Number questions

Question and mark-scheme extracts © Pearson Education Ltd. Reproduced for educational use; the original paper is linked on every question. Contact hello@oscarsongtutoring.co.uk for removal.

• Edexcel 1MA1 · November 2024 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Learners were generally able to write down the multiple of 9 that is between 20 and 30 as was required for this question. Incorrect answers were generally numbers between 20 and 30 that were not the required multiple of 9.

  Text version

  Write down the multiple of 9 that is between 20 and 30.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Almost all learners were able to correctly work out 500 + 145.

  Text version

  Work out 500 + 145.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  This question required learners to use information on the cost of a hire car per day and the cost of insurance in order to work out change from ten £50 notes. The majority of learners were able to do this successfully and often showed clear working. Where incorrect answers were seen, some came from errors in arithmetic and others came from not understanding how to work with the information provided to find the amount of change that would be received, leading to addition and subtraction of a variety of combinations of the figures provided. A small minority of learners misinterpreted the insurance as being per day and this led to an answer of −£250 or £250 this was awarded SC1.

  Text version

  Javid hires a car for 10 days. He pays £45 for each day and £30 for insurance. Javid pays with ten £50 notes.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q12 · 1 mark

  1 mark

  12

  
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  Examiner report

  Learners were asked to identify the error in a calculation. A slight majority of learners were able to give a correct explanation of the error in the method, with answers such as ‘he should have multiplied first’ and ‘he didn’t use BIDMAS’ being the common correct responses. Where incorrect answers were seen these commonly included correct reference to the need to do multiplication first, but then indicated that the calculation should be 12 −5 or showed 5 – 12 = 7 which was incorrect.

  Text version

  Olly was asked to work out 5 - 3 × 4. He first wrote 5 - 3 = 2 and then worked out 2 × 4.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q18 · 3 marks

  3 marks

  18

  
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  Examiner report

  This question asked learners to work out 818.4 ÷ 1.2. Many learners made an attempt to perform the division and working with 8184 ÷ 12 before considering the place value / position of the decimal place in the answer. In general, the division was attempted by use of the ‘bus stop’ method and there were a good number of learners who could perform this fully correctly to obtain the digits 682. Where errors in arithmetic were made these often lead to 6 as the first digit which was sufficient for the method mark to be awarded. There were learners who set up the division calculation, but were not able to complete this due to arithmetic errors or not being able to recall the method beyond the initial layout. The fully correct answer was only obtained by a minority of learners, this was often due to the final answer being given as 68.2 or 6.82.

  Text version

  Work out 818.4 ÷ 1.2.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q20 · 5 marks

  5 marks

  20

  
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  Examiner report

  This question differentiated well between learners. In part (a) learners were to perform a subtraction of mixed numbers. Slightly under half of the learners were able to correctly write both fractions over a common denominator, subtract them and give the answer as a mixed number. There were a significant minority of learners who had a partially correct response where they had attempted to write the fractions with a common denominator in order to subtract, but either gave the answer as an improper fraction or made an error in one of the numerators when writing the fractions with a common denominator. There were also a significant proportion of incorrect responses seen which sometimes made an attempt to write over common denominators but had no correct numerator due to errors in the method or where an incorrect method was attempted, often combining the whole number part of the fraction, numerator and denominator in some way. A few learners added rather than subtracted their fractions. In part (b), learners were asked to show a given result for the division of two mixed numbers. There were a minority of fully correct answers showing the required result. A similar number of responses gained 2 marks having converted one, or both, of the mixed numbers to improper fractions and then showing a method to divide by a fraction, but making an arithmetic error or not showing sufficient working to justify the required result. Many learners failed to achieve the third mark because they were unable to show how !"  = 2  . The ‘keep, flip, change’ approach to multiplying fractions was the more popular of the two. There were also a significant proportion of learners who gained 1 mark for conversion of one or both of the mixed numbers to improper fractions. Incorrect answers were common, with many incorrect attempts at converting mixed numbers to improper fractions and incorrect approaches to multiplication of fractions attempted.

  Text version

  Calculations with mixed numbers.

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• Edexcel 1MA1 · November 2024 · Paper 1F · Q22 · 4 marks

  4 marks

  22

  
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  Examiner report

  The first part of this question asked learners to use a given distance and speed to work out an estimate for the time taken by a car. There were relatively few fully correct answers, however many learners were able to start the process by rounding one or both of distance and speed. Following on from the rounding it was common to see incorrect calculations with 30 × 5 and 30 ÷ 5 being common. There were a significant number of learners who attempted to work with the exact values rather than rounding and others who rounded incorrectly. In some cases learners showed very little process for their calculation of the estimate. For those that did gain the second mark for dividing distance by speed (5 ÷ 30), many incorrectly calculated this to be 6. In part (b) learners were asked whether their answer to (a) was an over- or under-estimate. This was not well answered. Some learners only referenced rounding of one value in their answer, however they had rounded both and the nature of the calculation (division) meant that both needed to be considered in giving a decision. Many of the answers were not consistent with the rounding and process that had been used in (a). There were also a number of learners who incorrectly indicated that their answer to (a) was both an under- and over- estimate. Several just wrote over/under-estimate without an attempt at explanation. Learners need to be aware that it is ok to say I can’t tell whether it is an over or under estimate as long as they justify their answer.

  Text version

  A car travelled 4.96 miles at an average speed of 30.4 miles per hour.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  Examiner report

  Many learners used a formal method to divide a number with the digits 8184 by a number with the digits 12, usually 8184 ÷ 12, and most gained the first mark for making a correct start to the method and getting 6 as the first digit. Some went on to gain all three marks but having worked out 8184 ÷ 12 and obtained 682, many then gave the final answer as 68.2 or 6.82 and gained only two of the three marks. As they had multiplied both 818.4 and 1.2 by 10 before carrying out the division they possibly thought that they needed to divide 682 by 10 or by 100. If they had considered the relative sizes of the two numbers in the question then they should have realised that their final answer was not sensible. Arithmetic errors were common but those who had gained the first mark were still able to gain two of the three marks if the decimal place was correctly positioned in their final answer.

  Text version

  Work out 818.4 ÷ 1.2.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q3 · 5 marks

  5 marks

  3

  
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  Examiner report

  Part (a) was generally answered well. The most common method was to convert both mixed numbers into improper fractions and then write both fractions over a common denominator. Many learners gained at least one of the two marks for getting this far. The accuracy mark was sometimes lost because learners failed to write their answer as a mixed number or made an arithmetic error. Some chose to subtract the whole numbers and deal with the fractional parts separately and those that did were usually successful. A slightly smaller proportion of learners gained full marks in part (b) compared to part (a) but most gained at least one mark. The question required learners to show that the answer to the division is 2 4 so it was necessary for each stage of the method to be shown. Many gained at least two of the three marks for converting both mixed numbers into improper fractions (with at least one correct) and then showing a method to divide by a fraction. It was pleasing to see some learners making the arithmetic more straightforward by simplifying 21  to 3  before multiplying. Those that wrote 21   had to simplify 63 28 to 9 or write it as 2 28 in order to complete the working and gain the final mark. Having converted both mixed numbers into improper fractions some learners made the arithmetic unnecessarily complicated by choosing to use a common denominator of 12. Some wrote both mixed numbers as improper fractions and made no further progress; some flipped the wrong fraction or flipped both fractions. When no marks were scored this was often because learners had attempted to multiply the whole numbers and the fractions separately

  Text version

  Calculations with mixed numbers.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q5 · 4 marks

  4 marks

  5

  
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  Examiner report

  In part (a) it was pleasing that a good proportion of learners earned the first mark for rounding 4.96 to 5 or rounding 30.4 to 30 and it was very common to see both numbers rounded. Many went on to gain the second mark for 5 ÷ 30 or for a complete process to find the time. Some of those writing 5 30 were able to complete the process by multiplying by 60 but many could not. Some started with 30 ÷ 60 = 0.5 and then worked out 5 ÷ 0.5 and another successful approach was to write ‘30 miles in 60 minutes’ and divide both sides by 6 to get ‘5 miles in 10 minutes’. However, many learners could not demonstrate a full process to find an estimate for the time taken by the car. The first step was often 30 ÷ 5 = 6. Some gave 6 as the answer and others multiplied it by 60. These gained no credit. However, dividing 60 by 6 completed the process and earned the second mark. A significant number of learners did not understand the implications of the word ‘estimate’ and attempted to answer the question using 4.96 and 30.4. They gained no marks. In part (b) learners had to decide whether their answer to part (a) was an underestimate or an overestimate and give a reason for their answer. This was answered very poorly indeed. Many learners had rounded 4.96 up and rounded 30.4 down but only mentioned one of these in their answer. Answers such as “overestimate because I rounded the distance up” and “underestimate because I rounded down” were very common. Many learners did not consider how their rounding had affected the actual calculation they had carried out in part (a).

  Text version

  A car travelled 4.96 miles at 30.4 miles per hour.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  In part (a) a good proportion of learners evaluated both 25 and 8 correctly and gave the correct answer of 10. Some gained one of the two marks for either 25 = 5 or 8 = 2. Answers such as 200 and 200 were very common and gained no marks. In part (b) many of the learners who interpreted       as       went on to gain both marks for a correct answer of 1 8 . Some gave       as the final answer and scored just the method mark but the most common route to one mark was to work out   5 32 as 8 and then give 8 as the final answer. Those who started with 5 32 gained the method mark but were not able to complete the arithmetic to get a correct final answer.

  Text version

  Evaluate fractional powers.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q14 · 3 marks

  3 marks

  14

  
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  Examiner report

  Some learners gained the first mark for stating the value of sin30 or the value of sin45. Those who did not know these values were still able to gain the second mark for a correct sine rule statement such as 3 2 sin 45 sin30 AB  . More than half of those who gained the first two marks did not get a correct final answer, some because they had an incorrect value for sin30 or sin45, some because they could not rearrange their sine rule statement correctly and some because they could not combine the surds correctly. Many learners showed a lack of understanding of the mathematical requirements of the question with some using right-angled trigonometric calculations.

  Text version

  Triangle ABC has angle A=30°, angle C=45°, and BC=3√2 cm.

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• Edexcel 1MA1 · November 2024 · Paper 1H · Q16 · 6 marks

  6 marks

  16

  
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  Examiner report

  Part (a) was answered quite well by those with some understanding of surds and a good proportion of learners gained the method mark for multiplying both the numerator and the denominator by 5 . Some failed to gain the accuracy mark because they gave 15 5 as the final answer when the question asked for the answer in its simplest form, others because they made errors when trying to write it in its simplest form. In part (b), writing 7 5 as 5 3 was sometimes seen as the first step and sometimes it was seen later in the process. Some learners started by writing 7 5 as 5 3 and simplified the numerator of the fraction to 5 3 but no further progress. Those that realised they needed to rationalise the denominator were not always able to show a correct method to do so. Attempts at multiplying both the numerator and the denominator by 1  or by 3 were sometimes seen and gained no credit. Some of those that did multiply the numerator and denominator by 1  went on to expand the terms correctly but errors were frequently made, often when multiplying 5 3 by 2 3  . One error in the numerator or denominator was condoned for the third mark. Those learners who expanded all the terms correctly were usually able to give a correct final answer.

  Text version

  Manipulate surds.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  It was pleasing to see that the majority of learners could correctly convert minutes to hours and minutes successfully.

  Text version

  Write 140 minutes in hours and minutes.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Ordering decimal numbers by size was not as well answered as expected. The most successful approach seemed to be those who added trailing zeros to ensure each number had the same number of decimal places to allow an easier comparison to be made.

  Text version

  Order 0.57, 0.507, 0.5 and 0.05, smallest first.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  Finding the number halfway between the two given values was also well answered, with many responses showing the use of a list of numbers to identify the correct answer.

  Text version

  Find the number exactly halfway between -2 and 8.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  Whilst many correct responses were seen to this question, a lack of working often led to full marks not being awarded. This question directed learners to show all of their working, which meant evidence of working with both bead colours was required, but it was common to see only the red beads being worked with despite an often correct answer of 10 being shown. This level of working only gained the first mark. Learners showed a variety of approaches such as divisions of 52 ÷ 5 and 80 ÷ 7. The most commonly seen approach was repeated addition of 5 and 7 or repeated subtraction from the available beads. Whilst build-up and build-down methods did gain some credit, occasionally arithmetic errors were made in one or both lists so learners should be encouraged to use their calculators to save time and avoid such errors. A common incorrect approach was to divide the total number of beads available by the number required for one bracelet, 132 ÷ 12, giving an answer of 11. This gained no marks.

  Text version

  Each bracelet uses 5 red and 7 white beads. Jo has 52 red and 80 white beads.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  Both parts of this question required learners to use reasoning skills, with part (a) requiring a written explanation and decision and part (b) requiring learners to show a correctly evaluated counter-example. A lot of learners gave very good answers to part (a), demonstrating an ability to clearly explain why the statement was wrong. The most common ways that they did this were either to point out that 102 is 100 or to explain that 10 had been multiplied by 2 rather than by itself. The mark scheme shows other acceptable ways of answering the question, but these were less commonly seen. In part (b), many learners gave a wide range of acceptable examples of a division that produced an odd number or any non-integer. The result of the division did have to be evaluated correctly so unfortunately responses without showing the result or containing an arithmetic error did not get the mark. A significant minority of learners used odd numbers instead of even numbers, preventing the award of the mark. Learners had to give clear, correct answers to both parts of this question, and if there were incorrect elements to their statement, or contradictions, they did not gain the mark for that part of the question.

  Text version

  Junaid says 20 is square because 10²=20. Chloe says even÷even is always even.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q12 · 4 marks

  4 marks

  12

  
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  Examiner report

  This was the first multi-step question on the paper which combined the skills of finding a percentage of a quantity and using proportion, with a large number of learners being able to follow the necessary steps through correctly to gain an accurate answer. When errors were made after correctly finding 60% was 108, it was often due to becoming confused and selecting the wrong figures to use in their next set of calculations. Encouraging learners to label what intermediate figures are in their working would help here. Another common issue was incorrect percentage work. It still remains a problem for learners to simply write 60% of 180 or try to use a build up method, namely 10%, without using their calculators and without showing their calculations and therefore gaining no credit if arithmetic errors were made. Evidence also suggests some may be trying to use the percentage function of their calculator unsuccessfully.

  Text version

  180 concert tickets are sold; 60% are child tickets at £8 each. Total revenue is £1944.

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q20 · 2 marks

  2 marks

  20

  
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  Examiner report

  This very familiar use of a calculator question was very well answered by most learners, showing that they were able to use a variety of functions on their calculator to reach the accurate answer. Learners who showed figures that implied a partial evaluation, were awarded 1 mark for reaching an intermediate value or for an answer of 4.64 but a response gaining 1 mark only was rare compared to previous series. When errors were made, it was often due to incorrect use of the square root which was commonly only applied to the numerator rather than the whole fraction.

  Text version

  Use a calculator to evaluate √((208.3-15.7)/(5.694+1.8²)).

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• Edexcel 1MA1 · November 2024 · Paper 2F · Q27 · 2 marks

  2 marks

  27

  
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  Examiner report

  This question was not attempted well by the majority of the cohort. Learners often attempted to convert from standard form to ordinary numbers, which gained no credit and was not necessary, but rarely recognised that they should then be attempting a division. Sometimes a partial mark was awarded for finding the figures 3125 but this was rare. A very small minority were able to reach the accurate answer for 2 marks. Practising use of a calculator for manipulation of numbers in standard form would be helpful for learners.

  Text version

  1.25×10⁻¹² = k×(4×10⁻²⁰).

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• Edexcel 1MA1 · November 2024 · Paper 2H · Q1 · 2 marks

  2 marks

  1

  
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  Examiner report

  It was very common to see the correct answer on question 1. The use of a calculator is a familiar start for learners, and they did well. Those who didn’t gain full marks often only square rooted the numerator rather than the whole fraction. As ever, some were able to gain 1 mark for a correct partial evaluation.

  Text version

  Evaluate √((208.3-15.7)/(5.694+1.8²)).

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• Edexcel 1MA1 · November 2024 · Paper 2H · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  A slightly different approach to a standard form question which required learners to rearrange a simple formula to get the correct calculation. This was the cause of many learners losing the marks here as they completed the wrong calculation, either multiplying or dividing the wrong way round. Of those who were able to rearrange, all were able to gain at least one mark, either for stating the correct calculation, or for the digits 3125. A good number gained the second mark for correctly writing the answer in standard form, although some made an error changing 31 250 000 into standard form.

  Text version

  1.25×10⁻¹²=k(4×10⁻²⁰).

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• Edexcel 1MA1 · November 2024 · Paper 2H · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  A slightly more complex question than has often been seen testing the product rule for counting. There were two main approaches, the most common being to recognise that each of the 10 teams would play 9 games if playing each other team once and so to multiply 10 by 9, then multiply this total by 4 to reflect the fact that each team plays each other team 4 times. This method to 360 was seen and gained one mark. When using this method though learners needed to realise this was counting each game twice, and then halve to get the answer of 180. It was this step that was often missing. The alternative method was to recognise the issue of double counting in the initial calculation for the total number of games when playing each other once. This led to a value of 45, which again would score the first mark. Those who followed this method were more likely to gain the second by multiplying by 4 as they had understood the difficult concept of halving in their first step. However, the most common, and incorrect approach was to do 10 10 4   and this gained no marks.

  Text version

  10 football teams; each pair plays 4 times.

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• Edexcel 1MA1 · November 2024 · Paper 2H · Q19 · 5 marks

  5 marks

  19

  
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  Examiner report

  This was a particularly challenging bounds problem. The difficulty arose here due to the complexity of the denominator. Here they needed an upper bound of a paired with a lower bound for c or visa versa, and that is what we failed to see. Many gained the B1 for at least one correct bound. We often saw all 6, or at least 4. Learners struggled most with the bounds for w. however when it came to find the bounds for T, learners typically used all upper bounds, or all lower bounds and therefore no further marks could be awarded.

  Text version

  T=w/(a-c), with w=435 nearest 5, a=9.8 to 2 sf, c=2.5 to 2 sf.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  Examiner report

  This opening question was answered well with the majority of learners gaining 1 mark, usually for an answer of 700, although answers of hundreds or 700 written in words were also accepted and seen regularly. The most common incorrect answers were 3700 and 100.

  Text version

  Write down the value of the 7 in the number 3721.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  This cohort performed well on this question with almost all able to score 1 mark for an answer of 16.

  Text version

  Work out 1/6 of 96.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  This question was answered well with most learners able to gain B1 for 2 correct factors. A good number gave more than 2 factors which was allowed as long as they were all correct. Common incorrect answers were 2,3 and 4,4.

  Text version

  Write down two factors of 16.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  This question was answered very well with almost all learners gaining 1 mark for a correct answer. It was acceptable to give the list of numbers in descending order but this was rarely seen.

  Text version

  Write -3, 4, -7, 6 and 0 in order, starting with the lowest.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  This question was answered very well with almost all learners gaining 1 mark for a correct answer. Most gave their answer as 1.5 but some left in fraction form, e.g. 3 , which was also acceptable.

  Text version

  Find the positive square root of 2.25.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q8 · 6 marks

  6 marks

  8

  
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  Examiner report

  Part (a) of this question was answered well with the majority of learners gaining 3 marks. Each value was marked individually; for those that did not gain 3 marks, it was the total for tin of paint that caused most problems. For those that did not get the correct value of 49.9(0), there was a follow through for the 3rd B mark where if they added their 4 totals together accurately they could gain the mark and this was seen often. Part (b) also saw the majority of learners gain 3 marks for a correct answer of 771.45. Of those that didn’t, common errors included failing to use the correct operation for all 3 values e.g. adding 365.50 instead of subtracting and there was also a significant number of misreads seen, presumably due to the large number of digits involved in the question. A small number of learners saw the word interest and tried to work out 4.47% of 892.48.

  Text version

  Nina's DIY bill has 4 packs of screws at £29.99 each (total £119.96), 2 tins of paint at £24.95 each, wooden planks at £7.75 each (total £232.50), and a £14.95 delivery charge. Jeff starts January with £892.48, receives £4.47 interest, pays in £240 and spends £365.50.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q9 · 5 marks

  5 marks

  9

  
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  Examiner report

  This question was answered well with most of this cohort able to gain 5 marks for a correct answer. There were a variety of processes in the mark scheme for learners to gain credit from with the most common seen being to work out the number of child vegetarians and subtract from 80, and the number of adult vegetarians and subtract from 120, and add these two results together. Some of this cohort were unable to make any progress on this question, not being able to deal with finding 2 of 200 being the main issue. Many learners did not gain marks because they failed to show their process when finding fractions or percentages of amounts, for example 35% × 80 does not gain credit without an accurate result, whereas 0.35 × 80 is worth P1.

  Text version

  There are 200 people at a party. Two fifths are children and the rest are adults. 35% of the children and 45% of the adults are vegetarian.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q10 · 5 marks

  5 marks

  10

  
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  Examiner report

  Part (a) was answered well with a good number of learners able to give the correct answer of 19; incorrect answers were varied and showed no clear pattern. Part (b) saw more mixed results. In (i) a good number of the cohort were able to interpret the information correctly and gain a correct answer of 08 11. Some misinterpreted the information and added 6 and 8, then subtracted from 09 00, gaining 0 marks. There was a Special Case B2 available for an answer of 08 08 (the learner who chooses the correct train but does 08 14 – 6) and 08 09 (the learner who identifies 08 17 but subtracts 8 instead of 6) and these were seen often, 08 08 more so than 08 09. Some learners arrived at the answer of 08 11 but subtracted more time to allow for delays; centres should note that learners should work with the given information in the question and not include further interpretation of their own. (ii) also saw mixed results, although a good number gained B1 for a correct answer; common incorrect answers in the main talked about Barnie being able to leave later.

  Text version

  The aligned train timetable is: station | train 1 | train 2 | train 3 | train 4 | train 5 Horwich | 07:13 | 07:46 | 08:14 | 08:44 | 09:14 Lostock | 07:16 | — | 08:17 | — | 09:17 Bolton | 07:21 | 07:54 | 08:22 | 08:52 | 09:22 Salford | 07:36 | 08:05 | 08:36 | 09:05 | 09:36 Manchester | 07:47 | 08:15 | 08:45 | 09:15 | 09:45 Barnie walks 6 minutes from home to Lostock station and 8 minutes from Manchester station to his interview.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q16 · 4 marks

  4 marks

  16

  
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  Examiner report

  Part (a) saw a good number of learners score 2 marks for a correct answer. Of those that didn’t, it was common to see an incomplete factor tree (e.g. one that does not have prime numbers at the bottom of the branches) or a lack of understanding as to what is meant by prime factors. Part (b) saw 0, 1 and 2 marks awarded in almost equal measure. Of those that did not gain 2 marks, many gained 1 mark, usually for correctly identifying the prime factors of 210 or for an answer in the SCB1 list (2, 3, 6, 7, 14, 21). Some learners found the Lowest Common Multiple by listing multiples, gaining 0 marks.

  Text version

  Prime factors and highest common factor.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q18 · 2 marks

  2 marks

  18

  
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  Examiner report

  Part (a) was answered well with a large proportion of the cohort able to give a correct answer. Part (b) saw less success with very few correct answers seen; common incorrect answers included 8.026 × 10n where n was incorrect, often given as −4, and 0.8026 × 10n was also seen.

  Text version

  Standard form.

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• Edexcel 1MA1 · November 2024 · Paper 3F · Q23 · 2 marks

  2 marks

  23

  
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  This question saw very few learners scoring 2 marks. Some were able to gain one correct limit, usually 10.2. There were a variety of incorrect answers with 10.15, 10.25 being the most common.

  Text version

  Jana used a calculator to find a value t. The displayed answer began 10.2.

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• Edexcel 1MA1 · November 2024 · Paper 3H · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  A high percentage of candidates showed a good understanding of standard form. In part (a) nearly all candidates were able to convert from the numbers in standard form to ordinary numbers, although it will be of no surprise that (b) was answered less well than (a). In part (b) the most common incorrect answer seen was 8026×10-4

  Text version

  Standard form.

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• Edexcel 1MA1 · November 2024 · Paper 3H · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  This question was attempted by most but rarely resulted in full marks being awarded. Many were unable to appreciate that the question focused on truncation, rather than rounding and treated the question as if they had been told 10.2 was the result of a rounding process. As a result, they gave bounds of 10.15 and 10.25 which could not be given any credit. Where only 1 mark was scored, it was usually for the lower bound of 10.2(0); as an upper bound of 10.29 did not gain any credit.

  Text version

  Calculator answer for t began 10.2.

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• Edexcel 1MA1 · November 2024 · Paper 3H · Q14 · 3 marks

  3 marks

  14

  
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  A pleasing number of learners were familiar with the requirement of proving algebraically that the given recurring decimal was equal to the given fraction. Most chose to find the value of 10x and 1000x and subtract these. Where full marks were not awarded, this was invariably due to not showing the recurring nature of the given decimal and using terminating decimals throughout the working.

  Text version

  Prove recurring decimal 0.46262626... equals 229/495.

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  Candidates were generally able to write 18475 to the nearest thousand correctly. Common errors were giving the answer 19000, rounding to the nearest 10000 (answer 20000) or loss of the place value with an answer of 1800. Some candidates incorrectly gave an answer of 8000 as rounded to the nearest 1000.

  Text version

  Write the number 18 475 correct to the nearest thousand.

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  This question was answered well by candidates, with most being able to place the decimal values given in ascending order. Some candidates placed 0s in the hundredths column of the 0.2 and 0.1 to assist them in ordering the values, this was generally a successful strategy. Where incorrect answers were seen these were sometimes the result of ignoring the decimal point and the relative place value of the values leading to an answer of 0.1, 0.2, 0.03, 0.16, 0.21 or similar. Another common incorrect ordering was 0.03, 0.1, 0.2, 0.16, 0.21 which may have been the result of partial understanding of place value.

  Text version

  Write these numbers in order of size.

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Candidates were generally able to find the square root of 64 as was required in this question. Common incorrect answers were 32 (from 64 ÷ 2) or 4 (the cube root).

  Text version

  Find the square root of 64

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q6 · 4 marks

  4 marks

  6

  
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  A well answered question with many candidates able to correctly find that £1.50 was the cost of a single can of soup. It was also common to see slips in arithmetic in what was otherwise a correct process, candidates who showed their working clearly benefitted here as marks could still be awarded even when errors in evaluation were seen. An answer of £2.40 was relatively common, this came from candidates neglecting to take off the change from the £10 that they started with, but otherwise working correctly. Where candidates did not have a full correct process, they were often able to gain credit for subtracting the change (10 −1.80) or for a process to find the total cost of the 4 cakes (4 × 1.30). It was common to see just one cake being subtracted from the £10 rather than four. Where candidates reached the cost of the two cakes, it was common for candidates to miss the last step of the process leaving an answer of £3.

  Text version

  Ryan buys

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  In part (a) candidates were asked to calculate −12 ÷ −4. The majority of candidates were able to find the correct answer of 3, but there were also a significant proportion of candidates who incorrectly gave the answer −3. Other incorrect answers included 4 from an arithmetic error, 48 and −48 from working with multiplication rather than division. In part (b) candidates were asked to find the value of 25. The majority were able to give the correct answer of 32, often having shown their working. Common incorrect answers came from working with an incorrect number of 2’s when multiplying leading to answers of 16 or 64, or from incorrectly interpreting 25 as 2 × 5 and giving an answer of 10. Part (c) required candidates to add a single pair of brackets to the calculation to make the given answer correct. The majority of candidates gave the anticipated answer of 30 ÷ (3 + 2) −4 = 2, but a small number gave an alternative correct answer of 30 ÷ 3 + 2(−4) = 2. Where incorrect answers were seen these generally involved placing a single pair of brackets in an incorrect place in the equation, although some candidates did use more than one set of brackets.

  Text version

  (a) Work out -12 ÷ -4. [1 mark]

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q14 · 3 marks

  3 marks

  14

  
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  This was a standard question on multiplication of a 3 digit number by a 2 digit number. The majority of candidates were able to work accurately with their chosen method to obtain the correct answer. The most common approaches to multiplication were the column method and Napier’s bones. Where an accurate final answer was not obtained then this was often due to slips in arithmetic, but there were also a significant proportion of candidates who made errors in place value when attempting the multiplication.

  Text version

  Work out 273 × 54

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q18 · 1 mark

  1 mark

  18

  
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  A slight minority of candidates were able to correctly give the value of 100.The most common incorrect response was 0 which came from incorrectly interpreting this as 10 × 0. An answer of 10 was frequently seen.

  Text version

  Write down the value of 100^0.

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q21 · 3 marks

  3 marks

  21

  
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  In part (a) of the question candidates were asked to work out 3 5 −1 3. Many candidates started by writing the mixed numbers as improper fractions which wasn’t needed for this question, but could form part of a correct method. Many candidates attempted to write each fraction over a common denominator with 15 being the most frequently used common denominator. Candidates who identified the need to write over a common denominator were often able to do so correctly and went on to reach the correct answer with many leaving this as 15 (which was acceptable) and others converting back to a mixed number. There were some candidates who had reached 15 but made errors when attempting to convert back to a mixed number, as the mixed number was not required in this case the incorrect attempt at conversion was ignored. Common incorrect approaches involved subtracting numerators and denominators without writing over a common denominator, sometimes working with the original mixed numbers and sometimes after having converted to improper fractions. In part (b) candidates were presented with working for a product of fractions and asked to identify the mistake. Around half of candidates were able to correctly identify the issue with conversion from the improper fraction to the mixed number with many indicating that the answer should have been 1 24 rather than 1 24. The most common incorrect answers were indicating that they should have used a common denominator and that the initial conversion from the mixed number to the improper fraction was incorrect.

  Text version

  (a) Work out 3 4/5 - 1 2/3. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q24 · 4 marks

  4 marks

  24

  
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  Examiner report

  This question differentiated well between candidates. The estimation of the cost of fuel had two aspects that students needed to achieve – estimation and the calculation of cost. Where candidates were able to get full credit for this question they worked with a value correctly rounded to 1 significant figure and used a correct process to find an estimate of the total cost of fuel. The most common complete processes were 500 ÷ 10 × 0.8 = 40 and 510 ÷ 10 × 0.8 = 40.8, although some struggled to accurately evaluate their calculation due to arithmetic errors often in calculations working with decimals (0.8 or 0.81). A significant minority of candidates chose to round 0.81 euros to 1 euro which allowed for 2 marks to be awarded if used in a complete correct process. Some candidates worked with a value rounded to 1 significant figure in an incomplete or incorrect calculation and gained 1 mark. A common error was to attempt to work accurately with the values in the question before rounding the answer, where a correct process was used this could gain 1 mark. In part (b) candidates were asked whether their answer was an overestimate or an underestimate. Less than half of the candidates were able to give a decision that was consistent with their calculation in part (a) together with a reason that related to rounding up or rounding down. Some incorrectly referred to their rounding of the final answer. Where candidates rounded 513 and 0.81 down they were expected to indicate underestimate in (b) together with reference to rounding down. Where candidates rounded 0.81 to 1 and worked with 513 then overestimate and an indication of rounding up was required. Where a candidate chose to round 513 to 500 and 0.81 to 1 then credit was awarded in (b) for either indicating that the answer was an overestimate as they had rounded 0.81 up more than 513 had been rounded down (in relative terms) or that they could not tell if it was an overestimate or an underestimate as one value had been rounded up and the other rounded down. Many that rounded km down and euros to 1, only referenced rounding euros up in their explanation.

  Text version

  Sophie drives a distance of 513 kilometres on a motorway in France.

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• Edexcel 1MA1 · June 2024 · Paper 1F · Q26 · 5 marks

  5 marks

  26

  
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  Only a minority of candidates were able to correctly calculate the percentage of Kasim’s jars that were empty small jars. The majority of candidates who scored gained only 1 or 2 marks. A correct process to find 8 of 400 was the most commonly awarded mark, with a significant proportion of candidates able to also start to deal with the ratios and identify that number of small jars : number of medium jars : number of large jars could be written as 3:4:8. Having reached this point candidates generally struggled to find the number of empty small jars (30) with a range of incorrect attempts being seen. A very common incorrect combined ratio was to write the correct ratios, in the correct position in columns for S:M (3:4) and M:L (1:2). This gave an incorrect ratio of 3:4:2. Others added together the middle parts reaching 3:5:2. Having started with a process to find the number of empty small jars, many candidates worked with the ratios as given in the question and found 3+4+1+2 of 150 rather than 3+4+8 in an attempt to find the number of empty small jars. Where candidates did find that there were 30 empty small jars, a majority went on to incorrectly calculate what proportion of the empty jars were small, calculating 150 × 100, rather than what proportion were small empty jars, 400 × 100. There were a variety of other incorrect approaches seen.

  Text version

  Kasim has 400 jars. Of these, 3/8 are empty. For the empty jars, small : medium = 3 : 4 and medium : large = 1 : 2. Work out the percentage of all 400 jars that are empty small jars.

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q2 · 3 marks

  3 marks

  2

  
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  Part (a) was answered very well. The most common approach was to convert both mixed numbers into improper fractions and then add these fractions using a common denominator of 15. Errors were made when converting to improper fractions and when writing to a common denominator but one mark was awarded for a method to subtract using a common denominator with at least one correct numerator. Simple arithmetic errors when subtracting numerators were common. Many students did convert back to a mixed number even though it wasn’t required but any mistakes made converting 32 15 into a mixed number were not penalised. Students who chose to deal with the whole numbers and the fraction parts separately had a quicker method that resulted in fewer arithmetic errors. A small number of students did not know that a common denominator was needed. In part (b) many students were able to identify that Kevin had made a mistake when changing 24 into a mixed number. The most common approach was to work through the problem and compare the result with the given solution. Students who could do the multiplication then spotted that Kevin’s answer should be 11 124 . Some students started from 35 – 24 which should be 11 and not 9 and some considered 24 + 9 which should be 33 and not the 35 that is needed. A common incorrect explanation was that Kevin should have simplified his final answer and some students stated that he should have used a common denominator or that he should have used ‘keep, flip, change’. Very often the incorrect statements were from those students who had not tried to work through the problem themselves.

  Text version

  (a) Work out 3 4/5 - 1 2/3. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q5 · 4 marks

  4 marks

  5

  
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  Marks were often lost in part (a) because students did not understand the implications of the word "estimate". Most students were able to demonstrate a full process to find the total amount that Sophie pays which earned them one mark but there was a significant number of students who used very little rounding or no rounding at all and gained no further marks. As this question was testing estimation skills students were expected to round at least one value to 1 significant figure in order to get a calculation that they could work out in their heads. Rounding 513 to 500 and 0.81 to 0.8 was quite a common route to a correct estimate. Some students divided 513 by 10 to get 51.3 and then rounded this to 50 before multiplying by 0.8 or 0.81. Many students chose to round 0.81 to 1 rather than to 0.8 and although this made the calculation much easier it did not result in a very good estimate of the total amount. This approach scored at most two of the three marks. The working for this problem was very variable. The good responses generally clearly stated the estimates that they were working with. In some of the poorer attempts, students seemed to have taken multiple approaches in a bid to find an easier calculation but often their lack of estimation prevented them from finding an easier calculation. To be in a position to say whether their answer was an underestimate or an overestimate in part (b), students must have used a rounded value in a calculation in part (a). Many students did state that their answer was an underestimate and gave a suitable reason; for example, they had rounded both 513 and 0.81 down. Some students rounded one value up and the other value down but gave a reason that only mentioned rounding one value and they could not be awarded the mark. A small number of students were able to successfully explain that rounding 0.81 to 1 was more significant than rounding 513 down to 500 and could gain the credit here.

  Text version

  Sophie drives a distance of 513 kilometres on a motorway in France.

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q7 · 5 marks

  5 marks

  7

  
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  Most students made very good attempts at this multi-step question with many achieving at least three of the five marks. It was pleasing to see many well presented solutions with working out that was easy to follow. Most students worked with the number of jars with only a few choosing to take the more direct approach of working only with proportions. The majority of students gained the first mark by showing a process to find the number of empty jars. In order to make further progress students needed to associate corresponding parts from the two ratios. Many students realised that they needed to multiply both parts of the ratio 1 : 2 by 4 and they were able to write down the ratio 3 : 4 : 8 and gain the second mark. Using the ratio 3 : 4 : 8 to find the number of empty small jars gained the third mark. Some did this by finding 3 15 of 150, others by writing the ratio as 30 : 40 : 80. Having found that Kasim has 30 empty small jars, many students did not read the question with sufficient care. The question asks for the percentage of Kasim’s jars that are empty small jars so the required proportion is 30 400 . Many students, though, used 30 150 and it was very common to see 30 150  and an answer of 20%. Most of those students who did use 30 400 were able to find the correct percentage but arithmetic errors cost some students the final mark. A common error was to divide 400 by 30 rather than 30 by 400.

  Text version

  Kasim has 400 jars. Of these, 3/8 are empty. For the empty jars, small : medium = 3 : 4 and medium : large = 1 : 2. Work out the percentage of all 400 jars that are empty small jars.

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q15 · 4 marks

  4 marks

  15

  
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  This question was not answered as well as might have been expected and a surprising number of students failed to gain any marks at all. Many of those with some knowledge of sectors of circles went wrong at the first step, using πr2 or πr instead of 2πr and gained no marks. A good proportion of those who did make a correct start went on to get full marks. Marks were often lost because of arithmetic errors or poor algebraic manipulation. Students who cancelled down fractions before multiplying worked more accurately than those who left cancelling until the end. Those who started by forming the equation x     = gained the first mark but rearranging the equation correctly to find the value of x was a problem for some. Students who worked with proportion and found that the arc length is 5 of the circumference of the circle gained the first two marks. They could then complete the process to find the area of the sector by working out 12    although many chose to first work out the size of angle AOB. After gaining the first three marks for a complete process to find the area of the sector a significant number of students failed to get an answer of 15 because they could not evaluate    correctly. Those who used 12    made fewer arithmetic errors. Some students assumed that the sector was one third of a circle and worked with an angle of 120o and some measured the angle and used 130o in their calculations. These students gained no marks.

  Text version

  The diagram shows a sector AOB of a circle with centre O, radius 6 cm and angle AOB = 150°. Find the area of the sector, giving your answer in terms of pi.

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q17 · 3 marks

  3 marks

  17

  
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  Part (a) was generally answered quite well. Most students who knew about rationalising a denominator chose to multiply numerator and denominator by 7 although a few used − instead. The multiplying was usually carried out correctly. However, 7 was sometimes incorrectly simplified, often to 1, and the mark could not be awarded. It was common to see 1 7 as the final answer and this was awarded one mark. A common error was to find the reciprocal rather than rationalise. Incorrect manipulation of the surd was seen when students wrote 7 4 3 2 3 = + = or 2 + . In part (b) many students were able to gain at least one of the two marks for writing 80 as 16 5  or 16  or 4 5 . Although many went on to get the correct answer of 3 5 it was not unusual to see 4 5 − followed by an answer of 4 or to see 4 5 − given as the final answer. Writing 80 as 10 8  or 4 20  was a first step that often led to no marks being awarded although some students did get to 4 5 . A common mistake was to write 80 − as 75 and this often resulted in an answer of .

  Text version

  (a) Rationalise the denominator of 1/sqrt(7). [1 mark]

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q18 · 3 marks

  3 marks

  18

  
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  This was one of the better answered questions in the latter stages of the paper with most students gaining at least one mark. It was pleasing that many students were able to show a complete method leading to 25/66. Converting a recurring decimal to a fraction is a familiar type of question but here students had two recurring decimals to deal with. Adding the two decimals as a first step gives students only one recurring decimal to convert to a fraction but relatively few students chose this route. Those who did could often not add the recurring decimals correctly. The majority of students chose to convert both 0.15and 0.227 into fractions and most were able to gain the first mark for the start of a method to convert either decimal to a fraction. A common error at this stage was to follow x = 0.2272727 with 10x = 2.727272. After finding two appropriate decimals to subtract some students spoilt their solution by making careless arithmetic errors such as 1000x – 10x = 900x. Some students could recall the need to multiply the recurring decimal by powers of ten but were either unable to find the multiples needed to eliminate the recurring nature of the decimal or could not carry out the multiplications correctly. Many students, however, showed correct methods to convert both fractions to decimals and gained the second mark. Students still had to show that adding the two fractions gives an answer that can be written in the form 66 m . Some achieved this by adding the two fractions to get 375 990 and then simplifying, others simplified the two fractions before adding. Arithmetic errors in this final stage sometimes resulted in a fraction that was not 25 66 and the final mark could not be awarded. The presentation of working was often quite poor in this question.

  Text version

  Show that 0.151515... + 0.2272727... can be written as m/66, where m is an integer.

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• Edexcel 1MA1 · June 2024 · Paper 1H · Q20 · 3 marks

  3 marks

  20

  
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  This question was not answered as well as might have been expected. The expressions for 2x and 2y contained a combination of surds and indices and many students worked with surds but not with indices and made no meaningful progress. It was common, for example, to see ( ) written as 4 2 rather than as 2 . Many of the students who did get the first mark for 2 or for y = 2.5 were unable to write 3 n as n−. Those who got the second mark for an equation such as n = − + usually went on to give a correct answer although arithmetic errors cost some students the final mark. Any errors made when converting 35 6 into a mixed number were ignored as the improper fraction is acceptable as the final answer.

  Text version

  2^x = 2^n / cuberoot(2) and 2^y = (sqrt(2))^5. Given that x + y = 8, work out n.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  The opening question was accessible to all students and was well answered with very few students not being awarded the mark.

  Text version

  Write the following numbers in order.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  Writing a fraction as a decimal seemed to be answered by the majority of the cohort but a large number did not write in the correct format, writing their answer as a percentage instead or writing it as a decimal with the wrong magnitude.

  Text version

  Write 31/100 as a decimal.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  This question requiring the identification of a multiple between two given values was answered correctly by most of the cohort. When the mark wasn’t awarded, it was often due to including more than one value, some of which were not multiples of 7.

  Text version

  Write down the multiple of 7 that is between 30 and 40

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q9 · 4 marks

  4 marks

  9

  
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  This first multi-step problem proved challenging for many, with less students than expected gaining all 4 marks available. Students often struggled to interpret the distance readings from the car given in the question as two five-digit mileages, often treating them as single digit distances and simply adding the digits together rather than subtracting. With working shown supporting the method used, these students were frequently awarded two marks, a mark for [mileage] × 47 and a conversion from pounds to pence, pleasingly often seen as a single step of [mileage] × 0.47. For those who found the real mileage, by subtracting 47241 from 47879, and reached the figure £299.86, the final step of adding the £80 expenses was not always understood, with it either being ignored; being subtracted; or using incorrect magnitude. When partial marks were not awarded, it was often due to not showing the multiplication. For example, 188 or 1.88 without also showing 4 × 47 gained no credit for [mileage] × 47. Problem solving activities in lessons with real-life context such as this would be beneficial for students to understand what process is required. Students should also be encouraged to check if their answer makes sense in real life.

  Text version

  Anil has a job as a driver.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q10 · 2 marks

  2 marks

  10

  
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  Listing outcomes for events is frequently assessed on this tier and is often answered very well. However, it noted that success in this question was poor in comparison to previous series, often due to only two events rather than three being written as a combination. The most successful responses used a systematic listing approach to avoid repeated combinations and ensuring all possible outcomes were given. Those using T and H also appeared to be more successful to those writing heads and tails in full, but both were acceptable. Layout of the combinations also appeared to be a common cause of lost marks as the combinations were not always clearly defined in a standalone way making it difficult to see whether letters had been “grouped” together or not. For example, using brackets to define a group was clearer than using commas alone.

  Text version

  Anita throws a coin 3 times.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q12 · 3 marks

  3 marks

  12

  
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  Examiner report

  This question was answered well with the majority of students using correct processes to arrive at 8 × 35 and giving a fully correct answer of 280g. Some students achieved only two marks for an answer of 560g (using white chocolate bars rather than milk) and even fewer achieved only one mark for an answer of 840g (the total weight). For those students who achieved no marks this was either due to them not attempting the question, although this was rare, or not being able to make a correct start to find 3 of 24 due to simply writing which is insufficient as a process. A common incorrect answer of 12 from just dividing by 2 was also seen. The other common misconception in this question was the use of 0.6 as equivalent of 3. Students should be encouraged to show processes at all times, (e.g. 24 ÷ 3 × 2 or 2 ÷ 3 = …) rather than just writing “ 3 = …” as this will enable them to achieve the process marks even when they make mistakes.

  Text version

  Saira buys 24 bars of chocolate. Two thirds are white chocolate and the rest are milk chocolate. Each milk chocolate bar weighs 35 g. Work out the total weight of the milk chocolate bars.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q18 · 3 marks

  3 marks

  18

  
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  Examiner report

  Whilst many students gained all 3 marks available in this small problem, many students struggled to find 56% of 1800 using a valid method as the first step. Calculations attempted unsuccessfully were often a non-calculator method such as a build-up or partitioning method, with the working shown often being insufficient for students to be given credit. Students should be encouraged to use a calculator appropriately and be confident in using decimal multipliers. Of the students who could calculate 56%, many of those then misunderstood the question and did not subtract this from 1800 and some also did not divide by 66. The vast majority of students did, however, realise and therefore gained credit for using [44%] ÷ 66. As with the majority of questions requiring the use of percentages, many students still believe writing 56% of a number or 56% = … is sufficient evidence of a correct process but such statements gain no credit unless a correct value is given. Use of the percentage button on the calculator may account for this but there is evidence to support the conclusion that many students do not know how to use this function correctly.

  Text version

  Mrs Simpson organised a school trip for 66 children.

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q19 · 3 marks

  3 marks

  19

  
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  Examiner report

  It was pleasing to see that the majority of students gave a fully correct answer to part (a) of this standard use of a calculator question. Many of the students who gained the 2 marks for the question gave the full answer, which was acceptable for the award of the marks, but many showed no intermediary calculations for the numerator or denominator and gained no marks for an incorrect final answer. A method mark was often awarded for correctly evaluating either the denominator or the numerator, but this was less frequently seen compared to similar questions on previous series. Most students wrote down all the figures from their calculator as advised in the question without rounding unnecessarily which was also pleasing to see. A common error was to get a final answer of 1.809.... that resulted from evaluating the numerator and then typing ÷ 4.62 – 8.91 rather than calculating the denominator separately or making use of the fraction function in the calculator. This led to BIDMAS being applied incorrectly and often led to no marks being awarded due to not always showing the value of the numerator and providing only an answer. Other common incorrect answers suggested students were either not using the fraction button but using ÷ instead (−8.6106….), square-rooting the entire calculation (5.1499….) and only square rooting the 35.2 in the numerator (0.885….). Part (b) required the answer to part (a) to be rounded to 2 significant figures and whilst a follow through from part (a) was acceptable, the majority of students rounded to 2 decimal places instead. To improve success on this type of question, students need to be rigorous in showing their working through part calculations and should be encouraged to work out and write down the value of the numerator and denominator separately to ensure they are awarded for partial evaluation and to avoid order of operation errors. They also need to improve their ability to confidently use functions such as the fraction button when entering complex calculations into a calculator.

  Text version

  (a) Work out sqrt(35.2 + 1.7^3) / (4.6^2 - 8.91). Write all digits shown on your calculator. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  Writing a number as a product of prime factors in part (a) is a familiar and standard question that was answered perfectly by a significant number of students. The most commonly seen method was to use a factor tree, with many showing a complete tree, some including 1 on their tree which still allowed for at least the method mark to be awarded but some not completing the factorisation for 9. When all of the prime factors had been found, some went on to correctly write as a product, some wrote as a product but included 1 which was not condoned for the accuracy mark and some either wrote their answer as a list or as an addition calculation. When a mark was not awarded, it was often due to listing single factors or factor pairs of 90. It was rare to see more than one error in factor trees compared to previous series which was pleasing. There was less success in part (b) with the majority of students being unable to find the LCM of two values written as prime factor products. The most successful approach came from listing multiples of 12 and 18. When the mark was not awarded it was often due to candidates not knowing what to do with 12 and 18 or finding the HCF instead of the LCM. The use of Venn diagrams was rare but when used often led to a correct answer.

  Text version

  (a) Write 90 as a product of prime factors. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 2F · Q25 · 4 marks

  4 marks

  25

  
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  Combining the skills of applying fractions, percentages and ratio in this small problem appeared to be demanding for many students, with many often only being able to work with one of the three skills but not all in a correct way. Calculating 7 of 14 was by far the most common first step shown, earning 1 mark with these students either failing to advance further in the problem-solving process but many then using a correct process to find the number of sweets for Andy and Tina after the first exchange to gain 2 of the 4 marks. Of the students gaining 2 marks, a large number either stopped or were not able to work with 12.5% using a valid method. Very few students showed working for every step which often led to marks being unachievable if arithmetic errors occurred. Selecting a specific value to begin working with was more commonly seen than expected, with many multiplying each part of the ratio by 21 from adding the parts of the ratio together or using 100. Of these students, very few were successful due to increased arithmetic errors or decimal values when working with a starting value of 100. Unfortunately, the majority of the cohort gained no marks and this was often due to using 21 rather than 14 when working with 7. Centres should give more opportunities to students on practicing the best way to approach multi-step problems involving multiple skills, particularly involving ratio, and how to logically organise their calculations.

  Text version

  Andy, Luke and Tina share sweets in the ratio 1 : 6 : 14. Tina gives 3/7 of her sweets to Andy, then gives 12.5% of her remaining sweets to Luke. Tina says they now have equal numbers. Is she correct? Show your working.

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• Edexcel 1MA1 · June 2024 · Paper 2H · Q2 · 3 marks

  3 marks

  2

  
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  Examiner report

  Part (a) is another familiar question and was very well done. Most used factor trees to find the prime factor decomposition of 90. Some used a Venn diagram to good effect. Students were allowed to give their answer in expanded or in index form, and both were seen regularly. Only a small number listed the prime factors, rather than writing as a product, and this is something we have seen a real decrease in. These students scored 1 mark. As did the students who made a single arithmetic error in their trees. Unfortunately, those who ended branches on a composite, rather than prime, number typically scored zero. Part (b) was only worth a single mark and students did not perform well. Many didn’t know what to do to find the LCM with the numbers given in prime factor form. Those who gained credit typically did it by writing them as ordinary numbers and listing multiples, or by drawing a Venn diagram. Many gave the HCF of 6 or gave 216 as an answer.

