Pearson Edexcel GCSE Maths · Topic R
Ratio, percentages, compound measures and direct or inverse proportion. Every question below is the real Pearson question as it is printed on the paper, with its mark scheme. Then practise with the original printable pack.
Tier
Total recorded: 0 of 65 marks
20 original questions written in the style of the real papers. Attempt one on paper, then reveal the mark scheme and award yourself the marks. Marks you award are saved in this browser against that question.
1
In a car park there are 24 cars and 15 vans and no other vehicles.
(a)
(1)
(b)
(2)
(Total for Question 1 is 3 marks)
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2
This question is about writing ratios in their simplest form.
(a)
(1)
(b)
(2)
(Total for Question 2 is 3 marks)
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3
A tank is being filled with water. The volume of water V litres in the tank after t minutes is shown by a straight-line graph that passes through the origin and the point (5, 40).
(a)
(2)
(b)
(1)
(Total for Question 3 is 3 marks)
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4
The depth of water d cm in a container t seconds after filling begins is shown by a curve. The tangent to the curve at the point where t = 6 passes through the points (2, 10) and (10, 46).
(2)
(Total for Question 4 is 2 marks)
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5
A train travels 210 km in 1 hour 45 minutes.
(a)
(2)
(b)
(1)
(Total for Question 5 is 3 marks)
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6
A piece of oak has mass 480 g and density 0.75 g/cm³.
(2)
(Total for Question 6 is 2 marks)
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7
A jacket normally costs £80. In a sale the price is reduced to £68.
(a)
(2)
(b)
(1)
(Total for Question 7 is 3 marks)
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8
In a sale, all normal prices are reduced by 20%. The sale price of a coat is £72.
(3)
(Total for Question 8 is 3 marks)
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9
£4500 is shared between Amy, Ben and Carl in the ratio 2 : 3 : 4.
(a)
(2)
(b)
(1)
(Total for Question 9 is 3 marks)
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10
This question is about converting between units.
(a)
(1)
(b)
(2)
(Total for Question 10 is 3 marks)
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11
£2000 is invested in an account paying 3% per year compound interest.
(a)
(2)
(b)
(1)
(Total for Question 11 is 3 marks)
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12
y is directly proportional to x. When x = 4, y = 20.
(a)
(2)
(b)
(1)
(c)
(1)
(Total for Question 12 is 4 marks)
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13
Two shops sell the same brand of rice. Shop A sells a 2 kg bag for £3.20. Shop B sells a 5 kg bag for £7.50, marked '20% extra free' (so the bag contains 20% more rice than 5 kg at no extra cost).
(a)
(4)
(b)
(2)
(Total for Question 13 is 6 marks)
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14
£650 is invested in an account paying 4% simple interest per year.
(a)
(2)
(b)
(1)
(Total for Question 14 is 3 marks)
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15
To make a shade of green paint, blue paint and yellow paint are mixed in the ratio 5 : 3. To make some green paint, 40 litres of blue paint is used.
(a)
(2)
(b)
(1)
(Total for Question 15 is 3 marks)
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16
A 750 g box of cereal costs £2.40. A 1.2 kg box of the same cereal costs £3.60.
(3)
(Total for Question 16 is 3 marks)
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17
Here are the ingredients needed to make 8 flapjacks: 200 g oats, 120 g butter, 3 tablespoons of syrup.
(a)
(2)
(b)
(1)
(Total for Question 17 is 3 marks)
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18
A map is drawn to a scale of 1 : 25000.
(a)
(2)
(b)
(2)
(Total for Question 18 is 4 marks)
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19
A shop buys a bicycle for £120 and later sells it for £150.
(a)
(2)
(b)
(2)
(Total for Question 19 is 4 marks)
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20
The numbers of visitors to a museum in six consecutive months were: January 120, February 135, March 150, April 145, May 170, June 185.
(a)
(2)
(b)
(2)
(Total for Question 20 is 4 marks)
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619 questions shown as printed, 39 reference-only · newest series first
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 · Q1 · 1 mark
1 mark
Examiner report
The majority of learners were able to write 25% as a decimal.
Write 25% as a decimal.