  Text version

  (a) Write 90 as a product of prime factors. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 2H · Q6 · 4 marks

  4 marks

  6

  
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  Examiner report

  There were many different approaches seen to Question 6 which was really interesting to see. As the question was designed to lack structure, students had to plot a path through the problem themselves, and most did so with at least some success. The most common approach was to use the starting ratio of 1 : 6 : 14, and then to find 7 of 14 = 6, and to subtract and add to the ratio to give 7 : 6 : 8. The next step was to then find 12.5% of 8 = 1 and again subtract and add to give 7 : 7 :7 and show Tina was correct. However, some worked with the values as fractions of 14, and others scaled up the ratio to a different total and worked from there. All these methods were capable of gaining full marks, but the latter two often led to errors, either in arithmetic, or due to premature rounding. Some students lost marks, as although they were able to find 7 and 12.5%, they either did so of the wrong values or added to the wrong values, or lost track of which values linked to which of the three people. This is a question where working was required to gain credit and was asked for in the demand. Anyone giving a correct answer without supportive working would score zero. Some students chose to use their oven values (in the ratio 1 : 6 : 14) which could also lead to full marks being given.

  Text version

  Andy, Luke and Tina share sweets in the ratio 1 : 6 : 14. Tina gives 3/7 of her sweets to Andy, then gives 12.5% of her remaining sweets to Luke. Tina says they now have equal numbers. Is she correct? Show your working.

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• Edexcel 1MA1 · June 2024 · Paper 2H · Q9 · 2 marks

  2 marks

  9

  
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  Examiner report

  Part (a) was answered well, as error intervals normally are. This is one of the new topics that students have taken to well. Part (b) unfortunately, was answered less well. Students were required to recognise that there are an infinite number of values greater than 7.349 but still less than 7.350, and some did and articulated this well. Many didn’t though, and it was common to see poorly worded explanation either contradicting themselves or being mathematically incorrect.

  Text version

  A number N is rounded to 2 significant figures.

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• Edexcel 1MA1 · June 2024 · Paper 2H · Q15 · 2 marks

  2 marks

  15

  
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  A slightly different style of surds question to the ones we have seen previously, but it was approached well by students. A good number of the stronger students gained the first mark for a method to rationalise, and many of these then gained the second mark. However, some who had the correct algebra leading to the answer, attempted to simplify further often to expressions such as √𝑎 𝑎. This further incorrect working was not ignored and lost the A mark. Some students worked with a prime number, such as 3, in place of a. These students were able to gain the M1 if their method to rationalise was correct. The most common error was in trying to rationalise using √𝑎+ 1 rather than √𝑎−1.

  Text version

  Given that a is a prime number, rationalise 1/(sqrt(a) + 1). Give the answer in simplest form.

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  This question saw varied results; the majority of students were able to gain one mark for an answer of 8. A good portion of the cohort scored no marks, with the common incorrect answer being 80 - other incorrect responses involved multiplying by 10 or 100.

  Text version

  Change 800 centimetres to metres.

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  This question was answered well with most students gaining 1 mark, usually for an answer of 30. For those who didn’t, "tenths” or “3000” were the most commonly seen incorrect answers.

  Text version

  Write down the value of the 3 in the number 62 837

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  This question saw mixed results, though a majority still scored the 1 mark available. Of those that did not gain a correct answer, the most common mistake was to have 1 and 2 3 in the incorrect order. A small number of students ordered the fractions from biggest to smallest, yielding no marks.

  Text version

  Write 1/2, 2/3 and 1/4 in ascending order.

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  This question saw a majority of students gain the full 3 marks. There were various ways students could achieve a correct solution and all were seen. The most common method being to find the year that Aisha turned 18 (2011) and then count up in 5’s until reaching 2026 or 2031 and arriving at an answer of ‘no’. Some students found the difference between 2011 and 2030 (19) and explained or showed that 19 was not divisible by 5, which was enough to gain 3 marks - although some that found 19 missed the final mark because they did not state that 19 is not divisible by 5. Some found the difference between 2030 and 1993 but then didn’t know how to work with it to gain the rest of the marks. A minority of students gained 0 marks, with the most common incorrect process seen being to start at 1993 and count up in multiples of 5. Some attempted to find the year she was 18 by repeated addition but included 1993 so ended up with an answer of 2010.

  Text version

  Aisha was born in 1993

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q9 · 3 marks

  3 marks

  9

  
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  Examiner report

  This question was answered very well with almost the entire cohort scoring full marks. The most common process seen was to calculate the total for 5 days of ski hire, 4 days of lift passes and 8 hours of ski lessons and find the sum of the 3 totals, leading to an answer of 498. Of those that did not gain full marks, the most common errors were usually related to digits, e.g. writing down 23.5 × 8 = 180 instead of 188, presumably copying down incorrectly from the calculator. Some students opted to use a repeated addition method e.g. 26 + 26 + 26 + 26 + 26 = 130; this was a successful, although not efficient, process for some students; but led to errors for the majority who used it.

  Text version

  Lucia is going on a skiing holiday.

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  This question saw much success with most of the students scoring 2 marks. The most common method seen was to work out 45 × 8 = 360 then divide by 60 to reach the correct answer of 6. Common incorrect solutions were to reach 360 and be unable to convert to hours, some students treated an hour to be 100 minutes and did 0.45 × 8 and others attempted a build-up method of 8 lots of 45 but went wrong in the method.

  Text version

  There are 8 episodes in a TV series.

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  This question saw mixed results with a minority to gain 2 marks for 3 correct prime numbers. Of those that weren’t awarded full marks, some gained 1 mark for 2 out of 3 correct prime numbers. Many were only able to give 1 prime number or in some cases none at all; common incorrect prime numbers were 21, 25, 27 and 39. Few students demonstrated good strategies to identify prime numbers, either by using the times tables or by tests of divisibility.

  Text version

  Write down three prime numbers that are between 20 and 40

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q22 · 2 marks

  2 marks

  22

  
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  Examiner report

  The full range of marks out of 3 were awarded for this question. Some students were able to gain 2 marks for a correct answer of 21; the most common methods seen were to find the factors of 63 and 105 or to find the prime factors of 63 and 105 and go from there, sometimes listing the product of prime factors and on other occasions a Venn diagram. Of those that didn’t gain 2 marks, a good number gained 1 mark, often for an answer of 3 or 7 or for the correct prime factors of 63 and/or 105. Many found 3 and 7, then chose 7 as their final answer as the highest common factor of the two. The most common incorrect method seen was to find the LCM of 63 and 105 by listing multiples.

  Text version

  Find the highest common factor (HCF) of 63 and 105

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• Edexcel 1MA1 · June 2024 · Paper 3F · Q23 · 4 marks

  4 marks

  23

  
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  Examiner report

  It was pleasing to see most students pick up 1 mark for converting from an ordinary number to standard form at this late stage in the paper on (a)(i). Part (a)(ii) saw less success with fewer gaining the mark; common errors generally focused around an incorrect number of zeros or a misinterpretation of the power of ten e.g. taking the power to be positive instead of negative. A good portion of students were able to gain 2 marks in part (b) for an answer of 3.42 × 107. Of those that didn’t, many gained 1 mark, usually for an answer of 34 200 000 or 3.42 × 10n, n ≠ 7.

  Text version

  (a) Write as an ordinary number: (i) 5.3 × 10^4; (ii) 7.4 × 10^-5. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 3H · Q1 · 2 marks

  2 marks

  1

  
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  Examiner report

  Most students were able to score at least one mark normally for a correct factor tree for 63 or 105 with no more than one error. Although one error was condoned here, it was pleasing to see that most factor trees were accurate. Quite often a correct Venn diagram was drawn for one mark, though many were unable to use their Venn diagram to arrive at the solution required. Very common incorrect answers given were 3 and 7 and these gained one mark; an answer of 7 x 3 also just gained the one mark. The method mark could also be gained for listing factors of 63 or 105. Although many students gained full marks, a significant proportion chose the LCM of 315 rather than the HCF of 21. It was disappointing to see that some Higher Tier students showed that they did not fully understand the difference between factors and multiples and gained no marks for just listing the multiples.

  Text version

  Find the highest common factor (HCF) of 63 and 105

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• Edexcel 1MA1 · June 2024 · Paper 3H · Q2 · 4 marks

  4 marks

  2

  
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  Examiner report

  A high percentage of students showed a good understanding of standard form. In part (a) nearly all students were able to convert from the numbers in standard form to ordinary numbers, although it will be of no surprise that (ii) was answered less well than (i). Most students were able to use their calculator to work out the value of the calculation in part (b) and get, 34 200 000. These students scored at least one mark, but many of them were not then able to write the number in standard form, despite being able to convert from standard form to an ordinary number in part (a). Of those that gained no marks for part (b) of the question, it was usually because they attempted to do it without the calculator or did not know how to enter numbers in standard form into their calculator. These students often failed to take account of the differing powers of ten – this resulted in them adding 9.7 to 2.45 to arrive at 12.15 and then a final answer of this being multiplied by a power of ten, usually 12.15 × 1013

  Text version

  (a) Write as an ordinary number: (i) 5.3 × 10^4; (ii) 7.4 × 10^-5. [2 marks]

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• Edexcel 1MA1 · June 2024 · Paper 3H · Q13 · 2 marks

  2 marks

  13

  
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  Examiner report

  870 was the most commonly seen incorrect answer and was awarded one mark for the correct start of multiplying 30 by 29 to find the number of ways in which two students could be chosen as first and second. Many of these students then failed to recognise that their answer needed to be halved as the order of selecting the two students did not matter. Relatively few students scored full marks. A small number of students successfully used 30C2, which was surprising to see at this level. Commonly seen incorrect answers which could not be credited with any marks included 60 (= 30 × 2) and 900 (= 30 × 30).

  Text version

  There are 30 students in a class.

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• Edexcel 1MA1 · June 2024 · Paper 3H · Q19 · 3 marks

  3 marks

  19

  
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  Examiner report

  This question discriminated well with the full array of marks being awarded. The lower attaining students restricted their answer to calculating R by substituting in P as 5.88 10  and Q as 3.6 10  , with some then writing the lower bound of this value, but these responses were not awarded any marks. Most students recognised the need to state bounds for P and/or Q and hence gained the first mark for the digits 5875 or 5885 or 355 or 365. This was to allow a mark to be awarded to the students who ignored the  and  from P and Q respectively. Many students did not progress beyond the first mark as they attempted to calculate the lower bound of R by dividing the lower bound of P by the lower bound of Q. Of those who gained 2 of the 3 marks it was usually for having the incorrect upper bound for Q, usually as 3.64 10  or 3.649 10  with no recurring notation. There were some students who were only awarded 2 of the 3 marks as they gave a final answer in standard form instead of an ordinary number. The final mark was only awarded for a final answer in standard form if an answer within the accepted range was given as an ordinary number first.

  Text version

  R = P/Q. P = 5.88 × 10^8 correct to 3 significant figures and Q = 3.6 × 10^5 correct to 2 significant figures. Find the lower bound for R as an ordinary number, to the nearest integer.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  This question was answered well with the majority of students able to give a correct answer of 31. Of those that didn’t gain B1, 209 was the most common incorrect answer from adding instead of subtracting; 41 was also seen when students were unable to deal with the tens correctly.

  Text version

  Work out 120 - 89.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  The majority of this cohort were able to gain B1 for a correct answer of 60. Of those that didn’t, 50 and 150 were the most common incorrect answers seen.

  Text version

  Work out 1/5 of 300.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  The majority of students gained 3 marks for an answer of 2300 on this question. For those that didn’t it was an error in conversion which was often seen with 1 litre = 100 millilitres being the most common incorrect conversion used; these students could still gain 1 mark if they had a correct process to find the difference using one of the incorrect conversions stated in the mark scheme. Those students who converted 3 litres into millilitres were more successful than those who converted 700 ml into litres and errors in arithmetic were noted when doing 3000 – 700. A small number of students arrived at 2300 but spoiled their answer by then trying to convert to litres; this was still allowed if the student gave an answer of 2.3 litres but 2.3 on its own lost the A mark and this was seen on occasions. Some students also missed that the question was about 3 litres and instead subtracted 700 from 1 litre (1000 ml) obtained 300 ml and gained no marks.

  Text version

  There are 3 litres of oil in a can. Jermaine uses 700 millilitres.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q17 · 3 marks

  3 marks

  17

  
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  Examiner report

  The majority of students were able to gain at least 1 mark for correctly inverting the second fraction and multiplying. It was common to see the second mark gained too, usually for reaching 5 . Students who attempted to find a common denominator, e.g. 18  often made no further progress. The final step proved to be the most challenging for this cohort but some were able to successfully convert to a mixed number. Students should read the demand of the question carefully as 3.6 given as an answer was seen.

  Text version

  Work out 3/5 divided by 1/6.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q18 · 3 marks

  3 marks

  18

  
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  Examiner report

  The majority of students opted to use column multiplication for this arithmetic question. Some students managed correct place value in their structure and a good number of those managed to reach the digits 1512 to gain the first accuracy mark and place the decimal point correctly to the gain the full 3 marks. Common errors seen were incorrect place value in the columns, as well as incorrect arithmetic when adding the columns, usually arriving at the digits 378 or in trying to break down the components but only using 6 × 2 and 0.3 × 0.4, giving an answer of 13.2. Some students reached 1512 but were unable to place the decimal point in the correct place; centres need to continue to encourage students to use approximation to decide on a sensible place for their decimal point.

  Text version

  Work out 6.3 x 2.4.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q19 · 4 marks

  4 marks

  19

  
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  Examiner report

  It was rare to see a correct answer in (a)(i) with incorrect answers of 0 and 5 seen often. (a)(ii) also saw little success with the majority of students gaining B0; common incorrect answers included 0.05, −10 and −25. Part (b) saw mixed results, some students were able to make a correct first step, usually adding the powers for the numerator to reach 29. From there students either went onto gain 2 marks for a correct answer or incorrectly simplified, with 29 ÷ 23 = 23 most commonly seen. A good proportion of the cohort gained no marks, making an incorrect first step such as 25 × 24 = 49 or 25 × 24 = 220. Some students also evaluated the terms as ordinary numbers and worked from there; if 64 was reached this gained M1 and was seen regularly.

  Text version

  Use laws of indices.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q20 · 4 marks

  4 marks

  20

  
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  Examiner report

  Part (a) saw most students make a good attempt at a factor tree. A good number of students were able to complete their factor tree accurately and also write their prime factors as a product. The factor tree was attempted by most students and well set out. There was a good understanding of the need for prime factors and very few included 1. Of those that did not gain 2 marks, common errors included incorrectly considering 39 as a prime number and arithmetic errors when considering the next pair of prime factors. For part (b) it was more common to see 1 mark gained rather than 2. Students were able to produce either the prime factors of 130, at least 4 factors of 156 or 130 or a common factor of 156 and 130. Of those students who gained no marks, finding the lowest common multiple was the most commonly seen incorrect method.

  Text version

  Work with the numbers 156 and 130.

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• Edexcel 1MA1 · November 2023 · Paper 1F · Q26 · 3 marks

  3 marks

  26

  
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  Examiner report

  It was common to see students gain the first method mark for rounding one of the figures appropriately, 6 or 8 on the numerator being seen most often. The majority then struggled with the next step which was to carry out an accurate calculation. Some were able to reach the digits 16, from attempting 48 ÷ 0.3 but resulting in incorrect place value. Some students attempted to work out the accurate calculation and then round the answer, gaining no marks. A few students were able to deal with the decimal value of 0.3 in the denominator by multiplying both the top and bottom of their fraction by 10. This is a useful skill for centres to continue teaching their students but in general dividing by decimals is a skill that needs more practice. Some students rounded 0.26 down to 0 which led to 48 ÷ 0 and were confused with what to do with the calculation.

  Text version

  Estimate (5.7 x 8.2) / 0.26.

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  Examiner report

  The majority of students used a suitable method to multiply 6.3 by 2.4 and most commonly this was the traditional long multiplication method. Many students gained the first mark for a complete method with relative place value correct and most then went on to get two or three marks. Some students correctly came up with the digits 1512 but placed the decimal point incorrectly and gained two of the three marks. Students making arithmetical errors were also able to score two of the three marks by giving an answer with the decimal place correctly positioned, if this followed a correct method. Students who tried to answer this question by a less formal method were not as successful, often showing an incomplete method such as 6 × 2 + 0.3 × 0.4 and gaining no marks.

  Text version

  Work out 6.3 × 2.4

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q2 · 4 marks

  4 marks

  2

  
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  Examiner report

  Part (a)(i) was generally answered well. Common incorrect answers were 5 and 0. Fewer students were able to write down the value of 5–2 in part (a)(ii). The most common incorrect answer was –25. In part (b) many students made a good start by working out 25 × 24 as 29 and gained the method mark. Many of these students went on to give 26 as the final answer but some wrote 29 ÷ 23 = 23 and did not gain the accuracy mark. A common incorrect approach was 25 × 24 = 49 followed by 49 ÷ 23 = 26. Although this approach resulted in 26 it was awarded 0 marks because the “correct” answer had been obtained from incorrect working.

  Text version

  This question is about powers and index laws.

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q3 · 4 marks

  4 marks

  3

  
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  Examiner report

  In part (a) a good proportion of students gained two marks for writing 156 as a product of its prime factors, usually by using a factor tree, and relatively few students failed to gain at least one mark. Some students gained the method mark for drawing a correct factor tree with branches ending at 2, 2, 3 and 13 but then failed to write a correct product. Students who showed a complete method but made only one arithmetic error also gained the method mark. When no marks were awarded this was usually because the method was incomplete (often due to thinking that 39 is a prime number) or because there was more than one arithmetic error. Most students were able to gain the method mark in part (b) but only about half then went on to gain both marks for finding the highest common factor of 156 and 130. A very common incorrect answer was 13 and this gained one mark. Many students chose to draw a factor tree for 130, having already drawn a factor tree for 156 in part (a), and good use was made of Venn diagrams although some students were confused as to which section of the diagram represented the highest common factor. Those students who listed factors or factor pairs of 156 and 130 were less likely to score full marks because they often failed to find all the factors or factor pairs.

  Text version

  This question is about prime factors and the highest common factor.

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q14 · 3 marks

  3 marks

  14

  
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  Examiner report

  Students who gained the first mark for interpreting 27 as ( ) 3 27 or −       as 32 often went on to gain at least two of the three marks for evaluating either 23 as 9 or 2 as 8. A good proportion of students evaluated both correctly and gave a final answer of 17. When only one term was evaluated correctly it was more often 27 as 9. Students encountered more problems evaluating −       and common incorrect values were 1 8 , − and –8. Mistakes in the evaluation of 27 included 3 27 = 9 and 3 27 = 3 followed by 3 × 2 = 6.

  Text version

  Work out the value of 27^(2/3) + (1/2)^(-3)

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q20 · 4 marks

  4 marks

  20

  
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  Examiner report

  This proved to be a challenging question and finding the size of angle ABC was beyond most students. The first mark was awarded for using the cosine rule for any angle but many students could not even get that far despite the cosine rule formula being given on the formula sheet. Many lost marks for not using brackets when squaring 5 7 and this often resulted in 35 as only the √7 was squared. Many of those that did correctly substitute into the cosine rule for angle ABC could not then rearrange the equation to make cosB the subject. Mistakes in the order of operations and sign errors were very common. Relatively few students got as far as cosB = –0.5 and many of those that did then failed to give the answer as 120o. Many students showed a lack of understanding of the requirements of the question and attempted to use the sine rule or right-angled trigonometry.

  Text version

  In triangle ABC, BA = 10 cm, BC = 5 cm and AC = 5√7 cm.

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• Edexcel 1MA1 · November 2023 · Paper 1H · Q22 · 4 marks

  4 marks

  22

  
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  This proved to be a challenging question with very few students knowing how to work out the value of the common ratio of the sequence. Some of the students who were able to use the 2nd term and 3rd term to write down the common ratio 13 9 2 2 2 + + made no further progress but it was pleasing that there were others who showed a complete process and went on to gain full marks. When attempting to rationalise the denominator errors were sometimes made in expanding terms, most commonly in the numerator. One error was condoned for the third mark. Many students did not know how to use the 2nd term and 3rd term to find the common ratio. Summary Based on their performance on this paper, students should: ● practise their arithmetic skills, particularly division and operations with decimals ● consider whether or not an answer to a calculation is of a sensible size ● take care when interpreting the scales on the axes of graphs ● practise using the standard ruler and compass constructions ● understand the difference between standard and reverse percentage ● practise using the relationships between lengths, areas and volumes in similar figures

  Text version

  The 2nd term of a geometric sequence is 3 + 2√2. The 3rd term of the sequence is 13 + 9√2

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  A good accessible start to the paper with this question being well answered with most students scoring the mark.

  Text version

  Factors.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Another accessible question with the majority of students correctly writing the decimal as a fraction.

  Text version

  Convert 0.9 to a fraction.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Writing a square number between two given values appeared to be challenging for some. Common incorrect responses included 42, 52 and similar but gained no credit.

  Text version

  Square numbers.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  The majority of students were able to find a simple percentage of an amount in this question which was very pleasing to see.

  Text version

  Percentages.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q8 · 4 marks

  4 marks

  8

  
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  Examiner report

  The first multi-step problem on the paper was tackled well with most students able to work with the different multiples of objects and obtain the correct cost for at least 2 different items using the constraints given. The presentation and amount of explanation varied, with some showing calculations to gain £188.5 only and others annotating to explain that £188.50 is less than £200 or calculating the amount of money left over. Each of these responses were sufficient for the award of all four marks. Some mistakes were often made, the majority of which seemed to be related to misreading or misinterpreting the information. Common mistakes were that 4 tennis balls cost £4 rather than £5 or that the hockey sticks were £30 each. The majority of students who did not score full marks were able to score partial marks by clearly showing their processes for multiplication and addition, however there were a few who missed out on marks due to not clearly showing their process. For example, writing £80 for hockey sticks without showing where this came from.

  Text version

  A shop charges £9.50 per football, £30 for two hockey sticks, £23 per cricket bat and £5 for four tennis balls. Curtis buys 5 footballs, 6 hockey sticks, 2 cricket bats and 4 tennis balls, and has £200.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q9 · 2 marks

  2 marks

  9

  
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  Listing possible combinations was generally answered very well, with many students who took a systematic approach to listing the combinations, (eg starting with WP, WS, WC) having the most success. Some started with WP, BS, GC and sometimes went wrong or omitted one or more combinations or gave repeated combinations. Some responses showed the combinations written in full words, rather than using the letter given in the question. This was, of course, acceptable, but may have taken longer than necessary. Some answers failed to list all 9 combinations, and so students should be encouraged to check that they have the correct total based on the options available for each variable. A few students repeated combinations (eg WP and PW), which tended to score only 1 mark.

  Text version

  There are three shirts, white, blue and grey, and three ties, plain, striped and checked.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q15 · 3 marks

  3 marks

  15

  
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  Most students were able to find 72% of 120, but it was disappointing to note that many still used a build-up method with this topic as several correctly found 70% but struggled to find the 2% accurately using this method. If the full process was not shown, due to listing their values for e.g. 50%,10% and 1%, the process marks could not be awarded for incorrect values. Of those correctly finding 72% of 120, many went on to incorrectly subtract 30% of 120 from 86.4 rather than find 30% of the value just found. It was common to see an incomplete answer of £25.92 from correctly finding 72% then 30% of the answer, but not subtracting this to find the amount remaining. Centres should encourage students to write a valid process when calculating percentages of amounts and ensure they are aware that simply writing 120 × 72% is not acceptable unless an accurate answer is shown.

  Text version

  Martha receives 72% of £120, then spends 30% of the amount she receives.

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• Edexcel 1MA1 · November 2023 · Paper 2F · Q18 · 3 marks

  3 marks

  18

  
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  This familiar calculator use question was generally answered well and the award of 3 marks was common. Some students only scored one mark in part (a) for either 8.82 or 16.6 and some scored a mark for 1.88 rather than writing all of the digits on their calculator, as instructed in the question. As with previous similar questions, writing an answer containing at least 3 decimal places is sufficient to gain full marks in part (a). A small number gave a fraction so again only scored 1 mark for not fully evaluating their answer. Whilst the majority of students gave 1.88 in part (b) some rounded to 1.8, 1.87 or 1.90. Follow through from their answer in part (a) was allowed and this was frequently awarded when only partial marks were given in part (a). A small number of students multiplied their answer in part (a) by 10 or 100, but this was not very common.

  Text version

  Calculator evaluation.

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• Edexcel 1MA1 · November 2023 · Paper 2H · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  It was surprising to see how few students were able to gain marks on this question with it being such a familiar question on this specification. It is clear that many students need a greater understanding of rounding, and truncation, and the limits of accuracy.

  Text version

  A number x is written correct to 2 significant figures. The result is 1.9

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• Edexcel 1MA1 · November 2023 · Paper 2H · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  This is a very familiar style of question, but the decimal in question proved a challenge. The big point of note from candidates is to use the correct notation for recurring decimals. This could be in the form of repeating all the recurring digits at least twice or the correct dots above the recurring digits. Those who failed to use such notation scored at most 2 marks. Many when writing the decimal out often lost the ‘2’ as a recurring digit and used repeating 3 and 7. In this case they often scored zero.

  Text version

  Prove algebraically that the recurring decimal 0.0723723723... (digits 723 recurring, i.e. 0.0 followed by recurring block 723) can be written as 241/3330

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  This question was well answered with most candidates correctly rounding off to obtain 8100. The most common error was to round off to the wrong place value, normally to the nearest 1000 leading to 8000 as an answer. Several wrote 100 rather than 8100.

  Text version

  Round 8061.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  A question in which nearly all candidates gained the mark. A minority gave incorrect answers where the numerical component was less, such as −4.

  Text version

  Negative numbers.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  This received a variety of answers with many candidates unable to identify tenths. Stating 0.9 was a more successful approach. "Uniths" was a common incorrect answer.

  Text version

  The number is 27.963.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q7 · 3 marks

  3 marks

  7

  
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  Many candidates gained one mark for either 322 or 4450. But the next steps seemed to cause an issue for many candidates. If using 322 and 178, then the tendency was to add the two figures to get 500 laps, rather than subtract. If 4450 was subtracted from the initial distance and 3600 m found, then candidates struggled to convert this to lengths. Many candidates made arithmetic errors with subtraction even though it was a calculator paper.

  Text version

  Each swimming-pool length is 25 m. Miklos has swum 178 lengths and wants to swim 8050 m in total.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q9 · 5 marks

  5 marks

  9

  
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  The familiar context of this question meant that candidates were able to access it and make some good progress into the marks. The most common method seen was to take 105g and then multiply it through by 3 (portions) and by 7 (days in a week) to find the total dog food needed for one week of 2205g. From there candidates either systematically showed totals for multiple weeks getting to 11025g or then divided 12000 by 2205 to understand that the food would last 5.4... weeks. Many implied the first process mark, even if they didn't state that 12kg = 12000g and ran the risk of losing that first mark if they did not go on to get a correct solution or show enough workings to justify it, like a solution of "5.4 weeks". Alternatively, other candidates chose to work in weeks and arrive at 38.09... weeks, however they often left their solution as this and so either scored only 2 marks or 3 marks if they had stated that 12kg = 12000g. Other common misconceptions were seen such as; 12kg = 1200g or that candidates thought that there were only 5 or 6 days in a week.

  Text version

  A bag contains 12 kg of dog food. A dog has 3 meals per day and receives 105 g at each meal.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q11 · 2 marks

  2 marks

  11

  
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  A very well answered question. The most common mistakes were either giving the fraction over 18, found by incorrectly adding the other 2 numbers in the ratio, or choosing the wrong number from the 3 options as the numerator.

  Text version

  Counters are in the ratio red:blue:green = 2:16:7.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  Candidates always seem to struggle with time, and this paper was no exception. Although it was not uncommon to see the correct answer, there were also many examples of candidates treating 1 4 hour as 25 minutes, or in some cases 20 minutes. The temptation to reach for the calculator was too much for many, who simply worked out 14.1 – 3.25 or added time to 14 10 rather than finding the difference.

  Text version

  A chess match lasted 3 1/4 hours and finished at 14:10.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  It was pleasing to see many correct answers given, with the numbers (or their equivalents) given in the correct order. Candidates who attempted to convert to fractions quickly realised that this was a more difficult route since you then had to find fractions with common denominators in order to make a comparison. They usually joined the rest in converting the two fractions to a decimal, and then ordering their five decimals, though this was not always done correctly.

  Text version

  The five numbers are 0.56, 57%, 7/12, 0.558 and 6/11.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q17 · 3 marks

  3 marks

  17

  
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  Most candidates made a start on this and gained at least one mark by calculating how many Australian dollars were earned in a week, or the UK rate per hour. Frequently candidates then went on to compare unlike values. Few gained all 3 marks because candidates often swapped between rates per week and rates per hour. If they did get to comparable figures they occasionally lost the accuracy mark since they had prematurely rounded figures earlier in their working.

  Text version

  Blake works 32 hours per week in the UK for £473.28. An Australian job pays 26.40 Australian dollars per hour. £1 = 1.796 Australian dollars.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q20 · 2 marks

  2 marks

  20

  
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  Examiner report

  Part (a) was mostly answered correctly but several candidates failed to fully understand the need to use a number between 1 and 10 when converting to standard form and gave 468 × 103 as their answer. Generally, candidates showed they had counted the movement of the 'decimal point' to place it from the end to after the 4, and this usually led to the correct answer. When the wrong answer was given, it was usually due to counting the non zero digits and this gave the incorrect 4.68 × 103. In other instances candidates dropped the digits after the 4 to give 4 × 105. In part (b) it was common to see 4 zeros put in front of the 5 and the decimal point not moved, omitted, or put after the third 0 to give 000.05037. It was common to also see the answer of 0.005037. Some candidates either did not see or did not know how to work with the negative index in standard form and gave the answer 50370.

  Text version

  Standard form.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q24 · 3 marks

  3 marks

  24

  
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  Examiner report

  This was a very well answered question with most correct answers coming from listing multiples of 30 and 24, realising that 120 was a common multiple and giving the final answer of 4 and 5 for full marks. Occasionally candidates used a different common multiple but still commonly scored full marks. Candidates who did not score generally had tried using factors rather than multiples (just by listing them). Occasionally candidates attempting to list multiples made an error before they reached three multiples for each of 24 and 30, scoring zero.

  Text version

  Each pack contains 30 balloons and each box contains 24 pencils. Ali buys the same number of balloons and pencils.

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• Edexcel 1MA1 · November 2023 · Paper 3F · Q26 · 3 marks

  3 marks

  26

  
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  Many candidates were able to recall the formula for speed (mainly seen as a formula triangle) and use it to successfully find the time by dividing distance (143 miles) by speed (55 mph) to get 2.6 (1 mark). Unfortunately, most candidates were unable to convert this to hours and minutes, often stating 2 hour 6 mins (leading to a final answer of 7 hours 26 mins) or 2 hours and 60 mins (being changed to 3 hours and leading to 8 hours 20 mins) or 2 hours 40 mins (interpreting 2.6 hours as 2 3 hour). The build up method to try to find the time for travelling 143 miles often broke down. 2 hours = 110 miles was correct but candidates struggled to find the time for the remaining 33 miles often just writing 33 minutes giving a final answer of 7 hours 53 minutes.

  Text version

  Riley travels 143 miles by car at 55 mph, then travels 5 hours 20 minutes by aeroplane.

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• Edexcel 1MA1 · November 2023 · Paper 3H · Q1 · 2 marks

  2 marks

  1

  
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  A high percentage of students showed a good understanding of standard form. In part (a) the great majority of students were able to convert from the ordinary number to a number in standard form. The most common error was to include the integer 468 as part of the answer. For example, 468 × 103 was often seen. A slightly smaller proportion of students were successful in part (b) which involved converting a number in standard form with a negative index into an ordinary number. There was no single error which was commonly seen in responses to this part of the question.

  Text version

  This question is about standard form.

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• Edexcel 1MA1 · November 2023 · Paper 3H · Q5 · 3 marks

  3 marks

  5

  
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  Another well answered question with most students using the common multiple 120 and giving 4 packs and 5 boxes as their answer. Working was generally accurate. Alternative commonly seen acceptable combinations included 8 packs and 10 boxes, 12 packs and 15 boxes and 24 packs and 30 boxes. This latter pairing was given by those students who found 720 (30 × 24) as their common multiple. Very few students used factor trees or Venn diagrams to find a common multiple. Where these approaches were used, they were often not successful.

  Text version

  Ali buys packs of balloons and boxes of pencils. There are 30 balloons in each pack. There are 24 pencils in each box. Ali buys exactly the same number of balloons and pencils.

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• Edexcel 1MA1 · November 2023 · Paper 3H · Q7 · 3 marks

  3 marks

  7

  
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  This question testing the use of mixed units of time in the context of distance, speed and time was successfully completed by about a half of all students taking this paper. However, the vast majority of students gained a mark for using time = distance ÷ speed to get the time travelled by car. Unfortunately, the process of changing to consistent units of time defeated many students. In particular, when trying to work in hours and minutes, many students changed 2.6 hours to 2 hours 60 minutes which, in turn, often led them to a final answer of 8 hours, 20 minutes. Another common error was for students to write 5 hours, 20 minutes as 5.2 hours then add this to 2.6 hours to end up with the same 8 hours 20 minutes as their final answer. Teachers might find it useful to help students to recognise that the decimal part of an hour represents tenths of an hour by using a conversion table to emphasise that 0.1 hours = 6 minutes This may help students to understand that decimal part of an hour × 60 = number of minutes.

  Text version

  Riley travelled by car and by aeroplane. He travelled 143 miles by car at an average speed of 55 miles per hour. Riley then travelled for 5 hours and 20 minutes by aeroplane.

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• Edexcel 1MA1 · November 2023 · Paper 3H · Q16 · 3 marks

  3 marks

  16

  
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  Where lower attaining students attempted this question their answers were often restricted to listing the possible numbers for each digit of the passcode without writing down the number of options for each digit. These students could not be awarded any credit. Having said this, the question discriminated well between higher attaining students with each of the possible marks often being awarded. Only a small proportion of students scored full marks for a correct probability. A significant number of students used fractions with denominator 9 in their calculations. They did not appear to appreciate the importance of “Zia tells her friend Amber that...” The most common error leading to the loss of the final mark was for students to include 1 in their list of prime numbers which led to an answer of

  Text version

  Zia has to set a 4-digit security passcode on her phone. Each digit of the passcode is a number from 1 to 9. She can use each number more than once. Zia tells her friend Amber that: the first digit is a cube number; the second digit is a prime number; the third digit is greater than 6; the fourth digit is an odd number. One possible 4-digit passcode is 1 3 8 3. Amber is going to have one attempt at guessing Zia's passcode.

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• Edexcel 1MA1 · November 2023 · Paper 3H · Q22 · 4 marks

  4 marks

  22

  
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  Examiner report

  This question proved to be more of a challenge to the highest attaining students than any other question on the paper but there were still a good number of fully correct responses. Low attaining students often merely substituted values into the word formula without considering bounds. They could not be awarded any marks but of those students who did consider bounds, a large number of them wrote down at least one correct bound from the six bounds relevant to the three values given in the question. Only the best students could identify the correct bounds to use in order the minimise the profit (lower bound of selling price − upper bound of cost of materials). Students who showed a good understanding of the bounds needed for this could usually complete the process to find the lower bound of the hourly rate of pay and use it to give a statement to confirm that Ebony’s rate of pay was definitely more than £8.20

  Text version

  Ebony makes some bracelets to sell. The materials to make all the bracelets cost £190, correct to the nearest £5. Ebony sells all the bracelets for a total of £875, correct to the nearest £5. The total time taken to make and sell all these bracelets was 72 hours, correct to the nearest hour. Ebony uses this method to calculate her hourly rate of pay: hourly rate of pay = (total selling price - total cost of materials) ÷ total time taken. The minimum hourly rate of pay for someone of Ebony's age is £8.20.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  Many students failed to read this question carefully and offered an ordered list of the given numbers, often correctly. This was only accepted if the correct answer of 0.5 was then explicitly chosen as the smallest number. Some wrote 0.50 for their answer. This was perfectly acceptable.

  Text version

  Here is a list of numbers: 1.6, 1.4, 2.1, 0.5, 1.3.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Although –4 was the modal answer, answers of –14 and 4 were common.

  Text version

  Work out -9 + 5.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  Whilst, on the whole, this question was answered well, many students did try to over complicate their solutions by first constructing factor trees and some even giving 20 as a product of its prime factors; 22 × 5 or 2 × 2 × 5, both of which earned one mark for identifying two correct factors. Product pairs were often seen, eg 4 × 5, etc. and these were an acceptable alternative way of identifying the factors of 20. Some students listed multiples of 20 failing to understand what a factor was.

  Text version

  Write down three different factors of 20.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  It was very pleasing to see many students clearly reading and comprehending the demand of this question and achieving full marks. Repeated addition was a preferred method rather than multiplication. Other than losing marks through arithmetic errors, marks were lost if the student hadn’t fully understood the ‘special offer’ either by just finding the cost of 6 large plates and 6 small plates at their normal prices or by thinking that the offer applied to large plates as well as small.

  Text version

  A shop offers one small plate at half its normal price with each large plate bought. A large plate normally costs £2 and a small plate normally costs 80p. Max wants 6 of each and has £15.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q11 · 6 marks

  6 marks

  11

  
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  Examiner report

  The modal answer in part (a) was the correct answer 248 but a great many students showed a complete inability to compute this subtraction accurately. Answers of 252, 352 and 348 were very common. A mark was often obtained by writing out the subtraction even if the technique was poorly executed. In part (b) many students insisted on trying to find the exact cost of the 696 tickets and consequently spent an inordinate amount of time following long multiplication processes. This life skill of estimating calculations is clearly an area that needs to be addressed. The numbers in the question are chosen to encourage, in this case, rounding up to values of 300, 400, 10 and 20 enabling the calculation to be straightforward. Those that did this usually gained the mark in part (c) for a correct reason for their answer being an overestimate. Some candidates thought rounding to the nearest 10, 100 etc explained that they had rounded up. Many students correctly said it was an overestimate but followed it up saying it had been rounded to the nearest whole number.

  Text version

  A total of 700 tickets were on sale for a football match; 452 were sold. For another match, 297 tickets were sold at £9.50 each and 399 at £19.50 each.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q14 · 5 marks

  5 marks

  14

  
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  Examiner report

  Part (a) was answered well with very few failing to subtract 73 from 100 correctly. In part (b), 5 was the most common error made. Part (c) offered a different challenge and while many were able to find 70% of 500, fewer were able to find 8 of 720 and thus complete the solution. Some divided by 8 but were unable to then multiply their answer by 5. An interesting way round this was to find one half of the 720 and conclude that this was already larger than 350 and that as 8 was larger than one half then Kasim was wrong. Others multiplied by 8 first and then divided by 5. Some attempted to convert 5/8 to a percentage. Those achieving this correctly were often unable to calculate 62.5% of 720. Many students assumed that an equal number of people watched the film on each day and simply compared 70% with 8 , concluding that more children watched the film on Friday as 70% is greater than 8 . A number failed to state 'No' despite all workings being correct so did not gain the final mark.

  Text version

  Last week, 73% of cinema tickets sold were adult tickets. At another film the adult-to-child ratio was 2:5. On Friday 500 people watched a film and 70% were children. On Saturday 720 watched and 5/8 were children.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  Very few students started by cancelling the 6 and 12. Those who did invariably got full marks. The most common correct approach was to find the product of the numerators and the product of the denominators to give 84 although there were many arithmetic errors along the way. A great number then failed to cancel the fraction to its simplest form, often simply dividing by 2. Another common approach was to find a common denominator giving 84 × This gained no credit until the student demonstrated how to multiply two fractions together, which they rarely even attempted. A high proportion of incorrect answers showed an attempt to find equivalent fractions first followed by addition of numerators. Weaker students often crossed multiplied to get 72. This of course also gained no credit.

  Text version

  Work out (6/7) x (5/12).

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q17 · 4 marks

  4 marks

  17

  
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  Examiner report

  The vast majority of students were able to find the actual number of yellow and green counters in the bag (55 of each) but were unable to work this out as a percentage of 200. The usual answer was to simply offer 55 as their percentage. Very few showed their method for the final percentage which would have gained a method mark. When students attempted to write 55/200 as a percentage, they usually took the approach to halve numerator and denominator but often couldn’t divide 55 by 2, 22.5 being a common error.

  Text version

  There are 200 counters in a bag: 38 red, 52 blue, and the rest split equally between yellow and green.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q20 · 3 marks

  3 marks

  20

  
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  Examiner report

  Many students did not know how to approach long division, especially with decimals. Far too many arithmetic errors prevented many students getting more than maybe one mark in this question. Even when division was carried out correctly accurate placement of the decimal point was rare. Some were unable to deal with the remainder of 6 and an answer of 56.6 was common. Several students who found the correct answer 56.4 in their working then divided by 100 and wrote 0.564 on the answer line. Some students tried build up methods. These rarely resulted in a fully correct final answer but credit was often earned along the way with 5 as the first digit and often a correct size of their final answer.

  Text version

  Work out 8.46 / 0.15.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  It was pleasing to see many students making valiant efforts to work with the given fractions. The whole numbers 7 and 2 were usually correctly dealt with and the difference between and 2 ( 8) was usually correct although many left this as a positive one eighth leading to an answer of 5 8 Students who converted both mixed numbers to improper fractions often fared better and were able to give a correct final answer. The most common incomplete answer seen was 8 . Weaker students often gave answers of 5 6 or, if they had converted to improper fractions, However, in many solutions of students at all levels, simple arithmetic errors were made, 7 × 8 was often seen not equal to 56

  Text version

  Work out 7 3/8 - 2 1/2.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q22 · 4 marks

  4 marks

  22

  
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  Examiner report

  Many students found this question far too demanding, not realizing that the total surface area of a cube was 6 times the area of one face. 150 divided by 4 was a common error. Even when the area of one face was correctly found many were able to go no further, often giving the volume as 25 × 25 × 25 or attempting to divide 25 by 4 (rather than finding the square root). For the students who did gain credit on this question the vast majority only scored 1 mark for dividing 150 by 6.

  Text version

  A cube has total surface area 150 cm^2.

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• Edexcel 1MA1 · June 2023 · Paper 1F · Q29 · 2 marks

  2 marks

  29

  
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  Some did some good work showing an understanding of the rules of indices but ultimately often failed to work out the value as required; 42 was a common answer. 4 was often seen but rarely converted to 16. 13 was a common answer following from this. Whilst 42 was a common answer it had often been derived from incorrect working. 4 was often seen from incorrect working of the numerator. This then was usually simplified to 42 gaining no credit. Unfortunately, some candidates spent a lot of time trying to evaluate the separate elements.

  Text version

  Work out the value of (4^-6 x 4^9) / 4.

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  Most students used a formal method to divide a number with the digits 846 by a number with the digits 15 and usually gained the first mark for making a correct start to the method and getting 5 as the first digit. Many went on to gain all three marks. Some of those who divided correctly to get the digits 564 then positioned the decimal point incorrectly and gained only two of the three marks. Having divided 846 ÷ 15 and obtained 56.4 many students then gave the final answer as 0.564 or 0.00564, most likely thinking that they needed to divide 56.4 by 100 or by 10000 because they had multiplied both figures by 100 before dividing. If they had considered the relative sizes of the two numbers in the question then they might have realised that their final answer was not sensible. Arithmetic errors were common but students who had gained the first mark were still able to gain two of the three marks if the decimal place was correctly positioned in their final answer. A number of students did not know how to deal with the final remainder of 6 which often resulted in answers of 56.6. Some students chose to use a build-up method or repeated subtraction to carry out the division but these methods were rarely successful.

  Text version

  Work out 8.46 ÷ 0.15

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q2 · 3 marks

  3 marks

  2

  
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  This question was answered very well. The most common method was to convert both mixed numbers into improper fractions and then write the fractions over a common denominator. Many students gained at least two of the three marks for getting this far. The accuracy mark was often lost because students failed to write their answer as a mixed number or they made an arithmetic error. Many of the arithmetic errors occurred when converting the mixed numbers to improper fractions. Some students used 16 rather than 8 as the common denominator which increased the chances of them making an arithmetic error. Having written both mixed numbers as improper fractions some students made no further correct progress and gained one mark only. Far fewer students chose to subtract the whole numbers and deal with the fractional parts separately. The difficulty that some had with this method was subtracting a larger fraction from a smaller fraction which meant that − was often not evaluated correctly.

  Text version

  Work out 7 3/8 − 2 1/2. Give your answer as a mixed number.

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q3 · 4 marks

  4 marks

  3

  
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  Many students gained the first mark for dividing 150 by 6 to find the area of one face of the cube and very often they went on to score full marks for working out the volume of the cube. After finding the area of one face some students could make no further correct progress. It was common to see 25 divided by 2 or by 4 in an attempt to find the side length and some thought that the volume was given by 25 × 25 × 25. A significant number of students could not show a correct first step and gained no marks. Some attempted to draw the cube and gave a first step of 150 ÷ 3 (presumably the 3 visible faces). Some misinterpreted the question and assumed that 150 was the surface area of one face and wrote 150 or divided 150 by 4.

  Text version

  A cube has a total surface area of 150 cm².

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  Many students gained the first mark for simplifying either the numerator or the denominator with at least two of three terms correct in a product. At this stage the most common mistakes were 6x10y6 or 36x25y9 or ax7y5 instead of 36x10y6 in the numerator and 12x2y4 instead of 12x3y4 in the denominator. A good proportion of students completed the algebra correctly and arrived at an answer of 3x7y2. Some students made one error in the numerator or denominator and gained two marks for an answer of the form axbyc with two of a, b and c correct (of these the error was often an incorrect coefficient). A small number of students used a different approach and instead of simplifying the numerator and the denominator they chose to start by simplifying 6x5y3 ÷ 3x2y7 and 6x5y3 ÷ 4xy–3. A common error was for students to introduce plus signs into the numerator and then attempt to expand the two brackets, leading to more than one product for the numerator.

  Text version

  Write (6x⁵y³)² / (3x²y⁷ × 4xy⁻³) in the form ax^b y^c where a, b and c are integers.

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q14 · 4 marks

  4 marks

  14

  
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  Part (a) was answered quite well with many students able to write 1 16 as −. Common incorrect answers included −, − and 4 . In part (b), students who interpreted 8 as ( ) 3 8 or 9 as ( ) gained the first mark and usually went on to gain at least two of the three marks for evaluating 2 as 32 or 3 as 27. Most went on to evaluate both correctly and gave a final answer of 5. When only one term was evaluated correctly it was more often 9 as 27. Mistakes were more common in the evaluation of 8 and 25 = 64 was frequently seen. Some students found 3 8 =2 or 9 = 3 (or both) but then incorrectly multiplied by 5 and 3 respectively instead of raising to a power. Those students who interpreted 8 as 3 58 or 9 as 9 gained the first mark but were rarely able to evaluate either 3 58 or 9 correctly.

  Text version

  This question is about indices.

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q16 · 4 marks

  4 marks

  16

  
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  Most students started with a process to find the surface area of the sphere. Some made no further progress but many continued with 4πr2 = 200π or 4r2 = 200 and went on to find the radius and gained the first three marks. Inconsistent use of π was a problem for some. It was not uncommon to see a surface area of 200π followed by 4πr2 = 200. After showing a correct process to find the radius a significant number of students then failed to get the accuracy mark for finding the diameter of the sphere in the required form. Many could not write as 5 2 with 50 = 10 5 a common mistake and the radius was often given as the final answer . Instead of starting with a process to find the surface area of the sphere some students started by forming the equation r    = .

  Text version

  The surface area of a sphere of radius r is 4πr². 3/8 of the surface area of a sphere is 75π cm².

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q19 · 2 marks

  2 marks

  19

  
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  This question was answered very well with many students getting both marks for working out the value of x as 7. Some who gained the first mark for a statement such as 5 × 12 × x = 420 were unable to complete the arithmetic correctly. A common error was 420 ÷ 60 = 70. Misreads of the number 420 in the question were quite common. Students who misread 420 were still able to gain the process mark but not the accuracy mark. It was quite common to see 5 + 12 used within solutions and incorrect answers often involved an attempt at 5 + 12 + x = 420.

  Text version

  The menu in a restaurant has starters, main courses and desserts. There are 5 starters, 12 main courses and x desserts. There are 420 different ways to choose one starter, one main course and one dessert.

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• Edexcel 1MA1 · June 2023 · Paper 1H · Q23 · 4 marks

  4 marks

  23

  
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  This question involved writing two fractions with a common denominator, rationalising and simplifying surds. There were many valiant attempts achieving varying degrees of success and not many blank responses. Many students started with a method to write the two fractions with a common denominator and gained the first mark. A common mistake, which prevented the award of the second mark, was incorrectly simplifying 2 3 4 3 4 3 − − − − to 1 2 3 4 3 − − . Some students were unable to continue the solution any further and gave their single fraction as the final answer. A good number of students though went on to gain the third mark for a method to rationalise the denominator with some giving a fully correct solution. The alternative approach used by a good proportion of students was to start by rationalising the denominator of each fraction before writing the fractions with a common denominator. The main obstacle to a successful outcome for these students was making errors when manipulating the surds with common mistakes being √3 × √3 = 9 and √3(3√3) = 3√3 + 3. Those who used this approach were more likely to give a fully correct answer. Some students used a hybrid approach, rationalising one fraction before trying to achieve a common denominator and then rationalising again. This route had comparable success with the other routes.

  Text version

  Write 3√3/(4 − √3) − 2/√3 in the form (a√3 + b)/c where a, b and c are integers.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  A good accessible start to the paper with this question being well answered most students scoring the mark.

  Text version

  Write 6184 correct to the nearest hundred.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Another accessible question with a majority of students correctly writing the decimal as a fraction.

  Text version

  Write 0.7 as a fraction.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Most students could change between metres and centimetres but converting between metric units remains challenging for some students with many forgetting the conversion factor to use.

  Text version

  Change 9 metres into centimetres.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  This question was answered correctly by almost all students.

  Text version

  From the list 20, 40, 60, 80, 100, choose the multiple of 25.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q11 · 3 marks

  3 marks

  11

  
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  Using a frequency table to find the total weight was generally well answered, with most students understanding that they needed to multiply the weights by the number of people, before adding together to get the total weight. Some just added the weights in the weight column, ignoring the frequencies thus gaining no credit. Arithmetic errors cost a minority of students the accuracy mark (disappointing on a calculator paper) and some students only included 5 products, usually omitting a weight with frequency of one. Adding an extra column to the table proved very helpful for many students. It is important for students to have experience of working with data in tables and to understand how to extract the relevant information. Centres should also encourage students to make full use of a calculator to check their answers when in a calculator exam.

  Text version

  A hotel lift contains people with weights and frequencies: 40 kg: 1; 50 kg: 2; 60 kg: 4; 70 kg: 5; 80 kg: 3; 90 kg: 1.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q13 · 2 marks

  2 marks

  13

  
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  Success in this question was mixed, with understanding of the information provided being vital in the level of success. Whilst most of the cohort gained both the marks available, many scored no marks at all, often due to not identifying that 50 represented one sixteenth and subsequently dividing 50 by 16 rather than multiplying by 16. Of those who correctly interpreted the information given, some incorrectly thought they still needed to add or subtract the 50 teachers to their answer.

  Text version

  There are 50 teachers in a school, representing 1/16 of everyone in the school.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q14 · 4 marks

  4 marks

  14

  
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  This multi-step problem proved challenging for many students. Whilst many were able to start this question sensibly, very few were able to complete the processes required to find the correct answer. Partial marks were often awarded with many students successfully gaining marks for correctly calculating the volume of one or both shapes. This was usually done before any unit conversion. Fewer students worked accurately with one dimension between the shapes to find the number of packets that could fit along one edge of the box. Students who found the number of packets along each edge (9, 8 and 12), often misunderstood what to do with these values, with addition of 9, 8 and 12 being a commonly seen next step rather than multiplying. Students choosing to work this way often marked their values on the diagram and this approach is to be encouraged. Students who gained the unconditional accuracy mark for conversion between units usually converted units before working out the volume. Some students attempted to convert after calculating the volume and were often confused with volume conversion from mm3 to cm3 and vice versa and so were unable to go on and achieve full marks. Quite a few students calculated the surface area rather than the volume or simply added all the three lengths together for each shape.

  Text version

  Each sweet packet is a cuboid 80 mm by 60 mm by 20 mm. Each box is 72 cm by 48 cm by 24 cm.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q18 · 6 marks

  6 marks

  18

  
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  It was very pleasing to see that the majority of students could gain full marks in part (a). When full marks were not awarded, the most likely score was zero and was often due to a range of approaches being attempted. Most students chose to divide 180 by 12 and then multiply by 3. Occasionally a student would try a build-up method of 12 cans cost £3, 24 cans cost £6 etc. Unless completely correct, this approach rarely scored partial marks. The addition of an extra measure alongside money when using proportion appeared to cause great difficulty for many students in part (b). Fully correct solutions were rare in comparison with part (a) and many more students demonstrated a choice of approaches, often simply trying to make use of the values in the question using a range of operators. Of the students who correctly showed that each can cost 29p, many then struggled to know how to use this to calculate the cost of a proportion of the can, with many simply dividing by 3 as they thought 100 was a third of 330 ml. Whilst some students got as far as 0.088... or 0.09, unfortunately the accuracy mark was often lost for leaving their answer in pounds when it was requested in pence. Centres should encourage students to read the question again at the end of their calculations to ensure the final answer is given in the correct units or to the required level of accuracy.

  Text version

  Asha buys 180 cans in packs of 12 at £3 per pack. Ethan buys 24 cans of lemonade for £7, with 330 ml in each can.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q20 · 3 marks

  3 marks

  20

  
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  It was pleasing to see that the majority of students gave a fully correct answer to this question. Many of the students who gained the 2 marks for the question simply gave the full answer, which was acceptable for the award of the marks, but many showed no intermediate calculations for the numerator or denominator and gained no marks for an incorrect final answer. A method mark was often awarded for correctly evaluating either the denominator or the numerator but the values were then added or multiplied rather than divided. Most students wrote down all the figures from their calculator as advised in the question without rounding unnecessarily which was also pleasing to see. A common error was to get a final answer of 28.306.... that resulted from entering the calculation into the calculator in one go without brackets or proper use of fraction function. This led to BIDMAS being applied incorrectly on the calculator and often led to no marks being awarded. Students should be encouraged to work out and write down the value of the numerator and denominator separately to ensure they are awarded for their working out and to avoid order of operation errors. Working out the value of the reciprocal in part (b) appeared demanding, with very few students gaining the mark available. Many wrote the reciprocal of 0.625 as 0.625 but did not evaluate to give the answer as an acceptable value such as 1.6.

  Text version

  Evaluate (25 - sqrt(43.87)) / (6 + 2.1^2), and find a reciprocal.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q21 · 2 marks

  2 marks

  21

  
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  Around half of the cohort were successful in writing the value correctly as a product of prime factors and gaining the two marks available in this standard and familiar question. As with previous series, the most common reason for the loss of marks was due to writing factor pairs instead of finding prime factors, gaining no credit, or finding the prime factors but not writing these as a product. Listing the correct prime factors using commas or as an addition gained the method mark only. A number of students made careless arithmetic errors when writing their factor tree such as 6 = 3 × 3 or 10 = 5 × 5 and quite a few left 15 at the end of a branch, resulting in an incomplete factor tree which scored no marks. Some students included 1s in their factor trees, which was acceptable for the method mark, but not for the accuracy mark. However, this was less frequently seen than in previous series which is encouraging.

  Text version

  Write 60 as a product of prime factors.

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• Edexcel 1MA1 · June 2023 · Paper 2F · Q26 · 2 marks

  2 marks

  26

  
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  The majority attempted the question and but very few fully correct answers were seen. Of the students who gained partial marks for finding one correct value, usually 12.65, it was common to provide the incorrect upper bound of 12.74. In addition to blank responses, whole number answers of 12 and 13 or 12.6 and 12.8 were often seen as incorrect values that gained no credit. The most successful answers were often those where a number line was drawn showing 12.6 to 12.8 and subsequently identifying where the bounds would be. Therefore, to improve student outcomes, centres should encourage students to use a number line method where the number to add or subtract is half the degree of accuracy asked for. Students would also benefit from having a better understanding of inequality notation.

  Text version

  A number d rounds to 12.7 to 1 decimal place.

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• Edexcel 1MA1 · June 2023 · Paper 2H · Q1 · 3 marks

  3 marks

  1

  
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  Part (a) provided a very familiar start and was answered very well. It is clear however that candidates are attempting the calculation in a single step. This is of course perfectly acceptable, but it leads to them either getting full marks, or no marks, as not intermediate or partial calculations are seen. Part (b) was again answered well, but some candidates were unaware of what is acceptable when asked for a ‘value’. In this case we needed to see a decimal or a fraction that did not include any decimal values within it. For example, simply writing 0.625 was not acceptable.

  Text version

  This question is about calculator use.

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• Edexcel 1MA1 · June 2023 · Paper 2H · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  Another very familiar question and one that was answered well by almost all. The most common error leading to 0 marks was to see an incomplete factor tree, that is where a branch ended with a composite number and not a prime number. The most common method was to draw a factor tree. Some responses included commas or addition signs between the prime factors instead of multiplication, showing a lack of understanding of 'product'. On some papers it was difficult to distinguish between multiplication and addition signs so pupils should take more care with presentation. There were also some arithmetic errors such as 3 x 3 = 6 which had clearly not been checked and sometimes pupils wrote the wrong power of 2.

  Text version

  Write 60 as a product of its prime factors.

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• Edexcel 1MA1 · June 2023 · Paper 2H · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  This is now a familiar question, and one that was answered very well. Candidates typically do better on this version of the error interval question, rather than when tested on truncation.

  Text version

  A number, d, is rounded to 1 decimal place. The result is 12.7

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• Edexcel 1MA1 · June 2023 · Paper 2H · Q19 · 3 marks

  3 marks

  19

  
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  Many candidates, including some of the weaker ones, were able to gain a mark here for a suitable bound, it was good to see that they were applying their knowledge of error intervals into a more complex context. However, many then struggled to select the correct bound in their expression for sin(x) and so gained no further credit. Candidates who did select the correct bounds and achieved 2 marks, typically then did gain the final mark, although a number forgot to find the inverse sine and were left with an answer of 0.731... rather than 46.989… Some candidates attempted the question in the incorrect order and worked with sin(x) and then attempted to find bounds of this answer. This method gained no marks.

  Text version

  ABC is a right-angled triangle with the right angle at B. Angle ACB is marked x. AB = 9.3 cm correct to the nearest mm. AC = 12.6 cm correct to the nearest mm.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  This question was answered correctly by most candidates. In cases where zero marks were awarded it was most likely to be because of extra zeros which showed a lack of understanding of place value, for example 30001007 or 31007.

  Text version

  Write the number three thousand one hundred and seven in figures.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Common incorrect answers of 400 or 40000 were seen, from a misunderstanding of how many grams there are in a kilogram.

  Text version

  Change 4000 grams into kilograms.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  This question was answered well. Those that didn’t get the mark generally ordered the two negative numbers incorrectly, though some only wrote down four of the numbers.

  Text version

  Order the numbers 7, -5, 3, 9, -2 from smallest to largest.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  This question was well done by the majority of candidates with most gaining 3 or 4 marks. Most showed they needed to add all the times to 8.30 but for many this was not a strong point thus losing the C mark as their figures were not accurate. A lot of students obtained an answer of 9.15 rather than 10.15 for the first calculation when adding 1 hour 45 minutes to 8.30. Candidates also lost marks for forgetting the rest period when calculating the final time. A very efficient process seen on quite a few occasions was to add the times to give 3 hr 25m and then add that to 8.30, leading directly to 11.55. Mistakes crept in when carrying times over the hour, or when they attempted to use their calculators to do the arithmetic, or from arithmetic errors.

  Text version

  Wayne starts walking at 08:30, walks for 1 hour 45 minutes, rests 15 minutes, then walks 85 minutes to a cafe.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q24 · 3 marks

  3 marks

  24

  
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  Examiner report

  Most candidates struggled to access this question. Many confused the two skills and some stated the multiple as the factor and vice versa, confused by the terms "lowest" and "highest". At this level the numbers chosen for this problem also hindered candidates further. Hardly any tried to find factor pairs for part (a), however some did start to list multiples to find the solution for the second part. In part (b) most were rewarded with the method mark, but not many went far enough, or without error, to arrive at the solution of 15876. It was pleasing to see that more candidates, than in previous sessions, chose to utilise Venn diagrams and prime factor decomposition to solve these two questions. However, again many confused the two skills, and many were unable to use their Venn diagram to actually arrive at the two solutions required. Common incorrect answers were 7 in part (a), using the highest prime factor, and 3 in part (b) using the lowest prime factor. Those who gained full marks mostly did so using the Venn diagram method, rather than listing multiples.

  Text version

  A = 2^2 x 3^4 x 7 and B = 3^2 x 7^2.

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• Edexcel 1MA1 · June 2023 · Paper 3F · Q28 · 4 marks

  4 marks

  28

  
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  Examiner report

  Part (a) was not answered particularly well. The requirement to write the ratio in the form 1: n seemed to confuse many with few students achieving both marks. The majority attempted to convert both values into ordinary numbers with 9000 being the common error at this stage. Those that did convert the values correctly often failed to write them as a ratio losing both marks. Generally candidates found it hard to simplify to the 1 : n form with many at this point not realising they needed to divide both values by 90 000. In part (b) candidates found more success. Perhaps having a calculator made it more accessible to the students as the vast majority attempted to give an answer. It was pleasing to see how many students were able to convert standard form numbers into ordinary numbers though some clearly did not use their calculators to help them with this. This was by far the most successful approach to answering this question correctly with the majority who did the conversion gaining full marks. Where students did not get full marks, most were able to gain one mark for having no more than one error in the order, or for converting into ordinary numbers. A common incorrect approach was to put them in order by their index number. Summary On the evidence of performance on this paper, students need to: • Written work needs to be legible for examiners to consider awarding marks. Figures taken from the question, and taken from candidate’s own work, need to be transcribed accurately. • Candidates need to be trained to avoid rounding or truncating answers to calculations, and to use the most accurate values where possible. • There is a continued need for emphasis to be given to algebraic manipulation and derivation, and application of ratios, scaling and rates, and time in preparing for future examinations. • Candidates need to be trained to use their calculators for working with percentages, rather than always using a break-down / partitioned approach. • The inclusion of working out to support answers continues to need emphasis.

  Text version

  Work with standard form and ordering.

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• Edexcel 1MA1 · June 2023 · Paper 3H · Q2 · 5 marks

  5 marks

  2

  
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  The majority of students scored full marks on this question. There were a number of routes through the question and stages in the working could be seen in different orders. Most students started by calculating 68% of 800 then proceeded to take into account the other factors stated in the question. However, some students did not include all the factors, for example, forgetting that each person will drink 2 cups of coffee. In cases where a student did not get a correct answer for the amount of coffee needed, a common error made was dividing 1088 by 10.6 instead of multiplying to give a final answer of 103g. Nearly all students earned the mark in part (b) for stating that “more coffee would be needed”, or equivalent. Students should be reminded that if they calculate and use values to support their answer in part (b), the values must be correct.

  Text version

  Jonny wants to know how much coffee he will need for 800 people at a meeting. Each person who drinks coffee will drink 2 cups of coffee. 10.6 g of coffee is needed for each cup of coffee. Jonny assumes 68% of the people will drink coffee.

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• Edexcel 1MA1 · June 2023 · Paper 3H · Q5 · 3 marks

  3 marks

  5

  
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  Examiner report

  Students who had a good understanding of the concepts of highest common factor and lowest common multiple found this question to be straightforward. However, this was often not the case, with many students confusing the two terms or being unable to apply the concepts to numbers given in index form. A significant number of students gave a correct answer to part (a) on the answer line for part (b) and vice versa. They could not be awarded any marks. Many students used a Venn diagram approach but often they did not have a good understanding of how to use their diagram to answer the question. In both parts, answers left in index form or as a product of factors received full credit. In part (a) the most commonly seen incorrect answers included 3, 7 and 9. In part (b), common incorrect answers included 22 × 34 × 7 × 32 × 72 (or 1000188) and 2 × 2 × 3 × 3 × 7 (or 252). Some students were able to gain a mark for listing at least 3 multiples of 2268 and at least 3 multiples of 441 though these students were less likely to find a correct final answer.

  Text version

  A and B are numbers such that A = 2^2 × 3^4 × 7 and B = 3^2 × 7^2

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• Edexcel 1MA1 · June 2023 · Paper 3H · Q9 · 2 marks

  2 marks

  9

  
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  Examiner report

  This question was also well answered. A wide variety of successful approaches were seen using fractions or decimal multipliers or both. Of those, a small number of students who scored one of the two marks available, gave an answer of 0.56 or 5.6. Students who attempted the question but scored no marks for their responses usually added or subtracted the 70% and 80% or expressed one as a percentage of the other.

  Text version

  Some people were asked if they wanted a new television. 70% of the people said yes. 80% of the people who said yes wanted a television with a large screen. What percentage of the people asked said they wanted a television with a large screen?

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• Edexcel 1MA1 · June 2023 · Paper 3H · Q20 · 3 marks

  3 marks

  20

  
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  Examiner report

  There were many good attempts at this question. Most students who understood the method used either 1000x − 10x or 100x − x. The detail and presentation of the proof could have been clearer in some cases but it was usually good enough to award some marks for the response. For full marks, examiners expected to see an indication that recurring decimals were being used, for example, by the use of “...” at the end of the numbers or by dots above the 2 and the 3. Students who gave a correct and complete method without this were awarded 2 of the 3 marks available.

  Text version

  Prove algebraically that the recurring decimal 0.1232323... (with the digits 23 recurring) can be written as 61/495

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  This first question was generally well answered and served as a good introduction to the paper. Correct answers of 10 or 100 were the most common.

  Text version

  Write 0.3 as a fraction.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  This question was usually answered correctly although an answer of 6 (3×2) was a common mistake.

  Text version

  Work out 3².

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  Another well answered question with few mistakes. It was pleasing to see most able to follow the correct order of operations.

  Text version

  Work out 20 ÷ (3 + 2)

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Although 10 and/or 12 were seen more often than not, a number of students failed to gain the mark by offering extra, incorrect values. 6 being the most common seen.

  Text version

  Write down a factor of 60 that is between 8 and 14

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q6 · 4 marks

  4 marks

  6

  
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  Examiner report

  It was very pleasing to see so many students gaining good marks on this multi- step question. The vast majority gaining 2+ marks. In general, marks were lost through not reading the question carefully. Often just one child was considered, or two adults were included. Another common mistake was to omit the cost of petrol while in other cases it was seen as a cost for each person. Poor arithmetic often denied many full marks, mainly with the addition of two child tickets (the only non-integer), or with an inability to line up integers and non-integers successfully in a column addition method. Some gave the total cost of the trip instead of the change. The standard of presentation of answers was lacking, in some cases, with little structure or order to what they were doing

  Text version

  Fay is planning a trip to a theme park for 1 adult and 2 children. These are the costs for the trip. Total cost of petrol £23 Tickets to theme park £33 each adult £24.50 each child Meals £15 each adult £10 each child Fay has £200 to spend. She pays all the costs. How much money does she have left? £

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q10 · 3 marks

  3 marks

  10

  
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  Most students correctly worked out that 5 was the greatest number of jars of coffee that could be bought for £23 in part (a). In part (b), a large number of candidates lost the mark as they hadn’t read the question carefully enough, missing the word “exactly” in reference to the number of jars to be bought at half price. Many realised that Michael could now buy an extra 11th jar but then lost the mark because they answered ‘yes’ to the question “Is Michael correct?”.

  Text version

  A shop sells jars of coffee. Each jar of coffee costs £4 Michael has £23

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q12 · 5 marks

  5 marks

  12

  
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  Examiner report

  Again with this multi-step problem in part (a), it was pleasing to see many students gaining good marks, often 2 or more. In this question, students had to find a sixth and 20% of 120 minutes. When performing calculations of this type it is important for students to show their working, eg 120 ÷ 6 or 100 × 120 so that credit can be awarded for correct method if errors are made with accuracy. In solving this problem, some students subtracted 50 from 120 to give 70 minutes and used this as the time spent playing badminton. Arithmetic errors were seen far too often from students when subtracting from 120. In part (b), many ignored the good work they had done in part (a) and explained that Elana did not get to the café on time because she spent 2 hours at the sports centre making it 3.30pm when she left. This part followed through the working and answer in part (a) and the mark awarded if the reason and working were correct for the time given in (a).

  Text version

  Elena spent 120 minutes at a sports centre. She played badminton for 50 minutes, used the swimming pool for 1/6 of the 120 minutes, used the gym for 20% of the 120 minutes, and spent the remaining time in the cafe. She arrived at the sports centre at 1:30 pm and had arranged to meet her friend in the cafe at 3:00 pm.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q18 · 5 marks

  5 marks

  18

  
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  Examiner report

  Many students were unable to make any progress in this question by not reading the question fully and jumping in to either find a half and/or a twelfth of 240 or to divide 240 by 5, then 3 then 2. Those that correctly divided 240 in the ratio 5 : 3 : 2 usually went on to gain good marks. Many scored 3 marks for finding the numbers of cans remaining, 120, 36 and 44 but were then unable to find the required percentage of cola cans remaining. Finding one number as a percentage of another is an area that needs addressing. Those that did find a percentage were often successful by simplifying their fraction of 120/200 to 60/100.

  Text version

  There are 240 cans of cola, lemonade and orange drink in the ratio 5:3:2. One half of the lemonade cans and 1/12 of the orange cans are removed.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q19 · 3 marks

  3 marks

  19

  
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  Examiner report

  The factorising of 500 was usually carried out with the aid of a factor tree diagram, many of which were seen to be fully correct. Failure to gain full marks was usually down to not giving their product of prime factors as powers as requested, often just leaving the factors in a list. Many arithmetical errors in the construction of a factor tree and some misunderstandings in the concept were seen where the sum instead of a product was given. Centres should emphasise here that complete tree diagrams should have each final branch ending in a prime

  Text version

  Write 500 as a product of powers of its prime factors.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q20 · 4 marks

  4 marks

  20

  
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  Examiner report

  In part (a), those students who dealt with the fractions and whole numbers separately often gained greater success in achieving full marks, although an answer of 3 9 was not uncommon. Although no credit was given for simply converting the mixed numbers to improper fractions, many did so accurately and then were able to convert both to a common denominator with at least one correct numerator to gain one mark. However, the answer following this approach was often left as an improper fraction, 20 . Unfortunately, many just added the numerators and the denominators to give an incorrect answer of 9 . Part (b) proved to be a much greater challenge for many students, many tried to concoct means of dividing 2 3 by 6 to get 9 , a few students however correctly changed 3 to 9 and divided this by 6 to get 9. The most successful approach was 3 × 6 showing an ability to divide a fraction by a whole number. Some had success by transposing the problem to show that 9 multiplied by 6 is equal to 2 3 , although 54 was often seen. Many students seemed to not understand the requirements for this question.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q21 · 2 marks

  2 marks

  21

  
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  Examiner report

  It was clear that the rules of indices are known by many students but the application of them was very poor. (2−5 × 28) was often written as 43. This had to be carefully marked as 43 as a final answer was an acceptable Special Case answer for one mark. Sometimes 2−10 or 216 were seen but rarely both. Less able students often unsuccessfully tried to evaluate the terms before finding a product or squaring and had little understanding of negative indices. Occasionally 23 was seen for the method mark but this was followed by 25. Working with negative numbers continues to be a problem with -5+8 being evaluated as 13 or -13. Many worked exclusively with the powers and did not include the base number at all; -5 + 8 = 3 was often seen.

  Text version

  Simplify (2⁻⁵ × 2⁸)². Give your answer as a power of 2.

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q22 · 2 marks

  2 marks

  22

  
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  It was common to see the digits 128 quoted in the working or in an answer, but rarely was the fully correct answer of 0.00128 seen. Very few seemed to know the rule of finding the product of the numbers and then counting the decimal places in order to position the decimal point. Many used long multiplication techniques, usually to no avail. It was rare to see an answer given in standard form. Method marks were sometimes gained for arithmetic errors in working but with a correctly positioned decimal place.

  Text version

  Work out 0.004 × 0.32

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• Edexcel 1MA1 · November 2022 · Paper 1F · Q24 · 6 marks

  6 marks

  24

  
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  Examiner report

  Students at this level find the comparing of ratios particularly challenging. The most common error in part (a)(i) was to add the values of b in the ratios to give a triple ratio of 1 : 9 : 5 or used some of the numbers in the given ratios and gave an answer of 1 : 3 : 5. Some using a correct common multiple often spoiled their final answer by more arithmetical mistakes. Although (i) was poorly answered many picked up marks for correctly following through with their values for a, b and c in part (ii). In part (b), few students were able to make significant progress. Those who assigned values to m, n and p were often successful, but this was rare. The substitution of n = 2m into p = 5n was rare also but usually successful when seen. Occasionally answers lost the accuracy mark for an incorrect order of 10 : 1 or for including letters in their final answer, eg. 1n : 10n.

  Text version

  Rizwan writes down three numbers a, b and c a : b = 1 : 3 b : c = 6 : 5

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  The majority of students gained at least two marks for a complete factorisation of 500, usually by using a factor tree, with relatively few students failing to gain at least one mark. Answers of 2 × 2 × 5 × 5 × 5 did not gain the final mark because this question asked for 500 to be written as a product of powers of its prime factors. This requirement was often overlooked. Some students gained the two method marks for drawing a correct factor tree with branches ending at 2, 2, 5, 5, 5 but then made no further correct progress. Students who showed a complete method and made only one arithmetic error gained the first method mark. When no marks were awarded, this was usually because the method was incomplete or because there was more than one arithmetic error. Relatively few students used the division method to find the product of prime factors.

  Text version

  Write 500 as a product of powers of its prime factors.

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q2 · 4 marks

  4 marks

  2

  
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  Examiner report

  Part (a) was generally answered well. The most common method was to convert both mixed numbers into improper fractions and then write both fractions over a common denominator. Many students gained at least one of the two marks for getting this far. The accuracy mark was often lost because students failed to write their answer as a mixed number or made an arithmetic error. Fewer students chose to add the whole numbers and deal with the fractional parts separately but those that did were often successful. Considering that this is a familiar question early in the paper, a surprising number of students were unable to achieve both marks. A similar proportion of students gained full marks in part (b) as in part (a) but a greater number of students gained no marks. Students who showed a correct method usually went on to get full marks. Most of the successful students started with 8  and evaluated this as 8 or cancelled to get 4  . Some students answered the question by showing that  = or 4  = but these approaches were rare.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q3 · 2 marks

  2 marks

  3

  
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  Examiner report

  Many students made a good start by working out 2–5 × 210 as 23. Others gained the first mark for squaring 2–5 or 28. Not all these students went on to complete the simplification correctly. A common mistake was (23)2 = 46. A significant number of students could not show a correct first step and gained no marks. In some responses 2–5 was identified as –32.

  Text version

  Simplify (2⁻⁵ × 2⁸)². Give your answer as a power of 2.

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q4 · 2 marks

  2 marks

  4

  
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  Examiner report

  Multiplying 0.004 by 0.32 often resulted in an answer with the digits 128 and this was sufficient for the method mark to be awarded. Failure to place the decimal point in the correct position was a common error and this meant that many students did not gain the accuracy mark. Students making one arithmetical error were also able to score one of the two marks by giving an answer with the decimal place correctly positioned. This question exposed weaknesses in multiplying without a calculator, especially when decimals are involved.

  Text version

  Work out 0.004 × 0.32

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q5 · 2 marks

  2 marks

  5

  
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  Students who showed a correct method to work out how many model B cars the factory should make generally went on to give the correct answer. Some, however, made an arithmetical error when working out 40000 ÷ 80 × 15 and gained one mark only. A common incorrect method was 40 000 ÷ 15. Some students attempted to find 15% of 40 000 leading to an incorrect answer of 6000.

  Text version

  A car factory asks 80 people which model they are most likely to buy. The results are: A, 23 people; B, 15; C, 30; D, 12. The factory is going to make 40 000 cars next year. Work out how many model B cars it should make.

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q6 · 6 marks

  6 marks

  6

  
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  Examiner report

  In order to make progress in part (a)(i) students needed to associate corresponding parts from the two ratios. Those that wrote the ratio 1 : 3 as 2 : 6 were often able to go on and write down the ratio a : b : c as 2 : 6 : 5 although 2 : 6 : 10 was quite common. Some used a common multiple of 3 and 6 to get a common element representing the value of b and 6 : 18 : 15 was a common correct answer. Many students did not understand how to combine the two ratios. A very common incorrect answer was 1 : 9 : 5 from students simply adding the two values of b. In part (a)(ii) many students gained both marks for expressing a as a fraction of their three numbers a, b and c. When students gained one mark only this was usually because they made an arithmetic error when adding the values of a, b and c or they gave an answer such as 1 6.5 where the denominator is not an integer. Students who had not given a correct ratio in (a)(i) could still gain both marks in this part for writing a correct fraction for their values of a, b and c. Students found part (b) quite challenging. After writing p = 10m or n m = or 2 p m = and gaining the first mark many students did not find a correct ratio. The statement p = 10m was quite often followed by m : p = 10 : 1. By leaving their ratio as 2 n : 5n some students failed to achieve the final mark. A few students answered the question by assigning values in the ratio given and were often successful. A large proportion of the students were unable to make any meaningful progress with this question.

  Text version

  Rizwan writes down three numbers a, b and c a : b = 1 : 3 b : c = 6 : 5

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  A good proportion of students found a multiple of 5 and an even number with a highest common factor of 7, often with little or no working, and gained both marks. The most common correct pair of values was 35 and 14 but 35 and 28 and 35 and 42 were also seen quite often. When students scored one mark only it was often for either m = 35 or n = 14. Some scored one mark for finding a multiple of 7 and an even number with a common factor of 7, e.g. 70 and 70. Listing at least 5 multiples of 5 also gained the first mark but this didn’t always lead to a successful outcome. Nevertheless, many benefitted from this way of earning one mark.

  Text version

  Two numbers m and n are such that m is a multiple of 5 n is an even number the highest common factor (HCF) of m and n is 7 Write down a possible value for m and a possible value for n. m = n =

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q15 · 3 marks

  3 marks

  15

  
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  This question was not answered as well as might have been expected and a large number of students failed to gain any marks at all with many not attempting the question. Many of those with some knowledge of sectors of circles went wrong at the first step, using πr2 or πr instead of 2πr and gained no marks. A good proportion of those who did make a correct start went on to get full marks.

  Text version

  The diagram shows a sector of a circle of radius 18 cm. 18 cm 18 cm x° The length of the arc is 4π cm. Work out the value of x. x =

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q17 · 2 marks

  2 marks

  17

  
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  This was one of the better answered questions towards the end of the paper. Many students gained at least one mark and a good proportion of students gave the correct answer. A surprising number of students got as far as       but then failed to evaluate this correctly.

  Text version

  Work out (8/27)^(4/3).

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• Edexcel 1MA1 · November 2022 · Paper 1H · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  For a question towards the end of the paper part (a) was answered reasonably well. Some students started by using consecutive terms to find the common ratio. Having identified the common ratio as 2 5 many worked out the next term as 4000 but 400 5 2 5  = was a common error. Instead of finding the common ratio some students used alternating terms of the sequence and the calculation 200 × (200 ÷ 10) gave the next term without them having to deal with surds. Part (b) proved to be a challenging question with very few students knowing how to work out the first term of the sequence. Some students gained the first mark for finding the second term of the sequence and others gained it by finding the ratio of the 4th and 6th terms. Those who were able to show a complete process to find the first term usually went on to gain full marks. The most common misconception was to create an arithmetic sequence of the denominators of the fractions leading to the final answer being given as 5 2 − .

  Text version

  The first five terms of a geometric sequence are √5, 10, 20√5, 200, 400√5.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  A good accessible start to the paper. This question was well answered with most students scoring the mark.

  Text version

  Write the following numbers in order of size. Start with the smallest number. −7                7                0                −2                −1

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  3674 was the common inaccurate answer and students are advised to carefully read the question being asked.

  Text version

  Four cards show the digits 7, 4, 6 and 3.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q7 · 4 marks

  4 marks

  7

  
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  Examiner report

  Generally this question was answered well with the vast majority of responses gaining some marks and the modal score was full marks. While 49.01 or 4901, forgetting to convert to pounds was often seen, the most popular incorrect approach was to divide by 13 rather than multiply. Another error seen was to add the two mileage figures. Even students that did not know how to interpret the real life setting of the question often gained the B mark, many with the use of 0.13 in a calculation. Another issue seen was arithmetic errors due to students trying to work without a calculator. Please encourage students to use calculators on papers 2 and 3 as they are designed for calculator use.

  Text version

  Myles's car odometer reads 12 468 miles at the start of a journey and 12 845 miles at the end. Petrol costs 13p per mile travelled.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q10 · 5 marks

  5 marks

  10

  
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  Part (a) was answered well with most students gaining at least the first mark for correctly selecting the arrival time from the bus timetable with the intention to subtract. The accuracy marks were usually lost for arriving at a value of 89, using 100 minutes to the hour. The most successful working showed the use of timeline diagrams or used a build up or chunking method. Encouraging candidates to show working and use of the time function on a calculator would be beneficial to centres. Part (b) was variable for students, with many completely correct answers seen, the best often showing a sound understanding of the concept of the question with some excellent annotations. A step-by-step approach for the journey worked best here and again, timeline diagrams were useful. However, others only added 7 minutes to 8am and could not select a bus to work with. Others selected the correct starting time but did not read the timetable effectively and gave the wrong arrival time. Some even read across the timetable. One surprise was the number of students who scored 0 in part (a) and 3 in part (b), often not attempting part (a) but being able to show full working in part (b).

  Text version

  Relevant entries from a Wigan-to-Bolton bus timetable are: the 07:20 bus from Wigan reaches Lostock at 08:09; a later bus leaves Blackrod at 08:09 and reaches Bolton at 08:58.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q11 · 4 marks

  4 marks

  11

  
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  This was a well attempted question with most students gaining at least 2 process marks and the vast majority achieving full marks. However, some students did not subtract to find the total number of children first and some, despite the bold print, did not go onto find the number of children not wearing hats. For those not scoring full marks, it was common that they scored at least one mark for saying there were 200 children. Some students stopped at finding just 35% (70) and so were only able to achieve half the marks. Common errors were to find 35% of 214 and another common error was seen when students did the build-up method for percentages. Most candidates using this method did not show what calculations they have done and so, unless their answer is correct, can have no method marks. Centres would benefit from reminding students of the need to read the question carefully and check that their answer is reasonable. They should also be reminded to show their working out to find percentages as students often made arithmetic errors without showing the associated calculations.

  Text version

  214 people go on a school trip. The people on the trip are either adults or children. There are 14 adults on the trip. 35% of the children on the trip are wearing a hat. Find the number of children on the trip who are not wearing a hat.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q12 · 4 marks

  4 marks

  12

  
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  Examiner report

  Part (a) of this question was well answered with the majority successfully calculating the correct answer. Common errors leading to no marks being awarded were to change 8 to a decimal and divide or to divide by 5 before multiplying by 8. Some arithmetic errors were seen but these were rare. In part (b) the majority of students gained at least 1 mark for correctly ordering three of the four fractions or correctly converting at least 2 of the fractions to a common format, often decimals. Of the students that converted the fractions to a common format, the majority correctly ordered all four fractions to gain full marks. Students should be encouraged to show conversions to a common format as those who were awarded no marks often showed no attempt to convert to a common format.

  Text version

  Complete both parts.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q13 · 4 marks

  4 marks

  13

  
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  Examiner report

  Students attempted this best buy problem with varying levels of success. Two marks was the modal score. As such, partial marks were often awarded for using one or both of the special offers correctly, with many also gaining the third mark for finding a comparable number of pints. This was often for adding the cost of another 2 pint bottle to find the cost of 8 pints in total or, more commonly seen, for finding the difference in cost between the two offers and making a comment about being able to buy an extra 2 pints for only 42p more. However, this type of comparison did not make full use of both offers and so was not a full consideration of the best value offer. When full marks were awarded, it was often due to finding the unit price of a pint or by finding the cost of 48 pints, but these were less frequently seen. A small number of learners calculated the alternative comparable figure of the pints that could be bought per pound but were unable to select the correct offer due to misinterpreting that the lowest amount was the best value. Students should be encouraged to use a systematic way of using each type of offer, including to write down the number of items being bought, and ensure that they have used each offer fully before finally calculating a unit price rather than calculating at the difference in cost.

  Text version

  A shop has two different special offers on milk. MILK 2 pints MILK 4 pints 75p Pay for 2 bottles get 1 bottle free £1.28 Pay for 1 bottle get 1 bottle half price Which offer gives the better value for money? You must show how you get your answer.

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• Edexcel 1MA1 · November 2022 · Paper 2F · Q25 · 3 marks

  3 marks

  25

  
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  Both parts of this question proved challenging for this cohort with very few gaining any marks at all. In part (a) students did not seem to know what to do so a lack of understanding of the term reciprocal would seem to be the problem here In part (b) the use of the term significant figures seem to pose more of a challenge then when this type of question is set around decimal places. Students would benefit from being given examples of mathematical terms they need to know and practice in rounding to a fixed number of significant figures as often as they round to a given number of decimal places.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 2H · Q14 · 3 marks

  3 marks

  14

  
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  Examiner report

  A common set up of a question, but with a slightly different recurring decimal. This decimal meant that any two multiples could be used to make a terminating decimal. Also, with the value being greater than 1, it allowed candidates to work with the improper fraction, or just the fraction 14225. As it is November, it is possible that many candidates had not had a great deal of exposure to higher level content, but it was surprising to see so many who did not know how to approach this common style of question, with a significant proportion trying to work from the fraction to the decimal and having no success. Candidates should take care with their algebra and show their working clearly. Some did not show their work to demonstrate the difference that they were trying to find. This was acceptable if a correct value was found, but many were unable to complete the subtraction and ended up scoring only 1 mark. It is important for candidates to remember to use their calculators at appropriate times.

  Text version

  The decimal 1.062222... has the digit 2 recurring.

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• Edexcel 1MA1 · November 2022 · Paper 2H · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  Candidates really struggled to gain full marks with this question, and it was primarily down to time conversion that was required. A pleasing proportion had enough of an understanding of bounds to gain at least one mark for one correct bound either for distance, or for time in minutes and seconds, or just in seconds. The second mark was for either correctly finding a bound for time in hours, or for a correct process to find a bound in kilometres per minute or kilometres per second. Those working in minutes often struggled here as they gave their time as 31.485 or 31.475, which is clearly incorrect. The final process mark was for working in kilometres per hour, but was normally only seen when candidates had found the time in hours first. Due to premature rounding in the question, many who had gained the first 3 marks could not then gain the accuracy mark as their answer was outside of the acceptable range. The C mark was only awarded to a handful of candidates as so few were able to communicate that the value of V was 20 correct to 2 significant figures as both bounds agree.

  Text version

  A race is measured to have a distance of 10.6 km, correct to the nearest 0.1 km. Sam runs the race in a time of 31 minutes 48 seconds, correct to the nearest second. Sam’s average speed in this race is V km/hour. By considering bounds, calculate the value of V to a suitable degree of accuracy. You must show all your working and give a reason for your answer.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  Examiner report

  This question was not answered quite as well as one might expect. Whilst many gave the correct answer, a minority had 0.41, 0.46 in the wrong order.

  Text version

  Write the following numbers in order of size. Start with the smallest number. 0.41            0.5            0.46            0.408

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  A well answered question.

  Text version

  Write down the value of the 2 in the number 12 345

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  Nearly all candidates gave the correct answer.

  Text version

  Write 4 5 as a decimal.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  The main error here was when candidates thought they had to round up to 20.

  Text version

  Write 19.4949 correct to the nearest whole number.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  A well answered question.

  Text version

  Here is a list of numbers. 5            11            18            22            29 From the list, write down a multiple of 3

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q7 · 3 marks

  3 marks

  7

  
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  Examiner report

  The majority of candidates completed this question with no issues. Of those candidates who failed to gain full marks, the most common error was in failing to give their answer in correct money notation, that is stating £145.6 rather than £145.60. This lost the final accuracy mark. Some candidates lost marks by doing a variety of strange calculations which some checking would have spotted. This included 208 – 0.25, 52 × 93.6, or cases of finding 52 then showing 208 × 60p rather than 52 × 60p.

  Text version

  208 bars of chocolate were sold from a shop. 1/4 of these bars of chocolate were large bars. The rest of the bars of chocolate were small bars. All the large bars of chocolate were sold for £1 each. All the small bars of chocolate were sold for 60p each. Work out the total amount of money for which the 208 bars of chocolate were sold. Give your answer in pounds.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  Part (a) was a well answered question. In part (b) many candidates gained both marks. Common errors included attempting the question by summing the numbers, but not always summing all of them, or by dividing by 2, 3 or 5. A few candidates found the range or median. Some candidates lost marks because they did not extract the correct numbers from the table.

  Text version

  Four students play a game. Their points are: Ali 143, Barbara 121, Calliope 45 and Danesh 19. Barbara has more points than Danesh.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q15 · 5 marks

  5 marks

  15

  
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  Examiner report

  A significant number of candidates were able to score some marks on this question although only a small proportion of candidates were able to progress through this problem to achieve a conclusion based on correct comparable figures. Most candidates made a good start by finding the cost of 1kg of carrots. Those who were able to progress further then chose to isolate the cost of 2.5kg of onions. Where candidates scored the first P2, many struggled to scale 2.5kg to 4kg and were therefore unable to progress through the remainder of the question correctly. Of the candidates scoring 0 marks, many incorrectly halved the £2.36 to split the cost of the carrots and the onions equally. Common errors that stopped candidates from progressing correctly included the multiplying of different quantities by 2 to get 5kg of onions or 5kg of onions and 4kg carrots or 6kg of carrots. Some good responses might have gained full marks had the candidate fully answered the question by communicating the correct conclusion.

  Text version

  2.5 kg of onions and 2 kg of carrots cost a total of £2.36 3 kg of carrots cost £1.74 Stuart has £2 He wants to buy 4 kg of onions. Does Stuart have enough money to buy 4 kg of onions? You must show how you get your answer.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q17 · 3 marks

  3 marks

  17

  
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  Examiner report

  Part (a) showed poor understanding of rounding to significant figures with answers of 8, 80 and 87.6 being common. Many candidates gave answers such as 876 or rounded to the nearest thousand (88 000) or rounded down instead of up (87 500) whilst some candidates included a decimal point in their answer. In part (b), the majority of candidates answered this question correctly but a written method was rarely seen. There was some evidence of omitting to use brackets in the calculation. Of those who didn’t score full marks, many scored the method mark for calculating the numerator or denominator correctly. Indeed, those candidates who worked out the numerator and denominator separately would usually go on to gain full marks. It was surprising that a good number of candidates chose to arbitrarily round their answers to 1 or 2 decimal places and calculate an estimate. Some copied the answer from their calculator incorrectly putting 13.254 thus costing themselves 2 marks.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q20 · 4 marks

  4 marks

  20

  
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  Examiner report

  Most candidates were able to gain 2 marks for at least 3 correct ingredients for 25 scones. It would seem that asking them to go further caused some confusion and errors were made. Some candidates were able to get as far as 3 marks but failed to get the final mark as they had made an earlier inaccurate calculation for flour. Working was often set out poorly particularly that worked out the amount for 5 scones and then added two lots of amounts for 10 scones.

  Text version

  Here is a list of ingredients for making 10 scones. Ingredients for 10 scones   80 g butter 350 g self‑raising flour   30 g sugar 2 eggs Martin has 100 g butter 1 kg self‑raising flour 50 g sugar 4 eggs Martin wants to make 25 scones. He has not got enough of some of the ingredients. Work out how much more of each of these ingredients he needs.

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• Edexcel 1MA1 · November 2022 · Paper 3F · Q29 · 3 marks

  3 marks

  29

  
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  Examiner report

  In part (a), there were many answers which included the digits 675 but rarely the correct response. Too many candidates appeared to want to give the answer as a standard form number. Examples of incorrect responses included 67 500 where they had multiplied by 10 000 rather than divided by 10 000 and 0006.75, demonstrating an incomplete understanding of standard form. In part (b), many candidates struggled with the format of a number written in standard form. They were able to use their calculators to find 659 200 as the answer to the calculation but then struggled to put it into standard form; sometimes despite being able to convert from standard form to an ordinary number, gaining 1 mark instead of 2 marks, which was quite common. Those that failed to score often attempted to do it without the calculator or did not know how to enter numbers in standard form into their calculator.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 3H · Q9 · 3 marks

  3 marks

  9

  
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  Examiner report

  A high percentage of candidates showed a good understanding of standard form. In part (a) nearly all candidates were able to convert from the number in standard form to an ordinary number. A smaller proportion of candidates were successful in part (b) which involved a multi-stage calculation. A significant number of candidates scored only 1 mark out of the 2 marks available because they could work out the value of the numerical expression as an ordinary number but either did not attempt to put it in standard form or could not write it correctly in standard form. A significant number of candidates lost marks because they rounded prematurely.

  Text version

  Complete all parts of this question.

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• Edexcel 1MA1 · November 2022 · Paper 3H · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  There were many fully correct answers to this question. However, a significant minority of candidates could not take into account all the information given and were awarded just one of the two marks available for listing a correct set of integers for x (or y). A small number of candidates tried to use inequality signs, therefore ignoring or not understanding the statement that “x and y are integers”.

  Text version

  x and y are integers such that 3 < x < 8 4 < y < 10 and x + y = 14 Find all the possible values of x.

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• Edexcel 1MA1 · November 2022 · Paper 3H · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  A minority of candidates scored both marks on this question. Most candidates were unable to appreciate that the question focused on truncation, rather than rounding and treated the question as if they had been told “1.2” was the result of a rounding process. As a result, they gave the bounds as 1.15 and 1.25. These bounds could not be given any credit. Where only 1 mark was scored, it was usually for the lower bound, 1.2(0).

  Text version

  Martin used his calculator to work out the value of a number P. He wrote down the first two digits of the answer on his calculator. He wrote down 1.2 Complete the error interval for P. ≤ P <

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• Edexcel 1MA1 · November 2022 · Paper 3H · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  Most candidates scored full marks for their answers to this question. The most common error seen was where candidates used 7, 13 and 5 in a sum, for example as 7 + 13 + 5, rather than in correct products. Candidates who gained one of the two marks usually did so for giving the correct product leading to 455 but could not complete the question successfully. Some candidates tried unsuccessfully to work backwards from the 555.

  Text version

  A pet shop has   7 guppy fish 13 tetra fish   5 angel fish. David is going to choose one of the following combinations of fish a guppy fish and an angel fish or a tetra fish and an angel fish or a guppy fish, a tetra fish and an angel fish. Show that there are 555 different ways for David to choose his fish.

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• Edexcel 1MA1 · November 2022 · Paper 3H · Q17 · 4 marks

  4 marks

  17

  
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  Examiner report

  It was relatively rare to see a fully correct solution to this question. However, many candidates were able to write at least one or all three of the relationships as a ratio or as an equation to gain one or two marks. Only higher attaining candidates could go on to link all four weights for example by giving the equations 2 B B D D   + = +     , A = 3B and C = 4D. Some candidates spoiled their chances of getting the third mark by using the same variable, x, to represent two of the weights and gave an equation such as the one above with x substituted for both B and D. These candidates scored at least 3 of the 4 marks available. Any ratio equivalent to 42 : 63 : 15 : 20 was accepted and awarded full marks, for example 2.1 : 3.15 : 0.75 : 1. Using the common multiple 105 proved to be a successful strategy employed by some candidates.

  Text version

  There are four boxes on a shelf, A, B, C and D. The total weight of A and B is 3 times the total weight of C and D. The weight of A is 2/3 of the weight of B. The weight of C is 75% of the weight of D. Find the ratio weight of A : weight of B : weight of C : weight of D.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Most students correctly identified the value of the 6 as six thousand. 16000 and 600 were the most common errors.

  Text version

  Write down the value of the 6 in the number 16 007.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  This was answered well with many showing understanding of equivalent forms, A few gave the 3 values in reverse order and were penalised for not reading the question carefully enough. A common misunderstanding was for 0.5 to be less than 0.45 thinking perhaps that since 5 < 45 then 0.5 < 0.45. A small proportion did not convert all values to the same equivalent form which resulted in evaluating 2 as smaller than 45%.

  Text version

  Write 1/2, 0.55 and 45% in order of size, starting with the smallest.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q7 · 3 marks

  3 marks

  7

  
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  Examiner report

  Generally well answered, some with minimal working shown. Careless arithmetic was a major reason for some students not gaining full marks in this question. 20 – 6 = 24 or 20 – 6 = 12 were the most common errors made but by dividing correctly by 2 to get 12 or 6, 2 out of the 3 marks available were possible. A common approach was to list costs of candles in multiples of 2. However, it was not uncommon for some multiples to be omitted, thus affecting the final number of candles bought. Some weaker students got no further than working out the number of candles that could be bought for £20. To gain any credit £6 ÷ 2 also needed to be seen. Giving an answer of 14 on the answer line was also common following correct calculations, with 7 candles often being an embedded answer.

  Text version

  Each candle costs £2. Simon pays with £20 and receives £6 change.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q10 · 2 marks

  2 marks

  10

  
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  Examiner report

  Whilst many were able to find the required temperature of 27, −15 + 42 was often evaluated as −57 or +57. The drawing of a temperature scale was a common approach, sometimes leading to the correct answer but often leading to an answer of 26 (counting from −15 upwards 42 times). 33 was a very common answer were −15 + 42 was incorrectly calculated using column method. It is a concern that this question was poorly done by many students.

  Text version

  Norway's lowest temperature was −15°C and its highest was 42°C greater.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q11 · 4 marks

  4 marks

  11

  
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  Examiner report

  Many students did not realise that the number of units of electricity used in November was the difference in the two meter readings, and simply multiplied the November reading by the 16p. Two marks were still available here if a correct method for long multiplication was shown. Whilst a correct method of long multiplication was often seen, the number of simple arithmetic and place value errors in multiplying is a cause for concern. Place value errors were also common within the final answer, where £7360, £736.0 and £7.36 were seen on many occasions. Some managed to score 3 marks but lost the final mark as no units were included. Some students tried to find the difference in the readings by subtracting the larger value from the lower value.

  Text version

  Fiona's electricity meter rose from 88 738 kWh to 89 198 kWh. Each kWh costs 16p.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q12 · 4 marks

  4 marks

  12

  
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  Examiner report

  In part (a), there did seem to be some improvement in the addition of two fractions at this level, although the predictable incorrect answer of 18 and its simplifications were often seen. A common denominator of 72 was often preferred to the more straightforward 12. A number of students did change the denominators to 12 but then forgot to adapt the numerators appropriately. Whilst many were successful in multiplying the two fractions correctly in part (b), many again converted the fractions to equivalent fractions with a common denominator. Unfortunately, this was often followed by just the multiplication (or in some cases addition) of the numerators keeping the same common denominator. In this part of the question, the answer had to be given in its simplest form. Many students ignored this demand leaving 80 as their final answer or lost the accuracy mark for incorrect cancelling of 80. It was far too common to see division methods applied in this question, often accompanied by KFC written on the page. Overall, it was encouraging to see this question was attempted by almost all students, which is an improvement on previous series.

  Text version

  Work with fractions.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q15 · 3 marks

  3 marks

  15

  
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  Examiner report

  In part (a), either the concept of estimation seems to be poorly understood at this level or students are increasingly not reading questions carefully enough, but it was very common for students to attempt to find the exact product of the two given values. This gained no credit at all. Unfortunately, in part (b), many students used long multiplication techniques to find the value of 29.6 × 32, often making arithmetical errors along the way. Some, perhaps thinking this part was similar to the previous part, estimated the result, working out 30 × 30 = 900. This would have been an ideal approach in order to find the relative size of the answer but alone gained no credit.

  Text version

  Estimation and place value.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q16 · 4 marks

  4 marks

  16

  
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  Examiner report

  Distance, speed and time formulae were understood by many students and 50 ÷ 40 was often seen in part (a). Poor arithmetic then often followed with results such as 1.1 or 1.2 hours. Very few students were then able to convert the part hours to minutes and 1 hour 10 mins or 1 hour 20 mins were the usual results. When a correct division giving 1.25 was found, this was then incorrectly converted to 1 hour 25 mins by many students giving a final answer of 08:55. Build up methods were common for this question, with 1 hour associated with 40 miles. However, most of those who used this approach were unable to reconcile the remaining 10 miles with a correct time. Weaker students often wrote 50 ÷ 40 and then proceeded to divide 40 by 50 and many worked out 50 × 40. Others used 7.30 as the ‘time’ in the formula. A small minority of students clearly didn’t read the question carefully and gave an answer of 1hr 15mins for the time taken rather than the time of arrival. More students had success in part (b), realising that if the average speed was greater then the time of arrival would be earlier.

  Text version

  Savio leaves at 07:30 and drives 50 miles at an average 40 mph.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q20 · 3 marks

  3 marks

  20

  
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  Examiner report

  Many students found the demand of this question just too great, and where to start puzzled a great many. Some just worked with the given fractions, adding or subtracting and in some cases multiplying them together. Very few were able to tease out a process to find the required fraction. One mark was awarded for adding the two given fractions, this being just one step away from a correct solution. One mark was also available for identifying the fraction of the unshaded parts of rectangles A and C. However, many simply wrote 3 (instead of 8) and 2 (instead of 11 ) in the appropriate places. Fraction arithmetic remains an issue with many students writing 8 + 11 = 19 . Of those who did make a sensible start, 88 was a common answer which gained 1 mark. Also, 88 was a similar common incorrect answer.