Edexcel 1MA1 · November 2024 · Paper 1F · Q3 · 1 mark
1 mark
Examiner report
Most learners knew that 1cm = 10mm and were able to use this to successfully convert 15 centimetres to millimetres. There were a significant minority of learners who incorrectly used the conversion factor and gave an answer of 1.5 millimetres having divided rather than multiplied by 10. A number of students also incorrectly used a multiplier of 100 rather than 10, giving an answer of 1500.
Change 15 centimetres into millimetres.
Edexcel 1MA1 · November 2024 · Paper 1F · Q9 · 7 marks
7 marks
Examiner report
In part (a) learners were asked to use the information provided regarding the total number of stickers in order to complete the bar chart. This was answered correctly by the majority of learners. Where answers were seen that were not fully correct there was often working shown which allowed for the award of part marks. Common errors included reading one of the two given bar heights incorrectly, this was often the bar height for the football players which was sometimes incorrectly given as 16 or 18. In part (b) learners were asked to give the fraction of the 40 stickers that are stickers of tennis players and to give the fraction in its simplest form. The majority of learners were able to identify the required fraction and correctly simplify this to give the required answer. The most common reason for an incorrect final answer was to either give the unsimplified fraction or where errors were seen in the attempts to simplify the fraction. A small minority gave the fraction of stickers that were football players rather than the fraction that were tennis players. Part (c) of the question required learners to convert between ratio and fraction notation. The majority of learners were able to correctly complete the conversion. The most common incorrect answer was where learners did not sum the parts of the ratio to obtain the denominator of the fraction. In part (d) learners were asked to give the ratio 5: 4 in the form : 1. This proved challenging for learners with only a minority able to give the correct answer. Some learners made an attempt to write the given ratio in the required form but made errors when attempting to calculate 5 ÷ 4, others started the process to divide but did not reach the form : 1. Other incorrect responses included 1:0.8 (the form 1: ) and answers of 1.25 without n= or any attempt to write as a ratio. There were a significant number of incorrect answers of 5: 1 or where n had been introduced into the ratio in some way, for example 5: 4.
Milly has stickers of tennis, football and cricket players only. A bar chart shows 12 tennis-player stickers and 17 football-player stickers. She has 40 stickers in total. Ewan has large and small stickers in the ratio 5:4.
Edexcel 1MA1 · November 2024 · Paper 1F · Q17 · 3 marks
3 marks
Examiner report
Around half of learners were able to make some progress with this question, although only a minority were able to give the decision of ‘no’ together with correct supporting figures. Where fully correct responses were seen these generally worked from the required ratio for the paint and found the volumes of each paint colour needed to make 24 litres. Some learners made a start to a correct process by finding that 24 ÷ 8 = 3 or, having recognised that there were 24 litres of paints that could be mixed, by starting a process to scale down the ratio of the available paints (12:7:5) to compare it to the required ratio (4:3:1). In some cases, learners had made a start to a process, often by showing 12 ÷ 4 = 3, or appeared to have come to the correct conclusion, but did not show the figures to support their decision. Incorrect responses often identified that there were 24 litres of paint available to mix and concluded that there was sufficient paint available without considering the required ratio for the green paint. Many got the correct answer of 12:9:3 but then incorrectly stated that they needed more white paint.
Gita wants to make 24 litres of green paint by mixing blue, yellow and white paint in the ratio 4:3:1. She has 12 litres of blue, 7 litres of yellow and 5 litres of white paint.
Edexcel 1MA1 · November 2024 · Paper 1F · Q22 · 4 marks
4 marks
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.
A car travelled 4.96 miles at an average speed of 30.4 miles per hour.
Edexcel 1MA1 · November 2024 · Paper 1F · Q24 · 1 mark
1 mark
Examiner report
This question was very poorly answered with few learners able to give an explanation that related to rate of change of volume. Incorrect answers often described the relationship between the volume and time rather than interpreting the gradient, for example ‘as time increases the volume of water in the tank decreases’ or ‘negative correlation’. Others incorrectly described the change over a number of seconds or referenced specific values from the graph.
A graph shows the volume V litres of water in a tank against time t seconds.
Edexcel 1MA1 · November 2024 · Paper 1H · Q5 · 4 marks
4 marks
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).