  Text version

  Three identical rectangles A, B and C are aligned. In A the lower 5/8 is shaded; in C the upper 9/11 is shaded. In B, the shaded strip lies between the horizontal line aligned with the top of A's shading and the horizontal line aligned with the bottom of C's shading.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q22 · 3 marks

  3 marks

  22

  
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  Examiner report

  This question was answered poorly by all but a few students. Many recognized the radius as being 3 cm but were unable to find an expression for the area. The height of the cylinder was often taken as 6 cm instead of 5 cm. A common error was to correctly find the area of the plan, 9π, and then multiply it by the area of the front elevation. Some students used numerical values for π and this was acceptable in assessing the process but not in the final answer. Whilst many students did realise that they needed to use 𝜋𝑟2, or even 𝜋𝑟2ℎ they lacked the confidence to evaluate this with the given information. Weaker students did attempt to count squares in working out the area of the plan but this was usually accompanied by counting squares to find the area of the front elevation as well.

  Text version

  A cylinder's plan is a circle of radius 3 cm; its front elevation is a rectangle 6 cm wide and 5 cm high.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q24 · 2 marks

  2 marks

  24

  
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  Examiner report

  Many students gained at least one mark here for correctly identifying the prime factors of 124, usually by way of a factor tree diagram. However, so many failed to write these as a product. Many students faltered on their first factorisation, pairings of 2 and 64 being a common mistake. Of the students who completed the factor tree correctly, many then only wrote ‘2×2’ and seemed put off by ‘31’ as a prime factor (many then attempting to split 31 further, obviously unsuccessfully).

  Text version

  Write 124 as a product of prime factors.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q25 · 5 marks

  5 marks

  25

  
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  Examiner report

  Those students understanding the concept of ratio usually started correctly by dividing the 160 vehicles in the ratio 3 : 7, resulting in 48 (16 × 3) cars. Failure to then complete the solution correctly was generally a result of finding either 8 of 48 or 25% of 48 and then immediately subtracting the single result from 48 and then calculating either 8 or 25% of the remainder. Some students misinterpreted the first line of the question and assumed that here were 160 cars and then proceeded to find 8 and 25% of 160 leaving them with an answer of 100. This was marked as a special case with the award of two marks.

  Text version

  There are 160 vehicles with cars:vans=3:7. Of the cars, 1/8 use electricity and 25% use diesel; the rest use petrol.

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• Edexcel 1MA1 · June 2022 · Paper 1F · Q26 · 4 marks

  4 marks

  26

  
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  Examiner report

  Very many students had clearly not covered standard form in depth and therefore were unable to make any meaningful sense of this question. 1630 and 16300 were common errors in part (a). In part (b) 438 × 103 was often seen. In part (c), 4000 and 0.00006 were sometimes seen but no credit was given until a multiplication had taken place. Correct values of 0.24 and 24 × 10-2 were sometimes seen but rarely then put into standard form. Incorrect understanding of how the power changes was common with students writing 2.4 × 10-3 as their final answer. The majority of students appeared to score 1 mark for answers of the form 2.4 × 10n where n ≠ -1

  Text version

  Standard form.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  The majority of students gained two marks for writing 124 as a product of its prime factors, usually by using a factor tree, and relatively few students failed to gain at least one mark. Some students gained the method mark for drawing a correct factor tree with branches ending at 2, 2 and 31 but then failed to write a correct product. Answers such as 2, 2, 31 or 22 + 31 or 22 were quite common. Students who showed a complete method but made only one arithmetic error also gained the method mark. The most common arithmetic error occurred at the start of the process when 124 was sometimes split into 2 × 64 rather than 2 × 62. Some students failed to recognise 31 as a prime number and made errors trying to further divide it. When no marks were awarded this was usually because the method was incomplete or because there was more than one arithmetic error. Very few students used the division method to find the product of prime factors.

  Text version

  Write 124 as a product of prime factors.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q3 · 5 marks

  5 marks

  3

  
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  Examiner report

  Most students made very good attempts at this multi-step question with many achieving full marks. It was pleasing to see many well presented solutions with working out that was easy to follow. The majority of students started by using the ratio 3 : 7 to work out that there were 48 cars and gained the first two marks. Many students completed the process by finding of 48 and 25% of 48 and subtracting the numbers of cars that use electricity and the number of cars that use diesel from 48 to find the number of cars that use petrol. Arithmetic errors were quite common and were often made at the final stage when subtracting 6 and 12 from 48. It was surprising that a significant number of students used a build up method such as 10% = 4.8, 10% = 4.8, 5% = 2.4, etc. to find 25% of 48. Centres should note that incorrect statements such as 25% of 48 = 11 or 8 of 48 = 5 can get no credit unless the method for finding 25% of 48 or 8 of 48 is shown. Some students made the mistake of subtracting the number of cars using electricity from 48 and then finding 25% of 42, not 25% of 48. Instead of finding 8 of 48 and 25% of 48 some students chose to combine 8 and 25%, usually 8 rather than 37.5%, and then worked with 8 or 8. The award of the SCB2 for finding the fraction and percentage correctly but not working with the ratio was relatively common.

  Text version

  There are 160 vehicles with cars:vans=3:7. Of the cars, 1/8 use electricity and 25% use diesel; the rest use petrol.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q4 · 4 marks

  4 marks

  4

  
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  Examiner report

  In part (a) the majority of students knew how to write 1.63 × 10–3 as an ordinary number. Common incorrect answers were 1630, 0.0163 and 0.000163. Part (b) was also answered very well. Incorrect answers were often of the form 4.38 × 10n with an incorrect value of n. Many students started part (c) by working out 4 × 6 = 24 and 103 × 10–5 = 10–2. Some went on to give 24 × 10–2 or 0.24 or 2.4 × 10–3 as the final answer and gained one mark only. A very common error was changing 24 × 10–2 to 2.4 × 10–3 instead of to 2.4 × 10–1. Another common mistake with the indices was 103 × 10–5 = 10–15. Students who did not deal correctly with 103 × 10–5 could still gain one mark for an answer in the form 2.4 × 10n with an incorrect value of n. Those who converted 4 × 103 and 6 × 10–5 to ordinary numbers before doing the calculation often got into difficulties with place value and rarely gained any marks.

  Text version

  Standard form.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  In order to make progress students needed to link the probability of taking a lime flavoured sweet with the ratio 9 : 4 : x. Those who started by writing 3 = or formed an equation such as x = + were usually able to show a complete process to work out the value of x. Some marks were lost through careless arithmetic errors and those using an algebraic approach sometimes made mistakes when solving their equation, such as expanding 3(13 + x) incorrectly or incorrectly simplifying 13 + x to 13x. Of the students not scoring full marks few made the connection between 3 7 and 9 21 .

  Text version

  Lime:strawberry:orange sweets = 9:4:x and P(lime)=3/7.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q12 · 3 marks

  3 marks

  12

  
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  Examiner report

  This is a familiar type of question and most students were able to gain the first mark for showing an understanding of the recurring decimal notation. It was pleasing that many students were able to show a complete method leading to a correct fraction. Any subsequent incorrect cancelling of 990 was ignored. Some students got as far as 11.6 99 but were then unable to complete the method to arrive at a correct fraction. After finding two appropriate decimals to subtract some students spoilt their solution by making careless arithmetic errors such as 1000x – 10x = 900x. Some students could recall the need to multiply the recurring decimal by powers of ten but were either unable to find the multiples needed to eliminate the recurring nature of the decimal or could not carry out the multiplications correctly. It was common, for example, to see 10x = 1.17 followed by 100x = 11.1717.. or by 100x = 117.17 . Some students did not understand the recurring notation, writing 0.117117... or 0.171717...

  Text version

  Express the recurring decimal 0.1171717… (17 repeats after the first decimal digit) as a fraction. Show working.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q18 · 4 marks

  4 marks

  18

  
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  Examiner report

  This was one of the better answered questions towards the end of the paper. Many students gained at least one mark and a good proportion of students gave a fully correct solution. When just one mark was awarded this was usually the first mark for making some progress with the numerator or the third mark for showing that ÷ 2–3 is the same as × 8. After writing 5 9 −       as −       some students were unable to deal with the negative power and a common error was to ignore the minus sign and write 7 3 or treat the minus sign as a multiplier and write – 7 3 . A number who were able to find 3 7 made errors converting 4 2 3 to 14 3 . Those who simplified the numerator to 3 14  scored the first two marks. It was surprising to see some students then work with 42 21 rather than simplifying it to 2. An error here was 42 21 = 1 2 . Mistakes at the final stage when working with the denominator prevented some students from achieving the accuracy mark. Some used 21 ÷ 2–3 but combined the indices incorrectly or gave 24 as the final answer. A common error was to write the denominator 2–3 as –8. Students seemed to struggle with negative indices generally.

  Text version

  Work out [(5 4/9)^(−1/2) × (4 2/3)] ÷ 2^(−3). Show working.

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• Edexcel 1MA1 · June 2022 · Paper 1H · Q21 · 5 marks

  5 marks

  21

  
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  Examiner report

  This proved to be a challenging question with very few students showing any understanding of what was required to find the total area of the two shaded regions. Most students failed to find a successful strategy and working out was often messy and difficult for examiners to follow. Fully correct answers were seen only rarely but nevertheless it was pleasing to see some excellent solutions from the most able students taking this paper. The students who scored marks had generally drawn appropriate triangles on the diagram to help formulate their approach. Those who used 2 absinC to find the area of a triangle were usually able to recall the exact value of sin60o or sin120o. Some students made a good start and gained the first two marks by finding either the area of a triangle or the area of a sector but often they did not find both and were unable to make any further progress. It was pleasing to see many students attempting this question but often they simply found the area of one circle as 16or the area of three circles and then made incorrect assumptions about the proportion shaded in searching for a solution. Summary Based on their performance on this paper, students should: ● take care when carrying out arithmetic operations and check their working to avoid careless errors ● consider whether or not an answer is reasonable and of a sensible size ● read each question carefully and ensure that their final answer matches the question asked ● show their methods clearly when using graphs ● ensure that they know the difference between surface area and volume ● practise working out an estimate for the mean from a grouped frequency table ● practise answering probability questions that require the use of algebra and ratio

  Text version

  Three circles each have radius 4 cm. Centres A,B,C are collinear with AB=BC=4. The two shaded regions are the parts of the middle circle lying outside both the left and right circles.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  Examiner report

  A good accessible start to the paper with a question, that was well answered with most students scoring the mark.

  Text version

  Write 1476 to the nearest 10.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  Only about two thirds of the cohort was able to correctly answer this question. Some students added 1 and 10 instead of finding the difference.

  Text version

  Complete 1−3/10 = [fraction].

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Well over 90% of the cohort was able to answer this question correctly. The errors seen were to not give a 3-digit number or to give the first 3 multiples of 5.

  Text version

  Write down a 3-digit multiple of 5.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q6 · 1 mark

  1 mark

  6

  
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  Examiner report

  This question was exceptionally well answered with most students gaining the mark. A minority of students lost the mark by omitting a number from their answer or for getting confused on the negatives, giving answers such as -2, -7, -11, 3, 8, 10.

  Text version

  Order −11, −2, 8, −7, 3, 10 from smallest.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  This was generally well answered and the modal score was three marks. When full marks was not scored this was often due to arithmetic errors; it was disappointing to see so many arithmetic errors, particularly in the subtraction of £150 from £1428 when a calculator could be used. Students either did not have a calculator or chose not to use it. Centres should encourage students to use a calculator on the calculator papers. A few students decided to add together the £150 and the £1428 before dividing by six. Unfortunately, this was an incorrect process and gained no marks. Some students left two methods to be marked, in this case both will be marked and the lower of the two marks awarded. Students should be discouraged from this practice and make their own choice as to which method they want marking. In this question the choice was often either a fully correct answer or 1428 ÷ 6 and if nothing was written on the answer line then the student scored no marks.

  Text version

  A £1428 holiday is paid with a £150 deposit then 6 equal payments.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  Both parts of this question were well answered with part (b) scoring slightly higher. The symbols used seemed to be well understood by the vast majority of students.

  Text version

  Choose from =, <, >.

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• Edexcel 1MA1 · June 2022 · Paper 2F · Q23 · 2 marks

  2 marks

  23

  
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  Examiner report

  This error interval question was not well answered by students. Most students had an idea of what was being asked but struggled to find the upper and lower bounds due to not considering the place value of the initial value. The most successful answers were often those where a number line was drawn with the nearest metres shown and subsequently identifying where the bounds would be. In addition to blank responses, common errors included giving the values as 89 and 90, 85 and 95, 85.5 and 95.5 or 89 and 91. Finding 89.5 as the lower bound was seen as a single answer and awarded a mark more often than finding the upper bound. To improve student outcomes, centres should encourage students to use a number line method where the number to add or subtract is half the degree of accuracy asked for. Students would also benefit from having a better understanding of inequality notation. It is also worth reinforcing that numbers are not always rounded to the nearest 10.

  Text version

  A pitch length is 90 m correct to nearest metre.

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• Edexcel 1MA1 · June 2022 · Paper 2H · Q3 · 2 marks

  2 marks

  3

  
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  Examiner report

  Students are clearly getting used to this type of question, and it was pleasing to see so many scoring both of the marks. There are misconceptions that persist, and was still quite common to see ’80.5’ as an incorrect lower bound, and ’90.4’ for the upper bound.

  Text version

  A pitch length is 90 m correct to nearest metre.

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• Edexcel 1MA1 · June 2022 · Paper 2H · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  Another familiar question, and another answered well by many. A significant number of students did struggle, and it seemed it was the denominator of the fraction including the fractional power that caused the issues. They could gain a single mark for a correct partial evaluation, but it was common to either see no marks or both marks. Students need to make sure they are able use the power button correctly on their calculators so they are able to process complex calculations. There were many instances where just the answer was written down which lost possible marks for a partial evaluation. 1.43 was often seen as the cube root was taken of everything. Also 7.5 was multiplied by 2 rather than to the power. Another common incorrect answer was 1.427... which came from taking the cube root of the whole fraction rather than just the denominator.

  Text version

  Use a calculator to evaluate [cube root of (1.57⁴+tan60°)] / √7.2.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  Working out 1 4 of 28 wasn’t a problem for most students.

  Text version

  Work out 1/4 of 28.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  Most students answered this factors question correctly with many giving more than the requested two factors. This still gained full marks as did writing their answer as factors pairs being multiplied together. The most common incorrect answer was students giving multiples instead of factors.

  Text version

  Write down two factors of 12.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  Most students responded with the correct answer. Occasionally 13 10 was seen; students need to be reminded to turn off the fraction mode on their calculators, unless working with fractions.

  Text version

  Find √1.69.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q7 · 3 marks

  3 marks

  7

  
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  Examiner report

  This question was answered well, though there was a significant minority who did not attempt the question or fail to gain at least one mark. The main issues for students who did not earn full marks were either poor numeracy skills (not using a calculator), misreading numbers from the table, or only working out the difference for one week. They rarely opted for the method of finding the difference for each week, this method was very poorly executed as they tended to either ignore the −5 altogether or simply ignore the negative. A surprising number of students appeared not to use a calculator.

  Text version

  Weekly apples sold: 86,75,92. Weekly oranges: 68,80,76.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  This question was answered well by most students. A few students did not give a final conclusion and therefore could not achieve full marks. The most common approach was to multiply to find the number of nails needed and the number of nails they had. Other preferred methods included working out how many nails they had and divide by 4 to find the number of frames that could be made. A small number of students misunderstood what their values represented and therefore said she didn’t have enough and needed 4 more nails instead. Students need to ensure they use their calculator to check their final values as some showed a correct method, but their multiplication skills meant their values were not correct to get full marks.

  Text version

  35 frames need 4 nails each. Sinita has 3 boxes of 48 nails.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  This question was generally answered well. Most common errors included students rounding, not fully simplifying the fraction and incorrectly entering numbers into the calculator by multiplying the top, then dividing by 10 and then subtracting 1.97 The most successful approach is always to work out and state the numerator and denominator separately, and then divide them.

  Text version

  Work out (2.75×14.6)/(10−1.97).

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q18 · 2 marks

  2 marks

  18

  
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  Examiner report

  In part (a) most students were able to correctly round to 2 significant figures if they attempted the question, but a common incorrect response was 25 showing they thought 2 significant figures meant the first 2 digits. Part (b) was answered less successfully than part (a). Some incorrect responses included 0.1, 0.08, 0.0900 and 1, showing the students were less confident dealing with smaller numbers rather than larger ones.

  Text version

  Rounding.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q19 · 4 marks

  4 marks

  19

  
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  Examiner report

  The vast majority of students attempted this question with a fair proportion getting full marks. The majority found 150 for red, thus gaining the first mark. The most common approach was then to subtract this together with 82 from 400 to get 168 green counters and thus scoring two marks. Some just subtracted 82 from 150 getting 68 instead of 168. If they knew how to find the percentage of amount, they rarely made a mistake for the last two marks, so 3 out of 4 marks was rare. The most common error was to subtract the 82 from 400 as a first step and then try to find 3 of 318 which resulted in no marks. Another incorrect method seen was converting 3 8 to a decimal and then adding it to 82. It was very rare to see students using the alternative method of converting both 3 8 and 82 to percentages. Some students converted 3 8 to 0.375 or 37.5 and then added this to 82 before subtracting. There were a fair number of students who managed to add together 82 and 150 then covert this to a percentage (58%) but this was as far as they got, not realising that this was not the percentage of green counters. Generally, the major weakness was a failure of students to understand how to convert to a percentage for the final answer, which therefore limited the number of marks to just 2.

  Text version

  400 counters are red/yellow/green. 3/8 are red and 82 are yellow.

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• Edexcel 1MA1 · June 2022 · Paper 3F · Q21 · 2 marks

  2 marks

  21

  
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  Examiner report

  Those who had a clear idea of LCM usually wrote a list of multiples of 24 and 56 until they found the first multiple in common which was 168. This was the most successful method used, which usually resulted in the award of full marks. The other approaches were linked to the derivation of prime factors, using a variety of factor trees, Venn diagrams or tables, sometimes more than one. Whilst these were usually correctly presented for 1 mark, students rarely knew how to find the LCM from their prime factors, though Venn diagrams were sometimes successfully used.

  Text version

  Find LCM of 24 and 56.

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• Edexcel 1MA1 · June 2022 · Paper 3H · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  Just over a quarter of all students completed part (a) of this question successfully to gain all 3 marks. A commonly seen final answer was 10120. This could only score 1 mark. However, about two thirds of all students got as far as simplifying the expression to √10120. Some of these students left this as their answer while other students went on to evaluate it incorrectly. Answers to part (b) were often marred by a lack of clarity. Answers such as “Liam should have multiplied the numbers inside and outside the brackets” were commonplace but could not usually be rewarded with the mark available. Another common incorrect response was for a student to state that the 12 should be squared. More successful responses usually referred to the answer Liam should get, that is 12100 or that Liam should have multiplied 50 and 2, not worked out 50².

  Text version

  Indices.

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• Edexcel 1MA1 · June 2022 · Paper 3H · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  This question was generally well answered with most students scoring the full 2 marks. Where examiners saw errors, most either involved adding 16, 5 and 3 instead of multiplying, or multiplying the 16, 5 and 3 but then adjusting their answer by, for example dividing by 3 or dividing by 2, as they mistakenly believed that the 240 included repeats. This latter approach was given some credit for the 16 × 5 × 3.

  Text version

  Rayheem has 16 shirts, 5 pairs of jeans, 3 jackets; outfit uses one of each.

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• Edexcel 1MA1 · June 2022 · Paper 3H · Q16 · 3 marks

  3 marks

  16

  
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  Examiner report

  This question discriminated well between more able students sitting this paper with many students being awarded each of the 0, 1, 2 or 3 marks available. Some students did not attempt the question and many lower attaining students restricted their answer to working out the value of p by substituting e = 6.8 and f = 0.05. This gained no credit. Of those students who did score marks, many of them scored just one mark for writing down at least one of the bounds for e or f. Students who substituted bounds for e and f into the expression for p were split between those who calculated 2[UB of e] ÷ [LB of f], the correct expression and those who calculated 2[UB of e] ÷ [UB of f]. Some students who had the correct fraction, failed to take the square root or made an error in taking the square root and so lost the final accuracy mark. There was a significant number of students who calculated [UB of 2e] ÷ [LB of f], that is 13.65 0.045 instead of 13.7 0.045. These students could not be awarded full marks even though their final answer worked out to be in the range 17.4 to 17.5

  Text version

  p=√(2e/f), where e=6.8 correct to 1 dp and f=0.05 correct to 1 sf.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  Ordering of negative numbers was correctly carried out by most students.

  Text version

  Write the numbers 8, -7, -10, 1, 0, -2 in order of size, starting with the smallest.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  An incorrect answer of 0.9 was common.

  Text version

  Write 9/100 as a decimal.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  A very well answered question, although incorrect answers of 30 and 320 were common.

  Text version

  Write 327 correct to the nearest ten.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  This was surprisingly poorly answered with 14 as the most common incorrect response. A significant number of students just wrote 7 × 7 without giving a value.

  Text version

  Write down the value of 7^2.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  Few failed to get the correct answer of 14 when dividing 42 by 3 although a small minority insisted on halving then halving again thinking this was the correct method of finding a third of a quantity. This error was repeated in question 14 when trying to divide £1.80 by 3. Many students also used repeated addition or listed multiples, the majority eventually arriving at 42.

  Text version

  £42 is shared equally between 3 friends.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q9 · 3 marks

  3 marks

  9

  
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  Examiner report

  Failure to gain full marks in this question was usually a result of considering just one packet of cheese instead of two. However, arithmetical errors were made far too often in either the addition or in subtracting £6.50 from £10; £4.50 being a common incorrect result given. Some failed to give a conclusion and so failed to gain the final mark. Lack of working let some students down and the subtraction from £10 was incorrect in a significant number of cases.

  Text version

  Danny buys a loaf of bread for £1.20, a bottle of milk for 70p and two packets of cheese for £2.30 each. He pays with a £10 note and says, 'I should get £3.30 change.'

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q10 · 2 marks

  2 marks

  10

  
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  Examiner report

  It was pleasing to see many students dealing with the arithmetic of negative values well. Most were able to compute Wednesday’s temperature as – 2oC although many offered this as their final answer; clearly not having read the question carefully. While getting the negative temperature on Wednesday was good some students struggled to go from negative to positive integers and often missed counting 0 and got an answer of 6 degrees. Many used number lines and were usually successful. Quite a few students calculated -5 + 3 as -8. It was common to see 5 – 2 = 3 for the difference rather than 5 – (-2) = 7.

  Text version

  At noon on Monday the temperature was 5 °C. On Tuesday it was 10 °C less than on Monday. On Wednesday it was 3 °C greater than on Tuesday.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q11 · 6 marks

  6 marks

  11

  
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  Examiner report

  The vast majority of students answered part (a) correctly and thus showed clear understanding of the key. Part (b) was not as well answered, many students were happy to count the complete symbol as 8 but then thought that the smaller squares represented1 video game, giving 19 and 9 for Tuesday and Wednesday respectively. Many students were able to find the 22 or the 10 but not both or gave the answer 6 from 22 -16, the difference between Monday and Tuesday In part (c), there were very many correct solutions. Some reversed their diagrams for Thursday and Friday, some simply shared the 32 video games equally between the two days. Mistakes were also common in the division of (or inability to divide) 32 by 4.

  Text version

  A pictogram records video games sold. One full symbol represents 8 games. Monday has 2 symbols, Tuesday has 2 3/4 symbols and Wednesday has 1 1/4 symbols. Thursday and Friday are blank.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q14 · 4 marks

  4 marks

  14

  
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  Examiner report

  Most students knew to calculate the cost of one kilogram of carrots by dividing £1.80 by 3 and subsequently secure a second mark for working out the cost of four kilograms. Problems arose when trying to work out the cost of one kilogram of potatoes. Many subtracted £1.80 (instead of £1.20) from £3.45 and then divided by 5. Some subtracted £1.20 but then made an arithmetical error, usually resulting in a value of £2.20 giving 44p as the cost of one kilogram of potatoes. A considerable number ignored the 2kg of carrots and divided 3.45 by 5 to find the cost of 1 kg potatoes as 69p.

  Text version

  3 kg of carrots cost £1.80. 2 kg of carrots and 5 kg of potatoes cost £3.45 in total.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q17 · 5 marks

  5 marks

  17

  
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  Examiner report

  Whilst the context of this question was not unfamiliar, many students worked purely on complete batches of 12 biscuits in part (a), not realising that additional biscuits could be made from the remaining ingredients. Consequently, an answer of 36 was the modal answer which gained 3 of the 4 available marks. A variety of processes were seen in determining the greatest number of biscuits (or batches), build-up methods being most prominent. Work was often poorly laid out and not shown sequentially and many worked with only one or two ingredients, losing potential credit. In part (b) it was sufficient to identify ‘flour’ solely as the critical ingredient preventing more biscuits (or batches) being made. However, few did this, referring to “other ingredients” or butter as well as or instead of flour.

  Text version

  A recipe makes 12 biscuits using 125 g butter, 200 g flour and 50 g sugar. Heidi thinks she has 500 g butter, 700 g flour and 250 g sugar.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q20 · 6 marks

  6 marks

  20

  
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  Examiner report

  Complete solutions of this long multiplication of two decimal numbers in part (a) were scarce. With whichever method adopted, students need to be aware that initially ignoring the decimal points and multiplying, in this case, 367 by 42, was the best way to approach this calculation. Far too many students made place value errors in their chosen method largely by trying to include the decimal parts in their calculation. Where students had a correct method, it was common to see incorrect answers due to times table errors. In part (b), again fully correct solutions were few and far between. Simply dividing 59 by 16 was too great a demand for many. Those that attempted the division were often able to gain the first mark for the first digit being 3. In both parts, encouragement should be given to work out an estimate to identify the size of the answer and hence place the decimal point correctly.

  Text version

  Complete two non-calculator decimal calculations.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q22 · 3 marks

  3 marks

  22

  
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  Examiner report

  It was very pleasing to see many good attempts at this question. Many students scored at least one mark for either writing both fractions as improper fractions or for writing two fractions with a common denominator. In each case one error was condoned. Some students found it difficult to subtract 15   from 15   to give a negative value of െ 15   and simply wrote 15  . Some reached a solution of 15   but then failed to convert it into a mixed number. There were still many who simply subtracted the three separate components, whole number, numerator and denominator leading to a common incorrect answer of 2½. Where improper fractions were used, many students failed to realise that a common denominator was still required for the subtraction of the fractions, getting 5 െ 3 then subtracting to get ଶ .

  Text version

  Work out 4 1/5 - 2 2/3.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q26 · 4 marks

  4 marks

  26

  
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  Examiner report

  This question was not well answered. Some students gained a mark, usually for substituting 3 into the given formula for the surface area of the sphere. Some gave a numerical value for pi and attempted to find the surface area of the sphere, with varied success.

  Text version

  A cube has edges of length x cm. A sphere has radius 3 cm. The surface area of the cube equals the surface area of the sphere. You are given that the surface area of a sphere is 4πr^2.

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• Edexcel 1MA1 · November 2021 · Paper 1F · Q27 · 2 marks

  2 marks

  27

  
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  Examiner report

  Only a few students correctly found either bound for the length of the pencil; 7.1 and 7.2 or 7.3 were the best of the sensible incorrect attempts.

  Text version

  Freddie measured the length of a pencil as 7.2 cm correct to 1 decimal place.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q1 · 6 marks

  6 marks

  1

  
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  Examiner report

  In part (a) many students used a suitable method to multiply the two decimals, with relative place value correct. This meant that all of these students were able to gain the method mark and many went on to get two or three marks. Some students correctly came up with the digits 15414 but placed the decimal point incorrectly and gained two of the three marks. Students making arithmetical errors were also able to score two of the three marks by giving an answer with the decimal place correctly positioned, if this followed a correct method. Students who tried to answer this question by a less formal method were not as successful, often showing an incomplete method such as 3 × 4 + 0.67 × 0.2 and gaining no marks. Students were not quite as successful in part (b). Those who used a formal method to divide a number with the digits 5984 by a number with the digits 16 usually gained the first mark for making a correct start to the method and getting 3 as the first digit. Many went on to gain all three marks. Some of those who divided correctly to get the digits 374 positioned the decimal point incorrectly and gained two of the three marks. Arithmetic errors were common but, as in part (a), students could still gain two of the three marks if the decimal place was correctly positioned in their final answer. Some students rounded both 59.84 and 1.6, divided 60 by 2, and wrote 30 as the final answer. This gained no marks but it would have been a useful strategy for students to use when deciding where to position the decimal point in their final answer.

  Text version

  Complete two non-calculator decimal calculations.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q3 · 3 marks

  3 marks

  3

  
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  Examiner report

  This question was generally answered quite well. The most common method seen was to convert both mixed numbers into improper fractions and then write both fractions over a common denominator. Many students gained at least two of the three marks for getting this far. The accuracy mark was often lost because students failed to write their answer as a mixed number or made an arithmetic error. Having written both mixed numbers as improper fractions some students made no further correct progress and gained one mark only. Far fewer students chose to subtract the whole numbers and deal with the fractional parts separately. The difficulty with this method was subtracting a larger fraction from a smaller fraction which meant that − was often followed by an answer of or 2 10 − .

  Text version

  Work out 4 1/5 - 2 2/3.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q7 · 4 marks

  4 marks

  7

  
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  Examiner report

  This question was not answered particularly well. Many students gained one mark for using the given formula to write a correct expression for the surface area of the sphere, 4 × π × 32 for example, but not many of these students attempted to find the surface area of the cube. It was very common to see 4 × π × 32 followed by x  = . Those students who did find an expression for the surface area of the cube generally went on to form a suitable equation and complete the method to gain full marks. Some students found an expression for the area of one face of the cube rather than for the surface area, often writing x  = , and gained the first two marks only.

  Text version

  A cube has edge x cm. A sphere has radius 3 cm. Their surface areas are equal. Sphere surface area = 4πr^2.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  Part (a) was answered quite well with many students knowing that the value of 70 is 1. The common incorrect answers were 0 and 7. Slightly fewer students were able to find the value of 3 × 36 × 3–6 in part (b) with the most common incorrect answer being 27. In part (c), some of the students who knew that a negative power involved a reciprocal made arithmetic mistakes and gave incorrect answers such as 1 or 1 . In part (d), students not familiar with fractional indices often divided 27 by 3 instead of finding the cube root of 27 which resulted in 9 being a common incorrect answer.

  Text version

  Evaluate four index expressions.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  Since students were asked to find an estimate for the length of one side of each square in part (a) it should have been evident to them that they would need to use a rounded value. Some students did this at the start of the process, rounding the total area to 5400 before dividing by 6. Others started by dividing 5406 by 6 and then rounded 901 to 900 before attempting to find the square root. Many students gained the first mark for dividing by 6 but the next stage in the process proved to be beyond a considerable number of these students. Those who recognised that they needed to find the square root often went on to get full marks for an answer of 30 but the incorrect processes seen were many and varied. Often these involved division by 4 or by 2. Some students gained the first mark and gave 900 or 901 as the final answer. The mark in part (b) was not dependent on a complete process in part (a). To be in a position to say whether their answer was an underestimate or an overestimate, students must have used a rounded value in a calculation. Many students did state that their answer was an underestimate and gave a suitable reason; for example they had rounded the total area down or they had rounded 901 to 900. Some students chose underestimate or overestimate but gave no reason for their choice. Overall, part (b) was not answered particularly well.

  Text version

  A shape is made from six identical squares and has total area 5406 cm^2.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q13 · 1 mark

  1 mark

  13

  
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  Examiner report

  Some good evaluations of Ted’s method were seen. Successful students often explained that Ted should have used 100x and x or that he should have used 1000x and 10x. Some students gave acceptable explanations that focused on the recurring numbers after the decimal points. Any numerical examples given as part of an explanation needed to be correct for the mark to be awarded. This was often not the case. Some answers consisted only of a correct numerical method showing that the recurring decimal could be written as the fraction 99 and these were accepted. Some answers, such as “he should have used 100x” or “he needs to find 1000x”, did not go quite far enough. Many answers were simply incorrect. A common misconception was that Ted had made a multiplication error because the value he found for 10x was wrong. A significant number of answers consisted of a commentary of what Ted was doing but no evaluation of his method.

  Text version

  Ted tries to convert 0.434343... to a fraction by writing x=0.434343..., 10x=4.343434..., then subtracting 10x-x.

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• Edexcel 1MA1 · November 2021 · Paper 1H · Q19 · 4 marks

  4 marks

  19

  
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  Examiner report

  Writing 12 as 2 3 was sometimes seen as the first step and sometimes it was seen later in the process. Some of the students who started by writing 12 as 2 3 and simplified the numerator of the fraction to 8 2 3 + made no further progress. Those students who realised that they needed to rationalise the denominator were not always able to show a correct method to do so. Attempts at multiplying both the numerator and the denominator by5 + or by 3 were often seen and gained no credit. Those who did appreciate the need to multiply numerator and denominator by 5 − often went on to expand the terms correctly although some students made sign errors. Having got as far as (34 2 3) + some students gave this as the final answer and did not score the final mark because the question asked for an answer in the form ( 3) a + 𝑏 .

  Text version

  Show that (8+sqrt(12))/(5+sqrt(3)) can be written in the form (a+sqrt(3))/b, where a and b are integers.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  More students were successful on this question than on question 2. The vast majority were able to correctly order the decimal figures given.

  Text version

  Write 1.02, 0.12, 1.20 and 0.21 in order of size, starting with the smallest.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q6 · 2 marks

  2 marks

  6

  
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  Examiner report

  In this question part (b) was more often correct than part (a). In part (b) almost all answers were correct with just a few students giving 16 as an answer. Whilst this is a multiple of 8 it was not in the given list. However, for part (a) a wide range of incorrect answers were given using numbers from the list and it was disappointing to see that almost a third of the cohort could not recognise 25 as a square number.

  Text version

  Here is a list of whole numbers from 21 to 30: 21, 22, 23, 24, 25, 26, 27, 28, 29, 30.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q7 · 3 marks

  3 marks

  7

  
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  Examiner report

  This question was generally well answered with many correct answers seen. The major problem seen in this question was students stopping after subtracting 940 from 2500 and not dividing their answer by 2. This working allowed one mark to be awarded. The other issues seen in this question was arithmetic errors or some students thought that there were two bags of 940g so the third bag was 620g.

  Text version

  A baker has bags A, B and C. Bags A and B contain the same amount of flour. Bag C contains 940 g. The three bags contain 2500 g in total.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  A high proportion of students added the correct heights to give 35 and many went on to gain full marks by dividing by five. A few divided by six, so only gained one mark, and there were some arithmetic errors and misreading of the y-axis, causing the accuracy mark to be lost. There were also some students who used both the frequencies and the numbers on x-axis adding a mixture of both or adding all together whilst others incorrectly multiplied the number on the dice by the frequency. All these methods were incorrect and did not score any marks.

  Text version

  Five students each throw a die the same number of times. A vertical line graph shows frequencies 6, 4, 5, 8, 7 and 5 for die scores 1, 2, 3, 4, 5 and 6 respectively.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q9 · 1 mark

  1 mark

  9

  
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  Examiner report

  This question was answered very well with many students scoring the communication mark available. The most common correct responses were to perform the correct calculation stating that the true answer was 14 and state that multiplication should be done before addition. Many students wrote BIDMAS or BODMAS as part of their response and often giving the correct answer of 14 as well. Where the mark was lost it was often due to contradicting information being used or a calculation being shown which did not give the correct answer (14). Some students said that 20 was actually correct and scored no marks for just re writing the working given.

  Text version

  Alec works out 2 + 3 × 4 by doing 2 + 3 = 5 and then 5 × 4 = 20. Alec is wrong.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q12 · 3 marks

  3 marks

  12

  
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  Examiner report

  It was pleasing to see that a high proportion of students gained full marks on both parts of this question. A common incorrect answer to part (a) was 0.9156… from √13.82 4.06 i.e., failing to square root the whole calculation, this gained no marks. The students that wrote down intermediate stages in their calculations could gain a mark for their working eg √13.82 = 3.717…. Some students lost the mark for part (b) by writing 1.8, rather than 1.84. It was pleasing to see that many students gained the mark in part (b) by correctly rounding their answer, even if incorrect, from part (a).

  Text version

  Use a calculator to work out sqrt(13.82/4.06).

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  This question was not so well answered and proved quite difficult for many students. Those who gained both marks usually did so by converting the given fractions to decimals first then ordering correctly. However, many students only achieved one mark usually as a result of incorrect or incomplete conversions. It was common to see 5 and 8 correctly converted to a decimal but when converting the other two fractions students often only worked to 1 decimal place hence losing accuracy and gaining two values of 0.6 to compare. This method allowed the award of the method mark only for two correct conversions. Others showed no working but did list the fractions and some did so correctly, a high risk strategy, others with no working often scored one mark for three fractions ordered correctly. A small minority tried to work with equivalent fractions but this method often broke down and was rarely successful.

  Text version

  Write 5/8, 2/3, 4/9 and 3/5 in order of size, starting with the smallest.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q18 · 3 marks

  3 marks

  18

  
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  Examiner report

  This problem presented students with a slightly different approach to testing frequency tables and the question was well answered by many. When partial marks were awarded it was often for finding the total length of the planks represented in the table, continuing to subtract from 92 to find that the 2m lengths equated to 26m and then losing the final mark due to either forgetting to divide by 2 or because of arithmetic errors. Common incorrect approaches seen included adding the frequencies and subtracting this from 92, giving an answer of 55 or using a combination of adding both columns of the table. Less commonly seen incorrect approaches included looking for a pattern or sequence from the frequencies provided, usually arriving at 11, or giving an answer of 20 due to assuming that if 10 planks represented the 1 metre lengths then 20 planks must represent the 2 metre lengths.

  Text version

  Ben has planks: 5 of length 3 m, 8 of length 2.5 m, an unknown number of length 2 m, 14 of length 1.5 m and 10 of length 1 m. Their total length is 92 m.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q19 · 4 marks

  4 marks

  19

  
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  Examiner report

  This was a very accessible problem and allowed students to score a range of the available marks. The modal score was full marks. When full marks were not scored a common approach for this question was to find Rachel’s share (£240). Many then incorrectly calculated Samina’s share as ¼ of £240 or ¼ of 600 and not ¼ of (£600 - £240) as required. This then obviously led to Tom’s share for this method being incorrect but most students did find 600 ÷ 3 = 200 and so gain the third process mark. Of those who correctly calculated all three correct shares, the majority went on to gain the communication mark by giving a correct conclusion and accurate comparative figures. A few gave confused or ambiguous statements; again, succinct statements are recommended.

  Text version

  Rachel, Samina and Tom share £600. Rachel gets 2/5 of £600. Samina gets 1/4 of the money left. Tom gets the rest. Tom says he would have got more if they had shared £600 equally.

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• Edexcel 1MA1 · November 2021 · Paper 2F · Q22 · 4 marks

  4 marks

  22

  
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  Examiner report

  The majority of responses to the first part of this question scored at least one mark and a good proportion gave the correct answer of 12. When one mark was gained it was for the sight of one or both factor trees, but some students did not know how to use the results and so did not go on to gain the accuracy mark. The most successful method seemed to be listing factors and extracting 12 from the list. Part (b) was not so well answered but as with part (a), many students gained a method mark for a factor tree, but then were unable to use the results correctly. The most successful responses were from those who listed multiples of 24 and 40. A few students did confuse HCF and LCM.

  Text version

  Find an HCF and an LCM.

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• Edexcel 1MA1 · November 2021 · Paper 2H · Q1 · 3 marks

  3 marks

  1

  
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  Examiner report

  Part (a) was answered very well. Almost every candidate was able to extract the correct critical value, and most provided the correct inequality symbol too. It was not uncommon to see −1 < x as an acceptable alternative answer. Those who did drop marks were fairly equally spread between choosing < over > or for including an inclusive inequality. Part (b) was again very well answered. Almost all students scored at least one mark, either for a line of correct length, or for a closed circle at −3, with a large proportion gaining the second mark also. Those who failed to score typically had their circles the wrong way round, or the line stopping at 3 rather than 4.

  Text version

  A number line has an open circle at -1 and is shaded right.

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• Edexcel 1MA1 · November 2021 · Paper 2H · Q2 · 4 marks

  4 marks

  2

  
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  Examiner report

  Both parts (a) and (b) were similarly well answered. In both cases the vast majority of students gained the first mark for prime factors or a factor tree, many then continuing to gain the correct answers. When students didn’t score full marks it was very often because they mixed up HCF and LCM. There was a significant number who found correct prime factors, and entered these into a Venn diagram, but were then unsure how to use this to complete the question. Those who scored zero normally did so because they had chosen a listing method, but unfortunately listed multiples in place of factors or vice versa.

  Text version

  Find an HCF and an LCM.

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• Edexcel 1MA1 · November 2021 · Paper 2H · Q13 · 2 marks

  2 marks

  13

  
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  Examiner report

  Many students on this paper appear to have not been taught the product rule for counting, and as a result, had no real strategy to approach the question. Those who did correctly multiply the values, often then carried out another calculation, such as dividing by 3, and hence ended with an incorrect answer.

  Text version

  A school has 16 teachers, 120 girls and 100 boys. One of each is chosen.

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• Edexcel 1MA1 · November 2021 · Paper 2H · Q21 · 4 marks

  4 marks

  21

  
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  Examiner report

  This grade 9 problem was a struggle for most, however there was scope for a good number to gain a single mark for one correct bound. This was normally a bound for T rather than l. The bounds for l most commonly seen were 51.5 and 52.5. These were outside the range that was acceptable for the substitution mark, so those who made this error were unable to gain the third mark even if they chose the correct pair. The second mark was for rearrangement, either before or after substitution, and proved to be unattainable for the majority of students due to the complex nature of the stated formula. To gain the third mark students had to select the correct pairs, eg LB of l and UB of T, or vice versa, and substitute these into a formula. In Summary Based on their performance on this paper, students should: • ensure they are familiar with sufficient higher tier content to be able to access the paper • work on understanding standard topics such as trigonometry, graphs, and box plots • spend more time working with ratio and proportional reasoning to allow them to work confidently with problems relating to these areas. • be confident in the different applications of trigonometry, depending on the type of triangle presented • practise solving problems which require conversion between units, in particular here for time in minutes and hours • make use of the units given in questions to determine formulae eg density units of g/cm3 lead to density = mass/volume • use brackets around negative numbers when entering these into a calculator

  Text version

  Pendulum period T seconds and length l cm satisfy T=2πsqrt(l/g). Katie measures l=52.0 and T=1.45, both 3 s.f.; use π=3.142.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  Another well answered question. Where the mark was not gained by a small minority of students, values such as 2 and 3.5 were given. Some students wrote factors as paired products, which was acceptable.

  Text version

  Write down two factors of 35.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  A question in which nearly all students gained the mark.

  Text version

  What is the time 2 hours 40 minutes after 8:05 am?

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Most students gave the correct response. A common error was to see ଵ ଺ changed to a decimal which resulted in a decimal answer. It was evident that these students did not appreciate that multiplying by ଵ ଺ is the same as dividing by 6.

  Text version

  Work out 1/6 of 66.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  Those students who adopted a systematic approach to listing the outcomes were the ones who gained full marks most regularly. A common error was to repeat outcomes.

  Text version

  Bag A has cards E, F and G. Bag B has cards J and K. James takes one card from A and then one from B.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  This question was generally well answered with nearly all students gaining full marks. Most mistakes were in respect of accuracy of calculations rather than process, suggesting that some students were not using their calculator effectively, or perhaps did not have one. Those who just worked with one of each item were able to be awarded the first mark.

  Text version

  Sandy pays for 2 plane tickets at $600 each, 7 hotel nights at $120 each and 2 theme-park tickets at $250 each.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  Successful students used their calculator to divide 300 by 4.85 and rounded down to find 61 books could be bought, but 61.8 rounded up to 62 was often seen. Unsuccessful approaches were to either round the book price to 1 significant figures and estimate, or to multiply 300 by 4.85 instead of divide. Build up methods using repeated addition rarely earned method marks, as multiple calculations increased the risk of errors and students did not always make it clear where the end point was.

  Text version

  Corina has £300 to spend on books. Each book costs £4.85.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  In part (a) most students used a non-calculator method and obtained the correct answer. It was obvious when calculators were used where an answer of 196 ÷ 603 = 3 h 26 min was seen. Many gained 1 mark for getting as far as 3 hours. In part (b) it was very rare to see any correct answers. Some wrote down the formula triangle for speed distance but could not relate this to an algebraic expression. The closest many students got was 2x, the most common incorrect algebraic answer.

  Text version

  Complete a time conversion and an average-speed expression.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q14 · 3 marks

  3 marks

  14

  
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  Examiner report

  The most successful method here was to exclude zeros and work with 600 rather than 600,000,000. A number lost the final accuracy mark by virtue of recording an incorrect number of zeros even though the non-zero digits through their working were correct. Some students only gained 1 mark since they got as far as 520 (million) but failed to then subtract this from 600. Very few realised they could use ଶ ଵହ to get to the answer. Premature rounding again lost students marks as it was not uncommon to see ଵଷ ଵହ converted to 86% meaning their final answer was then incorrect. Many of those trying to find 86% using build up methods soon got into difficulties.

  Text version

  A stadium cost £600 million. 13/15 of this was for the building and the rest was for the land.

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• Edexcel 1MA1 · November 2021 · Paper 3F · Q23 · 4 marks

  4 marks

  23

  
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  Examiner report

  In part (a) most students secured the mark for this question. As this was a calculator paper many students may have correctly processed this value using a calculator. Only a minority of students secured the mark for part (b). There were many answers indicating that students had a limited knowledge of negative indices in standard form. In part (c) many of the responses scored one mark for 4730, either by entering the calculation into the calculator or converting to 4200 + 530 but did not secure the accuracy mark by recognising that the answer needed to be in standard form.

  Text version

  Complete three standard-form tasks.

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• Edexcel 1MA1 · November 2021 · Paper 3H · Q3 · 4 marks

  4 marks

  3

  
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  Examiner report

  A high percentage of students showed a good understanding of standard form. In part (a) nearly all students were able to convert from a number in standard form to an ordinary number. A slightly smaller proportion of students could convert from an ordinary number to a number in standard form which involved a negative index. Calculations in part (c) were usually carried out successfully but a significant number of students scored only 1 mark out of the 2 marks available because they did not convert 4730 to standard form or because they made an error in the conversion. The former error could have been avoided with a more careful reading of the question.

  Text version

  Complete three standard-form tasks.

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• Edexcel 1MA1 · November 2021 · Paper 3H · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  About a half of students scored both marks on this question. Where only 1 mark was scored, it was usually for the lower end of the interval and where the student had used 6.4 for the upper end of the interval.

  Text version

  Freya writes x=6.4 correct to 1 decimal place.

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• Edexcel 1MA1 · November 2021 · Paper 3H · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  This question was not well answered and only about a quarter of all students scored one mark or more. Students who scored one mark usually scored this for giving the correct value for n. In general, little working was seen in the working space so it was rare for examiners to be able to award the process mark where both answers were incorrect.

  Text version

  (a x^6)^(1/n) = 7x^3.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  Text version

  Write the following numbers in order of size. Start with the smallest number. 0.32 0.4 0.35 0.309

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Text version

  Here is a list of numbers. 5 11 18 22 29 From the list, write down a multiple of 3

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  Text version

  Write 4.666 correct to the nearest whole number.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Text version

  Write 3/4 as a decimal.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Text version

  Write down the value of the 7 in the number 8765

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q10 · 4 marks

  4 marks

  10

  
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  Text version

  Jenny has 12 marbles. 4 of these 12 marbles are large. The rest of these 12 marbles are small. Each large marble has a weight of 70 grams. Each small marble has a weight of 50 grams. Work out the total weight of the 12 marbles. ....................................................... grams

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q17 · 5 marks

  5 marks

  17

  
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  Text version

  In a shop, a TV has a normal price of GBP 500 The shop has a sale. On Monday, the normal price of the TV is reduced by 10% to give the sale price. On Tuesday, the sale price of the TV is reduced by 20% Chris wants to buy the TV. He has GBP 400 to spend on the TV. Does Chris have enough money to buy the TV on Tuesday? You must show how you get your answer.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q18 · 3 marks

  3 marks

  18

  
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  Text version

  Work out an estimate for (790 x 289)/49.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q21 · 3 marks

  3 marks

  21

  
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  Text version

  Show that 2 1/3 x 3 3/4 = 8 3/4.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q28 · 2 marks

  2 marks

  28

  
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  Text version

  Write these numbers in order of size, starting with the smallest: 6.72 x 10^5, 67.2 x 10^-4, 672 x 10^4, 0.000672.

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• Edexcel 1MA1 · November 2020 · Paper 1F · Q29 · 3 marks

  3 marks

  29

  
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  Text version

  Given a/b = 2/5 and b/c = 3/4, find a:b:c.

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q2 · 3 marks

  3 marks

  2

  
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  Text version

  Show that 2 1/3 x 3 3/4 = 8 3/4.

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q5 · 3 marks

  3 marks

  5

  
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  Text version

  Sean pays GBP 10 for 24 chocolate bars. He sells all 24 chocolate bars for 50p each. Work out Seans percentage profit. ....................................................... %

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q9 · 2 marks

  2 marks

  9

  
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  Text version

  Write these numbers in order of size, starting with the smallest: 6.72 x 10^5, 67.2 x 10^-4, 672 x 10^4, 0.000672.

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q11 · 6 marks

  6 marks

  11

  
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  Text version

  Evaluate each expression.

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q20 · 4 marks

  4 marks

  20

  
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  Text version

  Show that (sqrt(180) - 2sqrt(5))/(5sqrt(5) - 5) can be written as a + sqrt(5)/b, where a and b are integers.

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• Edexcel 1MA1 · November 2020 · Paper 1H · Q23 · 3 marks

  3 marks

  23

  
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  Text version

  There are four types of cards in a game. Each card has a black circle or a white circle or a black triangle or a white triangle. number of cards with a black shape : number of cards with a white shape = 3 : 5 number of cards with a circle : number of cards with a triangle = 2 : 7 Express the total number of cards with a black shape as a fraction of the total number of cards with a triangle.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  Text version

  Write 0.37 as a fraction.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Text version

  Write 29 381 correct to the nearest 1000

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  Text version

  Here is a list of numbers. 3 4 9 18 27 30 36 From the numbers in the list, write down a cube number.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Text version

  Liz is watching a film at the cinema. The film started at 14 30 The film is 105 minutes long. When the film ends, Liz takes 20 minutes to get to the bus stop. A bus leaves the bus stop at 16 45 Does Liz get to the bus stop in time to get this bus? You must show all your working.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q9 · 4 marks

  4 marks

  9

  
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  A conversion scale shows 40 kilometres as approximately 25 miles. An approximate rule says: divide kilometres by 10, then multiply by 6.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q12 · 2 marks

  2 marks

  12

  
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  Lucy uses a code to open a lock. The code is a letter followed by a 2-digit number. The letter is L or U. The number is a prime number between 20 and 30 Write down all the possibilities for Lucys code.

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q13 · 3 marks

  3 marks

  13

  
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  A machine fills bags with sweets. There are 4275 sweets. There are 28 sweets in each full bag. The machine fills as many bags as possible. How many sweets are left?

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q16 · 4 marks

  4 marks

  16

  
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  An exam has two papers, Paper 1 and Paper 2 Paper 1 has 60 marks. Paper 2 has 90 marks. The pass mark is 2 3 of the total number of marks. Danielle gets 70% of the marks for Paper 1 How many of the marks for Paper 2 must Danielle get in order to get the pass mark?

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q19 · 2 marks

  2 marks

  19

  
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  Adam, Linda and Rytis share money. Linda gets three times Rytis and half as much as Adam. What fraction of the total does Linda get?

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q20 · 4 marks

  4 marks

  20

  
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  Pens and pencils are sold in a shop. 12 pencils cost GBP 1.80 The ratio of the cost of a pen to the cost of a pencil is 7 : 3 Work out the cost of 5 pens. GBP .......................................................

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• Edexcel 1MA1 · November 2020 · Paper 2F · Q21 · 4 marks

  4 marks

  21

  
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  Write 84 as a product of its prime factors.

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• Edexcel 1MA1 · November 2020 · Paper 2H · Q1 · 4 marks

  4 marks

  1

  
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  Write 84 as a product of its prime factors.

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• Edexcel 1MA1 · November 2020 · Paper 2H · Q10 · 4 marks

  4 marks

  10

  
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  Simplify each expression.

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• Edexcel 1MA1 · November 2020 · Paper 2H · Q11 · 2 marks

  2 marks

  11

  
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  Jack is in a restaurant. There are 5 starters, 8 main courses and some desserts on the menu. Jack is going to choose one starter, one main course and one dessert. He says there are 240 ways that he can choose his starter, his main course and his dessert. Could Jack be correct? You must show how you get your answer.

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Work out 1/3 of 24.

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Work out 2.5^2

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q5 · 1 mark

  1 mark

  5

  
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  Write the following numbers in order of size. Start with the smallest number. 1 - 4 0 7 - 6 - 3 2

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Karim buys 200 tiles. The tiles are sold in boxes. There are 25 tiles in each box. Each box of tiles costs GBP 9.75 Work out the total cost of the boxes of tiles Karim buys. GBP ................................................

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q9 · 3 marks

  3 marks

  9

  
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  Work out the value of 300 2 x 5

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q15 · 5 marks

  5 marks

  15

  
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  Shop A sells packs of 4 batteries for GBP 1.60; Shop B sells packs of 6 for GBP 2.70. Harry needs at least 30 batteries. Single batteries actually cost 40p at A and 45p at B.

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q20 · 4 marks

  4 marks

  20

  
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  Akhtar, Ben and Carl each have some money. Akhtar has GBP 65 Ben has GBP 100 Carl has three GBP 5 notes, one GBP 20 note and some GBP 10 notes. The mean amount of money per person is GBP 80 How many GBP 10 notes does Carl have?

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q24 · 3 marks

  3 marks

  24

  
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  Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes. ........................ hours ........................ minutes

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• Edexcel 1MA1 · November 2020 · Paper 3F · Q25 · 2 marks

  2 marks

  25

  
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  A number, m, is rounded to 1 decimal place. The result is 9.4 Complete the error interval for m. .................................................. m < .................................................

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q2 · 3 marks

  3 marks

  2

  
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  Andy cycles a distance of 30 km at an average speed of 24 km/h. He then runs a distance of 12 km at an average speed of 8 km/h. Work out the total time Andy takes. Give your answer in hours and minutes. ........................ hours ........................ minutes

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q3 · 2 marks

  2 marks

  3

  
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  A number, m, is rounded to 1 decimal place. The result is 9.4 Complete the error interval for m. ................................................ m < ................................................

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q10 · 4 marks

  4 marks

  10

  
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  A person's heart beats approximately 10^5 times per day and a person lives about 81 years. Separately, 2 x 10^12 red blood cells have total mass 90 g.

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q15 · 2 marks

  2 marks

  15

  
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  Prove algebraically that 0.7333... (with 3 recurring) can be written as 11/15.

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q18 · 4 marks

  4 marks

  18

  
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  In a cube, A and H are opposite vertices, so AH is a body diagonal through the cube. AH=11.3 cm correct to the nearest millimetre.

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• Edexcel 1MA1 · November 2020 · Paper 3H · Q20 · 1 mark

  1 mark

  20

  
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  The five numbers are 98^53, 98^64, 98^73, 98^88 and 98^91.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  This question was quite well done with a big majority of students giving the correct answer “70”. Examiners accepted the answer “7 tens” but did not accept the word “tens” alone. Some students gave other incorrect responses such as “tenths” or “7 tenths”.

  Text version

  Write down the value of the 7 in the number 1074

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  This question was also answered well. Incorrect responses seen included 5, 4.5, 4.60 and 45.8.

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  Write 4.58 correct to 1 decimal place.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  The majority of students answered this question correctly. 0.317, 317 and 31700 were the most commonly seen incorrect responses but some students introduced zeros between one or more of the digits in 31.7 and gave answers such as 3100.7.

  Text version

  Work out 31.7 x 100.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  This question was not done very well. Answers given were often not equivalent to ଶ଼ ଻଴. A significant number of students who did some correct working did not give the fraction in its simplest form, most commonly leaving it as ଵସ ଷହ.

  Text version

  Write the fraction 28/70 in its simplest form.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q6 · 4 marks

  4 marks

  6

  
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  This question was generally answered well. Nearly all students could use the representation to write down the number of pictures sold in January in part (a) of the question. In part (b) a similarly high proportion of students could represent the number of pictures sold in April on the diagram. Most students could also score the two marks available in part (c) though a significant proportion of responses contained mistakes in arithmetic, usually in one of the totals for a particular day. These responses normally got one mark for adding the four totals 24, 28, 20 and 12, three of which were correct.

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  A pictogram uses one complete symbol to represent 8 pictures. January has 3 symbols, February has 3.5 symbols, March has 2.5 symbols, and the April row is blank.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q7 · 2 marks

  2 marks

  7

  
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  Most students scored both marks for their answer to this question though a surprisingly low proportion of students took the shorter route of writing 1¼ hours as 1 hour 15 minutes then comparing it with 1 hour 25 minutes. Students generally preferred to convert both times to minutes. This approach was often successful but there was a significant number of students who wrote 1¼ hours as 1.25 hours then changed this to 85 minutes. Their resultant final answer was “0” and the sense that this must be wrong was usually missing. Another error seen was writing ¼ of an hour as 45 minutes. This led to a final incorrect answer of 20 minutes.

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  Work out the difference, in minutes, between 1 hour 25 minutes and 1 1/4 hours.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q8 · 3 marks

  3 marks

  8

  
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  Over a half of all students scored the full three marks for their responses to this question. The majority of students worked in grams, starting by converting 3 kilograms to 3000 grams. Only a small number of students worked in kilograms. Most of the errors seen in working were in the calculation of 4 × 650. Students making a mistake here usually scored two of the three marks available. The most common error seen in the method to solve this problem involved students dividing the 650 grams by 4 as part of their solution. Some other students subtracted the weight of one block from the total weight of all five blocks to give an answer of 2350 grams.

  Text version

  Prasha has five blocks of wood. The total weight of all five blocks of wood is 3 kilograms. 4 of the blocks of wood each have a weight of 650 grams. Work out the weight, in grams, of the other block of wood. ....................................................... grams

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q11 · 2 marks

  2 marks

  11

  
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  This question was a good discriminator. More able students scored two marks for a complete list without any repeats. About a third of students scored one mark for listing at least 4 correct outcomes but were not able to provide a fully correct answer. A total of 6 combinations was commonly seen. Some students listed the possibilities of how many heads and how many tails could occur without making it clear the order of the heads and tails within these possibilities, so for example, stating 1 heads and 2 tails without differentiating between HTT, THT and TTH. Of the students who could not be awarded any marks, a good proportion of them gave outcomes for only 2 throws.

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  Mason throws a coin 3 times. The outcome of each throw is either Heads or Tails. List all the possible outcomes of the 3 throws.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q12 · 5 marks

  5 marks

  12

  
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  Part (a) of this question was well answered and many students showed clear working together with a clear conclusion based on supportive figures. Most students stated that Rehan did not have enough money and gave their reason as either “he would need $215” or that “he only has $65 left”. Part (b) was less well answered but differentiated well between the most able students sitting the paper. Many students failed to “use a suitable approximation” so could not be awarded any marks for their response to this part of the question. Only a relatively small proportion of the students who did use an approximation guaranteed the statement that “Rehan is wrong” by using a value below £0.749, for example 0.74 or 0.7.

  Text version

  Rehan has $200. Trainers cost $60, three T-shirts cost $25 each, and a jacket costs $80. The exchange rate is $1 = GBP 0.749.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q14 · 2 marks

  2 marks

  14

  
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  Students usually scored two marks for a fully correct response to this question. There were several different methods seen and no one method was used much more frequently than any of the other methods. Students who could demonstrate a correct method scored at least one mark. Errors in the evaluation of 10 × 20 were commonplace. Of those students who could not be awarded any marks, a common approach was to calculate 20 × 10 + 3 × 5.

  Text version

  Work out 23 x 15.

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q20 · 3 marks

  3 marks

  20

  
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  Many students made a good start to this question by either starting with a prime factor decomposition of at least one of the numbers 108 and 120 or by writing down multiples of each of the numbers. Some allowance was made for arithmetic errors and students who used one of these two approaches generally scored at least one mark. Students who listed multiples were more likely to obtain full marks than those who used prime factor decomposition. It did seem that students who used the latter approach lacked confidence in how to use their products of prime factors to find the lowest common multiple. Final incorrect answers of 2 (lowest common factor) and 12 (highest common factor) were often seen.

  Text version

  Find the Lowest Common Multiple (LCM) of 108 and 120

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• Edexcel 1MA1 · November 2019 · Paper 1F · Q22 · 3 marks

  3 marks

  22

  
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  This question discriminated well at the top end of the ability range with many students getting each of the possible marks for their response. Some students realized the need to change the mixed numbers to improper fractions and demonstrated they could do this for at least one mixed number but could get no further. They scored 1 mark. Students who successfully multiplied the two mixed numbers but left their answers as improper fractions, for example ଶ଼ ଵଶ, scored 2 marks. Correct answers in the form of a mixed number scored full marks. They did not need to be fully simplified so, for example, 2 ସ ଵଶ scored full marks. Many students benefitted from this. Disappointingly, there were a large number of students who tried to reach the answer by multiplying the whole numbers and the proper fractions separately to get an answer of 1 ଵ ସ or equivalent. Some confusion between multiplying and dividing fractions was evident in a significant number of student’s responses where inverting the second fraction before multiplying or cross-multiplying was seen quite often.

  Text version

  Work out 1 3/4 x 1 1/3. Give the answer as a mixed number.

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  Most students gained at least two marks on this question, usually for producing two factor trees with no more than one error. It was common however to see answers of 12 (finding the HCF) or 2 where many students thought that the lowest common factor was required. The listing of multiples was often seen, but unfortunately this was often littered with arithmetic errors.

  Text version

  Find the Lowest Common Multiple (LCM) of 108 and 120

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q3 · 3 marks

  3 marks

  3

  
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  Examiner report

  Although a correct mixed fraction was found by many students, a large number still find great difficulty in working with fractions. The less able students, instead of working with “top heavy” fractions, split the fractions to multiply them and working of 1 (1×1) and ଷ ଵଶ (3 ൈ ଵ ସሻ was sometimes seen. Other students tried to add the fractions with ଶଵ ଵଶ൅ ଵ଺ ଵଶൌ ଷ଻ ଵଶ regularly seen. Many answers were left as 28/12, when the question clearly stated that a mixed number was required.

  Text version

  Work out 1 3/4 x 1 1/3. Give your answer as a mixed number.

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  This question was poorly answered with the majority of students simply attempting to find the mean of the weights 5, 9 and 6. Their resulting conclusion did relate to the question asked but no credit was given unless a correct process was applied. A number of students found the mean to be 7.1 kg but then failed to conclude that Donna was incorrect in her assertion, thus only gaining two marks. A number of students worked out the total weights correctly but then added them together with the 6 in the tens column leading to an answer of 125 instead of 71.

  Text version

  4 red bricks have a mean weight of 5 kg. 5 blue bricks have a mean weight of 9 kg. 1 green brick has a weight of 6 kg. Donna says, The mean weight of the 10 bricks is less than 7 kg. Is Donna correct? You must show how you get your answer.

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q15 · 3 marks

  3 marks

  15

  
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  Examiner report

  Students are familiar with this type of question and at least one mark was usually gained for showing an understanding of the meaning of the recurring decimal notation, although 0.418418…was not uncommon. Many identified two decimals with a terminating decimal difference but were unable to accurately find the difference. Any subsequent incorrect cancelling of ସଵସ ଽଽ଴ was ignored.

  Text version

  Express 0.4181818... (with 18 recurring after the initial 4) as a fraction. Show all working.

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q16 · 5 marks

  5 marks

  16

  
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  Examiner report

  It was pleasing to see many students, in part (a), attempting to multiply the given expression by √ଵଵ √ଵଵ, some just wrote ൈ√11 but credit was given if the intention was clear. Student should be encouraged to write ൈ√ଵଵ ൈ√ଵଵ. Many students correctly worked out the surd product but then failed to fully simplify, leaving ଶଶ√ଵଵ ଵଵ as their answer. This was not awarded the final accuracy mark. In part (b), students who knew to multiply numerator and denominator by 2√3 ൅1, gained one mark but were often unable to complete the simplification to gain further credit.

  Text version

  Rationalise each denominator.

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• Edexcel 1MA1 · November 2019 · Paper 1H · Q19 · 3 marks

  3 marks

  19

  
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  Examiner report

  The correct answer to this question was seen only very occasionally. Some students were able to gain credit for 9ି భ మ = ଵ ଷ or equivalent. Only a very few were able to write 27 భ ర in any useful format.

  Text version

  Given 9^(-1/2) = 27^(-1/4) / 3^(x + 1), find the exact value of x.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  Most students were able to write the numbers in order of size.

  Text version

  Write these five numbers in order of size. Start with the smallest number: 8, -4, 1, -7, -2.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  This question was answered well with many students able to write 8375 correct to the nearest thousand. The most common mistake was to attempt to write it to the nearest hundred.

  Text version

  Write the number 8375 correct to the nearest thousand.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  This question was well answered with most students able to find the square root of 17.64

  Text version

  Find the value of sqrt(17.64).

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  The majority of students were able to find the value of 65.

  Text version

  Find the value of 6^5.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  This question was well attempted and a pleasing number of students were able to show a complete process to work out the number of tickets that were not sold. A common approach was to subtract the number of tickets that had not been sold (1274 ÷ 6.50) from the total number of seats in the cinema (14 × 15). The other common approach was to start by working out the total cost of all the seats in the cinema (14 × 15 × 6.50) and then subtract the total cost of the tickets that were sold (1274) to get 91. Dividing 91 by 6.50 completed the process. A common mistake made by students using this approach was to miss out the final step and give 91 as the answer.

  Text version

  There are 14 rows of seats in a cinema and 15 seats in each row. Each ticket cost £6.50. The tickets sold cost a total of £1274.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  Students who divided 8.40 by 0.024 had an efficient process to find the length of time spent in the car park in minutes and gained the first mark. This was the most common first step. Some students started by multiplying 0.024 by 60 to find that the cost per hour was 1.44 euros. Dividing 8.40 by 1.44 completed the process to find the length of time in hours and the first mark could be awarded. Some students used 1.44 in a build up method and attempted to reach 8.40 but few completed the method correctly. The next stage of the problem involved adding the length of time to 10 45. This was done by adding on 350 minutes in steps or by first converting it to 5 hours 50 minutes. However, this stage proved to be the downfall of many students. It was common to see 350 minutes converted to 3 hours 50 minutes or to see 5.83 (from 350 ÷ 60 or 8.40 ÷ 1.44) interpreted as 5 hours 83 minutes or 6 hours 23 minutes or 5 hours 8 minutes. Some of the students who added the length of time to 10 45 correctly gave the answer as 4 35 rather than as 4 35 pm or 16 35 and lost the accuracy mark. Students should be encouraged to use the time button on their calculator to deal with this type of question.

  Text version

  A car park in Spain charges 0.024 euros per minute. Jon drove into the car park at 10:45 and paid 8.40 euros when he drove out.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  Many students gained the first mark for writing 1/10 and 3/5 as decimals or as percentages or for converting them to fractions with a common denominator. Those who used 0.1 and 0.6 tended to be more successful even though some students wrote out a list of decimals from 0.1 to 0.6 and were still unable to identify the halfway number as 0.35. Those who used fractions often struggled to complete the process and those using percentages sometimes failed to gain both marks because they gave 35 as the final answer. Some students gave the final answer as 3.5/10, not understanding that this is not an acceptable format for a fraction.

  Text version

  Find the number that is exactly halfway between 1/10 and 3/5.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q15 · 3 marks

  3 marks

  15

  
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  Examiner report

  This question was not answered particularly well. Many students were not able to use the scale correctly. The length of the plane was often multiplied by 24 instead of being divided by 24 and it was common for students to add 1 and 24 and then multiply or divide the length of the plane by 25. The conversion from metres to centimetres caused more problems than expected. Common mistakes were dividing by 100 instead of multiplying by 100 or using 1 metre = 10 centimetres or 1 metre = 1000 centimetres. Some students used the scale correctly and divided 19.2 by 24 to find the length of the scale model but forgot to convert their answer to centimetres. Many students gained just one mark for 19.2 × 100 = 1920.

  Text version

  The length of a plane is 19.2 metres. A scale model is made at a scale of 1:24.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q22 · 2 marks

  2 marks

  22

  
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  Examiner report

  This question was answered surprisingly poorly with many students unable to complete the error interval correctly. Those who used 127.5 as the lower value sometimes used 128.4 as the upper value. Answers that used integers, such as 128 ≤ length < 130 or 127 ≤ length < 129, were very common. In many responses the number on the left of the error interval was larger than the number on the right.

  Text version

  The length of a pencil is 128 mm correct to the nearest millimetre.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q27 · 2 marks

  2 marks

  27

  
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  Examiner report

  Many students were able to enter the calculation into a calculator to obtain 0.0456 and they were awarded the method mark. The question required the answer to be given in standard form but it was common to see 0.0456 given as the final answer. Those who did attempt to write 0.0456 in standard form were often unsuccessful. Some students did not show 0.0456 but scored one mark for an answer of the form 4.56 × 10n with an incorrect value of n. Some students made hard work of this question and attempted to convert to ordinary numbers before doing the calculation. They usually got into difficulties.

  Text version

  Work out (3.42 × 10^-7) ÷ (7.5 × 10^-6). Give your answer in standard form.

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• Edexcel 1MA1 · November 2019 · Paper 2F · Q29 · 5 marks

  5 marks

  29

  
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  Examiner report

  This question proved to be beyond most students on this Foundation tier paper and it was frequently not attempted. Many that did make an attempt were unable to do anything other than find the volume of the cuboid. On its own, this was insufficient to gain any marks. Many of the students who appreciated the need to work out the surface area of the cuboid could not show a complete process to do so. A common mistake was to include either four 6 by 18 faces or four 8 by 18 faces in the surface area calculation. Relatively few students were able to progress beyond a surface area calculation to find the side length of the cube but it was pleasing that some who did so were able to carry on and give a fully correct solution.

  Text version

  A cuboid measures 18 cm by 8 cm by 6 cm. A cube has the same total surface area as the cuboid. Janet says the cube and cuboid have equal volumes.

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• Edexcel 1MA1 · November 2019 · Paper 2H · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  There remains a lot of misunderstanding about the values used to state an error interval. The most common error was 128.4 as the top of the interval. Many who were unprepared for this topic gave 127 and 129 as their answers or writing the largest number first.

  Text version

  The length of a pencil is 128 mm correct to the nearest millimetre.

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• Edexcel 1MA1 · November 2019 · Paper 2H · Q7 · 2 marks

  2 marks

  7

  
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  Many were awarded a single mark for 0.0456, since they were then unable to change this to a number in standard form. Common errors included 4.56 × 10-14 or 4.56 × 102.

  Text version

  Work out (3.42 × 10^-7) ÷ (7.5 × 10^-6). Give your answer in standard form.

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• Edexcel 1MA1 · November 2019 · Paper 2H · Q9 · 5 marks

  5 marks

  9

  
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  It was disappointing to find that so many students did not know how to find the surface area. Many only found volumes, which resulted in no marks being awarded. Of those who attempted to find the surface area, many found two of 6×8 and 4 of 6×18, but this still earned credit once they showed that they then wanted to add. Any remaining credit was only awarded for correctly processing their total surface area figure, usually by dividing their total surfaced area by 6 and then taking the square root to get their volume of the cube. Some students assumed that it was the volumes that were equal or that the cube was half the cuboid.

  Text version

  A cuboid is 18 cm by 8 cm by 6 cm. A cube has the same total surface area. Janet claims their volumes are equal.

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• Edexcel 1MA1 · November 2019 · Paper 2H · Q14 · 2 marks

  2 marks

  14

  
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  Many students were unprepared for the requirements of this question. Some were able to get one mark for a correct first step. A very common incorrect response was 19 + 25 = 44, then 3325 ÷ 44.

  Text version

  A car choice has 19 body colours, an unknown number of roof colours and 25 wheel types, giving 3325 combinations.

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• Edexcel 1MA1 · November 2019 · Paper 2H · Q20 · 4 marks

  4 marks

  20

  
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  Examiner report

  Those who stated 10.85 and 10.95 often went on to get three marks. Of those that stated 160 very few gave a correct reason. The vast majority did not consider bounds, and used 10.9 A significant minority quoted 18.94 instead of 19.95 Of those who did arrive at two correct bounds the final mark was often lost due to no reason or a poor reason given for appropriate level of accuracy.

  Text version

  d = c^3/8 and c = 10.9 correct to 3 significant figures.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  The one mark was awarded for students being able to find two different factors of 12. Most students were successful either listing factors or writing a pair as a product. Those who didn’t gain the mark had usually mixed up the word factor with multiple.

  Text version

  Write down two factors of 12.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  A very well answered question showing students have a good understanding of basic fractions of amounts. Almost all students knew that to find ଵ ଷ they had to divide by 3, and it was only those making an arithmetic error that typically failed to score the mark. This was a real shame when a calculator was available.

  Text version

  Find 1/3 of 30.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  This question required students to be able to convert between basic decimals and fractions. Again, it was well answered by students with most scoring the available mark.

  Text version

  Write 0.7 as a fraction.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Another well answered question; most students scored the mark.

  Text version

  From 7, 8, 15, 16, 18, 22, write down the multiple of 6.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q11 · 5 marks

  5 marks

  11

  
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  Examiner report

  Part (a) saw the first problem solving question on the paper, and it was one that was answered very well. Students are really starting to get a solid understanding of money based problems and have good success. It was pleasing to note that only a small minority showed arithmetic errors or incomplete processing. Students who failed to score any marks simply subtracted the cost of one set of lights from 20 and chose to ignore the multiple lights and multiple £20 notes given in the question. Part (b) was testing students ability to find a fractional change of an amount. Those who failed to get any marks usually tried to subtract ଵ ହ or 0.2 from 120, rather than finding ଵ ହ of 120 and subtracting that. Very few students followed the more efficient method of finding ସ ହ.

  Text version

  Dylan buys 13 bicycle lights at £7.50 each and pays with five £20 notes. A bicycle normally costs £120 and is reduced by 1/5.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q12 · 3 marks

  3 marks

  12

  
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  Examiner report

  Another problem solving question answered well by many students. The full range of marks was awarded. The initial mark was for a first step in the process, finding the weight of the small boxes, which almost all students were able to score. The next process was to find the number of large boxes. The most efficient method was to subtract the weight of the small boxes and divide by 750. However, with this being a foundation paper, more inefficient build up methods were regularly seen (and catered for in the mark scheme) and the second mark was regularly awarded. In most cases, once the second mark was awarded, so was the third. This tended to not be the case only when arithmetic errors occurred. Again, with proper calculator use this error could have been eradicated.

  Text version

  Small cornflake boxes weigh 450 g and large boxes 750 g. Rae buys 3 small boxes plus some large boxes, total 5850 g.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q15 · 4 marks

  4 marks

  15

  
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  This item posed many problems for students, with many unable to get beyond two marks. The best responses were the more structured ones, and it was good to see students using two-way tables or frequency trees, to structure their response. Typically, students scored one or both of the first two process marks (which could be awarded in either order) by finding either the number of boy or girls, along with the number of school dinners or packed lunches. It was from this point that many were unable to progress and often we saw incomplete processes. It was also unfortunate to see students mis-assigning values, eg girls = 0.55 × 800 = 440, which made the processes incorrect. Students should be encouraged to take real care in how they present their responses; those who approached the question in a logical and structured way, ticking off information in the question at each stage were more successful.

  Text version

  A school has 800 students. 31% have packed lunches; 55% are boys; 60% of boys have school dinners.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q20 · 4 marks

  4 marks

  20

  
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  The Venn diagram question was answered really well by many students and the award of three or four marks was common. Generally speaking a good proportion of students were able to score at least three marks, normally for a correctly labelled diagram with at least 2 regions correct. When mistakes were made, it was often from values in more than one region, or quite commonly, for the region (A ∪ B)’ to be either incomplete, or containing all the values.

  Text version

  Universal set U={1,...,13}; A={multiples of 3}; B={even numbers}.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q23 · 3 marks

  3 marks

  23

  
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  A good number of students were able to gain both marks. Of those who didn’t a large proportion gained no marks, often because no intermediate work was shown. Students really should be encouraged to show intermediate steps of working as good exam technique and ensure the method mark can be awarded. In part (b) students were asked to round their answer to part (a) to 4 significant figures. This mark could be awarded whatever was seen in (a) provided the value had at least 5 significant figures. It is clear many students have no real understanding of what significant figures means, with many giving 4 decimal places, or including trailing zeros.

  Text version

  Use a calculator for (29^2-4.6)/sqrt(35-1.9^3).

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q27 · 4 marks

  4 marks

  27

  
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  Questions involving time and conversion of time are always a challenge and this problem solving question was no exception. A good number of students were able to gain the first mark for finding the time difference of 1 hour 18 minutes, or 78 minutes. The next two processes were interchangeable. A calculation of speed was required, but unfortunately in many cases could not be awarded as the division was often completed the wrong way round. The other mark was for a conversion of either time (if done before the speed calculation) or speed. It was this step that students found most challenging with many either not completing it at all, or often multiplying by 100.

  Text version

  At 13:30 Nimer is 65 miles from a hotel. He arrives at 14:48.

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• Edexcel 1MA1 · November 2019 · Paper 3F · Q28 · 3 marks

  3 marks

  28

  
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  Examiner report

  Part (a) and (b), which involved conversion to and from standard form, were generally answered well and worth a single mark each. Part (c) was another interpretation question, and like the questions earlier in the paper, it was answered quite well. Students were expected to realise that the major contributor was the power of 10 and hence B is bigger, and many were able to articulate this well enough. However, there were a number of misconceptions that became evident through responses. Some students made the same mistake as the person in the question and felt the number of decimal places was key. A good number also felt it was to do with the number of zeros, rather than the magnitude of the number and also scored no marks. Unfortunately, some students left the decimal point in when converting to ordinary numbers and therefore often lost the mark in their explanation.

  Text version

  Standard-form questions. Let A=6.212×10^8 and B=4.73×10^9. Asma claims A>B because 6.212>4.73.

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• Edexcel 1MA1 · November 2019 · Paper 3H · Q2 · 3 marks

  3 marks

  2

  
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  Text version

  Use a calculator for (29^2-4.6)/sqrt(35-1.9^3).

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• Edexcel 1MA1 · November 2019 · Paper 3H · Q7 · 3 marks

  3 marks

  7

  
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  Text version

  Let A=6.212×10^8 and B=4.73×10^9. Asma claims A>B because 6.212>4.73.

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• Edexcel 1MA1 · November 2019 · Paper 3H · Q21 · 2 marks

  2 marks

  21

  
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  Text version

  For a biased coin, P(4 heads in 4 throws)=16/81.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  A good opening question that was accessible to almost all students.

  Text version

  Write 180 minutes in hours.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  This question was well answered. The vast majority of students just wrote down the answer but some did not evaluate the bracket first and so gave an incorrect answer.

  Text version

  Work out 10×(3+5).

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  This was well answered with the majority of students being awarded the mark. However, some incorrect answers were seen and 25 was a common incorrect answer.

  Text version

  Write down a prime number between 20 and 30.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  This question was well answered but some students did find it more challenging than the previous questions. Many showed working, listing the numbers and looking for the ‘middle’. Of those that gave an incorrect answer, 11.5 was a common error.

  Text version

  Find the number exactly halfway between 7 and 15.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q6 · 4 marks

  4 marks

  6

  
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  Examiner report

  This question was the first on the paper to be classified as a problem. Most students scored well on this question. Successful students set their work out in a methodical way, making sure that the answer to each component was clear so that they knew which numbers to add at the end. Many students added the prices for one person then multiplied by 4, this seemed to be quite a popular way to tackle the problem. However, some students found the use of 7 nights and 4 people challenging. They appeared unsure when to use which number as a multiplier and so just multiplied all the numbers together. Others forgot to multiply the 50 by both 7 and 5 meaning that £1950 was a popular incorrect answer which gained three out of the available four marks. Unfortunately, there were lots of arithmetic errors seen in the multiplication, meaning the loss of the accuracy mark even when a full correct set of processes were seen. The numbers in this question were easy for manipulation so errors should not really have been so common.

  Text version

  A holiday for 4 people lasts 7 days. Per-person costs: travel £150, hotel £50 per day, spending money £250.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q8 · 2 marks

  2 marks

  8

  
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  This question was generally answered well and most students scored at least one mark. This was available either by converting to percentages, comparable fractions or equivalent decimals, or for a list with one misplaced fraction – usually 7/12. Lists were often given unaccompanied by working, so more than one misplacement resulted in no mark being awarded. There was little evidence of the list given in descending rather than ascending order, though many weaker students simply ordered on the size of the denominator. Attempts by drawing diagrams are to be discouraged, as these are rarely of a consistent size, or accurate enough depictions of the fractions. Accurately stating ½ = 0.5 or 50% and ¼ = 0.25 or 25% was sufficient for the method mark to be awarded, so it was in the student’s interest to show their working and stating these simple conversions is a better strategy than poorly drawn diagrams.

  Text version

  Fractions: 1/3, 3/4, 1/4, 7/12, 1/2.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  In part (a) most students managed to use a time difference and multiply it by 4. Those students who used a method starting with 4miles in 1 hour and 2 miles for the 30 minutes were generally successful although 4.5 instead of 6 was seen on some occasions. In addition, doing 1.5 × 4 = 6 was usually successful however far too many students tried to work in minutes and used 90 × 4 = 36; they then seemed to realise that this answer was too big and divided by 100 to get 3.6. Many students had trouble manipulating the speed-distance-time formula choosing to divide rather than multiply, with 90 ÷ 4= 22.5 being seen often. The use of time in calculations still remains an area that students find difficult and centres are advised to revise this topic well with students. For part (b) most students gained one mark as they could work with time well enough to reach the time when Ruth left the library. Some students could not convert 1 and 1/4 hours correctly often using 1 hour 25 minutes, hence giving an answer of 12:45. Some students gave the final answer as 12:35am losing the accuracy mark.

  Text version

  Ruth walks from 9:00 to 10:30 at 4 mph, stays 50 min, then takes 1.25 h to walk home.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q11 · 2 marks

  2 marks

  11

  
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  This was well answered and all three of the approaches given on the mark scheme were commonly seen. The main issue was the accuracy mark which was most often lost because of a single simple arithmetic error. A small number of students struggled with this question and clearly didn't understand how to multiply the two numbers together; some just multiplied 70×50 and added this to 4×8. This was the most consistent conceptual error seen.

  Text version

  Work out 74×58.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q13 · 1 mark

  1 mark

  13

  
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  This question was very poorly answered. Only a relatively small proportion of students were able to express multiply x by 10 in an acceptable format. Some mixed up multiply with divide, e.g. x/10 was seen, others knew the connection was a factor of 10 but were unable to write an expression, e.g x cm = 10 mm was given and another incorrect response was x = 10x. There were many instances of units being included within the expression they offered and this often made the expression invalid. Sometimes m was also given in the expression. It is fair to say that the majority of foundation students found this question challenging.

  Text version

  A line has length x cm.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q14 · 2 marks

  2 marks

  14

  
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  Part (a) was well answered by most students. There were some errors seen but there was no common pattern. However, part (b) was not well answered by students. Some students could not see the fault within Fiona’s working and thought the answer was correct. The two most frequent incorrect responses were that there are not two halves in one, and that there are only two halves in any number ie. in 48 there are two halves, and both are 24. Thus, finding half of 48 not the number of halves in 48. Those who did answer correctly often worked out that there were 96 halves. The most successful students explained that dividing by half is the same as multiplying by two and therefore there are 96 halves in 48

  Text version

  Fraction questions. Fiona claims 48÷(1/2)=24 because there are 24 halves in 48.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  Both parts of this question were well answered. In part (b) 15 was seen as an incorrect answer and occasionally an arithmetic error was seen.

  Text version

  Powers and roots.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q18 · 4 marks

  4 marks

  18

  
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  Many fully correct justifications were seen. There were some well organised attempts clearly earning three method marks where an arithmetic error was obviously the only mistake. The most commonly used starting points were either to find the area of the rectangle or the number of paving stones needed to cover a side of the rectangle. The second step then caused difficulty, the area of the rectangle was often divided by the length of a stone, rather than the area of one stone, or the number of stones on each side was added rather than multiplied. Students using the second approach were more successful if they worked out the cost of covering one length eg 20× (£)2.50, then said they needed 4 rows like this to find £200. This kind of approach using the diagram and drawing in the rows seemed to add scaffolding for many students. Some students tried to work with perimeter which is not a correct first step and so no marks could be awarded.

  Text version

  A rectangular path is 600 cm by 120 cm. Square paving stones have side 30 cm, cost £2.50 each; budget £220.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q19 · 4 marks

  4 marks

  19

  
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  Many students did part (a) well although some common mistakes were to change the denominator to 15 but forgot to multiply the numerator, some added the fractions instead of subtracting and some subtracted the numerators and denominators and got ½. For part (b), students who attempted this question answered it well and were able to simplify fully. However, the most common mistake seen was for students to find a correct answer and not simplify fully i.e. leaving the answer as 3/6 or simplifying incorrectly 6/12 = 3/6 = 1/3 was seen often. It is worth noting that some students wrote and tried to use KFC (Keep, Flip, Change). As this was multiplication rather than division no marks were gained by those students and this showed a lack of understanding of the concept of calculating with fractions.

  Text version

  Fraction arithmetic.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  Many students appeared to read the question carefully and produced a simple well organised solution for full marks. Many who could not complete the question were able to make a creditworthy start to part (a), usually for finding 150g of flour was needed for 15 biscuits, or for deciding that 60 ÷15 would tell them how many batches of biscuits were needed, although this was not always given as 4 as a counting error often occurred, with 15+15 = 30, 30+30=60 and so 3 batches are needed. Many students also found the amount of butter required while doing part (a) and went on to score full marks, but others did not label their quantities and became confused when attempting part (b). Students should be advised to set out their working carefully with values and mark what values represent, again to aid their own working but also to ensure correct methods in longer question can be clearly seen and part marks awarded. A few students tried to use a unitary method here, many mixed up the ordering but some did use it correctly although premature of rounding often meant that their answer was not accurate enough, in these cases process marks were awarded. A common error seen in part (b) was to confuse butter and flour and use 600g of flour so 3 packets. Occasionally 100g was used as the butter, if this was clearly stated and then 1 pack required a process mark could be awarded. As stated in the mark scheme instructions and general guidance, if 2 was given on the answer line but came from incorrect working no marks were awarded.

  Text version

  50 g sugar makes 15 biscuits; flour is 3× sugar and butter 2× sugar. Deon makes 60 biscuits; butter packs are 250 g.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q24 · 2 marks

  2 marks

  24

  
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  Examiner report

  This question was attempted by almost all students and some fully correct answers were seen. The modal mark was however one. Very few students listed all factor pairs successfully but most were able to find at least 4 correct factors of both 72 and 90. Many found prime factors but were not able to translate this into a correct final answer. The most successful students were those who used prime factor decomposition and a Venn diagram. There was still a bit of confusion between factors and multiples here with the LCM of 360 given as the answer. 6 and 9 were common answers, often without any indication of working out.

  Text version

  Find HCF of 72 and 90.

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• Edexcel 1MA1 · June 2019 · Paper 1F · Q27 · 4 marks

  4 marks

  27

  
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  This question was not well answered. Many students were able to obtain one mark for calculating the number of each colour pen but then failed to progress any further with anything creditworthy. A common incorrect method seen was to add together 7, 3 and 4 and to divide 212 by the sum of the parts as they would to divide into a given ratio. It was common to see 212 ÷14 and then an answer of 60. Some students did put 24 as an answer but did not always support this with working and all the three figures of 14,15 and 24 were required for the first mark. Again, a good number of arithmetic errors were seen in this question.

  Text version

  Packs contain black2, red5, green6 pens. Packs sold ratio black:red:green=7:3:4; total pens 212.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q2 · 5 marks

  5 marks

  2

  
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  Examiner report

  In part (a) the vast majority of students were able to start the process to calculate the amount of flour by dividing 60 by 4 or by multiplying 50 by 3 and gain the first mark. Most then went on to complete the process to find the amount of flour Deon needs and score full marks. Those who used a unitary approach, starting with 50 ÷ 15 to find the amount of sugar to make one biscuit, rarely got the correct answer because of arithmetical errors and rounded values but often gained two of the three marks for showing a complete process. Part (b) was also answered well with most students able to work out that Deon needs 400 g of butter and therefore needs to buy 2 packs. A few students gave the final answer as 1.6 and lost the accuracy mark. Students who made a mistake when calculating the amount of butter could still gain one mark if they divided their amount of butter by 250. A few students did not read the question with sufficient care and divided 600 g (the amount of flour) by 250 and gained no marks.

  Text version

  50 g sugar makes 15 biscuits; flour is three times the sugar and butter twice the sugar. Deon will make 60 biscuits; butter is sold in 250 g packs.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q3 · 2 marks

  2 marks

  3

  
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  Examiner report

  Many students started by drawing factor trees to find the prime factors of 72 and 90 and were then usually able to use the prime factors to find that the highest common factor of 72 and 90 is 18. Sometimes, though, the prime factors were not used in the correct way and the accuracy mark was lost. Effective use was made of Venn diagrams with students generally scoring at least one of the two marks and often both marks. Some students were confused as to which section of the diagram represented the highest common factor. Those students who started by listing factors or factor pairs of 72 and 90 were less likely to score full marks because they often failed to find all the factors or factor pairs. Nevertheless many of these students gained one mark for finding at least 4 factors of 72 and of 90 or for an answer of 6 or 9. Some students found multiples of 72 and 90 rather than factors and gained no marks.

  Text version

  Find the highest common factor (HCF) of 72 and 90.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q6 · 4 marks

  4 marks

  6

  
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  Examiner report

  This ratio question was answered quite well. In order to make progress students needed to associate corresponding parts from the two ratios and work out 2 × 7, 5 × 3 and 6 × 4. Those that found the ratio of the number of pens of each colour sold, 14 : 15 : 24, were often able to complete the process to work out the number of green pens sold. Most did this by dividing 212 by 53 and then multiplying by 24 but some went from 14 : 15 : 24 to 28 : 30 : 48 and then to 56 : 60 : 96 and usually selected the correct value to give as the final answer. Some students though, found 14 : 15 : 24 but failed to make any further meaningful progress and scored one mark only. Common incorrect methods used included dividing 212 by 14 (from 7 + 3 + 4) and multiplying the result by 4 or dividing 212 by 4. These approaches made no use of the information about the number of pens in each pack. Students frequently tried different approaches in their attempts at a solution with the result that working out was often very difficult for examiners to follow.

  Text version

  Packs contain 2 black pens, 5 red pens and 6 green pens. The numbers of packs sold are in ratio black:red:green=7:3:4. A total of 212 pens were sold.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q8 · 4 marks

  4 marks

  8

  
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  Examiner report

  Last year’s report advised that “centres and students should be aware that rounding values to 1 significant figure in order to estimate is not always the most appropriate way to solve a problem”. Those students who rounded 63.5 to 60 and 101.7 to 100 in part (a) usually gained only one of the two marks because they could not deal with 6000 . Many went on to give an answer in surd form. Students who rounded 63.5 to 64 and 101.7 to 100 were far more successful and 80 was the most common answer. Some students did not understand the implications of the word “estimate” and chose to multiply 64 by 102, gaining no marks. Part (b) was answered very poorly indeed. Most answers did contain the digits 148 but the decimal point was usually incorrectly placed. The most common incorrect answer was 14.8. Students were much more successful in part (c). Not surprisingly, the most common incorrect answer was –25.

  Text version

  Estimation, powers and indices.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q9 · 3 marks

  3 marks

  9

  
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  Examiner report

  Many students gained at least two of the three marks for converting both mixed numbers into improper fractions (with at least one correct) and then multiplying correctly. The requirement for the answer to be given as a mixed number in its simplest form meant that the final accuracy mark was often not awarded. Answers of 5 6 and 28 were common. Some answers were spoilt by arithmetic errors. Having converted both mixed numbers into improper fractions some students chose to use a common denominator of 10. Unfortunately 35 × 16 was often followed by 560 or by 51 rather than by 560 . A few students decided to use decimals and they were often successful. When no marks were scored this was usually because students had chosen to multiply the whole numbers and fractions separately, giving an answer of 3 3 .

  Text version

  Work out 3 1/2 × 1 3/5.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  Students who gave the exact value of either tan30º or sin60º gained the first mark. Various strategies were used to find these values. Some students worked them out by drawing an appropriate triangle; some used patterns in a table with angles of 0º, 30º, 45º, 60º and 90º and some simply recalled them from memory. Sometimes sin30º ÷ cos30º was used to find the value of tan30º. However, the strategies used were not always successful and incorrect values were very common. When only one of the two values was correct it was more often sin60º = 3 . In some responses the values were not labelled. If only one value was correct examiners had to assume from the calculation shown that the order was tan30º×sin60º. Some of the students who got to 1 × 3 did not go on to get full marks because they gave 3 as the final answer or simplified it to 2. The question required the answer to be given in its simplest form. Some students used incorrect values such as tan30º = 1 and sin60º = 0.5 which just happened to give an answer of 0.5. When the “correct” answer clearly came from incorrect working a mark of 0 was awarded.

  Text version

  Find the exact value of tan 30° × sin 60°.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q15 · 4 marks

  4 marks

  15

  
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  Examiner report

  Most students were able to gain the first method mark for using a volume formula with the correct substitution. A common mistake at this stage was to use a radius of 6 cm instead of 3 cm. It was also not uncommon to see 32 instead of 33 substituted into the formula for the volume of a sphere. Having substituted correctly many students failed to gain the second method mark because they found the total volume of a cone and a sphere, not the total volume of a cone and a hemisphere. However, many of these students were still able to gain the third method mark for simplifying the volume of the cone to 30π. Incorrect answers of 66 or 66π, from adding 30π and the volume of the sphere were very common. Many students struggled to simplify their expressions for volume because they had difficulty dealing with the fractions within the calculations. Some left the volume of the cone as 1/3π × 90 and 4/3×27 and 1/2×4/3×27 were often evaluated incorrectly. Generally, answering in terms of π was understood well. Students who used a value for π usually got into difficulties and made little progress.

  Text version

  A cone of height 10 cm and base diameter 6 cm sits on a hemisphere of diameter 6 cm. Cone volume=(1/3)πr^2h; sphere volume=(4/3)πr^3. Total volume is kπ cm^3.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q16 · 4 marks

  4 marks

  16

  
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  Part (a) was a straightforward question for those who realised that the number of different three digit numbers is given by 53 although a surprising number of errors were made in evaluating 53. Students often included extra working with 53 which invalidated their method, for example 53 × 3 or 53 × 5 or 53 – 20, and they gained no marks. A method of 53 – 1 was acceptable because there are 124 three digit numbers that are different to the one in the diagram (553). Common incorrect methods included 5 × 4 × 3 × 2 × 1 and 5 × 3 × 5. A few students used listing as part of their method, listing all the three digit numbers starting with 1 for example and then multiplying by 5. Attempts at listing all the possible three digit numbers were hardly ever successful. Students were less successful in part (b) when finding how many of the possible three digit numbers have three different digits. A common strategy was to subtract the number of three digit numbers that do not have three different digits from the answer to part (a). However, the number subtracted was frequently not 65 and 125 – 5 = 120 was a common incorrect response. As in part (a) many incorrect methods were seen and attempts at listing were usually not successful.

  Text version

  A combination lock has three dials. Each dial can be set to 1,2,3,4 or 5.

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• Edexcel 1MA1 · June 2019 · Paper 1H · Q18 · 5 marks

  5 marks

  18

  
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  In part (a) many students were able to gain at least one of the two marks for writing 12 as 4  or . Although most went on to get the correct answer of it was not unusual to see 3 + followed by an answer of or . Common mistakes were to write 12 as or to write 3  as 15 and give an answer of . Some students started part (b) by attempting to deal with the power and many were able to obtain . Different strategies were used to find  . Writing out 3 seven times and working through the multiplication in a systematic way tended to be a successful approach. The second step for these students was to rationalise the denominator. Instead of multiplying numerator and denominator by 3 some students chose to multiply by which resulted in . This fraction is not in the required form and the students gained only two of the three marks unless they simplified it to 3 . Students who attempted to deal with the power first but went wrong, obtaining for example, sometimes went on to gain a method mark for rationalising the denominator of their fraction. Some students chose to start by rationalising the denominator. Usually this involved multiplying both the numerator and denominator of 1 by 3 to give 3 . Many students could get no further but those who simplified       to 2187 scored full marks as this fraction is in the required form. Some students started by multiplying the numerator and denominator of 1       by   and frequently got into difficulties. Rationalising the denominator seemed to be much more accessible to students than dealing with the power of 7.

  Text version

  Surds and fractional indices.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  The correct answer 75 100 or 3 4 was the most common seen with very few incorrect answers.

  Text version

  Write 0.75 as a fraction.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Again, most students gained the mark here; a small minority thought that –1 is smaller than −3.

  Text version

  Write -3, 4, 0, -1, 2 in order of size, starting with the smallest.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Only a very few students made any errors in this question. Incorrect factors of 9 and 10 were sometimes seen. A few students listed multiples of 15 by mistake.

  Text version

  Write down two factors of 15.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q5 · 1 mark

  1 mark

  5

  
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  The correct value for two million was usually seen although the omission or addition of 0s was common.

  Text version

  Write the number two million in figures.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  Whilst many students gained at least two marks, and often three, it was alarming to see errors in arithmetic on a calculator paper. Some students failed to note that there were two coffees purchased and results of 4.35 (10 – 2.75 – 2.9) were common. A significant number of students, having correctly calculated Dave’s change, said that Dave was not correct or gave no final decision, clearly not reading the question carefully enough.

  Text version

  Dave buys 2 coffees at £2.75 each and a cake for £2.90. He pays with £10 and thinks his change will exceed £1.50.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q10 · 2 marks

  2 marks

  10

  
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  The most common error here was to get the inequalities the wrong way round. Some said that 4 + 7 was less than 103 – 92. Most students gained at least one mark, usually for 22 = 2 × 2 and one other correct sign.

  Text version

  Use <, = or > once in each blank.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q12 · 3 marks

  3 marks

  12

  
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  Part (a) was usually answered correctly. In part (b), although generally well done, many students confused time notation with decimal notation and incorrectly wrote 9.00 – 7.22 = 1.78 This gained one mark for clearly showing the intention to find a time difference. However 1.78 or 2hrs 38mins were often seen without working and these gained no credit. Some students gave an answer of 1.38 or 1:38 showing an actual time and not a length of time. This gained one mark with or without working. Some only worked out the minutes at 38 with no regard for hours; this gained no marks.

  Text version

  Train timetable from Brighton to London: 07:22→09:00, 07:29→08:32, 07:32→08:48. Graham reaches Brighton station at 07:15.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  Many students answered this question successfully. Students who recognised that the length of the side of each square is 2cm generally went on to get full marks. Some students took the whole diagram to be a square whilst some found the area, usually in shaded squares (30) A few students measured the length of the square (1.7cm). Others divided the length (12) by the number of squares (9). Some students misread the question and thought the whole shape was a square which resulted in a wrong answer of width 12. The majority of students either scored full marks or zero marks in this question.

  Text version

  Nine identical squares form a stepped arrangement inside a rectangle. The rectangle's 12 cm length spans 6 square side-lengths; its width spans 5 square side-lengths.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q15 · 4 marks

  4 marks

  15

  
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  Although a few students did work with perimeter instead of area, the vast majority gained at least one mark for 90 × 60. Many, failing to read the question carefully, then simply found the area of the garden where flowers are grown. It was however pleasing to see so many fully correct solutions. Many used non calculator methods to find 40% (or 60%). Some found 40% or 60% of both dimensions as opposed to just one before finding the area.

  Text version

  A rectangular garden is 90 m by 60 m. Flowers occupy 40%; the rest is grass.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q16 · 5 marks

  5 marks

  16

  
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  In part (a), it was rare to see both parts answered correctly. B was often identified as the least likely coin to land on Heads but A and D were very common choices for the most likely. Many students correctly said that Julie was wrong in part (b) but their reasoning varied widely. Simply saying that coin C was biased was insufficient since this was given in the question. It needed to be clear that the student was referring to the probability of the ଵ ଷ given in the table. Students using decimal or fraction equivalents for ଵ ଷ often made errors in the conversion; 30% was a common error. A number of students referred to even chances or 50-50 chances or ‘odds’ rather than using the correct probability language. Part (c) was often answered well. Many students tried to convert 0.033 to a fraction or a percentage usually making an error in their subsequent working. Many did not understand the use of the word “estimate” in the context of probability and believed they were required to round off the numbers before calculation. Students who found the correct answer of 132 and then rounded to say 130 were not penalised, provided 132 was seen. A number of students were not explicit in the use of 0.033 and so any rounding made (eg. 0.03) without first writing 0.033 was given no credit.