A car travelled 4.96 miles at 30.4 miles per hour.
Edexcel 1MA1 · November 2024 · Paper 1H · Q7 · 1 mark
1 mark
Examiner report
This question was not answered well with many learners unable to explain what the gradient of the graph represents. Correct explanations contained a reference to 'rate' or 'speed' or 'how fast' or 'each second', for example ‘the rate at which the tank is losing water’. Some of the incorrect explanations did refer to the volume of water and to time but described what the graph shows, not what the gradient represents. Explanations such as ‘the volume of water decreases as time increases’ and ‘the volume of water leaving the tank in 50 seconds’ were very common. There were also many incorrect explanations such as ‘negative correlation’ and ‘direct proportion’ that did not mention the context at all.
A graph shows tank-water volume V litres against time t seconds.
Edexcel 1MA1 · November 2024 · Paper 1H · Q8 · 3 marks
3 marks
Examiner report
Many learners made a good start, most often dividing 720 by 80 to find the area of the base of the rectangle and this earned them the first process mark. To complete the solution, they needed to divide the area of the base by 2 to find the length of the rectangle. A good proportion managed to work out the length as 4.5 cm and scored full marks. Some lost the accuracy mark due to an arithmetic error, most commonly 720 ÷ 80 = 90, but they could still gain the second process mark for dividing by 2. After finding the area of the base many learners made no further correct progress and some gave 9 as the final answer or multiplied by 2 instead of dividing by 2. It was very common to see b × h ÷ 2 being used in an attempt to find the length of the base. Presumably this was prompted by the triangular cross section of the prism. Some learners used the pressure formula incorrectly, working out 720 × 80, and gained no marks.
A triangular prism rests on a rectangular face of width 2 m. It exerts 720 N and pressure is 80 N/m². pressure = force/area.
Edexcel 1MA1 · November 2024 · Paper 1H · Q9 · 6 marks
6 marks
Examiner report
In part (a) a good proportion of learners gained at least one mark but there were a large number who knew what a box plot looks like but couldn't find the necessary values from the cumulative frequency graph and scored no marks. Those that had a good understanding usually gained three marks for a fully correct box plot although some lost a mark because of inaccuracies in plotting values. When two marks were awarded for a box drawn and three correctly plotted values these values were usually the lowest mark, the highest mark and the median. Some learners earned just one mark for identifying one of the three values needed which tended to be the median. Box plots with the LQ, median and UQ plotted at 15, 30, 45 or at 20, 40, 60, i.e. quarters of the cumulative frequency or mark range, were often seen. In part (b) many learners gained one mark for working out 30% of 60 as 18 or for reading a value from the graph at mark = 40 but fully correct solutions were not as common as might have been expected. Some worked out 30% of 60 but failed to obtain a comparative statistic and errors were sometimes made when reading from the graph, most often 44 instead of 42 for the cumulative frequency at a mark of 40. Some interpreted the value 42 read from the graph as the number who passed the test which therefore led to an incorrect conclusion being drawn. A significant number made no attempt to use the graph. It was sometimes not clear whether or not a value had been read from the graph. Learners should be encouraged to show a clear method on the graph if they are reading a value from it.
EXCLUDED FROM TEXT-ONLY STUDENT DELIVERY: the official item requires readings from a cumulative-frequency curve and drawing a box plot on a blank scale. The batch schema has no faithful graph/image field. The graph represents marks for 60 students; the lowest mark is 8 and the highest mark is 74.
Edexcel 1MA1 · November 2024 · Paper 1H · Q12 · 4 marks
4 marks
Examiner report
It was pleasing to see some fully correct solutions but, overall, this question was answered very poorly with relatively few learners showing that they understood the relationships between lengths, areas and volumes in similar solids. Starting the process to find the ratio of the radius of A to the radius of B by finding 3 64 or 3 125 gained the first mark and some learners reached the ratio 4 : 5. The second mark was awarded for using the information about the radius of sphere C and working out 5 ÷ 2 or for starting to work with area and working out 42. A process to find the ratio of the area of A to the area of C, such as 42 : 2.52, was needed for the third mark but few were able to get this far. Some of those that did gave 16 : 6.25 as the final answer and were not awarded the accuracy mark because the question asked for an answer in the form a : b where a and b are integers. A successful route used by a few learners was to combine the ratios 4 : 5 and 2 : 1, giving the ratio of the radii as 8 : 10 : 5 from which they could easily see that the required ratio is 82 : 52. Many learners could not make a correct start. It was common to see 125, the volume of sphere B, divided by 2 and then 64 : 62.5 given as the final answer. Since the question involved three spheres some learners attempted to use the formulae for the surface area or volume of a sphere.