  Text version

  Four biased coins have P(heads): A=0.33, B=0.033, C=1/3, D=30%. Julie claims coin C is equally likely to land heads or tails. Coin B will be thrown 4000 times.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q17 · 4 marks

  4 marks

  17

  
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  There are many ways to start to solve this problem. Many gained two marks usually for correctly finding the number of calories in the 150g of yogurt; the calculation for banana was a little more demanding depending upon the process chosen. A significant number of students found the “correct rounded” answer from simply ‘playing’ with the numbers in the question, eg. 84 – (100 – 60) + 87 + (150 – 100) = 181 This gained NO credit. A number of students had no appreciation of proportion as a multiplicative relationship. Those that began with 100/87 = 1.14 received one mark for working with proportion, but they nearly always proceeded with multiplying by150 rather than dividing, depriving them of any further marks.

  Text version

  Banana has 84 calories per 100 g; yogurt has 87 calories per 100 g. Priti eats 60 g banana and 150 g yogurt.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q23 · 4 marks

  4 marks

  23

  
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  It was pleasing to see many good solutions to this question. There was, however, some misunderstanding of what was required. Some found the number of cups required to fill the whole container (2 marks maximum) and some found the number of cups needed to fill the final third of the container (3 marks maximum). The final accuracy mark was often not gained through not rounding down to a number of completely filled cups. Incorrect conversions between millilitres and cubic centimetres were condoned if the process was correct. A number of students converted ଶ ଷ to a decimal or a percentage. This was accepted provided the conversions were correct to two significant figures. Often weaker students worked with surface area or perimeter or found 2/3 of 275 and thus gained no credit.

  Text version

  A 30 cm by 6 cm by 19 cm cuboid container is 2/3 full of water. Each cup holds 275 ml.

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q25 · 2 marks

  2 marks

  25

  
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  Examiner report

  Only a very few students gained the full two marks in this question. Some did earn one mark for one correct entry, usually 8.3. Near misses included answers of 8.25 ≤ y < 8.35 indicating some understanding of error intervals but from a rounded rather than a truncated number.

  Text version

  A calculator display for a number y began 8.3 (so 8.3 is the displayed truncation to one decimal place).

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• Edexcel 1MA1 · June 2019 · Paper 2F · Q27 · 2 marks

  2 marks

  27

  
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  Examiner report

  Understanding of standard form was good. Many students earned at least one mark, usually for a correct answer to part (b).

  Text version

  Standard form conversions.

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• Edexcel 1MA1 · June 2019 · Paper 2H · Q4 · 4 marks

  4 marks

  4

  
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  Examiner report

  This was the first problem type question on the paper and was answered very well. The problem required the students to carry out three steps which could be interchangeable in order, as the mark scheme shows. Typically, students followed the path of finding the total volume, then finding 2 3 of this volume, before finally dividing by 275 and rounding down to find the number of cups. There were a number of errors that brought the loss of one or two marks. Some students worked with the total volume only and were able to score two marks at best. Others worked with ଵ ଷ rather than ଶ ଷ of the total volume. These students could gain three marks only. Finally there were the students who rounded the answer up to 9 rather than down to 8, again these lost the final mark. Alongside these problems, some students thought there was a need to convert units due to a misunderstanding of the conversion between cm3 and millilitres. This was catered for in the mark scheme and students were still able to score all the process marks despite incorrect unit changes. Some students mis-interpreted this as a bounds question and calculated the volume as 30.5 × 6.5 × 19.5. Another incorrect method seen was to calculate the surface area of the cuboid instead of the volume, gaining no marks.

  Text version

  A 30 cm by 6 cm by 19 cm cuboid container is 2/3 full of water. Each cup holds 275 ml.

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• Edexcel 1MA1 · June 2019 · Paper 2H · Q6 · 2 marks

  2 marks

  6

  
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  Examiner report

  It is clear that students have practised error intervals from rounding but not from a truncated number. This question was answered very poorly, with lots of students giving the answers of 8.25 and 8.35 which gained zero marks. Centres need to spend time on this new topic and ensure students know the difference between the two types of error interval.

  Text version

  A calculator display for a number y began 8.3 (so 8.3 is the displayed truncation to one decimal place).

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• Edexcel 1MA1 · June 2019 · Paper 2H · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  Both parts of this question were answered very well, with the vast majority of students being able to correctly convert to and from standard form.

  Text version

  Standard form conversions.

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• Edexcel 1MA1 · June 2019 · Paper 2H · Q17 · 4 marks

  4 marks

  17

  
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  This explain question was probably the worst answered of the three. Most students realised that the number of cubes must be a multiple of 8 and 11 (the sum of the two ratios) but most missed the crucial part that 88 was the lowest common multiple. Without this acknowledgement, the mark could not be awarded. Students generally struggled to find a way through part (b). Some used the structure of a two- way table or a probability tree, and when this was the case, were often successful. Most other students worked with numbers of cubes, but struggled to find one of the correct pairs that would lead them to the number of large yellow cubes.

  Text version

  A bag contains small/large cubes, each red/yellow. Small:large=4:7 and red:yellow=3:5. All small cubes are yellow.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  A very well answered question. Most students gave the correct answer of 500 but 400 was sometimes seen.

  Text version

  Write 478 to the nearest hundred.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  The majority of students gave either 48 or 56 (or both) as their answer. Some gave multiples that were not within the stated range.

  Text version

  Write down a multiple of 8 that is between 41 and 60.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  There were few correct answers for this question. Most students appeared to want to give the numbers that were multiples of 3, rather than powers of 3. Some gave just one of the numbers, and not both.

  Text version

  Here is a list of numbers: 4, 6, 9, 10, 15, 27, 30, 40.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q6 · 2 marks

  2 marks

  6

  
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  Examiner report

  Many students gave the correct answer. Less successful methods were those where students used partitioning methods which introduced more opportunity for error. This included those who divided 8 by 2 and gave the answer of 4 on the answer line, or those who just found 10% as 8 and made errors from there. Some treated this as an increase or decrease percentage, giving answers of 64 or 96, but were still credited for method.

  Text version

  Work out 20% of 80.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  A frequent incorrect answer was 10, where the students had only dealt with the circles, perhaps from not reading the question carefully. Many gained full marks, but it was not uncommon for one mark to be given for showing 33 or 27 from the first stage of subtracting two numbers logically from the table. There was much evidence of unnecessary errors, such as 33 – 27 = 7 or 26 + 7 = 34.

  Text version

  A bag contains 16 red circles, 26 green circles, 11 red squares and 7 green squares. There are more green counters than red counters.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  There were many correct answers which gained full marks. Many realised that 1/4 was 13 (litres) and gave this as their final answer; use of quantities such as 13 rather than a fractional approach was far more popular. Those who scored no marks often subtracted the 1/4 from the number of litres, that is 52 – 0.25, or divided 52 by 1/4.

  Text version

  A car's fuel tank holds 52 litres when full. The tank is 1/4 full.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  Most students got at least one mark for summing the values in some form. Marks were lost by either using the incorrect value of 120 (eg 120/400) or leaving the answer as 240/400. A few went on to express the answer as a decimal or percentage, or an unsimplified fraction and so lost the final mark, since the answer had to be given as a fraction in its simplest form. Overall a well answered question.

  Text version

  Bill has 400 counters. He gives 35 to Sameena, 50 to Henry and 75 to Lucas.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q11 · 4 marks

  4 marks

  11

  
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  This was very much a question of two halves. Part (a) was well understood and many saw it through to an accurate conclusion. A small minority chose to do this by multiple addition, presumably without a calculator, and usually lost the final mark due to arithmetic error. Some just found the difference between the given costs. Too many mis-copied the figures from the table. In part (b) few gained the mark as their explanation was frequently incomplete: reference must be made to both the number of parcels and the cost. Just working out the accurate calculation was also insufficient. The crucial feature was that both figures had been rounded down.

  Text version

  Sending one parcel costs £15.25 by Express and £35.38 by Rapid.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  This was very well answered with the majority gaining both marks. Common errors included not showing working, writing a shortened answer such as 2.4 or 2.5, premature rounding/truncation, or copying the figures incorrectly from the question. Using an incorrect order of operations led to the answer of 1.3530… The most successful students were those who worked out the value of the numerator (and wrote it down) then worked out the value of the denominator (and wrote it down) then did the division. Students need to be careful when using their calculators. Many misinterpreted their calculators and included recurring notation with some of their figures, which was condoned on this occasion. There was no penalty for students who interpreted the question demand by not only showing the figures on the calculator display, but also showed all other figures that could be generated by the calculator, sometimes to 50 or more decimal places.

  Text version

  Find the value of (5.27 + 3.5) / (7.9 - 4.36). Give your answer as a decimal and write down all the figures on your calculator display.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  This was well answered with many getting the final answer of 28, though some lost the final mark by rounding in the wrong direction, or not giving their answer as an integer. The most common errors were 850 × 200 or 850 ÷ 18.53

  Text version

  Liz wants to change £850 into South African rand and get as many 200-rand notes as possible. The exchange rate is £1 = 18.53 rand.

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• Edexcel 1MA1 · June 2019 · Paper 3F · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  Setting out methodical and clear working was essential in this question. The majority gained the first mark for calculating either 28% or 112 packets for Alan, but it was not usual to find students working out 32% and 40% and just adding them. Equally, many went on to show 6/10 or 300 for Beryl, but again there were those who just worked with 4/10. As in other questions there were too many cases of poor arithmetic or mis-copying figures, though this did not prevent the award of the process marks. The ratio calculation was the more challenging aspect of this question with many just trying a ratio division using 3 : 4, usually involving a division by 7.

  Text version

  Three shop owners buy packets of mints. Alan buys 400 packets: 32% are small and 40% are large. Beryl buys 500 packets: 3/10 are small and 1/10 are large. Charlie buys 150 small packets, with small : medium = 3 : 4.

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• Edexcel 1MA1 · June 2019 · Paper 3H · Q7 · 2 marks

  2 marks

  7

  
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  This question was done well by the great majority of students who were awarded both marks. Some students gave an answer of 0.32 believing this was correct to 3 significant figures. These students were given full marks provided they had shown a more accurate version of the answer in the working space. The request to give the answer correct to 3 significant figures served as a guide to students and correct answers given to more than 3 significant figures gained full credit. Students are therefore advised to write down their full calculator display before rounding.

  Text version

  Work out the square root of ((2.5 x sin 43 degrees) / (8.2^2 - 50.5)). Give your answer correct to 3 significant figures.

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• Edexcel 1MA1 · June 2019 · Paper 3H · Q10 · 3 marks

  3 marks

  10

  
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  Examiners were able to award full marks to about a half of students for their answer to this question involving percentages. Most students showed a good understanding of the problem and calculated that the total interest added to Marie’s account was £144. Not all of these students could express this as a percentage interest rate. The most common error was for students to express £144 as a percentage of £8144 instead of £8000. It was noticeable that a large number of students used a multiplier approach, interpreting 0.018 or 1.018 as a 1.8% increase. The most common errors seen were working out 20% of 8000, or using an incorrect reverse percentage process.

  Text version

  Marie invests £8000 in an account for one year. At the end of the year, interest is added to her account. Marie pays tax on this interest at a rate of 20% She pays £28.80 tax. Work out the percentage interest rate for the account. %

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• Edexcel 1MA1 · June 2019 · Paper 3H · Q11 · 3 marks

  3 marks

  11

  
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  Questions involving standard form are often well answered and this question was no exception. Students usually expressed their answer to part (a) as an ordinary number (130) with a small minority of students giving their answer in standard form (1.3 × 10²). Most students worked in standard form and did not convert the distance and speed to ordinary numbers before dividing one by the other. The most common error seen in the method was for students to multiply the distance by the speed but this was not commonplace. However, there were a significant number of students who identified the correct calculation (3.9 × 107) ÷ (1.3 × 105) but who expressed it without the brackets. This usually led to the incorrect answer 1.3 × 1012 because students were not careful about the order of operations when they used their calculator to evaluate their answer. These students could usually be awarded one of the two marks available. Most students were able to gain the mark in part (b) for stating that their answer to part (a) would be increased or equivalent, for example that the signal will take longer to get to Mars.

  Text version

  The distance from Earth to a spacecraft is 3.9 x 10^7 km. Assume a signal travels at 3 x 10^5 km/s.

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• Edexcel 1MA1 · June 2019 · Paper 3H · Q12 · 1 mark

  1 mark

  12

  
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  About two thirds of students were able to give an acceptable reason why 64 భ ర is not equal to ଵ ସ of 64, usually by explaining that 64 భ ర can be interpreted as the fourth root of 64 or √64 ర or by evaluating the value of √64 ర as 2.828. The reason “ ଵ ସ of 64 is not the same as 64 to the power ଵ ସ” was not deemed sufficient to score the mark because it is the same as merely rephrasing the statement in the question.

  Text version

  Work out 64^(1/4). Patrick says that 64^(1/4) = 16 because 64 divided by 4 is 16.

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• Edexcel 1MA1 · June 2019 · Paper 3H · Q19 · 5 marks

  5 marks

  19

  
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  Examiner report

  Part (a) of this question discriminated well between more able students sitting this paper. Some students did not attempt the question and many weaker students restricted their answer to working out the value of D by substituting u = 26.2 and a = 4.3 This gained no credit. Of those students who did score marks, many of them scored just one mark for writing down at least one of the bounds for u or a. Students who substituted bounds for u and a into the expression for D were split between those who calculated [UB of u]2 ÷ [2 × LB of a], the correct expression, those who calculated [UB of u]2 ÷ [LB of a] and those who calculated [UB of u]2 ÷ [2 × UB of a]. Part (b) was not answered well and only a small proportion of students gave the correct answer of 80. Even fewer students were able to say why. The most common incorrect approach by far was to add their answer to part (a) to 78.6003 and then divide by 2, accompanied by an explanation of this being the mid-point or the average. Centres may wish to highlight this misconception.

  Text version

  D = u^2/(2a), where u = 26.2 correct to 3 significant figures and a = 4.3 correct to 2 significant figures.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q1 · 1 mark

  1 mark

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  This question was quite well done. The most common error was for students to write 0.152 at the end of their list presumably because these students mistakenly thought that the number was bigger than the others because it was the only number with 3 decimal places.

  Text version

  Write the following numbers in order of size. Start with the smallest number. 0.4 0.02 0.37 0.152 0.2

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q3 · 1 mark

  1 mark

  3

  
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  The vast majority of students answered this question correctly. Some students confused factors with multiples and mistakenly wrote that 20 is a factor of 10.

  Text version

  Here is a list of numbers. 3 5 7 12 15 18 20 From the list, write down a factor of 10

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q4 · 1 mark

  1 mark

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  Nearly all students correctly rounded 7829 to 8000.

  Text version

  Write 7829 to the nearest 1000

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q5 · 3 marks

  3 marks

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  All parts of this question were answered well. Parts (a) and (b) were answered correctly by almost all students. A small proportion of students incorrectly placed brackets round the 7 and 2 in part (c).

  Text version

  (a) Work out 3 × 5 + 7 (1) (b) Work out 23 (1) (c) Write brackets ( ) in this statement to make it correct. 7 × 2 + 3 = 35 (1)

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q6 · 3 marks

  3 marks

  6

  
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  This question was generally answered well. Many different approaches were possible but most students either showed that only 7 tins of cat food were needed to feed the 2 cats for 14 days or that the cat food available would feed the cats for 16 days. Students working was generally clear but when diagrams were used they were not always well annotated or accompanied by clear explanations. A small proportion of students produced correct working but wrote down an incorrect conclusion, that not enough food had been bought.

  Text version

  Each of two cats eats 1/4 of a tin of cat food each day. Oscar has 8 tins of cat food.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q10 · 2 marks

  2 marks

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  There were many fully correct answers to this question but also many students who scored one mark for giving two numbers which have a sum of 32, only one of which was prime. 9, 15, 21 and 27 were commonly mistaken as prime numbers. Some students included 1 as one of their two numbers. The great majority of students gave numbers with a sum of 32 but a small proportion of students gave two numbers with a product of 32, for example 2 and 16.

  Text version

  Write down two prime numbers that have a sum of 32 ,

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q11 · 3 marks

  3 marks

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  Well over four in every five students could identify the fraction not equivalent to 4 in part (a). Part (b) provided more of a challenge. A majority of students obtained a correct answer, namely 12, or a fraction equivalent to this. 72 was the most often seen equivalent fraction. A large number of weaker students merely added the numerators and added the denominators, giving 18 as their answer.

  Text version

  Consider the fractions 9/12, 6/8, 18/24, 10/16 and 15/20.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q20 · 2 marks

  2 marks

  20

  
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  Students were asked to “work out the value of a numerical expression in this question. Unfortunately, a substantial number of students who used laws of indices to simplify the expression left their answer in the form “32” and denied themselves full marks. Students using the laws of indices were generally more successful than students who attempted to work out the values of 37, 3−2 and 33 as their starting point. This was probably not surprising in a non-calculator paper. A large number of students evaluated 3−2 as −9. Many students “simplified” 37 × 3−2 to 95 then followed this by “simplifying” 95 ÷ 33 to 32. These students, of course, could not be given any credit.

  Text version

  Work out (3^7 x 3^-2) / 3^3.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q22 · 5 marks

  5 marks

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  There were many good attempts at this multi-step question with a majority of students scoring at least 3 of the 5 marks available. Most students got as far as working out the share that each of the 7 salesmen would get if 60% of the bonus was shared out between them. These students often then incorrectly calculated 25% of 210 rather than 25% of 180 so no further marks could be awarded. Some student’s answers were affected by arithmetic errors in the subtraction of 840 from 2100 or when dividing 1260 by 7. Only a very small proportion of students approached the problem by considering the total amount shared by the salesmen under each scheme. Examiners noticed that the working in this question was often poorly organized and scattered around the page.

  Text version

  A bonus of £2100 is shared by 10 people who work for a company. 40% of the bonus is shared equally between 3 managers. The rest of the bonus is shared equally between 7 salesmen. One of the salesmen says, “If the bonus is shared equally between all 10 people I will get 25% more money.” Is the salesman correct? You must show how you get your answer.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q24 · 4 marks

  4 marks

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  There were some good answers to this question from students who obtained full marks in part (a) but it was rare to see a correct response to part (b). Where students did not score all three marks in part (a) they often gained one mark for converting one hour to seconds or for using the relationship between time, distance and speed correctly. However, a significant number of students used an incorrect relationship between speed, distance and time, commonly attempting to calculate 213 ÷ 60 or 213 ÷ 1. In some cases, this incorrect application was accompanied by a correct distance, speed, time “triangle”. Responses to part (b) were usually restricted to stating that the estimate was an underestimate because the speed had been rounded down and it seems that most students could not see the link between dividing by a smaller number and getting a bigger answer

  Text version

  A plane is travelling at 213 miles per hour.

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• Edexcel 1MA1 · November 2018 · Paper 1F · Q26 · 4 marks

  4 marks

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  This question was not done well. A small proportion of students quoted a correct formula for the area of a circle. Unfortunately, they were usually unable to use the formula to find the area of a semi-circle of radius 10 cm or the area of a quarter of a circle with radius 20 cm. Many students quoted an incorrect formula, often citing the formula for the circumference of a circle instead. Many students found the area of a square of side 20 cm but this was by itself not enough to score any marks. Very few students scored 2 marks or more for their answers.

  Text version

  ABCD is a square of side 20 cm, with A bottom-left, B bottom-right, C top-right and D top-left. AB is the diameter of an inward semicircle of radius 10 cm above AB. AC is the quarter-circle arc from A to C with centre B and radius 20 cm. The shaded region is inside this quarter-circle sector but outside the semicircle.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q1 · 2 marks

  2 marks

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  This question was poorly answered simply because many students failed to actually evaluate their answer of 32 to 9 and so gained only one mark. Students need to be advised to read questions carefully. The most common error was to write 95 for 37 × 3-2, this was usually followed by 95 ÷ 33 = 32 giving a correct result from incorrect working thus gaining no marks. Some students tried to evaluate the given powers of 3 but 3-2 was often written incorrectly as -9. However, if two out of the three powers of 3 were evaluated correctly then one mark was awarded. Students who wrote these powers as full products often struggled to cancel them out due to not knowing how to deal with the 3-2; the majority of students who attempted this method gained no marks.

  Text version

  Work out (3^7 x 3^-2) / 3^3.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q3 · 5 marks

  5 marks

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  Students gained good marks here, many scoring three or more marks. 40% of 2100 was usually correctly evaluated, and the most popular approach was to then find the share for each salesman. A good number of students then in error found 25% of 210 instead of 25% of 180 and so gained no more credit. Some calculated all relevant values correctly but then made an incorrect statement.

  Text version

  A bonus of £2100 is shared by 10 people who work for a company. 40% of the bonus is shared equally between 3 managers. The rest of the bonus is shared equally between 7 salesmen. One of the salesmen says, “If the bonus is shared equally between all 10 people I will get 25% more money.” Is the salesman correct? You must show how you get your answer.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q5 · 4 marks

  4 marks

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  In part (a), many students never realised that the easier approach here was to round the speed of 213 to 200, preferring instead to carry out their calculations using the 213. A common approach was to find the distance travelled in one minute and then in one second. This was often not seen through to its completion as final division into one mile was rarely seen. In part (b), many students followed a correct answer in part (a) by claiming an underestimate since they had rounded 213 down. Centres should note and communicate to their students how approximations can affect the results of different calculations.

  Text version

  A plane travels at a speed of 213 miles per hour.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q7 · 4 marks

  4 marks

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  Many students correctly found the area of the semicircle (radius 10cm) and then often used this to compare with the area of the square, never realising the need to find the area of the quadrant (radius 20cm). A significant number introduced their own value for pi, often 3, but were usually unable to complete the proof. The fact the given result was in terms of pi should have deterred students from this approach.

  Text version

  ABCD is a square of side 20 cm, with A bottom-left, B bottom-right, C top-right and D top-left. AB is the diameter of an inward semicircle of radius 10 cm above AB. AC is the quarter-circle arc from A to C with centre B and radius 20 cm. The shaded region is inside this quarter-circle sector but outside the semicircle.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q11 · 3 marks

  3 marks

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  Very few students were able to understand what this question was asking for. However, a good number were able to pick up one mark for 125% or 1.25 with regards to Jack’s increase in the amount cereal. A sound approach followed by some students was to introduce their own values of amount and cost of cereal; this approach was often successful. A common incorrect answer was 25%; a lot of students assumed that if Jack increased the amount of cereal by 25% then the price must decrease by 25%.

  Text version

  Jack and Sadia work for a company that sells boxes of breakfast cereal. The company wants to have a special offer. Here is Jack’s idea for the special offer. Put 25% more cereal into each box and do not change the price. Here is Sadia’s idea. Reduce the price and do not change the amount of cereal in each box. Sadia wants her idea to give the same value for money as Jack’s idea. By what percentage does she need to reduce the price? %

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q14 · 4 marks

  4 marks

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  Those students who understood the meaning of a power of 4 usually went on to gain full marks in part (a). Students attempting to find the cube of 16 and 81 before finding the 4th root generally failed. Arithmetic errors in cubing 2 or 3 accounted for a number of students gaining one mark only. In part (b), of those who actually attempted this question many were able to score one mark for finding two of the values of a, b, c. The value of b proved difficult and so few were able to complete the question.

  Text version

  Work with fractional indices and powers of 3.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q16 · 3 marks

  3 marks

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  This question was often well answered. Most gained at least one mark for showing understanding of the recurring decimal notation. Some students, without fully finding the difference between two relevant recurring decimals, tried to “fiddle” their solution by working back from the given answer; this gained no credit. Centres are advised to explain to their students the need to show repetition in digits to display understanding of recurrence.

  Text version

  Prove that the recurring decimal 0.256565656... can be written as 127/495.

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• Edexcel 1MA1 · November 2018 · Paper 1H · Q20 · 3 marks

  3 marks

  20

  
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  Very few gained full marks in this question. Expansion of the numerator was often good however the correct value of 32 was not often seen owing to arithmetic errors along the way. Those knowing how to rationalise a denominator usually did it correctly to gain one mark. This was independent of a correct expansion for the numerator.

  Text version

  Show that ((sqrt(18) + sqrt(2))^2) / (sqrt(8) - 2) can be written in the form a(b + sqrt(2)), where a and b are integers.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q1 · 1 mark

  1 mark

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  This question was answered well with many students able to write down the value of the 4 in 542.3. The most common incorrect answer was tenths.

  Text version

  Write down the value of the 4 in the number 542.3

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q2 · 1 mark

  1 mark

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  Many students wrote down a square number that is also an odd number with the most common correct answers being 9 and 25. Some students gave an answer such as 32 which gained no credit unless it was evaluated in the working. Most incorrect answers were odd numbers such as 3 and 5 that are not square numbers.

  Text version

  Write down a square number that is also an odd number.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q4 · 1 mark

  1 mark

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  This question was answered quite poorly with fewer students than might have been expected able to work out the cube root of 64. Some students with the right idea gave the answer as 43 and lost the mark. The most common mistake was to work out the square root instead of the cube root.

  Text version

  Work out the cube root of 64

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q5 · 1 mark

  1 mark

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  The majority of students were able to write 0.31 as a fraction.

  Text version

  Write 0.31 as a fraction.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q6 · 2 marks

  2 marks

  6

  
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  This question was well answered. Many students were able to write the decimals in order of size and conversions to decimals were often shown in the working space. When the correct order was not given some students gained the method mark for listing any three of the fractions in order or for converting at least two of the fractions into decimals. Some incorrect answers were based on ordering the numerators or ordering the denominators. In some cases students attempted to compare by drawing diagrams, but this was generally unsuccessful.

  Text version

  The four fractions are 3/4, 5/7, 19/25 and 11/15.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q11 · 3 marks

  3 marks

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  Most students were able to gain the first mark for working out 30% of £80 as £24 and the majority then went on to give the correct answer. Some students added £80 to each bonus before subtracting but this did not affect the final answer. Having worked out Adam’s bonus as £24 some students could not complete the method correctly. A common mistake was to subtract £24 from £80 rather than from the £28 comparative bonus and then find the difference between £56 and £28 or give £56 as the final answer. A relatively small number of students could not work out 30% of £80 and gained no marks at all.

  Text version

  Adam gets a bonus of 30% of £80 Katy gets a bonus of £28 Work out the difference between the bonus Adam gets and the bonus Katy gets. £

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q13 · 5 marks

  5 marks

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  Part (a) was answered quite poorly. As a first step, most students either found the square root of 81 or divided 81 by 4. Unfortunately, far too many took the latter approach, often giving 20.25 as the final answer, and gained no marks. Many of those who found the square root of 81 went on to find the perimeter of the square but some did not and 9 was often given as the final answer. Rather surprisingly the number of fully correct responses seen in part (b) was very similar to the number seen in part (a). Many students gained one of the three marks. Some students gained the first method mark for finding the area of the triangle but could not use the area correctly to find the area of the parallelogram. A very significant number of students worked out the area of the triangle as 9 × 16, forgetting to divide by 2. These students could still gain the second method mark for using their area of the triangle correctly to find the height of the parallelogram, generally reaching an answer of 24. A number of students forgot to multiply the area of the triangle by 5 to find the area of the parallelogram. Others did not know how to find the area of a parallelogram and couldn’t get any further after multiplying by 5.

  Text version

  Answer both parts.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q17 · 3 marks

  3 marks

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  This question was answered very well with most students gaining at least two of the three marks. It was pleasing that working was generally well set out and easy to follow. The most widely used approach was to work out the number of kilograms of cement, sand and stone in the bags that Adrian already has. Some students chose to work out the number of bags of cement, sand and stone that are going to be used. Many students were then able to interpret their values to reach a correct conclusion that Adrian needs to buy 2 bags of stone. When the final mark was lost this was sometimes because students listed the total numbers of bags that Adrian will use instead of what bags he needs to buy. Other errors at this stage included stating that he needs to buy more stone without specifying the number of bags and giving a non-integer number of bags.

  Text version

  Adrian is going to make concrete. He is going to use 180 kg of cement 375 kg of sand 1080 kg of stone Cement, sand and stone are sold in bags. 1 bag cement 1 bag sand 1 bag stone 25 kg 22.5 kg 50 kg Adrian already has 10 bags of cement 20 bags of sand 20 bags of stone Work out what bags he needs to buy to make the concrete.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q18 · 2 marks

  2 marks

  18

  
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  Some good explanations were seen in part (a). Many students identified that Bill had used an incorrect multiplier and explained that he should have used 1.03 or that he had increased 150 by 30% rather than by 3%. Statements that he should have used 0.03 or that 3% is 0.03 were accepted since the student had identified that the multiplier was wrong. Instead of focusing on the multiplier some students increased 150 by 3% and explained that Bill is wrong because his answer should have been 154.5. These explanations were also accepted. Many answers were incomplete and didn’t explain why Bill’s method is wrong, e.g. “he needs to find 3% and subtract it from 150” or “he needs to find 1% and multiply it by 3”. Others were simply incorrect, e.g. “he increased 150 by 13%, not by 3%” or “he should have used 0.3” or “he should have divided not multiplied”. Part (b) was answered quite poorly with many students unable to complete the statement correctly. Although many could decrease 150 by 3% they did not know how to do so using a suitable multiplier in a single stage calculation. A common incorrect answer was 150 × 0.03 = 4.5, often with 150 – 4.5 = 145.5 written underneath. Some students wrote 150 × 0.3 = 45 or 150 × –3% = 145.5.

  Text version

  Bill wants to increase 150 by 3% He writes down 150 1.3 = 195 Bill’s method is wrong.

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• Edexcel 1MA1 · November 2018 · Paper 2F · Q27 · 4 marks

  4 marks

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  Part (a) was answered quite well with many students knowing how to write a number in standard form. Incorrect answers were often of the form a × 10n with a usually containing the digits 7547. Some students gave an answer of the form 7.547 × 10n with an incorrect value of n. Students were more successful in part (b). Incorrect answers did usually contain the digits 342, with either an incorrect number of zeros or with the decimal point incorrectly placed. In part (c) it was pleasing that many students gave the correct answer, usually in standard form but sometimes as an ordinary number and often with no intermediate working. Those that didn’t get the correct answer often scored 1 mark for correctly evaluating the numerator as 154 100 000. The division of 154 100 000 by 5 × 10-8 resulted in an incorrect answer of 0.3082 when the numbers were entered into the calculator without brackets around 5 × 10-8. Many students, though, made hard work of this question which could have been done easily with the correct use of a calculator. Those who converted to ordinary numbers before doing the calculation often got into difficulties, particularly with the denominator. Summary Based on their performance on this paper, students should: ● know and be able to use area formulae for triangles and trapezia ● practise giving reasons for answers using correct mathematical vocabulary, particularly for transformations and angle questions and in the context of probability ● understand the difference between simple interest and compound interest and know how to use multipliers to simplify percentage calculations ● practise completing Venn diagrams and learn the necessary set notation ● read each question carefully and ensure that they answer the question asked ● structure their working clearly, particularly when solving multi-step problems

  Text version

  Work with standard form.

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• Edexcel 1MA1 · November 2018 · Paper 2H · Q7 · 3 marks

  3 marks

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  Part (a) was usually well answered, but in part (b) there were few answers that gained full marks. Most attempted to convert the given figures to ordinary numbers which was usually done correctly, but the final step of conversion to an answer in standard form was not done well, frequently with the power of 10 given incorrectly.

  Text version

  Answer both parts.

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• Edexcel 1MA1 · November 2018 · Paper 2H · Q9 · 2 marks

  2 marks

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  This was poorly answered. Students showed confusion between truncation and upper/lower bounds, with most using (incorrectly) the figures 6.5 and 7.5

  Text version

  Martin truncates the number N to 1 digit. The result is 7 Write down the error interval for N.

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• Edexcel 1MA1 · November 2018 · Paper 2H · Q11 · 3 marks

  3 marks

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  Students found more success with this question, the main inhibitor being a failure to write down all the steps and working needed to “show that” 1335 was the resulting number. There were some 2-way tables used, but students did not know what to do with such a diagram, once complete.

  Text version

  In a restaurant there are 9 starter dishes 15 main dishes 8 dessert dishes Janet is going to choose one of the following combinations for her meal. a starter dish and a main dish or a main dish and a dessert dish or a starter dish, a main dish and a dessert dish Show that there are 1335 different ways to choose the meal.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q1 · 2 marks

  2 marks

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  Part (i), almost all students were able to access this simple one mark question that required them to subtract. The answer of 43.7 was seen almost on every script. Part (ii) was also answered well, although some students struggled to work with the fractions as the question required.

  Text version

  Write a number in each box to make each calculation correct.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q3 · 1 mark

  1 mark

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  This question required students to be able to use the square root button on their calculators to evaluate √1.44 and again, the vast majority of students were more than able. The required answer was acceptable as either a decimal or a fraction.

  Text version

  Find sqrt(1.44).

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q4 · 1 mark

  1 mark

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  Question 4 assessed students’ understanding of fractions as an operator. Like the previous items most students understood what was asked of them and were able to find 8 by dividing by 8.

  Text version

  Work out 1/8 of 720.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  This was the first question that really started to test students with a number struggling to convert between mm and cm. However, many were able to make the conversion, but some then subtracted rather than added. In this case they typically got the method mark for either 188 or 0.06, highlighting the importance of showing their method. Of those who did add, there were a number who failed to get the accuracy mark because they didn’t state the correct units with their answer.

  Text version

  Shaun is 1.88 m tall. David is 6 cm taller than Shaun. How tall is David?

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q8 · 4 marks

  4 marks

  8

  
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  Examiner report

  The first problem question on the paper required students to work with proportion and money to see if someone had sufficient funds to make a specific purchase. It was very pleasing to see how well students dealt with this question, and that is credit to the work done on such problems in centres. A score of four marks was very common. Of those who failed to score full marks it often came down to inefficient methods being used. Rather than using multiplication and their calculators, some students used repeated addition, and whilst there is nothing wrong with this approach it often led to arithmetic errors and therefore loss of marks. A small number of students failed to give a final conclusion to go with their correct figures, but this was far less common than it has been previously.

  Text version

  2 pens cost £2.38 5 folders cost £5.60 Ben wants to buy 20 pens and 20 folders. He only has £50 Does Ben have enough money to buy 20 pens and 20 folders? You must show how you get your answer.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q11 · 3 marks

  3 marks

  11

  
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  This second problem question caused significantly more issues than the first for students. A good number were able to start to work with percentages and realised that the proportion of men was 70%, however that was as far as many were able to get. Common incorrect methods included finding either 30% or 70% of 28, rather than realising that 70% related to the 28 women. Of those who were able to complete the problem, it was often by finding the number of men first rather than working from 70% straight to 100%.

  Text version

  There are men and women at a meeting. There are 28 women. 30% of the people at the meeting are men. Work out the total number of people at the meeting.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q13 · 4 marks

  4 marks

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  Another problem question and another one accessed well by the students. Most were able to gain at least two marks by finding the total cost of the calendars bought. Many students then struggled to find the number of calendars, possibly as this meant dividing by a decimal (even with a calculator); many multiplied by 0.9 instead of dividing. However, there were a good number who were able to take the final step and get to the 50 calendars.

  Text version

  Annie sold 45 books at £1.20 each 34 candles at £1.50 each some calendars at 90p each She got a total of £150 Work out how many calendars Annie sold.

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• Edexcel 1MA1 · November 2018 · Paper 3F · Q15 · 3 marks

  3 marks

  15

  
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  Examiner report

  This problem divided students, but most were able to get some credit for listing multiples of 3 and 5. Those who gained no marks typically divided 100 by 3 and then divided 100 by 5 and added the two answers. The student who had success normally worked by finding multiples of both 3 and 5 and identifying the common multiples. Very few students attempted to divide 100 by 15.

  Text version

  Bert has 100 cards. There is a whole number from 1 to 100 on each card. No cards have the same number. Bert puts a star on every card that has a multiple of 3 on it. He puts a circle on every card that has a multiple of 5 on it. Work out how many cards have both a star and a circle on them.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2018 · Paper 3F · Q18 · 4 marks

  4 marks

  18

  
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  Examiner report

  This problem was generally answered well. There were some failures seen in the attempts to find 20% and some students subtracted rather than added their percentage. The third process mark was the most commonly awarded for those students who knew to subtract the deposit after increasing the price. There was also a special case for those students who missed the percentage change altogether but knew to subtract the deposit and then divide by 10.

  Text version

  Trevor buys a boat. The cost of the boat is £14 200 plus VAT at 20% Trevor pays a deposit of £5000 He pays the rest of the cost in 10 equal payments. Work out the amount of each of the 10 payments. £

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2018 · Paper 3F · Q20 · 3 marks

  3 marks

  20

  
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  Examiner report

  Rounding to a given number of significant figures appeared to be a struggle for many students, with many giving answers of a completely different magnitude. Time spent on the understanding of what significant figures are would be well spent for centres. Part (b) assessed understanding of the order of operations and the ability to use their calculators. Most were able to gain at least one mark for one of the suitable intermittent values or for a correct value given to less than 4 decimal places. It is important that students read the guidance carefully as this question required all the figures on the calculator display to be written down. A common incorrect answer seen was 0.78692... where students took the square root of the whole fraction instead of the denominator only.

  Text version

  Answer both parts.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2018 · Paper 3H · Q1 · 3 marks

  3 marks

  1

  
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  Examiner report

  For part (a) many correct answers were seen and this should be expected from students sitting a higher paper. Part (b) was also generally well answered by the students, many of whom gained full marks. The most popular incorrect answer was 0.7869... This came from a misunderstanding of the square root sign with the square root applied to the whole calculation and not just the numerator.

  Text version

  Answer both parts.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2018 · Paper 3H · Q8 · 5 marks

  5 marks

  8

  
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  Examiner report

  Some fully correct answers were seen but this problem solving question was not well answered by the majority of students. Many students confused surface area and volume at some point within their working. Some students failed to find the correct values of 9, 5, 3 for the dimensions of large cuboid, often just deciding to multiply 45, 27 and 15 together as the volume. Although a good majority of the students did score one mark for using 2.53 as the volume of the smaller cube. But they then often used this with the surface area of the larger cuboid.

  Text version

  The diagram shows a solid metal cuboid. The areas of three of the faces are marked on the diagram. The lengths, in cm, of the edges of the cuboid are whole numbers. 27 cm2 15 cm2 45 cm2 The metal cuboid is melted and made into cubes. Each of the cubes has sides of length 2.5 cm. Work out the greatest number of these cubes that can be made.

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• Edexcel 1MA1 · November 2018 · Paper 3H · Q18 · 5 marks

  5 marks

  18

  
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  Examiner report

  Some students gained one mark by giving one of the correct bounds for either the distance or the time. A few students did not convert the time into minutes before finding the bounds so could not gain any further marks, 2.5 hours and 3.5 hours were seen as incorrect bounds of time. A minority of students were then able to combine the bounds in the correct way to obtain the values 2.7158… and 2.695…. Unfortunately, some of the students who obtained these results then averaged them and lost the final mark as this is not a valid method.

  Text version

  A high speed train travels a distance of 487 km in 3 hours. The distance is measured correct to the nearest kilometre. The time is measured correct to the nearest minute. By considering bounds, work out the average speed, in km/minute, of the train to a suitable degree of accuracy. You must show all your working and give a reason for your answer. km/minute

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• Edexcel 1MA1 · June 2018 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  Examiner report

  Very few incorrect answers were seen to this question although an answer of 6300 was a common error.

  Text version

  Write 6324 correct to the nearest thousand.

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• Edexcel 1MA1 · June 2018 · Paper 1F · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  Students had more success with ordering the integers in part (a) than in ordering the decimal numbers in part (b).

  Text version

  Write the following numbers in order of size. Start with the smallest number. -6 6 -5 0 12

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• Edexcel 1MA1 · June 2018 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  The majority of students gave the correct answer to this question; and to a lesser extent were the most common incorrect choices.

  Text version

  The fractions are 4/16, 2/8, 15/60 and 3/9. Write down the fraction that is not equivalent to 1/4.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q5 · 1 mark

  1 mark

  5

  
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  Examiner report

  Most students identified the first even multiple of 7 as 14. Students failing to do this often correctly listed multiples of 7 and then chose 28.

  Text version

  Write down the first even multiple of 7

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• Edexcel 1MA1 · June 2018 · Paper 1F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  Most students gained at least two marks in this question by following either process shown in the mark scheme. Failure to gain full marks was generally due to poor arithmetic skills. Some students were unable to divide by 4 (particularly 220), clearly missing their calculators. Many wrote 2140 / 4 but did not attempt to work this out. A few thought that the cost of the flight was per person and multiplied by 4 before adding and dividing.

  Text version

  Four friends share equally: GBP1280 flights, GBP640 villa and GBP220 car hire.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  Both parts to this question were answered well although a number of students did not appear to know the difference between even and odd numbers. In part (a), the odd number factors did not have to be explicitly identified; it was acceptable to show them in a product or a list or a factor tree diagram, if it was clear to which even number they referred. In part (b), some students were confused and gave a list of odd numbers or again carried out factor decomposition of numbers, even and odd. These lists did sometimes contain correct responses but were not identified providing examiners with choice. Some students mistakenly carried the criteria for part (a) over to part (b) and listed factors. Some students misunderstood this question, and gave examples to show the statements were correct.

  Text version

  Give counterexamples to two statements.

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• Edexcel 1MA1 · June 2018 · Paper 1F · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  Very many students were able to score at least two and often three marks in this question. Some carelessly read the question as requiring just one length of 45 cm to be removed before working out the number of 40 cm pieces remaining. One mark could be gained for this if a correct process was complete. Any incorrect length for the remaining piece of wire after the removal of the 40 cm pieces was ignored. A few students did not engage with 45 at all and just removed 40 cm pieces; this gained no marks.

  Text version

  A 240 cm wire has two 45 cm lengths removed. The remainder is cut into as many 40 cm lengths as possible.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q15 · 2 marks

  2 marks

  15

  
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  Examiner report

  The most common approach in finding the percentage of a quantity on a non- calculator paper is by a ‘build up’ method. Most students correctly quoted 10% of 160 as 16 but many were unable to correctly find 5%, some divided by 10 again and some found 1% and then made errors in multiplying by 5. When using a build up method it is important to show all working. This advice was often ignored and it was impossible to award the method mark. Some students quoted to gain the method mark but were then unable to correctly cancel to find the correct answer. Some students attempted repeated halving finding 50% 25% and 12.5% which was unhelpful. A significant number of students correctly found 15% but then proceeded to subtract it from or add it to 160 which lost them the accuracy mark.

  Text version

  Work out 15% of 160 grams.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q17 · 2 marks

  2 marks

  17

  
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  Examiner report

  The correct answer of 1 : 3 was given by about 40% of students; frequently with no method shown. The ratio 1 : 4 was the most common incorrect answer. This shows the common misunderstanding of the relationship between ratios and fractions. Some students were confused by the reference to n in the question and felt that their answer should contain an element of n. So answers of 1 : 3n and n : 3 were sometimes seen. Some students used a value for the number of chocolates in the box and worked out the value of the separate parts often not reducing to the form 1 : n.

  Text version

  There are some chocolates in a box. One quarter contain nuts and the rest do not contain nuts.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q19 · 4 marks

  4 marks

  19

  
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  Examiner report

  Converting the mixed numbers to improper fractions was the most common approach in part (a). This often lead to arithmetic errors where at least one of the fractions with a common denominator was incorrect. The more economical approach of dealing with the whole numbers separately and then writing the fractions with a common denominator usually got the correct answer. However, the most common error was to add the two whole numbers and then simply to add the numerators and denominators of the fractions to give an incorrect answer of 3 . In part (b), many students simply did not know how to divide by a fraction with just under 75% of students unable to gain any credit in this question. Of those that did, the greatest loss of marks was for not reading the question carefully enough and failing to give the answer as a mixed number in its simplest form; answers of and 1 were common. Many unsuccessful students were aware they needed to ‘flip’ but were unclear which fraction this referred to (sight of KFC on scripts was common). Conversion of the first fraction to an improper fraction as a first step was regularly missed out by students.

  Text version

  Work out each mixed-number calculation.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q21 · 4 marks

  4 marks

  21

  
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  Examiner report

  This question was quite well attempted and the majority of students gained at least one and often two marks. By a variety of methods, a correct number of bags (20) was found. This was then usually multiplied by 65p to find the selling price of the sweets. Although many were able to correctly quote a £3 profit, fewer were then able to convert this to a percentage; 3% and 13% were common incorrect answers given. However, it was pleasing to see that some students got 30%, often by realising £1 was 10% so £3 would be 30%. The use of repeated addition/subtraction was commonplace in dividing 5000 by 250 but this approach often introduced many arithmetic errors. An alternative approach, frequently seen, was finding the profit on 1 bag or on 1kg and then multiplying up to 5kg. It was disappointing to see that some students did not know how many grams were in a kilogram.

  Text version

  Renee buys 5 kg of sweets for GBP10. She puts 250 g into each bag and sells every bag for 65p. Work out her percentage profit.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1F · Q22 · 4 marks

  4 marks

  22

  
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  Examiner report

  A great many students did not seem to understand the concept of estimating values to enable a simple calculation. Students need to be encouraged to estimate the numbers given in the question rather than part way through. Many students used inappropriate rounded values such as 4000 and many wasted a great amount of time trying to compute accurate results. It was very common to see 15.12 × 8 = 120.96 followed by repeated addition/subtraction in an attempt to divide into 3069.25 Although rounding to one significant figure was not essential in gaining full marks it certainly did ease the calculations. Many students did use correctly estimated values, but then could not perform the relevant multiplication and division correctly. In part (b), many students simply did not try to answer the question posed. Many said that Juan would get there faster or quicker instead of words relating to time; their statement may have been a correct one but did not answer the question.

  Text version

  A cycle race is 3069.25 miles. Juan usually averages 15.12 mph and cycles 8 hours per day. After training his speed rises to 16.27 mph.

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• Edexcel 1MA1 · June 2018 · Paper 1H · Q1 · 4 marks

  4 marks

  1

  
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  Examiner report

  Part (a) was generally answered well. The most common approach was to convert both mixed numbers into improper fractions and then add these fractions using a common denominator of 28. Errors were made when converting to improper fractions and when writing to a common denominator. Any mistakes made converting 28 into a mixed number were not penalised because writing the answer as a mixed number was not required. Students who chose to add the whole numbers and add the fractions not only had a quicker method but also one that resulted in fewer arithmetic errors. There were of course some students who did not know that a common denominator was needed. A common error was to add the denominators 4 and 7. In part (b), the requirement for the answer to be given as a mixed number in its simplest form meant that many students gained only one of the two marks. Most students started by converting 1 5 into an improper fraction. This was not always done correctly. The standard method 5 × 3 usually resulted in 15 and final answers of either 115 or 5 were very common. Some students appeared confused as to which fraction had to be inverted; occasionally both were. Students who chose to start by writing 20 ÷ 20 gained the first mark but were usually unable to complete the method successfully. Attempts at using decimals were rarely seen and seldom successful.

  Text version

  Work out each mixed-number calculation.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1H · Q3 · 4 marks

  4 marks

  3

  
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  Examiner report

  Most students made very good attempts at this question with about two thirds of students achieving full marks. It was pleasing that working out was usually easy to follow. The first two process marks were usually gained by working out the number of bags of sweets that Renee sold (20) and multiplying this number by 65p to find that she got a total of £13 from selling all the bags. A few students were unable to multiply 65 by 20 correctly, usually due to place value errors. Some students decided to work out the cost price of each bag of sweets (50p) or to work out both the cost price (£2) and the selling price (£2.60) of 1 kg of sweets. Relatively few students failed to use 1000 g = 1 kg Many of those who worked out that Renee made a profit of £3 were able to go on and work out her percentage profit although a number of students did get stuck at this stage. Some students used 3 ÷ 10 × 100 and others argued that since £10 = 100% then £3 = 30%. It was not uncommon, though, to see 3 ÷ 10 × 100 incorrectly evaluated to give an answer of 33.3%. Some students used 13 ÷ 10 × 100 = 130 and those who forgot to subtract 100 and gave a final answer of 130 gained 3 of the 4 marks. Students who did not know how to work out the percentage profit often gave a final answer of 3%. A method for finding the percentage was not always shown. Students who had made an earlier arithmetic error were still able to gain the third mark for using percentages correctly but they needed to show their process in full; those using a build-up method tended not to do this.

  Text version

  Renee buys 5 kg of sweets for GBP10. She puts 250 g into each bag and sells every bag for 65p. Work out her percentage profit.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1H · Q4 · 4 marks

  4 marks

  4

  
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  Examiner report

  Marks were often lost in part (a) because students did not read the question carefully or did not understand the implications of the word “estimate”. Most students were able to demonstrate a full process to find the number of days which earned them one mark but there was a significant number of students who used very little rounding or indeed no rounding at all. As this question was testing estimation skills students who used no rounding at all gained a maximum of one mark. The most common approach was to round 3069.25 and 15.12 to 3000 and 15 respectively. Some students then worked out 3000 ÷ 15 and divided the result by 8 whereas others first worked out 15 × 8 and divided 3000 by the result. Either way students had straightforward calculations to carry out which they usually managed successfully. Many different and valid examples of rounding were seen. 3069.25, for example, was rounded to 3000, to 3100, to 3070 and to 3069. Some students chose to round 15.12 to 15, others chose to round it to 20, and 8 was sometimes rounded to 10. Sensible rounding of intermediate values also took place, the most common being 15.12 × 8 = 120.96 which was then rounded to 120 or 121. A few students rounded 3069.25 to 4000 which is not an appropriate rounded value and these students were not awarded the accuracy mark. Centres and students should be aware that rounding values to 1 significant figure in order to estimate is not always the most appropriate way to solve a problem. Some students lost time trying to find the answer without rounding, before realising they needed to use rounded values and crossed out all their original working. Those who attempted division without rounding often used chunking or build-up methods that took considerable time. Part (b) was well answered with most students explaining that the time taken would be less as Juan’s speed has increased. Some students explained that the answer would not be affected because they would round both 15.12 and 16.27 to 20. Answers such as “Juan will do more miles per day” or “Juan will be quicker” gained no credit because they do not explain how the answer to part (a) is affected. This part of the question was well answered even when students had not achieved a fully correct approach in (a).

  Text version

  A cycle race is 3069.25 miles. Juan usually averages 15.12 mph and cycles 8 hours per day. After training his speed rises to 16.27 mph.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1H · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  Part (a) was answered well. A common incorrect answer was 18. Students were even more successful in part (b). Not surprisingly, the two most common incorrect answers were 0 and 23. In part (c), many students were able to gain at least one of the two marks. Most commonly one mark was awarded for working with a cube root with fewer students showing understanding of working with a reciprocal. A common approach was to deal first with the power of 2/3, for example, 3 27 = 3, 32 = 9, but many students then failed to deal with the negative power. The most common error made in this question was 3 27 = 9. Some students got as far as 3-2 but then gave the answer as –9 or –6. Students who attempted to square 27 before finding the cube root usually got into difficulties. A common incorrect first step was to write . A number of students merely found 1/3 of 27 or 2/3 of 27 instead of using indices properly.

  Text version

  Evaluate the following powers.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 1H · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  The most common method was to start by expanding the bracket and many students gained the first mark for 40 + 90 . A very common mistake was to follow this with 130 which meant that no further marks were awarded. Another error was to write 40 + 90 as + . Students who got to    usually went on to complete the solution. Some students started by simplifying 8 + 18 to + . It was common to see 8 + 18 = 26 . The question asked for the value of a. Students who wrote on the answer line rather than just 5 lost the accuracy mark.

  Text version

  Simplify sqrt(5)(sqrt(8)+sqrt(18)) = a sqrt(10).

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• Edexcel 1MA1 · June 2018 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  15.9 was a very common error; 2.0 was also sometimes seen.

  Text version

  Write 1.59 correct to 1 decimal place.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  This question well answered with the vast majority of students just giving the answer without working so presumably using their calculator effectively.

  Text version

  Work out 3^5.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Examiner report

  Whilst the majority of students gave a correct answer there were a good number of incorrect responses; a few used numbers such as 4327.23 which was acceptable. However, those students that were incorrect often used fewer than 6 digits or occasionally more than one 4 in the answer. It is worth centres asking students to be careful with the placement of commas and decimal points as some were very difficult to decipher.

  Text version

  Write a six-digit number whose thousands digit is 4, using digit 4 only once.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q5 · 3 marks

  3 marks

  5

  
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  Examiner report

  This question involved converting between metric units; some students still struggle with this as a concept. Part (a) was often correct although a popular incorrect answer was 3.5, suggesting the student had divided by 10 instead of multiplying by 10. Part (b) saw a variety of answers including 77, suggesting that some students used 100 millilitres in a litre. The placement of the decimal point was not always clear and centres are asked to remind students to write as clearly as possible to ensure their answers are correctly interpreted. Part (c) was not as well answered as parts (a) and (b); only 50% of students gave the correct answer. Students seem less comfortable with the knowledge that there are 1000 grams in a kilogram. When correct, the accuracy of this answer may have been helped by the fact that multiplication was required for the conversion.

  Text version

  Convert the measurements.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Examiner report

  The majority of students were able to give at least one correct answer and many both correct answers. However, there was little evidence of students approaching the question systematically by listing factors of 36, multiples of 3 and odd numbers, so few method marks were awarded. The most common error was to give at least one even number in their answer. Students sometimes wrote out factor pairs of 36 and then chose two of them. Common incorrect pairs were 3 & 12, 4 & 9, 6 & 12 and 6 & 9.

  Text version

  Margaret is thinking of a number. She says, "My number is odd. It is a factor of 36 and a multiple of 3" There are two possible numbers Margaret can be thinking of. Write down these two numbers.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  This was generally well attempted with most students realising that they needed to find different combinations of the three names, many using abbreviations particularly M, Y and L. Whilst many students were able to correctly identify the 6 outcomes, a significant number gave fewer than 6, often stopping after just 3. Students who listed the outcomes in a systematic way were more successful, with those using a random approach often repeating an outcome or listing only 5 outcomes.

  Text version

  Mohsin, Yusuf and Luke finish first, second and third with no ties.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q8 · 5 marks

  5 marks

  8

  
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  Examiner report

  The majority of students showed appropriate working hen working through this problem which allowed them to pick up at least three process marks even if accuracy or one stage of working was not correct. Calculating the cost of rulers was very successful. Occasionally students would miss out one item when adding up. A variety of approaches were seen but when using the cost per item method many students rounded too soon which meant losing the final accuracy mark. The most common errors seen were in the incorrect use of place value e.g. 90p being added as £90. Also incorrect addition suggested that many students did not use their calculators appropriately for this question. Another common error was to multiply everything by 30 or to multiply 0.82 by 6, rather than by 5.

  Text version

  Neil buys 30 pens, 30 pencils, 30 rulers and 30 pencil cases. Price list pens pencils rulers pencil cases 6 for 82p 15 for 45p 10 for GBP1.25 37p each What is the total amount of money Neil spends?

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  Part (a) was answered well by students, with 186 ÷ 3 often written in the body with 62 on the answer line. There were a lot of distance, speed, time triangles, but not all were correct and those that were written in the correct orientation were not always used correctly. Some students chose to convert 3 hours to 180 minutes and then do 186 ÷ 180, this gained the method mark but not the accuracy as the answer was required in miles per hour. The most common error seen was to multiply the figures. A few students did not use their calculator and tried to round the given figures; this was not appropriate for this question. For this question an exact answer was required. If students are expected to estimate they will be told to do so in the question. In part (b), as with part (a), the majority of students worked correctly with the relationship between distance, speed and time and arrived at the correct distance travelled in 4 hours. A small number divided speed by time or converted the 4 hours to minutes before doing speed × time. These students arrived at answers of 14.5 or 13920, both results being very unrealistic for the distance travelled by a car in 4 hours. It is a good idea for students to check answers at the end to see if they are sensible.

  Text version

  Emily drives 186 miles in 3 hours. Sarah drives at 58 mph for 4 hours.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q10 · 3 marks

  3 marks

  10

  
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  Examiner report

  In part (a) students tended to list all odd numbers in the range 20 to 30, no doubt with the intention of identifying those that were prime numbers. Unfortunately, one or more numbers not prime were often included in their final answer. The most common misconception was to believe that either 27 or 21 or both were prime numbers. Some students did not read the question correctly and listed all the prime numbers up to 30. Others ignored the range given and listed prime numbers below 20. In part (b) both a decision and an explanation were required. It was answered well by some students but the majority were unable to use appropriate mathematical vocabulary to support their decision, such that whilst they could demonstrate some understanding that even numbers are divisible by 2, the statement was incomplete or referred to a single even number other than 2 and did not refer to even numbers in general. Common incorrect statements seen were that other even numbers divided into 2 or even numbers go into 2, rather than even numbers are divisible by 2; these gave some, although confused, evidence of understanding. Lots of responses repeated the statement that ‘2 is the only even prime number’, which did not answer the question. Many students clearly defined why 2 is a prime number but again didn’t explain why it is the only even prime by not referring to other even numbers and therefore giving an incomplete statement. A small minority stated that 2 was not a prime number or continued from part (a) and said prime numbers had to be between 20 and 30. It was also interesting to note that a significant number of students gave the wrong decision and stated that there were other even prime numbers, usually followed by a list of what they believed to be prime numbers, 26 was a popular choice for another even prime number.

  Text version

  Consider prime numbers between 20 and 30 and the claim that 2 is the only even prime.

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• Edexcel 1MA1 · June 2018 · Paper 2F · Q16 · 3 marks

  3 marks

  16

  
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  Examiner report

  On the whole, a very well answered question with many students achieving full marks. The number 5 was usually seen in the table with limited working. Occasionally 5 was a rounded answer from incorrect working and so could not gain the marks. A common misconception was to add all the buttons and divide by the sum of the frequency or to look for a sequence of numbers in the frequency column. Unfortunately, some students reached an answer of 95 but then did not divide by 19; these students scored only 1 mark.

  Text version

  Bags contain 19, 20, 21 or 22 buttons. Frequencies for 20, 21 and 22 are 7, 3 and 1. Total buttons: 320.

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• Edexcel 1MA1 · June 2018 · Paper 2F · Q19 · 5 marks

  5 marks

  19

  
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  Examiner report

  This question proved challenging for many students and some blank responses were seen. This was a problem solving question where a fully correct solution would involve finding three costs, for the labour, the fencing on the straight edge and the fencing around the semi-circle. This final aspect was often not found. It was common to see responses that confused area and circumference for the circle. The most successful start seen was to calculate labour cost for three days i.e. £180 × 3 = £540. Also, many of these students were able to work out one cost 50 × 29.86 = 1493 and then add two costs which resulted in the award of three process marks. Other students used a structured approach to calculate the perimeter of the semicircle but forgot to add the diameter length when calculating the total perimeter of the semicircle. Overall students who attempted this question seemed to miss out one aspect of the question. Students are advised, especially on the longer questions, to continually refer back to the question to check they have dealt with all the aspects of the problem set.

  Text version

  A field is a semicircle of diameter 50 m. Fencing costs GBP29.86 per metre plus GBP180 for each of 3 days.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2F · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  For part (a) the most successful students were those who listed multiples of 40 and 56 and identified the lowest one common to both lists. Many students broke down the two numbers into their prime factors but were unable to use this to find the lowest common multiple. A very common incorrect answer given was 2. Part (b) was not well understood by many students. The most common incorrect responses were 30 or 120. Very few students realised the relationship between prime factors and the HCF. Many found the values for A and B of 120 and 300 then decomposed into prime factors using factor trees; not recognising that they had already been given this information. Others attempted to find the LCM instead or just gave a factor of both numbers, often 5 as this was the highest prime factor but 3 and 2 were also seen on the answer line.

  Text version

  Find the LCM of 40 and 56. Also A = 2^3 x 3 x 5 and B = 2^2 x 3 x 5^2.

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• Edexcel 1MA1 · June 2018 · Paper 2F · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  This question was attempted by the majority of students and the full range of marks awarded. Many students scored one mark for either finding the total of the monthly payment or the 20% VAT. Many were able to show both of these skills and so scored two marks. It was pleasing to see a significant number of students able to find the deposit and thus score three marks. Some did engage with the ratio and the fourth and fifth marks were awarded to some of these students. The common errors seen were to try to partition by finding 10% of 8500, this often led to an incorrect answer of 85. Some just did 8500 – 6375 and did not engage with the percentage at all. A number of responses reached 51:85 but then stopped there evidently not being able to cancel any further. A few students tried to work in monthly values and then put these into a ratio. This method was rarely successful.

  Text version

  Raya buys a van for GBP8500 plus VAT at 20% Raya pays a deposit for the van. She then pays the rest of the cost in 12 equal payments of GBP531.25 each month. Find the ratio of the deposit Raya pays to the total of the 12 equal payments. Give your answer in its simplest form.

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• Edexcel 1MA1 · June 2018 · Paper 2H · Q2 · 3 marks

  3 marks

  2

  
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  Most students were able to score at least one mark in part (a), normally for two correct factor trees, although they could gain the mark for listing multiples of 40 and 56, or quite often a correct Venn Diagram was drawn. Although a large number of students gained full marks, a significant proportion chose the HCF (8) rather than the LCM. In part (b), a good number of students were able to gain the mark here usually giving the answer as 60 rather than working directly with the prime factors only (although this was seen). However, many students gave answers such 2 or 4.

  Text version

  Find the LCM of 40 and 56. Also A=2^3 x 3 x 5 and B=2^2 x 3 x 5^2.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 2H · Q20 · 2 marks

  2 marks

  20

  
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  Those students who had a good understanding of surds did typically find the mistake and explained it clearly. Some thought the error was multiplying by 2 െ √3 However, many students had clearly used their calculator to find the final answer, and failed to identify the mistake. Giving the correct answer without identifying the mistake made did not gain the mark. This was typically answered slightly better than part (a), with a good number realising than Sian had made her mistake in the simplification of √12.

  Text version

  Martin writes 14/(2+sqrt(3)) = 14(2-sqrt(3))/((2+sqrt(3))(2-sqrt(3))) = (28-14sqrt(3))/(4+2sqrt(3)-2sqrt(3)+3) = (28-14sqrt(3))/7 = 4-2sqrt(3). Sian writes 5/sqrt(12) = 5sqrt(12)/(sqrt(12)sqrt(12)) = 5 x 3sqrt(2)/12 = 5sqrt(2)/4. Each solution contains an error.

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• Edexcel 1MA1 · June 2018 · Paper 2H · Q21 · 5 marks

  5 marks

  21

  
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  Examiner report

  The final question on the paper really tested students understanding of bounds and accuracy although most students made an attempt. Many were able to score the first mark for correctly identifying at least one bound, although the less able students did not consider error bounds at all. Students struggled to find the bounds for mass where the figures given had been rounded to the nearest 5. Getting any bound wrong restricted a student to a maximum of three marks. The other bound that was typically wrong was the width, with many students giving these as 15.5 and 16.5. If a student made two mistakes on the dimensions of the cuboid they often gained no further marks. Of those who got correct bounds for the length, width and height, most gained the second mark for a correct upper or lower bound for volume. A good number of students were able to gain the third process mark for correctly finding a bound for density with many students understanding that a quotient required LB/UB and UB/LB, although some had the wrong formula and multiplied. Many students got no further than here due to having at least one incorrect bound and this fourth mark being for accuracy. A significant proportion of those who gained four marks were unable to gain the final communication mark as they either didn’t round properly (it needed to be to 2 decimal places or significant figures, not 1), or even if they did, they didn’t state the degree of accuracy to which they were working. Summary Based on their performance on this paper, students:  should be encouraged to use the most efficient methods when there is more than one available.  learn how to use calculators properly, especially in relation to the substitution of negative numbers into formulae that require them to be squared, and in working to a high degree of accuracy, rather than rounding too soon and losing accuracy.  spend greater time practising new content such as vectors, functions and estimated speed from a distance time graph.  continue to practise questions targeting AO3 (problem solving questions), and learn to structure solutions clearly.  use correct mathematical language when giving reasons in questions targeting geometry.

  Text version

  Jackson measures a cuboid as 13.2 cm by 16.0 cm by 21.7 cm, each correct to the nearest millimetre, and its mass as 1970 g, correct to the nearest 5 g.

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  A very well answered question. Most common errors were writing as 0.09, writing as an equivalent fraction or writing a percentage

  Text version

  Write 9/10 as a decimal.

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Examiner report

  This was a well answered question. Common incorrectly rounded answers included 3000 or 2600.

  Text version

  Write the number 2538 correct to the nearest hundred.

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q5 · 2 marks

  2 marks

  5

  
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  Examiner report

  Part (a) was generally well done, however some failed to get the mark because they wrote a four-digit number. In part (b) some added up all the different pairs of numbers, showing little understanding of place value, but still the majority gained the mark.

  Text version

  Here are four digits. 7 3 4 9

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q6 · 2 marks

  2 marks

  6

  
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  Examiner report

  The most successful responses that scored full marks, opted for a systematic pairing of the factors. When there was no clear method seen, students often missed some of the factors required; 1 or 30 being commonly missed factors. Some students confused the requirements of this question and instead expressed 30 as a product of its prime factors; when this was completed correctly then there were able to pick up one mark for finding three factors. It was rare to see any other numbers that were not factors of 30.

  Text version

  Write down all the factors of 30

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  The correct response of 24 was common and gained both marks. Some gained a mark by identifying the need to work with 6, 2 and 2. Those who made errors tended to get an answer of either 12 as they only multiplied by 2, or 18 because they added 6 three times rather than doubling.

  Text version

  David has twice as many cousins as Becky. Becky has twice as many cousins as Nishat. Nishat has 6 cousins. How many cousins does David have?

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  Both parts were answered well, with very little working shown. In part (b) this meant that if their answer was incorrect they lost two marks. A number of students did not use the brackets and so gave an answer of −1.4776 or squared the terms in the brackets separately and so gave an answer of 7.514. Other students multiplied 2.58 by 2 rather than squaring. Some students, as the question was two marks, tried to complete the question in stages in order to achieve both marks. This sometimes led to students rounding early and not using all of the numbers on their calculator display.

  Text version

  Use a calculator to work out the following values.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 3F · Q9 · 4 marks

  4 marks

  9

  
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  In part (a) very few methods were seen. Some used a number line method, showing 08.25 to 09.00 and 09.00 to 10.05. 80 minutes was the most common wrong answer, probably obtained from an attempt on the calculator to subtract 0825 from 0905. Part (b) differentiated well with the complete range of marks awarded. The responses for this question varied in the amount of working out given by students, even though the question required them to show all working. The best students showed all steps of the journey in a logical well-laid out way, which ensured that, given they had used the correct timings, they received all the marks. Generally, students were able to add 17 mins to the leave time of 8.45. Where students had used the length of the bus journey and added this to the two walking times, they often missed off the two minutes waiting time, meaning they could not achieve full marks. A number of students did not take into consideration the length of bus time and so got there around 9.17. A few indicated the bus time from Bury to get to Manchester at 9.35. There were very few responses that started at 10am and worked backwards. Some students did not use a bus time at all and used only the walking times with the start time. It was encouraging to find that nearly all students gave a conclusion with their answer.

  Text version

  A bus timetable gives journeys from Bury through Whitefield, Heaton Park and Cheetham Hill to Manchester. One service leaves Bury at 08:25 and arrives in Manchester at 09:05. A later service leaves Whitefield at 09:04 and arrives in Manchester at 09:35. Daniel leaves home at 08:45, takes 17 minutes to reach Whitefield bus stop, and then takes 15 minutes from Manchester bus stop to work.

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q10 · 3 marks

  3 marks

  10

  
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  This question was answered well as most students were able to understand the context of this question. The omission of the final zero in £190.40 was condoned, however students should be encouraged to use correct money notation. Further work that led to students stating the difference was not necessary. Some students that did not understand the context of the question decided to share the 8 or 20 hours between days, while others multiplied the two numbers given in the question by the two rates stated. The most common error was to simply multiply one of the hourly rates by 20.

  Text version

  Bronwin works in a restaurant. The table gives her rates of pay. Day Rate of pay Monday to Friday GBP8.40 per hour Weekend GBP11.20 per hour Bronwin worked for a total of 20 hours last week. She worked 8 of these 20 hours at the weekend. Show that Bronwin was paid less than GBP200 last week.

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• Edexcel 1MA1 · June 2018 · Paper 3F · Q15 · 2 marks

  2 marks

  15

  
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  About half of all students gave a correct response in part (a), this rose to around three quarters of all students in part (b). In part (a) many indicated that multiplication should be done first; but stating BODMAS or BIDMAS alone was insufficient. A common error for some students was to indicate multiplication first then −12 which then made the calculation incorrect. Those who merely gave the correct solution did not gain the mark unless they showed the correct order of operations used. In part (b) the mark was gained by either stating that the largest and smallest numbers were needed or commenting on putting the numbers in order. Saying it should be 8 – 1 = 7, or commenting that 5 and 3 were not the highest and lowest numbers were all frequently seen The explanation of why 5 – 3 was wrong seemed to be more accessible that asking for the range of a list of numbers. A few students tried to find the median or mean but the main mistake involved contradictions such as 7 – 1 = 6

  Text version

  Jenny evaluates 12 - 2 x 4 as (12 - 2) x 4. Rehan finds the range of 3, 1, 8, 7, 5 as 5 - 3.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 3F · Q16 · 5 marks

  5 marks

  16

  
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  Examiner report

  Fractions and ratios are a weakness in many students, but here there was a genuine attempt by many to see what they could do. In part (a) many arrived at the correct answer of 10. If they did not get that far then many were capable of showing the working 8 × 2.50 for 1 mark. Fraction work was rare. Some obviously had not read the question carefully and assumed they were going to be asked for Chan's amount and gave £7.50 on the answer line although Bispah and £10 could be seen in their working. Some calculated £20 – £2.50 but then shared it equally. In part (b) 2.50 : 7.50 was commonly seen, but a significant minority were unable to convert this to a ratio involving whole numbers as required. Many went on to give the correct ratio of 1:3 and some did well giving an equivalent ratio e.g. 250 : 750 or 5 : 15. Many gained 1 mark for Chan’s £7.50; if this was seen in part (a) it was still credited. Of those who did not gain the final mark, some replaced Chan with Bispah, possibly confused by the form a:b. Some misunderstood giving the answer as whole numbers and rounded up to 3:8. Many students assumed that units should be left in a ratio, giving £2.50 : £7.50, or even 2.50a : 7.50b.

  Text version

  Alan gets 1/8 of a sum, Bispah gets 1/2, and Chan gets the rest. Alan receives GBP2.50.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 3F · Q18 · 2 marks

  2 marks

  18

  
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  Many students were able to use their calculator to work out the value of the calculation and get 2300000. These students scored at least one mark, but many of them were not then able to write the number in standard form, or perhaps failed to notice that this was the requested form of the answer. But it was also evident that a significant minority of students did not use a calculator. Common incorrect answers here were 23 × 105 and 2.3 × 1012. Few students wrote down the intermediate steps showing 2645000000 and 1150. A common misconception was that the number of zeros equates to the index number resulting in 2.3 × 105 as the most common incorrect answer.

  Text version

  Work out (2.645 x 10^9)/(1.15 x 10^3).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2018 · Paper 3H · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  This question acted as a good discriminator. The most able students were able to provide a correct and complete answer to both parts of the question. Most students were able to make a start on the evaluation of T for the given values of w and d. Students generally showed a proficiency in being able to use their calculators with numbers in standard form and found a correct value for T. Unfortunately a significant proportion of these students did not give their answer in standard form so scored one of the two marks for their answers. There were some students who did not cube their value of d. Examiners were able to award one mark to students who worked out the correct value of ට ௗ and gave their answer in standard form. Part (b) of the question, involving percentage increases in the values of w and d was found to be more challenging and many students attempted to give an explanation of why Lottie was wrong without sufficient justification. Examiners expected to see either a re-calculation of T with increased and correct values of w and d followed by a comparison with the answer the student gave in part (a) or a full explanation involving a comparison of the effect of the 10% increase in w and the 5% increase in d on the value of T. This may have been demonstrated through a calculation of the total scale factor for the change in value of T or by a comparison of the effect of the percentage increases of 10% and 5% on the values of w and d³. Most students who were successful in part (b) took the re-calculation route.

  Text version

  T=sqrt(w/d^3), w=5.6 x 10^-5, d=1.4 x 10^-4.

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• Edexcel 1MA1 · June 2018 · Paper 3H · Q10 · 3 marks

  3 marks

  10

  
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  The most popular approach to answering this question was by writing down multiples of 20, 45 and 120 to find out how long it would take for the three lamps to flash again at the same time (360 seconds). This approach proved to be successful for many students and where the correct answer was not obtained, at least one mark was usually earned for writing down at least 3 multiples of 45 and 3 multiples of 120. Some students used minutes as their unit of time and found that the three lamps flashed together again after 6 minutes. A minority of students split 20, 45 and 120 into prime factors but often they were unable to proceed any further. These students also earned at least one mark. Some weaker students found the number of times that each lamp flashed in one hour but were unable to make any further progress or score any credit for their attempts. A small number of students did reach the answer “10” from a flawed method. These students, could not be awarded any marks.

  Text version

  Three lamps flash every 20, 45 and 120 seconds and start flashing together.

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• Edexcel 1MA1 · June 2018 · Paper 3H · Q14 · 2 marks

  2 marks

  14

  
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  Examiner report

  Most students scored at least one mark in this question. 480 was the most common answer seen and was awarded one mark for the correct strategy of multiplying 16 by 15 to find the number of matches played then multiplying by 2 as students did not realise that 16 × 15 would include each team playing two matches against each of the other teams. 120 was also credited with one mark, students giving this answer having divided the correct answer, 240, by 2. Commonly seen incorrect answers which could not be credited with any marks included 32 (= 16 × 2), 256 (16 × 16) and 512 (16 × 16 × 2), though some students worked out the correct answer by evaluating 16² − 16.

  Text version

  There are 16 hockey teams in a league. Each team played two matches against each of the other teams. Work out the total number of matches played.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Whilst this tested the order of operations, far too many students gave an answer of 90 and did not follow the rules of arithmetic.

  Text version

  Work out 2 + 7 x 10

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q4 · 1 mark

  1 mark

  4

  
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  The question was very well answered with the vast majority of students scoring the mark. −9 + 2 was the most common answer seen and students were happy to write in the answer boxes given.

  Text version

  Here are four numbers. -9 -2 2 9 Write one of these numbers in each box to make a correct calculation.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1F · Q9 · 1 mark

  1 mark

  9

  
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  This question was not well answered. Many students just worked out the correct answer. This did not answer the question set. The mistake must be identified to satisfy the assessment objective on this specification. Very few students identified that you should multiply 348 by 2 rather than divide. Centres can help students by looking at questions of this style and discussing the mistakes made in the working, they can then help them to articulate the mistake rather than finding the correct numerical answer. It is also worth pointing out to students that a 1 mark question should not take too long and is unlikely to require two or three calculations.

  Text version

  Jacqui wants to work out 3480 / 5 She knows that 3480 / 10 = 348 Jacqui writes 3480 / 5 = 174 because 10 / 5 = 2 and 348 / 2 = 174 What mistake did Jacqui make in her method?

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q11 · 3 marks

  3 marks

  11

  
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  This question was well answered with most students able to score at least 1 mark. In part (a) the most common error was to not realise 30÷8 gave an answer of 4 adults required rather than just 3. Most students showed some working either counting in eights or giving a division if working is seen a process mark can be awarded. In part (b) the follow through allowed an incorrect answer in part (a) to be correctly interpreted and still gain marks. A common approach seen was to consider adding the extra children to the adult without a full allocation often showing 6 + 2 = 8 or equivalent. Part (c) seemed to be understood but sometimes the students found it hard to articulate their answer.

  Text version

  There are 30 children in a nursery school. At least 1 adult is needed for every 8 children in the nursery. (a) Work out the least number of adults needed in the nursery. 2 more children join the nursery. (b) Does this mean that more adults are needed in the nursery? You must give a reason for your answer.

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q13 · 4 marks

  4 marks

  13

  
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  This question was not well answered and many responses were blank. Surface area is an expected skill and knowledge that a cube has six faces is also required but most students failed to realise this and so did not divide 294 by 6. Even when drawing a diagram students often still could not see the 6 faces. Some divided by 4 or 2 or even divided by 2 and divided by 4, adding the answers together, in the possible belief that this was the same as dividing by 6. Of those few that did divide by 6 most found the answer 49, although 48 was a popular incorrect figure, most did not realise this was the answer for the area of a square face and did not go on to find the square root. Some other incorrect methods included 49 × 49 × 49 and 294 × 294

  Text version

  The total surface area of a cube is 294 cm2. Work out the volume of the cube.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1F · Q14 · 3 marks

  3 marks

  14

  
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  Examiner report

  Students often secured some marks for this question, but very few scored full marks. A number of approaches were seen with the most successful being those who decided to convert the fractions to equivalent fractions with a common denominator (normally 35); these candidates scored well. Some students did try to use 100 as a common denominator and this approach was usually unsuccessful. A different approach seen was to try to draw diagrams for comparison, but these were often drawn without any consistency for the fractions and scored 0 marks. The other common approach seen was to convert the fractions into decimals and this was very successful for those that were able to accurately show the division calculations. Some students had difficulty with 5÷7 and so the overall approach scored a variety of marks dependent on the arithmetic skills of the student. 1 mark was awarded to those students who decided to write 7 as 2 but unfortunately they usually stopped at this point. A common incorrect approach seen was to say 5 because it was less than 1 with no consideration of the ‘gap’ to 1.

  Text version

  The fractions are 7/5 and 5/7. Work out which is closer to 1, showing all working.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1F · Q16 · 5 marks

  5 marks

  16

  
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  Examiner report

  In part (a) a good number of students were awarded the mark available for stating that both values had been rounded up. However a significant number only stated that one amount was rounded, with some not stating in what way. Another error commonly made was to state what the answer should have been and therefore not communicating anything about rounding or estimation. The correct answer was not asked for; the knowledge of estimation was being assessed. For the second part of the question a good number of fully correct answers were seen, with clear processes and good accuracy in the calculations. Of those that did not score full marks many lost the accuracy mark due to calculation errors when carrying out the initial multiplication but were able to gain process marks for correctly finding either 10% or 90% for their figures. Students who chose to use a build-up or repeated addition method rather than a grid method often lost marks due to confusion when adding their values. Arithmetic errors when subtracting £20.30 from £203 were also common. Those students who only achieved 1 of the 4 marks available rarely showed a method for calculating 10%, with £23 rather £20.30 seen frequently. Some students also correctly calculated 10% then failed to use it to find 90% and stated the 10% discount as their final answer. A small minority of students did not read the question carefully, finding the cost of 30 t-shirts rather than 35, candidates are reminded of the importance of careful reading and then checking they have answered the question asked.

  Text version

  Berenika wants to buy 35 T-shirts. Each T-shirt costs GBP5.80 Berenika does the calculation 40 x 6 = 240 to estimate the cost of 35 T-shirts. (a) Explain how Berenika's calculation shows the actual cost will be less than GBP240 There is a special offer. T-shirts GBP5.80 each. Buy 30 or more T-shirts. Get 10% off the total cost. (b) Work out the actual cost of buying 35 T-shirts using the special offer. GBP

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q20 · 3 marks

  3 marks

  20

  
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  Examiner report

  This question was answered in a variety of ways. An approximation was required but a few number of students tried to work out the actual calculation. This is a non–calculator paper and as such students should realise that complex arithmetic would not be set. There were also some who said 4² = 8, however this misconception was not seen too often. For those who tried to approximate many rounded to 600 or used 5 thus securing 1 mark. Others went further and got to 600÷21, some then just wrote an answer of Ami or Josh without further justification, this gained 2 marks. The most successful correct answer was to get to 600÷21 and then to show 600÷20=30 or 20×30=600 thus allowing the student to justifiably select Ami or 27.1115 as the appropriate answer.

  Text version

  Ami and Josh calculate 595/(4.08^2 + 5.3). Ami gets 27.1115 and Josh gets 271.115. Use approximations to decide which answer is correct.

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  A small number of students were able to gain 2 marks out of 3 for putting all the given numbers in standard form. Some also gained 2 marks for 0.0018 as their answer, not realising the need to give the answer in standard form as requested. A few students gained a mark for rewriting one number in standard form or for showing 1.8 × 10n. A common mistake seen when attempting to write numbers in standard form was to write, for example, 6−2 rather than 6 × 10−2

  Text version

  Work out (0.06 x 0.0003)/0.01. Give the answer in standard form.

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q22 · 3 marks

  3 marks

  22

  
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  Examiner report

  In part (a) very few blank responses were seen. However, the responses were mixed and mainly scored either full marks or no marks at all. A variety of methods were seen to create equivalent fractions with common denominators but a large number of students were unable to find the correct numerators, leading them to the incorrect answer of 3 . Students who created fully correct equivalent fractions were sometimes then unable to add the numerators correctly but were awarded a mark for a valid method. Other common errors included simply adding the numerators and then adding the denominators and giving 3 as their answer. In part(b) it was surprising to see –8 as a common incorrect answer. This question was not well answered and centres are advised to practice the use of negative indices.

  Text version

  (a) Work out 2/5 + 1/4. (b) Write down the value of 2^-3.

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• Edexcel 1MA1 · November 2017 · Paper 1F · Q23 · 2 marks

  2 marks

  23

  
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  Examiner report

  This was well answered by a majority of students. Of those students who didn’t score well, errors included listing the factors of 36, arithmetic errors and not using the multiplication sign in their final answer. A significant minority found the correct prime factors but then instead of multiplying they put addition signs between the factors or just listed the prime factors, both of these approaches lost the accuracy mark. Some did not factorise fully leaving 4 or 9 as an incorrect prime factor.

  Text version

  Write 36 as a product of its prime factors.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1H · Q1 · 2 marks

  2 marks

  1

  
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  A familiar question to students, and one where a larger percentage of students were able to score full marks for a correct prime factor decomposition, either using index form or not. When full marks were not scored many gained one mark for a correct partial method.

  Text version

  Write 36 as a product of its prime factors.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1H · Q4 · 4 marks

  4 marks

  4

  
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  Examiner report

  The second problem question on the paper proved to be a huge challenge for many in this cohort. In particular students providing just a written explanation relating to 1 circle out of 3 so it is 1 . Those who started to work with πr2 typically got at least 2 marks for a method to find the shaded area, which was very pleasing to see. Of those who got this far it was about even as to whether they could then draw a correct conclusion and compare to 1 . Noticeable was the error that occurred when students believed 33 to be equal to 1 .

  Text version

  A logo is three concentric circles with radii 4 cm, 7 cm and 10 cm. The annulus between 4 cm and 7 cm is shaded. Is exactly 1/3 of the logo shaded? Show working.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1H · Q8 · 2 marks

  2 marks

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  A question ordering recurring decimals has never been set before, but most students were able to gain some credit. One was the most common score seen. This was normally gained for having three of the decimals in the correct relative order, although many gained the mark for showing understanding of the notation, eg 0.2464646…

  Text version

  Order from smallest: 0.2(46), 0.24(6), 0.(246), and terminating 0.246. Parentheses denote the recurring block.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1H · Q9 · 5 marks

  5 marks

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  Examiner report

  This speed problem was too much for many students, and typically the best score seen was 1 mark only. This was awarded for a method to find the correct speed for James, eg 50 ÷ 2.5 or in minutes 50 ÷ 150. Unfortunately many of those who attempted this were unable to divide by 2.5, or when working in minutes completed the division the wrong way round and were unable to get further. A small number of students were able to get further, using time in hours and minutes to get to Peter’s 40 minutes for 15km. Those who did get this far generally went on to get the correct answer.

  Text version

  James and Peter cycled along the same 50 km route. James took 2 1 2 hours to cycle the 50 km. Peter started to cycle 5 minutes after James started to cycle. Peter caught up with James when they had both cycled 15 km. James and Peter both cycled at constant speeds. Work out Peter's speed.

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• Edexcel 1MA1 · November 2017 · Paper 1H · Q10 · 3 marks

  3 marks

  10

  
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  Part (a) of this question was answered quite well, with a good number knowing that the power of 1 is the square root. The common incorrect response was to halve 100 and get 50 In part (b) fractional indices to this degree proved harder. There were a large number of students who dealt with the power simply as a fraction and attempted to find 2 of 125. However, getting as far as 5 allowed many to score 1 mark. A small proportion of students were able to complete the solution to 25

  Text version

  (a) Find 100^(1/2). (b) Find 125^(2/3).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 1H · Q13 · 4 marks

  4 marks

  13

  
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  Examiner report

  The concepts of proportion within part (a) of this question were too complicated for most students; many started with the fraction of 15 rather than 4 , and as a result failed to score marks. Those who started correctly normally scored full marks. Part (b) was very poorly answered with almost no one scoring two marks. For those who scored 1 mark, it was normally for stating a correct bound (5.5 or 6.5).

  Text version

  A factory makes 450 pies. A representative sample has 15 pies. (a) If 4 sample pies are chicken, find total chicken pies. (b) If the number of steak pies in a sample is 6 correct to the nearest whole number, find the lower bound for the probability a random pie is steak.

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• Edexcel 1MA1 · November 2017 · Paper 1H · Q15 · 3 marks

  3 marks

  15

  
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  Another familiar question from the legacy specification and one where we would expect to see more correct algebra. Most students understood the need to find multiples of x, unfortunately these were either often wrong, or the wrong multiples were found. For example finding 1000x but not 10x. There were though a good number of students that were able to follow the algebra through to the correct fraction.

  Text version

  x=0.436363... with 36 recurring. Prove algebraically that x=24/55.

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• Edexcel 1MA1 · November 2017 · Paper 1H · Q21 · 3 marks

  3 marks

  21

  
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  Examiner report

  Again, very few students understood how to rationalise a complicated denominator such as this. Those who had some understanding often used – 1 rather than + 1 and therefore gained no credit. Those who knew which surd expression to use were normally able to gain at least two marks for the correct expansion of the numerator, many being unable to then simplify fully.

  Text version

  Show that (6-sqrt(8))/(sqrt(2)-1) can be written as a+b sqrt(2), where a and b are integers.

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q1 · 1 mark

  1 mark

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  A well answered question to start, where the only common error was a misplaced decimal point eg 0.7 or 0.007

  Text version

  Write 7/100 as a decimal.

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q2 · 1 mark

  1 mark

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  Nearly all students gained this mark.

  Text version

  Write down a multiple of 6 that is between 40 and 50

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q4 · 6 marks

  6 marks

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  Examiner report

  Part (a) was generally well done, with the common error in not carrying out the final division by 90 correctly. Some students failed to extract all the information correctly, for example not finding the total weight of each item of fruit. In part (b) the most popular choice of method was 75 × 15 with a conclusion. Some students showed 13 tomatoes at 975 and 14 tomatoes at 1050. The conclusion was sometimes written in part (ii), but marks were still credited for this in part (i). The last part was very poorly done, with many students just repeating what they had done in part (i); it was clear few understand the mathematical concept of an assumption.

  Text version

  Ken buys some fruit. He buys apples, bananas, peaches and oranges. Ken buys 4 apples weighing 125 g each 2 bananas weighing 170 g each 3 peaches weighing 135 g each Each orange has a weight of 90 g. The fruit has a total weight of 1.785 kg. (a) Work out how many oranges Ken buys. Jane wants to buy 15 tomatoes. She asks for 1 kg of tomatoes at a shop. Jane assumes that each tomato has a weight of 75 g. (b) (i) If Jane's assumption is correct, will she get 15 tomatoes? You must show how you get your answer. (ii) If Jane's assumption is not correct, could she get 15 tomatoes? Justify your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2F · Q6 · 2 marks

  2 marks

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  In both parts of this question there was confusion as to which numbers to include in their answer. In part (a) answers ranged from 3 , 4 and the incorrect fraction 4 for Annie. In part (b) there was similar confusion with ratio being given the wrong way around (eg 1 : 3) or use of the wrong numbers (eg 1 : 4, 3 : 4).

  Text version

  (a) Annie and Lily share money in ratio 4:3. What fraction does Lily get? (b) Dan gets 1/4 of some sweets. Find Rosie:Dan.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  A large proportion of students gained full marks by correctly identifying the relevant prime numbers, but some failed in this process by including a non- prime number. Weaker students confused prime numbers with square numbers, and sometimes included numbers between 1 and 10.

  Text version

  Steve says, "There are more prime numbers between 20 and 30 than there are between 10 and 20" Is Steve right? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2F · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  Most students were able to arrive at the correct values of 250, 100, 500 to put into a ratio, though many then failed to simplify it correctly or fully. Some errors were seen in arriving at these values, most often the “100”.

  Text version

  The table shows a cricket club's income in 2016 from a fete, a quiz and membership fees. Income Fete GBP250 Quiz Entry fees 13 at GBP5 each Refreshments GBP35 Membership fees 25 at GBP20 each Express as a ratio the income from the fete to the income from the quiz to the income from membership fees. Give your ratio in its simplest form.

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  This question was well answered. Students calculated the hourly rate for both people or calculated the equivalent amount earned for comparison with the £266; some did both! It was disappointing to find a common misread of the £266, usually replaced with £226.

  Text version

  Ellie makes hats. She makes at least 17 hats per hour. She is paid 46p for each hat she makes. Reaze is a waiter. He works 35 hours and is paid a total of GBP266 Show that Ellie's hourly rate of pay is more than Reaze's hourly rate of pay.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2F · Q14 · 4 marks

  4 marks

  14

  
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  Examiner report

  In part (a) students had to give an example by choosing two odd numbers in the given expression, and calculate an answer that was a multiple of 4. This was usually done well, sometimes using the same odd number, though errors were not uncommon. It was surprising to see even, rather than odd numbers being used, and merely substituted and not worked out. In part (b) students had to show some reasoning by explaining how the use of (any) odd number in the expression could give a multiple of 4. Marks in this part were rare. Nearly all students thought that they just had to give multiple examples as in part (a). Some gained the first mark (only) by reasoning that doubling an odd number always gave an even number.

  Text version

  a and b are odd numbers. (a) Give an example to show that the value of 2(a + b) is a multiple of 4 (b) Show that, when a and b are both odd numbers, the value of 2(a + b) will always be a multiple of 4

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q15 · 5 marks

  5 marks

  15

  
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  Students had to read and analyse the information given in this question, and then formulate a strategy for its solution; for many this caused too many problems. The most common misconception was with students finding an incorrect amount of oil purchased in both November and February with very few finding the 1500 and then subsequently adding 400 to this value to gain the total value of 1900. Many gained the process mark for showing a method to find an increase of 4%, though again there were many common errors including use of a 1.4 multiplier, division by 4 and partitioning methods that failed to add to give a 4% increase. Very few students provided a full solution leading to the correct answer.

  Text version

  Mr Page uses oil to heat his home. At the beginning of November there were 1000 litres of oil in his oil tank. Mr Page bought enough oil to fill the tank completely. He paid 50p per litre for this oil. He paid a total amount of GBP750 At the end of February Mr Page had 600 litres of oil in the tank. He bought enough oil to fill the tank completely. The cost of oil had increased by 4%. Work out the total amount Mr Page paid for the oil he bought in February. GBP

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• Edexcel 1MA1 · November 2017 · Paper 2F · Q21 · 4 marks

  4 marks

  21

  
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  In part (a) addition was required; some multiplied and gave the answer as 3. In part (b) multiplication was required; some added and gave the answer as 8. Students very rarely scored marks in part (c). A clear lack of conceptual understanding of standard form (or indices) was evident with most students missing the powers of 10 link to gain the correct algebraic power. Many tried to solve the equation to gain a numerical value with the use of the 3 and 2 as coefficients of 100 and 1000 rather than showing their derivation.

  Text version

  (a) pi^3 x pi^x = pi^9; find x. (b) (7^2)^y=7^10; find y. (c) If 100^a x 1000^b=10^w, show w=2a+3b.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2F · Q23 · 3 marks

  3 marks

  23

  
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  Examiner report

  There was a poor success rate for part (a). It was clear that some were just entering figures on their calculator without any forethought as to how to get the calculator to process part values. Those who worked out the four values and wrote them out, then moving on to the rest of the process of calculation frequently gained the final correct answer. Some lost marks due to premature rounding of the figures from their calculator. Good rounding in part (b) frequently led to the mark in this part being awarded. There were errors for some who used the wrong number of decimal places.

  Text version

  Use a calculator to work out sqrt((sin25 degrees + sin40 degrees)/(cos25 degrees - cos40 degrees)). (a) Give all display figures. (b) Round to 2 decimal places.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2H · Q6 · 4 marks

  4 marks

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  Examiner report

  Most students were successful in parts (a) and (b) of this question. In part (a) the most common incorrect response was “3” with “8” occurring quite frequently as a response in part (b). Part (c) was not well answered. Only a small proportion of students stated that 100௔ can be written as 10ଶ௔ or that 1000௕ can be written as 10ଷ௕ or that 100 = 10² and 1000 = 10³ and scored the mark for a first stage in the reasoning needed. Few students were able to complete this part of the question by showing that the product 10ଶ௔ × 10ଷ௕ leads to the given result.

  Text version

  (a) pi^3 x pi^x=pi^9. (b) (7^2)^y=7^10. (c) Show that 100^a x 1000^b=10^(2a+3b).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2H · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  A large proportion of students were successful with this question. However, many students were unable to apply the correct order of operations and did not apply the square root to the full numerical expression or were unable to use their calculator to get a correct value for the expression within the square root. Students are advised to give themselves more practice using the bracket function on their calculator. Some students omitted to calculate the square root altogether and simply gave their final answer as 7.5958… Part (b) of the question was done surprisingly badly. A significant number of students simply truncated their answer to part (a) to 2dp, and often those students applying rules for rounding not only increased the second decimal place by one but also their first decimal place by one. A significant number of those students rounding 7.597… gave their final answer as 7.6, instead of the correct 7.60 .

  Text version

  Work out sqrt((sin25 degrees+sin40 degrees)/(cos25 degrees-cos40 degrees)); give all display figures and then 2 d.p.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2H · Q15 · 3 marks

  3 marks

  15

  
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  For part (a) of this question examiners expected students to make a decision about whether Tracey is correct and then explain that the numbers 8 and 7 needed to be multiplied, and not added, to work out the different number of ways of choosing a main course and a dessert. The question was quite well answered with many students giving clear and concise answers though some responses were too vague to be awarded the mark. For example, some students merely stated that there would be more than 15 ways with no further explanation. Many different approaches to work out the total number of games played were seen in part (b) of the question. Some students used a listing method or a diagram, equivalent to adding the integers from 1 to 11 inclusive. Students who used a multiplication method often calculated 12 × 11 and did not take into consideration that this would include each team playing each other team twice. “132” was consequently a commonly seen incorrect answer. Examiners were able to give some credit for this answer. Other incorrect responses seen included 144 (12 × 12), 72 ( ଵଶൈଵଶ ଶ ), 78 (12 + 11 + …+ 1) and 24 (12 + 12).

  Text version

  (a) Tracey chooses one of 8 mains and one of 7 desserts and says add 8+7. Is she right? (b) Twelve teams each play every other team once. Find total games.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 2H · Q23 · 5 marks

  5 marks

  23

  
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  Examiner report

  The vast majority of students could make no progress with this question designed to test top grade students. Some students confused the geometric sequence with an arithmetic sequence and involved addition of the terms (rather than multiplication). For part (b) there were again few attempts worth any credit with some students starting their working by using their calculator to write down the value of 7 + 5√2 as a decimal. The best students gave clear, concise and full solutions to this question. Summary Based on their performance in this paper, students should: • practise solving linear equations. • learn standard techniques such as working out values in problems on compound growth by using a multiplier method. • carry out a common sense check on the answers to calculations, so for example you should expect the number of hours each of 3 cleaners need to clean all the rooms in a hotel to be more than the number of hours that each of 5 cleaners need to clean the same number of rooms. • use tracing paper to help in questions involving rotations. • check any readings taken from graphs to make sure scales on the axes have been interpreted correctly.

  Text version

  A geometric sequence starts sqrt(x)-1, 1, sqrt(x)+1. (a) Find x. (b) Show its fifth term is 7+5sqrt(2).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q1 · 1 mark

  1 mark

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  Very few incorrect answers here although 3800 was a common error.

  Text version

  Write 3758 correct to the nearest 1000

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q3 · 2 marks

  2 marks

  3

  
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  Examiner report

  The majority of students scored at least one mark in this question for identifying at least 3 factors of 18. A significant number of students failed to include 1 and/or 18 in their list. Pleasingly, unlike in previous years, candidates clearly showed that they knew the difference between a factor and a multiple.

  Text version

  Write down all the factors of 18

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q4 · 5 marks

  5 marks

  4

  
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  Examiner report

  This was answered well and many fully correct solutions were seen. On many occasions, incorrect monetary notation prevented full marks; it was common to see answers of 0.90p or just 0.90. £1.10 was a common incorrect answer found as a result of incorrect subtraction. Many students failed to read the demand of the question carefully enough and after fully correct arithmetic, often simply said “the family ticket is the cheaper”, without working out the required difference in cost. A significant number of students never actually showed their final subtraction and so incorrect differences quoted failed to gain any the second method marks since the method was never seen. Some candidates worked out the cost of 4 child tickets and one adult ticket or two child tickets and one adult ticket. These were deemed inappropriate attempts and received no credit. Despite this being a calculator paper, there were errors in calculating 5.80 + 5.80 + 5.80 + 7.80. Part (b) was also answered well. Students who realised that 102 minutes is equal to 1 hour 42 minutes usually went on to correctly complete the solution. Some converted 102 minutes to 1 hour and 2 minutes and failed to score, and some students converted to a decimal, 1.7, gaining some credit but rarely full marks. There was also evidence of poor mental arithmetic, with addition errors common. This should not happen on a calculator paper when students can, and should be encouraged to, check their calculations.

  Text version

  The table gives information about the prices of cinema tickets. Cinema ticket Price adult ticket GBP7.80 child ticket GBP5.80 family ticket (for 4 people) GBP24.30 Mr Edwards and his 3 children go to the cinema. It is cheaper for Mr Edwards to buy 1 family ticket rather than 4 separate tickets. (a) How much cheaper? The film starts at 6.45 pm. The film lasts 102 minutes. (b) What time does the film finish?

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q5 · 3 marks

  3 marks

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  A significant number of students converted 2 litres incorrectly to 200ml. Such attempts failed to gain any credit since this error trivialised the question. Others realised that division was required, but did 150 divided by 2 to reach 75. However, many students demonstrated a good understanding of what was required and either divided 2000 by 150 or used build up methods to reach the 2000 ml. Answers then varied, many giving 14 (often from premature rounding of 1000/150 to 7) and sometimes 12 as their answer and others gave an answer of 13.3 not realising that they needed a whole number answer. Many responses attempted a method of calculating 1 litre; some did not complete the process of doubling up (giving an answer of 6) or failed to account for the extra bottle when they did double their answer.

  Text version

  Thais has a large bottle of shampoo. There are 2 litres of shampoo in the large bottle. Thais also has some empty small bottles. Each small bottle can be completely filled with 150 ml of shampoo. How many small bottles can be completely filled with shampoo from the large bottle?

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q9 · 2 marks

  2 marks

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  Examiner report

  At least one mark was gained by most students for either correctly identifying two prime numbers or two numbers whose sum is a square number less than 30. An answer of 1 and 3 was a common error where students assumed the number 1 to be a prime number, similarly 7 and 9 was quite common with many students regarding 9 as a prime number.

  Text version

  Nidah writes down two different prime numbers. She adds together her two numbers. Her answer is a square number less than 30 Find two prime numbers that Nidah could have written down.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q10 · 2 marks

  2 marks

  10

  
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  Examiner report

  This question was poorly answered with many students simply finding either five sixths of 48 (= 40) or two thirds of 48 (= 32). A few attempted to use decimals usually getting inaccurate answers due to premature rounding.

  Text version

  2/3 of a number is 48. Find 5/6 of the number.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q11 · 3 marks

  3 marks

  11

  
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  Examiner report

  Most students gained one mark for a correct cost of £264 for Offer 1. Those failing to get this answer usually ignored the free lesson and just worked out £24 × 12 (£288). Working out the cost of 12 lessons with the 5% discount in Offer 2 proved more of a challenge. Some used 50% instead of 5%, a common error seen was simply subtracting 0.05 or 0.95 from 24 or from 288 and some calculated the cost of 11 lessons with this offer. Others thought “off” means “of” and assumed the cost of a driving lesson in Offer 2 was 5% of £24. A few students having shown fully correct calculations, failed to answer the question and quote the cheaper offer thus denying themselves an easy final mark. A small number did not state ‘Offer 1’ and just circled their choice. Centres must understand that this is not acceptable.

  Text version

  Jack's driving school has two offers. Offer 1 Offer 2 First driving lesson free All driving lessons All other driving lessons normal price 5% off the normal price The normal price of a driving lesson is GBP24 Douglas is going to have 12 driving lessons. Which is the cheaper offer for 12 driving lessons, Offer 1 or Offer 2? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q23 · 3 marks

  3 marks

  23

  
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  Examiner report

  In part (a), those students understanding the meaning of ‘reciprocal’ usually found the correct answer. Very many students did not. Fewer numbers of students understood the term ‘error interval’ in part (b). Some scored 1 mark for quoting either 9.75 or 9.85. Those few giving inequalities with the correct limits often made mistakes with the actual inequality signs chosen.

  Text version

  (a) Find reciprocal of 1.6. (b) x rounds to 9.8 to 1 d.p.; give the error interval.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3F · Q25 · 2 marks

  2 marks

  25

  
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  Examiner report

  The digits ‘7452’ were often seen and many students gained one mark for this. Often the answer was correctly given in Standard Form instead of as an ordinary number and often correct Standard Form was converted incorrectly; 0.00007452 and 74520000 were common errors.

  Text version

  Work out (13.8 x 10^7)(5.4 x 10^-12) as an ordinary number.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3H · Q3 · 3 marks

  3 marks

  3

  
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  Examiner report

  Many students were unable to use volume = mass ÷ density. A very common error was to multiply the mass by the density in an attempt to find the volume and some students divided the density by the mass. Those that did use volume = mass ÷ density frequently gained only one mark because they gave no consideration to the units or because they dealt with the units incorrectly. Many students forgot to multiply by 1000.

  Text version

  A gold bar has a mass of 12.5 kg. The density of gold is 19.3 g/cm3 Work out the volume of the gold bar. Give your answer correct to 3 significant figures.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3H · Q5 · 3 marks

  3 marks

  5

  
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  Examiner report

  In part (a) many students were unable to find the value of the reciprocal of 1.6 and a wide variety of incorrect responses were seen. In part (b) one mark was often scored for showing 9.75 or 9.85 or both of these values but relatively few students went on to give a fully correct error interval. Those that attempted to write an error interval frequently made mistakes with the inequality signs. Some students used 9.84 rather than 9.85. Those that wrote the upper bound as 9.849 failed to indicate the recurring nature of the final digit.

  Text version

  (a) Find reciprocal of 1.6. (b) x rounds to 9.8 to 1 d.p.; give the error interval.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3H · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  This question was well attempted. The main obstacle to a correct answer for many students was the inability to write 7.452 × 10-4 as an ordinary number. In many responses 7.452 × 10-4 was either converted incorrectly to an ordinary number or given as the final answer. Many students scored one mark for showing the digits 7452. Although the calculation is one that can be entered directly into a calculator there were a number of students who attempted, often unsuccessfully, to first write the numbers in the question as ordinary numbers.

  Text version

  Work out (13.8 x 10^7)(5.4 x 10^-12) as an ordinary number.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · November 2017 · Paper 3H · Q16 · 3 marks

  3 marks

  16

  
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  Examiner report

  Most students failed to identify from the question that they needed to work with bounds and it was very common to see 11.8 and 148 substituted into the formula for petrol consumption. There were no marks for this approach which completely ignored the topic that the question was actually assessing. Identifying at least one upper bound or one lower bound was sufficient for the first mark. A few students used 148.49 instead of 148.5 but made no attempt to show that the 9 is recurring. Some students with the correct bounds did not appreciate that they needed to use the upper bound for litres of petrol and the lower bound for distance. Some substituted the two upper bounds or the two lower bounds into the formula. Those that did substitute the two correct bounds usually went on to make the correct decision.

  Text version

  Petrol consumption=100 x litres used / kilometres. Distance 148 km and fuel 11.8 L are each correct to 3 s.f. Could the true consumption be at least 8 L/100 km? Show working.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  Examiner report

  The majority of students were able to score the mark on this question for an answer of 16. There were however a significant proportion of students that didn’t understand the index notation fully, leading to common wrong answers of 8 and 32.

  Text version

  Work out the value of 2^4.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  A good proportion of students achieved the mark for rounding, but it is clear that a large number of students do not understand what rounding to decimal places means. Common errors included rounding or truncating to 2 decimal places and many moved the decimal point rather than rounding at all, or added three zeros to the end.

  Text version

  Write 7.26451 correct to 3 decimal places.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q5 · 2 marks

  2 marks

  5

  
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  Examiner report

  Another question where almost all students were able to show a good understanding of what is required to find a percentage, with a large proportion getting both marks. Of those who failed to gain full marks, a good number were able to get a mark for showing a suitable method to find 60%. This was commonly from finding 10% and multiplying by 6 or adding 6 lots. However, students continue to show a lack of method in their working, so the process of dividing by 10 is not stated. In most cases this didn’t cost marks but, for a number of students, finding 50% and adding 10%, the first calculation was not shown and was often incorrect. E.g. 50% = 45, which results in zero marks, whereas if they had written 50% = 70 ÷ 2 = 45 they could still have gained the method mark if this had been accompanied by a correct method for the 10% as well. Poor recall of tables also caused problems here with statements like 6 × 7 = 52. It was also common to see students read the question as “60% off 70” and so give an answer of 28

  Text version

  Work out 60% of 70

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q7 · 3 marks

  3 marks

  7

  
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  Examiner report

  This is the first of the new problem solving questions and it was pleasing to see so many students being able to score marks. In many cases both method marks were scored by dealing suitably with the items listed, and for understanding the need to multiply or divide by 3 in relation to the sausages. With the accuracy mainly being dealt with in the final mark, it meant that arithmetic errors or slightly incomplete processes were still able to gain marks. The failure to score all three marks was usually down to one of a few things; arithmetic errors, not using all the items (for example only costing the price of one pack of bread rolls not two) or for failing to write a conclusion.

  Text version

  Fahima buys 2 packets of bread rolls costing GBP1.50 for each packet 1 bottle of ketchup costing GBP1.60 3 packets of sausages Fahima pays with a GBP10 note. She gets 30p change. Fahima works out that one packet of sausages costs GBP2.30 Is Fahima right? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  Many students scored the mark for correctly multiplying fractions in part (a). Those who didn’t often either added or mixed up the method for adding and multiplying. Another common incorrect process was to cross multiply, doing 5 × 4 and 8 × 3 leading to an answer of ଶ଴ ଶସ. Others were confused between the method for multiplication and addition and attempted methods involving a common denominator. In part (b) students commonly forgot to use a common denominator leading to an incorrect answer of ଵ ଵ = 1. Of those who had a denominator of 12, some forgot to multiply the numerators correctly to get an equivalent fraction. Another common misconception was to confuse with division and attempt to work out ଶ ଷ െ ସ ଵ

  Text version

  (a) Work out (5/8) x (3/4). (b) Work out 2/3 - 1/4.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q9 · 4 marks

  4 marks

  9

  
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  Examiner report

  The next of the problem solving questions and again a large proportion of students were able to gain marks. Almost all scored the first mark for doing something correct with time, usually 8 × 12 (=96). The second mark caused more problems because it meant students had to work with the quarter which many were unable to do. Many were then able to gain more credit for adding two lots of their overtime figure to 96. There was a relatively small proportion who were able to pull it all together, along with correct arithmetic and get to the correct final answer.

  Text version

  Sean's normal rate of pay is GBP12 per hour. For each hour beyond 8 hours in a day he is paid 1 1/4 times his normal hourly rate. On Monday he worked 10 hours. Work out his total pay.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q13 · 3 marks

  3 marks

  13

  
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  Examiner report

  It is apparent that many students have no real understanding of metric units at all. Centres need to take note to ensure that students are familiar with all common metric units of length, mass and capacity. This will help students, not only in questions like this, but also to recognise suitability of answers on other questions working in metric units. In relation to this question, surprisingly few students scored in part (a) for a suitable estimate for the height of the man. Many students were then more successful in part (b) however as they were able to multiply their answer to (a) by a suitable scale factor.

  Text version

  A tree and a man are drawn to the same scale. (a) Estimate the real height of the man in metres. (b) The tree is between 5 and 6 times as tall as the man in the printed diagram. Estimate its real height.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q17 · 4 marks

  4 marks

  17

  
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  Examiner report

  Although a good number of fully correct solutions were seen, this question proved demanding for a number of students despite the easy first mark for a correct process to find the weight of one tin of soup. Unfortunately, those who understood the steps in the process to solve this problem often failed to gain all four marks as they were unable to cope with the necessary arithmetic. A common incorrect starting point was to subtract the two total weights given or to divide by an incorrect amount of tins.

  Text version

  5 tins of soup have a total weight of 1750 grams. 4 tins of soup and 3 packets of soup have a total weight of 1490 grams. Work out the total weight of 3 tins of soup and 2 packets of soup.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q18 · 5 marks

  5 marks

  18

  
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  Examiner report

  This problem solving question involved estimation in a context. As with the previous problem questions most were able to get some marks for suitable processes. Typically these marks were awarded for evidence of estimation or for dividing an area by a coverage figure. Many students were unable to correctly recall the formula for the area of a circle; this is a formula that must be learnt by students. For some reason, a number of students thought that they needed to use 360o somewhere in their solution. In part (b) the common response was to discuss the rounding done in the final step, i.e. rounding to a whole number of bags, which was not the essence of the question. To gain marks students had to discuss the effect of their estimation of either π or the coverage figure. Commonly when discussing the latter, students wrongly stated that rounding up to 50 would give an overestimate, where it would actual bring about an underestimate.

  Text version

  Balena has a garden in the shape of a circle of radius 10 m. He is going to cover the garden with grass seed to make a lawn. Grass seed is sold in boxes. Each box of grass seed will cover 46 m2 of garden. 10 m Balena wants to cover all the garden with grass seed. (a) Work out an estimate for the number of boxes of grass seed Balena needs. You must show your working. (b) Is your estimate for part (a) an underestimate or an overestimate? Give a reason for your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q22 · 2 marks

  2 marks

  22

  
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  Examiner report

  Many foundation students are familiar with this type of question and almost all of those who scored marks did so through the use of a factor tree. A single arithmetic error was allowed for the method mark, but any more resulted in no marks. Students do need reminding that 1 is not a prime factor so should not be included when writing a number as the product of its prime factors. It is frustrating that some students continue to drop the accuracy mark by failing to state give correct prime factors as a product; the final answer was frequently given as a list of the prime factors or as a sum rather than product.

  Text version

  Express 56 as the product of its prime factors.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1F · Q23 · 3 marks

  3 marks

  23

  
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  Examiner report

  Most students used a suitable method, with correct relative place value, to multiply the two decimals. This meant that all of these students were able to score at least one mark, many then went on to get two or three. Generally the placement of the decimal point in the final answer was correct so for most one mark became two. It is essential that students set out their work in an ordered fashion that can be followed through by the examiner; this is particularly pertinent for those that work with a number of individual products. Those employing this method frequently failed to find all the necessary products, thus an incomplete method was offered which gained no marks.

  Text version

  Work out 54.6 x 4.3

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q2 · 2 marks

  2 marks

  2

  
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  Examiner report

  The most common approach was to create a factor tree. Many candidates opted to start with 8 and 7 and then correctly completed this approach. Poor arithmetic stopped some candidates from gaining full credit but they were able to pick up a method mark for completing their tree to prime number ends provided there was only one error. Many candidates were able to express the prime numbers as a product, but some lost the final mark by writing the prime factors as a list. Some candidates chose to use index notation to tidy up their final answer; this was not required to score full marks and any errors in doing this were not penalised.

  Text version

  Express 56 as the product of its prime factors.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q3 · 3 marks

  3 marks

  3

  
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  Examiner report

  Most candidates attempted this question using partitioning, Napier’s bones or vertical methods. Usually when candidates made arithmetical errors they were still able to score two out of the three marks by giving an answer with the decimal place correctly positioned, if this followed a correct method. Candidates who tried to answer this question by a less formal method were not as successful often doing only a partial calculation such as 54 × 4 and 0.6 × 0.3 gaining no marks. Some candidates correctly came up with the correct digits 23478 but placed the decimal point incorrectly usually to give 23.478

  Text version

  Work out 54.6 x 4.3.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  In part (a) there were many correct responses, but sometimes spoilt by insufficient care taken to count zeros. Only a few took the unnecessary step of rounding the 7.97, thereby rendering their answer incorrect. In part (b) a large number of candidates had problems dividing 2.52 by 4 or they left it as a fraction without any calculation attempted. It was also common to see the 2.52 and 4 multiplied to 10.08. There was more success dealing with the indices, though 105 ÷ 10-3 was sometimes given as 102. It was not always clear whether this was a failure to deal with subtracting a negative number, or if addition was being applied rather than subtraction. Some candidates left their answer as 0.63 × 108.

  Text version

  (a) Write 7.97 x 10^-6 as an ordinary number. (b) Work out (2.52 x 10^5) / (4 x 10^-3), in standard form.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q12 · 4 marks

  4 marks

  12

  
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  Examiner report

  In part (a) many candidates knew to use the reciprocal or to find the square root of 81 and were rewarded with a method mark. The correct value was seen less often. Part (b) was less successful with candidates required to show the need to both cube root and square to score the method mark. Of the candidates that did find the cube root of the fraction some then chose to double their numerator and denominator rather than square the values. Perhaps encouraged by part (a) some candidates incorrectly used the reciprocal at some point.

  Text version

  (a) Find 81^(-1/2). (b) Find (64/125)^(2/3).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q14 · 4 marks

  4 marks

  14

  
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  Examiner report

  This proportional reasoning problem proved a step too far for many candidates. Most were unable to access the question and chose to add the ratio parts for circles to incorrectly express as a fraction of the total ratio parts. Candidates that had some idea of what they needed to do often incorrectly multiplied the fraction of white circles by the fraction of black circles. Of the few candidates that were successful, most took a fractional approach and realised that they needed to multiply the fraction of white shapes by the fraction of white circles and add that to the fraction of black shapes multiplied by the fraction of black circles. Other candidates chose to use a nominal total to calculate the relevant fractions, however some could not overcome the difficultly this posed when 30% of their chosen total was not a multiple of 9 or when 70% of their chosen total was not a multiple of 7

  Text version

  White shapes and black shapes are used in a game. Some of the shapes are circles. All the other shapes are squares. The ratio of the number of white shapes to the number of black shapes is 3:7 The ratio of the number of white circles to the number of white squares is 4:5 The ratio of the number of black circles to the number of black squares is 2:5 Work out what fraction of all the shapes are circles.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 1H · Q15 · 4 marks

  4 marks

  15

  
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  Examiner report

  Candidates had varying degrees of success with this question. Many did much of the work using the original values and introduced estimated values only after they had completed nearly all their manipulation. When substituting the values into the formula, many omitted to square the radius. A significant number of candidates failed to write out a full equation, many calculating individual parts as opposed to using the given formula. There was poor rearrangement of the equation sometimes ending with subtraction rather than division. π = 3.14 was common, but without estimating this as 3 they then had difficulty cancelling π with 1 ; many kept 98 rather than rounding to 100. Those who gained full marks usually gave an answer of “4” from a calculation of 100 ÷ 25, because the actual working here was very simple for those who recognised what the question was asking. In many cases working was often poorly set out and difficult to follow. Candidates need to consider how they present their solutions. Using a systematic and logical sequence of steps leading to a final answer is highly recommended. In part (b) only the most able candidates were able to explain concisely the result of their division, which required a real understanding of the effects on calculation of rounding in both the numerator and denominator. Reference to the numerator and denominator was rarely seen. The majority stated that if they rounded more values down than up then their answer would be less, or that John would be more accurate as he had used a calculator.

  Text version

  A cone has volume 98 cm^3 and radius 5.13 cm. Use V=(1/3)pi r^2 h. (a) Estimate h. (b) State whether the estimate is above or below the calculator value, with reasons.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Examiner report

  Few students were successful in this question with 56.8 being a very commonly seen response, that is rounding to one decimal place instead of one significant figure. Some students gave the answer 60.00 which of course is 4 significant figures.

  Text version

  Write 56.78 correct to one significant figure.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q4 · 2 marks

  2 marks

  4

  
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  Examiner report

  The instruction to “start with the smallest fraction” was treated as guidance only and examiners also accepted lists starting with the largest fraction. The question attracted many fully correct answers. Students were usually able to put at least three of the fractions in correct order, the most common method seen being to convert the fractions into decimals. Nearly all the students presented their answers in fraction form but examiners also accepted correct decimal or percentage form.

  Text version

  Put 2/5, 11/30, 1/2 and 7/15 in ascending order.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q6 · 4 marks

  4 marks

  6

  
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  Examiner report

  This multi-step question proved to be a good discriminator between students of different abilities taking this paper. A large majority of students made a good start by either finding the number of £1 coins or by finding the total value of the 50 p coins. Many of these students were then able to show a correct process for working out the number of 20 p coins. However, some students added 165 (number of £1 coins) to £62 (the value of the 50 p coins) then subtracted this from 495 in an attempt to find the number of 20 p coins. A number of students used 0.3 or 30% for 3 in their attempt to find the number of £1 coins. This was not accepted by examiners. Students who used 0.33 (or better) or 33% (or better) for 3 were able to score some marks but this did not result in an integer number of £1 coins. Most students scored at least 2 marks overall for their response to this question, with a good proportion of students securing full marks. It was encouraging to see that nearly all students converted between pence and pounds without any trouble. Those students who did use inconsistent units usually obtained a large total sum of money but this did not seem to ring any alarm bells with the students concerned.

  Text version

  There are 495 coins. One third are GBP1 coins, 124 are 50p coins, and the rest are 20p coins. Work out the total value.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q8 · 3 marks

  3 marks

  8

  
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  Examiner report

  Most students scored at least two of the three marks available in this question and many students scored all three marks. Parts (a) and (b) were answered correctly by a large majority of students. For part (c), it seemed that most students understood what a prime number was but they often included at least one extra inappropriate number, for example 27

  Text version

  Here is a list of numbers. 21 22 23 24 25 26 27 28 29 (a) From the numbers in the list, write down a square number. (b) From the numbers in the list, write down a number that is a multiple of both 4 and 6 (c) Write down all the prime numbers in the list.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  This question discriminated well between students. Many students could find the cost of 150 envelopes at one of the shops, usually Letters2send and scored 2 marks for this. A much smaller proportion of students could take into account the special offer at Stationery World and £31.50 was often seen as the total cost of the 150 envelopes at this shop. This led to an incorrect conclusion. Nearly all students approached the problem by finding the cost of 150 envelopes at each shop. However, a small number of students found the cost of one envelope at each shop and compared these costs (13.96 p and 14 p). Rounding one of these values sometimes led to students giving the incorrect conclusion that both shops gave the same value.

  Text version

  Suha is going to buy 150 envelopes. Here is some information about the cost of envelopes in two shops. Letters2send Stationery World Pack of 25 envelopes for GBP3.49 Pack of 10 envelopes for GBP2.10 Buy 2 packs get 1 pack free Suha wants to buy the envelopes as cheaply as possible. Which shop should Suha buy the 150 envelopes from? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q11 · 4 marks

  4 marks

  11

  
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  Examiner report

  Students were usually able to use the graph with accuracy to change 74 cm to inches though some students gave 28 or 20.9 as their response. These could not be awarded the mark available. Part (b) proved to be more of a challenge to students who could often change 6 feet 3 inches to inches but could not clearly show with enough detail a correct strategy to use the graph to convert this to cm. Examiners needed to see the use of an appropriate method, for example 25 inches = 63 cm, so 75 inches = 3 × 63 or 189 cm to award the second method mark as allowed on the mark scheme. Responses outside the range stated on the mark scheme were awarded full marks provided a correct strategy was clearly shown and used without error. For example, though using the conversion of a small number of units can lead to less accuracy, responses such as 5 inches = 12 cm so 75 inches = 15 × 12 = 180 cm were accepted for full marks but only provided a clear method was shown.

  Text version

  You can use this graph to change between inches and centimetres. 140 120 100 80 60 40 20 0 0 10 20 30 40 50 (a) Change 74 cm to inches. Daniel's height is 6 feet 3 inches. 1 foot = 12 inches (b) What is Daniel's height in centimetres?

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q12 · 2 marks

  2 marks

  12

  
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  Examiner report

  A majority of students gave a fully correct answer to this question requiring the use of a calculator. Most students wrote down all the figures from their calculator display as advised in the question. A significant number of students who did not score full marks scored one mark for recording a correct value for the denominator or for the numerator of the fraction. However, many students just wrote down an incorrect answer. It appears that many of them had put the whole calculation into their calculator in one go and either had not respected the order of operations or had missed out operations (such as squaring the denominator). Students should be encouraged to work out and write down the value of the numerator and denominator separately.

  Text version

  Find sqrt(13.4 - 1.5) / (6.8 + 0.06)^2. Write all figures shown on your calculator display.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q15 · 3 marks

  3 marks

  15

  
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  Examiner report

  Only a small proportion of students could write 4.7 × 10−1 as an ordinary number. 47 was a common incorrect answer seen. Most students were able to use their calculator to work out the value of the calculation in part (b) and get 2 280 000 000. These students scored at least one mark, but many of them were not then able to write the number in standard form. Common incorrect answers here were 22.8 × 108 and 228 × 107.

  Text version

  (a) Write 4.7 x 10^-1 as an ordinary number. (b) Work out (2.4 x 10^3) x (9.5 x 10^5), in standard form.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q18 · 5 marks

  5 marks

  18

  
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  Examiner report

  Examiners saw a small but significant number of concise, clear and accurate answers to this question. However, for many students, a clear strategy was absent and many responses could attract only one mark for the calculation of 60% of 2600 or for a correct process to find the total number of children (468). The most successful students usually calculated the total number of children and the total number of adults then either compared the total number of people to the number of seats occupied or expressed it as a percentage of 2600. Many students had difficulty dealing with the 4 and it was common to see an attempt to divide 117 by 3

  Text version

  On Saturday, some adults and some children were in a theatre. The ratio of the number of adults to the number of children was 5 : 2 Each person had a seat in the Circle or had a seat in the Stalls. 3 4 of the children had seats in the Stalls. 117 children had seats in the Circle. There are exactly 2600 seats in the theatre. On this Saturday, were there people on more than 60% of the seats? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2F · Q23 · 2 marks

  2 marks

  23

  
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  Examiner report

  A sizeable number of students made no attempt at this question and it was rare to see a fully correct answer. However, many students were able to state at least one bound (either 4.755 or 4.765) and were rewarded with one mark out of the two marks available. Where inequality signs were used by students, and this was not very common, they were often used incorrectly.

  Text version

  A number, n, is rounded to 2 decimal places. The result is 4.76 Using inequalities, write down the error interval for n.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2H · Q2 · 5 marks

  5 marks

  2

  
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  Examiner report

  Those students that started their solution by realising that the 117 children in the Circle equated to one quarter, giving 468 as the total number of children, usually went on to complete a fully correct solution. Many students, however, started by dividing the 2600 seats available in the ratio 5 : 2 and rarely made any further progress. Some students applied the ratio 5 : 2 to individual areas of the theatre which then led to decimal values which were often incorrectly rounded. Percentage calculations, finding 60% of 2600 were usually correct. A number of students gave a fully correct account and then neglected to actually answer the question posed and were consequently denied full marks. Some students used a two-way table to help them organise their solution which often proved useful. Too many did not read the question carefully enough and assumed the 4 related to the total amount of people and not just children. There was evidence that some students got lost in their own workings through lack of commentary.

  Text version

  Adults:children in a theatre are in ratio 5:2. Three quarters of children sit in the stalls and 117 children sit in the circle. The theatre has 2600 seats. Were more than 60% occupied? Show working.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2H · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  Many students had clearly never covered this topic and did not know the meaning of an error interval. Of those students who knew what they were doing failure in giving the correct inequalities prevented full marks being achieved. One mark was often awarded for sight of either 4.755 or 4.765 It was not uncommon for students to give the difference between the bounds as their final answer, losing the accuracy mark. Incorrect use of inequality signs (getting them the wrong way around) was also common even when correct endpoints had been identified.

  Text version

  n rounds to 4.76 to 2 decimal places. Write its error interval using inequalities.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2H · Q10 · 4 marks

  4 marks

  10

  
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  Examiner report

  In part (a), the great majority of students correctly gave an answer of Jupiter. The most common wrong answer was Uranus, with weaker students just looking at the initial digits and ignoring the powers of 10 It was clear in part (b) that those able to use their calculator for standard form calculations had no trouble finding the correct answer. Many place value errors were the cause of incorrect answers where students simply found the difference between 4.869 and 3.302 (1.567). Other errors were due to selecting the wrong data, such as for the wrong planet, or distance from the earth, rather than the mass of the two planets. In part (c), many students seemed to think that it was sufficient simply to say that 109 has “two more 0s” than 107 or pointing out that 102 = 100, without relating it to the actual numbers. A large number of students found the difference between the two distances showing they didn’t understand what 100 times greater meant. Those students whose first step was to divide the distance of Neptune from Earth by that of Venus from Earth usually gained full marks.

  Text version

  The table shows some information about eight planets. Planet Distance from Earth (km) Mass (kg) Earth 0 5.97 x 1024 Jupiter 6.29 x 108 1.898 x 1027 Mars 7.83 x 107 6.42 x 1023 Mercury 9.17 x 107 3.302 x 1023 Neptune 4.35 x 109 1.024 x 1026 Saturn 1.28 x 109 5.68 x 1026 Uranus 2.72 x 109 8.683 x 1025 Venus 4.14 x 107 4.869 x 1024 (a) Write down the name of the planet with the greatest mass. (b) Find the difference between the mass of Venus and the mass of Mercury. Nishat says that Neptune is over a hundred times further away from Earth than Venus is. (c) Is Nishat right? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2H · Q16 · 3 marks

  3 marks

  16

  
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  Examiner report

  There were a variety of acceptable approaches to the solving of this question but full marks demanded an algebraic approach at some point. Most students were able to at least begin to convert each of the given recurring decimals to a fraction and thus gain credit. A popular incorrect approach however was to let say x be equal to the given product followed by, for example, 10x = 1.3636… × 2.222… This gained no marks.

  Text version

  Using algebra, prove that 0.1[36 recurring] x 0.[2 recurring] = 1/33.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 2H · Q18 · 3 marks

  3 marks

  18

  
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  Examiner report

  Very few students attempted to convert the three terms to a common base in this question preferring to use their calculators in an attempt to find the value of 2x. Of those students that did, many then failed to apply the index laws correctly. Others tried to apply the index laws without converting to a common base. It was not unusual to see 2x = 2.73….. but few were able to complete the solution to find x = 1.45 Some did by a trial and improvement approach and some by applying logarithmic skills (outside this specification but still a valid method). A number of students misinterpreted the values in the question as mixed numbers and converted them into improper fractions.

  Text version

  16^(1/5) x 2^x = 8^(3/4). Work out the exact value of x.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q1 · 2 marks

  2 marks

  1

  
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  Examiner report

  Part (a) was nearly always correct. A few students started with the longest river, not with the shortest river. Part (b) was answered well and it was rare to see a response where a mathematical calculation was not attempted. The most common approach used to show that Ami is correct was to work out 112 × 3 = 336. Some students chose to divide the length of the River Thames by 3 and some divided the length of the River Thames by the length of the River Don. A few students made arithmetic errors which meant that the mark could not be awarded and there were some with correct working who contradicted the question by stating that Ami is wrong. Other incorrect answers that were commonly seen included 112 × 4 and 354 – 112

  Text version

  The table shows the lengths of five rivers. River Length (km) Trent 297 Don 112 Severn 354 Thames 346 Mersey 113 (a) Write down the rivers in order of length. Start with the shortest river. Ami says, "The River Thames is more than three times as long as the River Don." (b) Show that Ami is correct.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q3 · 2 marks

  2 marks

  3

  
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  Examiner report

  Q3(i) was answered very well. Incorrect answers included 10 and 19. Some students misread the question and wrote down a four digit number. Q3(ii) was also answered very well. Incorrect answers included 195 and 270

  Text version

  Here are four digits. 5 6 1 9 (i) Write down the smallest possible two digit number that can be made with two of the digits. (ii) Write down the three digit number closest to 200 that can be made with three of the digits.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q4 · 2 marks

  2 marks

  4

  
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  Examiner report

  This question was answered quite well. The most common method was to start with 32 ÷ 4 = 8 followed by either 8 × 5 or 32 + 8. Some students worked out 32 × 5 = 160 and then 160 ÷ 4. It was common to see a correct first step leading to either 8 or 160 and then for this value to be given as the final answer. This scored one mark. There were also responses in which 40 was seen embedded in the working, eg 40 ÷ 5 × 4 = 32, but not given as the final answer and these also scored one mark. The most common incorrect method used was 32 ÷ 5 × 4 = 25.6 because many students assumed that 4/5 of 32 was required.

  Text version

  4/5 of a number is 32. Find the number.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  Examiner report

  The majority of students wrote down all nine possible combinations and it was pleasing that many of the lists were systematic and written in a logical order. Those that did not use such a logical approach were more likely to miss out or repeat combinations. Answers with one or two of the combinations either missing or repeated were sometimes seen and these were awarded one mark. Very few students failed to score at least one mark.

  Text version

  Priti is going to have a meal. She can choose one starter and one main course from the menu. Menu Starter Main Course Salad Fish Melon Pasta Rice Burger Write down all the possible combinations Priti can choose.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q8 · 2 marks

  2 marks

  8

  
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  Examiner report

  This question was answered very well, with the majority of students subtracting 36 from 372 and dividing the result by 4. It was surprising, on a calculator paper, to see 372 – 36 sometimes evaluated incorrectly. However, a mark could still be earned for a correct method provided the calculation being attempted was shown. A significant number of students did not deal with the deposit correctly. Some added the deposit before dividing by 4 and some simply ignored the deposit and worked out 372 ÷ 4

  Text version

  Joanne wants to buy a dishwasher. The dishwasher costs GBP372 Joanne will pay a deposit of GBP36 She will then pay the rest of the cost in 4 equal monthly payments. How much is each monthly payment? GBP

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q9 · 3 marks

  3 marks

  9

  
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  Examiner report

  The majority of students were able to get at least one mark on this question and many went on to give a fully correct response. Many different methods were seen. The most widely used approach was to start at 9 am and add on the five times to find the time that Davos would finish cleaning. Another common method was to find the total of the five times and compare it with the length of the day. Time lines were often used but students did not always account for the minutes correctly. Mistakes were often made when adding on times, eg 2.55 pm + 75 minutes = 4.05 pm, and the use of unconventional time notation, eg writing 1 hour 40 minutes as 1.40, also led to many errors. The inclusion of a break caused confusion for some students about whether to add or subtract 75 minutes. Some felt that it should be split up into shorter breaks but were unable to record this accurately. Some of the students who found the total of the five times as 430 minutes divided 430 by 60 to get 7.16 hours and interpreted this as 7 hours 16 minutes. Students were generally very good at providing a statement as to whether Davos would finish cleaning by 4 pm although some students made no decision and could not be awarded the final mark.

  Text version

  A cleaner needs 2 h, 1 h 40 min, 1 1/2 h and 45 min for four rooms, plus 75 min of breaks. Starting at 9 am, will he finish by 4 pm? Show working.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q14 · 6 marks

  6 marks

  14

  
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  Examiner report

  Students generally made good attempts at part (a) with many achieving full marks. The main stumbling block to a successful outcome was an inability to use the exchange rate appropriately to deal with the two currencies. The majority of those that attempted a conversion chose to change from dollars into pounds, which was not surprising as the question asked for the answer to be given in pounds. A few changed £1500 into dollars and found the total cost in dollars before converting it into pounds. The majority of students gained the first two marks for finding the total cost of the hotel room ($2744) and the total cost of the wifi ($60). Those that realised they needed to divide by 1.90 to change dollars into pounds often did so at this stage. A common mistake was to add 2744, 60 and 1500 and divide the total by 1.90. Those who decided to deal with the currency conversion as the first step and changed $196 and $5 into pounds were more likely to have an answer affected by rounding errors. When attempting to change dollars into pounds a common mistake was to multiply by 1.90 and some students even multiplied by 0.90 In part (b) a few students thought that having fewer dollars to £1 would have no effect on the total cost of Andy’s holiday. The majority of the students, however, were split between those who thought it would be cheaper and those who thought it would be more expensive. Success in this part did not appear to depend on the number of marks gained in part (a).

  Text version

  Andy went on holiday to Canada. His flights cost a total of GBP1500 Andy stayed for 14 nights. His hotel room cost $196 per night. Andy used wifi for 12 days. Wifi cost $5 per day. The exchange rate was $1.90 to GBP1 (a) Work out the total cost of the flights, the hotel room and wifi. Give your answer in pounds. GBP (b) If there were fewer dollars to GBP1, what effect would this have on the total cost, in pounds, of Andy's holiday?

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q18 · 5 marks

  5 marks

  18

  
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  Examiner report

  It was pleasing to see many fully correct and well-presented solutions to this multi-step question. Many students were able to work out either 2 of 420 to find the number of vanilla cakes or 35% of 420 to find the number of banana cakes and often they did both. A common mistake was to subtract the number of vanilla cakes from 420 and then find 35% of 300, not 35% of 420. However, students who did this were still able to gain three of the five marks if the processes that followed were correct. Some converted 2 to a percentage but premature rounding often led to a loss of accuracy. Despite this being a calculator paper, a surprising number of students attempted to use a non- calculator method for the percentage calculation, often with incomplete or inadequate working shown. Students who got as far as subtracting the numbers of vanilla cakes and banana cakes from 420 to find the total number of lemon cakes and chocolate cakes then had to divide this total in the ratio 4 : 5. A common error at this stage was to divide the total by 4 and by 5 instead of by 9. Some students attempted to use the ratio 4 : 5 on a quantity that was not the total number of lemon cakes and chocolate cakes, eg finding 4 of 420

  Text version

  Of 420 cakes, 2/7 are vanilla and 35% are banana. The remaining lemon and chocolate cakes are in ratio 4:5. Find the number of lemon cakes.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3F · Q23 · 4 marks

  4 marks

  23

  
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  Examiner report

  Part (a) was not answered very well. Students were more successful at writing down the least possible value of the house than the greatest possible value of the house. A variety of incorrect answers were seen. These included 159 000 and 159 999 in Q23(a)(i) and 164 000 and 169 999 in Q23(a)(ii). Students who recognised that 210 000 = 105% in part (b) not only gained the first mark but usually went on to get the correct answer. Not surprisingly, the most common mistake was to work out 5% of 210 000 and then subtract the result from 210 000 or, less frequently, to add it to 210 000 Summary Based on their performance on this paper, students should: ● Practise writing algebraic expressions and formulae ● Practise setting up algebraic equations to solve a problem ● Use a calculator to check calculations that are carried out manually ● Practise completing Venn diagrams and learn the necessary set notation ● Read the information given in each question very carefully

  Text version

  Harley's house has a value of GBP160 000 correct to 2 significant figures. (a) (i) Write down the least possible value of the house. GBP (ii) Write down the greatest possible value of the house. GBP The value of Rita's house increased by 5%. Her house then had a value of GBP210 000 (b) Work out the value of Rita's house before the increase. GBP

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3H · Q4 · 5 marks

  5 marks

  4

  
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  Examiner report

  A very well answered question with the vast majority of students scoring full marks The most common method used was to calculate using the fraction and then the 35%. These students then correctly subtracted and split the remaining number of cakes in the given ratio of 4 : 5. The most popular alternative approach used was to convert the fraction into a percentage. Accuracy was sometimes lost through premature rounding with this method. Centres are advised to encourage students to calculate with fractions. Another alternative approach was to add the 2 and the 35% together, either in percentage or fraction form, to then work out the remainder as a percentage/fraction of 420 and then split into the correct ratio. Again some inaccuracies through rounding were seen if the percentage approach was used. The most common mistake seen was to find 2 of 420 as 120 then to do 420−120 = 300 and then to find 35% of this, rather than the original amount of 420. A student who did this could still score 3 marks, not gaining the process mark for finding the correct percentage or the correct fractional value and then going on to subtract these values from 420 It was pleasing to see the number of students who successfully used ratio at the end of this problem. This question was accessible to all students.

  Text version

  Of 420 cakes, 2/7 are vanilla and 35% are banana. The remaining lemon and chocolate cakes are in ratio 4:5. Find the number of lemon cakes.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3H · Q11 · 2 marks

  2 marks

  11

  
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  Examiner report

  This question targeted a new area of the specification and it was pleasing to see the majority of students scored at least one mark on this question. Many students obtained one mark for 215 ÷ 17 = 12.647.. and some went on to correctly indicate that it is not possible to have 0.647.. of a rose tree or that the answer was not an integer when an integer would be required. An alternative method seen was to show 12 × 17 (=204) and 13 × 17 (=221) and an explanation that there could not be a number of trees between 12 and 13 The main errors seen in this question, were to show a correct calculation with no interpretation scoring one mark, or to show 17 × 17=289, which has no meaning in this question or to give a vague reason eg ‘215 can’t be divided by 17’ the latter two do not score any marks.

  Text version

  Jeff is choosing a shrub and a rose tree for his garden. At the garden centre there are 17 different types of shrubs and some rose trees. Jeff says, "There are 215 different ways to choose one shrub and one rose tree." Could Jeff be correct? You must show how you get your answer.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · June 2017 · Paper 3H · Q17 · 5 marks

  5 marks

  17

  
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  Examiner report

  Most students attempted this question, although in part (a) a small number of students tried to work without finding any bounds failing to identify from the question that they needed to write down upper and lower bounds for both the time and track length. Others successfully gave the correct bounds for the track length but used the same rounding for the time bounds, thus not distinguishing between rounding to the nearest 5 and rounding to the nearest 10. When showing a division some students did not appreciate that they needed to divide the upper bound for distance by the lower bound for time - upper/upper and lower/lower were commonly seen. Different misconceptions seen were not to work in consistent units of time or to convert incorrectly. Centres need to continue to emphasise that time is not a decimal base. The use of a number line to work out the bounds was very successful when used. In part (b) many students indicated that the average speed would drop and this was sufficient for the award of the mark. Whilst others were too vague only referring to ‘it would change’ and not specifying what would change or indeed how it would change.

  Text version

  A train travelled along a track in 110 minutes, correct to the nearest 5 minutes. Jake finds out that the track is 270 km long. He assumes that the track has been measured correct to the nearest 10 km. (a) Could the average speed of the train have been greater than 160 km/h? You must show how you get your answer. Jake's assumption was wrong. The track was measured correct to the nearest 5 km. (b) Explain how this could affect your decision in part (a).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q1 · 1 mark

  1 mark

  1

  
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  Text version

  Write the following numbers in order of size.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q2 · 1 mark

  1 mark

  2

  
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  Text version

  Write 0.037 as a fraction.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q4 · 2 marks

  2 marks

  4

  
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  Text version

  Write down all the factors of 20

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q5 · 3 marks

  3 marks

  5

  
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  Text version

  Tanya needs to buy chocolate bars for all the children in Year 7

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q8 · 2 marks

  2 marks

  8

  
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  Text version

  Work out 15% of 80

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q10 · 1 mark

  1 mark

  10

  
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  Text version

  There are only black pens and green pens in a box.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q11 · 2 marks

  2 marks

  11

  
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  Text version

  Sally has three tiles.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q13 · 4 marks

  4 marks

  13

  
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  Text version

  Paul organised an event for a charity. Each ticket for the event cost £19.95 Paul sold 395 tickets. Paul paid costs of £6000 He gave all money left to the charity.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q16 · 5 marks

  5 marks

  16

  
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  Text version

  Sam buys 20 boxes of oranges.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q18 · 4 marks

  4 marks

  18

  
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  Text version

  Work out each expression.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q21 · 3 marks

  3 marks

  21

  
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  Text version

  Work out 6.34 × 5.2

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1F · Q25 · 4 marks

  4 marks

  25

  
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  Text version

  In a company, the ratio of the number of men to the number of women is 3:2

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1H · Q1 · 3 marks

  3 marks

  1

  
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  Text version

  Work out 6.34 × 5.2

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1H · Q9 · 2 marks

  2 marks

  9

  
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  Text version

  Work out the value of (9 × 10⁻⁴) × (3 × 10⁷).

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1H · Q10 · 3 marks

  3 marks

  10

  
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  Text version

  Evaluate each expression.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1H · Q11 · 4 marks

  4 marks

  11

  
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  Text version

  One uranium atom has a mass of 3.95 × 10–22 grams.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 1H · Q23 · 3 marks

  3 marks

  23

  
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  Text version

  Show that 1/(1 + 1/√2) can be written as 2 − √2.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  Text version

  Write down the value of the 3 in 4376.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Text version

  Write 7/16 as a decimal.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q3 · 1 mark

  1 mark

  3

  
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  Text version

  Here is a list of numbers

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q4 · 2 marks

  2 marks

  4

  
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  Text version

  Find (2.8 − 0.45)² + ∛5.832.

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• Edexcel 1MA1 · sample · Paper 2F · Q6 · 3 marks

  3 marks

  6

  
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  Text version

  Jan writes down

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• Edexcel 1MA1 · sample · Paper 2F · Q7 · 2 marks

  2 marks

  7

  
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  Text version

  ABCD is a square.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q11 · 3 marks

  3 marks

  11

  
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  Text version

  Adam says, “When you multiply an even number by an odd number the answer is always an odd number.”

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q14 · 5 marks

  5 marks

  14

  
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  Text version

  A cuboid tank is full of oil; an empty cuboid container will receive the unspilled oil.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q16 · 2 marks

  2 marks

  16

  
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  Text version

  Find the Highest Common Factor (HCF) of 24 and 60

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q19 · 3 marks

  3 marks

  19

  
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  Text version

  Jane made some almond biscuits which she sold at a fete.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2F · Q22 · 5 marks

  5 marks

  22

  
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  Text version

  A tin of varnish costs £15. A 6 m by 11 m floor is to be covered. Helen assumes each tin covers 12 m².

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2H · Q1 · 3 marks

  3 marks

  1

  
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  Text version

  Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 2H · Q4 · 3 marks

  3 marks

  4

  
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  Text version

  A motorway sign gives a distance and average journey time.

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• Edexcel 1MA1 · sample · Paper 2H · Q15 · 2 marks

  2 marks

  15

  
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  Text version

  The decimal 0.2 with recurring digit 5 is 0.25555…

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• Edexcel 1MA1 · sample · Paper 2H · Q18 · 5 marks

  5 marks

  18

  
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  Text version

  m = √s/t, where s = 3.47 (3 s.f.) and t = 8.132 (4 s.f.).

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• Edexcel 1MA1 · sample · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  Text version

  Write 2148 correct to the nearest 100

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 3F · Q3 · 3 marks

  3 marks

  3

  
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  Text version

  There are 6760 people at a rugby match. Of the children, 1/4 are girls.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 3F · Q5 · 3 marks

  3 marks

  5

  
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  Text version

  Faiza buys

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• Edexcel 1MA1 · sample · Paper 3F · Q10 · 2 marks

  2 marks

  10

  
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  Text version

  Here are four numbers.

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• Edexcel 1MA1 · sample · Paper 3F · Q11 · 2 marks

  2 marks

  11

  
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  Text version

  Here is a list of five numbers. 14 15 16 17 18 From the list,

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• Edexcel 1MA1 · sample · Paper 3F · Q15 · 3 marks

  3 marks

  15

  
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  Text version

  There are 25 boys and 32 girls in a club.

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• Edexcel 1MA1 · sample · Paper 3F · Q19 · 5 marks

  5 marks

  19

  
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  Text version

  Asif is going on holiday to Turkey. The exchange rate is £1 = 3.5601 lira. Asif changes £550 to lira.

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• Edexcel 1MA1 · sample · Paper 3H · Q2 · 5 marks

  5 marks

  2

  
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  Text version

  Asif is going on holiday to Turkey. The exchange rate is £1 = 3.5601 lira. Asif changes £550 to lira.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 3H · Q5 · 5 marks

  5 marks

  5

  
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  Text version

  Henry is thinking of having a water meter.

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• Edexcel 1MA1 · sample · Paper 3H · Q6 · 3 marks

  3 marks

  6

  
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  Text version

  Liz buys packets of coloured buttons.

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• Edexcel 1MA1 · sample · Paper 3H · Q8 · 1 mark

  1 mark

  8

  
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  Text version

  Write 0.000068 in standard form.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · sample · Paper 3H · Q15 · 3 marks

  3 marks

  15

  
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  Text version

  There are 17 men and 26 women in a choir. The choir is going to sing at a concert. One of the men and one of the women are going to be chosen to make a pair to sing the first song.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · specimen2 · Paper 1F · Q3 · 3 marks

  3 marks

  3

  
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  Text version

  Work out each value.

  Pearson does not publish a direct link to this question paper.

• Edexcel 1MA1 · specimen2 · Paper 1F · Q9 · 5 marks

  5 marks

  9

  
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  Text version

  The five fractions are 2/8, 10/40, 12/48, 5/24 and 20/80.

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• Edexcel 1MA1 · specimen2 · Paper 1F · Q11 · 2 marks

  2 marks

  11

  
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  Text version

  Write down three different multiples of 4 that add up to 40.

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• Edexcel 1MA1 · specimen2 · Paper 1F · Q12 · 4 marks

  4 marks

  12

  
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  Text version

  Helen has 80 books. Fiction : non-fiction = 3 : 1. Every book normally costs £10; every non-fiction book is sold at half price. She sells all 80 books.

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• Edexcel 1MA1 · specimen2 · Paper 1F · Q13 · 3 marks

  3 marks

  13

  
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  Text version

  Ryan and Carl each earn basic pay of £60 per day. Ryan gets a bonus of 25% of basic pay; Carl gets £20 in tips.

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• Edexcel 1MA1 · specimen2 · Paper 1F · Q23 · 4 marks

  4 marks

  23

  
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  Text version

  One sheet of A3 card has area 1/8 m² and mass per unit area 160 g/m².

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• Edexcel 1MA1 · specimen2 · Paper 1F · Q25 · 3 marks

  3 marks

  25

  
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  Text version

  Write 504 as a product of powers of its prime factors.

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q5 · 4 marks

  4 marks

  5

  
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  One sheet of A3 card has area 1/8 m² and mass per unit area 160 g/m².

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q6 · 4 marks

  4 marks

  6

  
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  Use each of 3, 4, 5 and 6 once where required.

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q7 · 4 marks

  4 marks

  7

  
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  A microwave is one-third off and sells for £90. A combination oven is 40% off and sells for £84.

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q8 · 3 marks

  3 marks

  8

  
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  Estimate √(4.98 + 2.16 × 7.35).

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q14 · 2 marks

  2 marks

  14

  
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  Show that ((4−√3)(4+√3))/√13 simplifies to √13.

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• Edexcel 1MA1 · specimen2 · Paper 1H · Q15 · 5 marks

  5 marks

  15

  
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  Evaluate or solve.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q1 · 1 mark

  1 mark

  1

  
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  Write 6819 to nearest 1000.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q2 · 1 mark

  1 mark

  2

  
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  Order the temperatures 7°C, −2°C, 10°C, −5°C, 3°C.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q3 · 2 marks

  2 marks

  3

  
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  Write 0.075 as a fraction in simplest form.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q4 · 1 mark

  1 mark

  4

  
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  Find 5⁴.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q5 · 2 marks

  2 marks

  5

  
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  One in three of the 720,000 babies born last year is expected to live to 100.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q6 · 2 marks

  2 marks

  6

  
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  A timetable gives these Swindon-to-London departure and arrival times: 06:10–07:16, 06:27–07:32, 06:41–07:44, 06:58–08:02, 07:01–08:07, 07:17–08:14 and 07:28–08:33.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q7 · 4 marks

  4 marks

  7

  
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  Tracy buys 2 coffees at £1.10 each, 3 teas at £0.95 each and 5 sandwiches at £2.15 each. The total cost is shared equally among 5 people.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q12 · 3 marks

  3 marks

  12

  
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  Martin has 8 pints of soup and fills 24 bowls with 0.3 pint in each bowl.

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• Edexcel 1MA1 · specimen2 · Paper 2F · Q21 · 2 marks

  2 marks

  21

  
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  Find HCF of 32,48,72.

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• Edexcel 1MA1 · specimen2 · Paper 2H · Q12 · 5 marks

  5 marks

  12

  
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  Answer both counting questions.

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• Edexcel 1MA1 · specimen2 · Paper 2H · Q16 · 2 marks

  2 marks

  16

  
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  Evaluate each expression.

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• Edexcel 1MA1 · specimen2 · Paper 2H · Q17 · 4 marks

  4 marks

  17

  
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  A right-angled triangle has hypotenuse a = 8.3 cm, correct to the nearest millimetre, and one leg b = 6.1 cm, correct to the nearest millimetre. The other leg has length c.

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• Edexcel 1MA1 · specimen2 · Paper 2H · Q18 · 3 marks

  3 marks

  18

  
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  Simplify (√a+2√b)(√a−2√b).

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q1 · 1 mark

  1 mark

  1

  
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  Change 4500 g to kilograms.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q2 · 1 mark

  1 mark

  2

  
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  Write 0.19 as a fraction.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q3 · 1 mark

  1 mark

  3

  
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  Write down an even number that is a multiple of 7.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q6 · 5 marks

  5 marks

  6

  
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  Coffee is sold in 200 g jars. Ben makes 8 cups each day and wants enough for 28 days.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q7 · 2 marks

  2 marks

  7

  
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  Write down three different factors of 18 that add to a prime number.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q8 · 2 marks

  2 marks

  8

  
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  A model plane is 17 cm long at scale 1:200.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q9 · 3 marks

  3 marks

  9

  
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  Evaluate both expressions.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q12 · 3 marks

  3 marks

  12

  
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  Ibrar buys 3 kg apples and 0.4 kg mushrooms for £6.93. Apples cost £1.95 per kg.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q17 · 3 marks

  3 marks

  17

  
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  Three students take a test marked out of 75. Amelia scores 56%, Hayden scores 8/15 and Sophie scores 43/75.

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• Edexcel 1MA1 · specimen2 · Paper 3F · Q25 · 2 marks

  2 marks

  25

  
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  Jim rounds a number, x, to one decimal place. The result is 7.2.

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• Edexcel 1MA1 · specimen2 · Paper 3H · Q4 · 2 marks

  2 marks

  4

  
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  Jim rounds a number, x, to one decimal place. The result is 7.2.

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• Edexcel 1MA1 · specimen2 · Paper 3H · Q10 · 3 marks

  3 marks

  10

  
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  The surface gravity of a planet is given by g = 6.67 × 10⁻¹¹m/r², where m kilograms is the mass of the planet and r metres is its radius. For Earth, m = 5.98 × 10²⁴ and r = 6.378 × 10⁶. For Jupiter, m = 1.90 × 10²⁷ and r = 7.149 × 10⁷.

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• Edexcel 1MA1 · specimen2 · Paper 3H · Q19 · 2 marks

  2 marks

  19

  
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  The recurring decimal is 0.3181818…, where the digits 1 and 8 recur after the initial 3.

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