Solid spheres A and B have volumes 64 cm³ and 125 cm³. Sphere C's radius is 50% of sphere B's radius.
Edexcel 1MA1 · November 2024 · Paper 2F · Q1 · 1 mark
1 mark
Examiner report
The opening question was accessible to all learners and was well answered with very few learners not being awarded the mark, often due to writing 17% as a decimal rather than a fraction or having an incorrect denominator such as 10 or 1000 with 17 as the numerator.
Write 17% as a fraction.
Edexcel 1MA1 · November 2024 · Paper 2F · Q9 · 2 marks
2 marks
Examiner report
Success with this familiar style of question on writing figures in a ratio in its simplest form was evident, with many fully correct responses being seen. Most learners correctly showed 90 : 150 and gained the first mark. They usually then tried to simplify it, with varying degrees of success. Some made errors in the simplification, others stopped too early, and others carried on to successfully reach 3 : 5 for full marks. A small number of learners seemed unaware of correct ratio notation and, although some began by writing a correct starting ratio, chose to then write it as a fraction and were then unable to gain any marks. It was quite rare for learners to write the numbers the wrong way round. Where they did this, they could gain a maximum of 1 mark if they simplified all the way to 5 : 3.
A bag has 90 red and 150 yellow counters.
Edexcel 1MA1 · November 2024 · Paper 2F · Q12 · 4 marks
4 marks
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.
180 concert tickets are sold; 60% are child tickets at £8 each. Total revenue is £1944.
Edexcel 1MA1 · November 2024 · Paper 2F · Q15 · 3 marks
3 marks
Examiner report
Performance in this question assessing the use of a ratio scale was poor but in line with similar questions in previous series and fully correct responses were rarely seen. A large number of learners were able to get started, usually by using 14 cm with the scale partially to gain the first mark but many were then unable to convert between cm and km, often just dividing by 1000 and not able to show an understanding that 25 000 represented cm rather than metres. When full marks were awarded, learners often showed the required division by 100 000 in stages of dividing by 100 followed by 1000. Some learners attempted no conversion at all. In some cases, there was confusion about how to use the scale, with wrong attempts such as 25000 ÷ 14 as a first step but this was less commonly seen.
Map scale is 1:25000. A road is 14 cm on the map.
Edexcel 1MA1 · November 2024 · Paper 2F · Q17 · 6 marks
6 marks
Examiner report
Part (a) of this question was well answered, with many learners successfully performing the percentage decrease accurately. Most began by calculating the 7% and then subtracting it, rather than working directly with 93% but both methods were acceptable. The most common cause of the loss of marks was to work with percentage methods that were inefficient and avoided use of the calculator such as using partitioning to build-up towards 7%, often via amounts such as 10%, 5% and 1%. Such methods are frequently used and often lead to inaccurate values being calculated compared to learners using a more efficient method such as decimal multipliers. Part (b) was poorly answered but in line with performance in questions from previous series using this skill. Whilst some learners were able to find the bonus of £400 which also gained the first mark, many were then unable to continue with a correct calculation to demonstrate that £400 represented 5% and use this to work back towards 100%. A very common error was to find 20% of 400, and these responses only gained the first mark, but it was more common to see learners gain no credit due to either working out 5% of £1700 and adding it on or finding 5% of £2100 and subtracting it. The most successful learners were those who wrote statements such as £400 = 5% and then continued to either divide by 5 then multiply by 100 or used a build-up method to show £800 = 10% and continued to build until 100% was reached.
Emma's £285 insurance falls by 7%. Peter earns £1700 plus a 5%-of-sales bonus and was paid £2100.
Edexcel 1MA1 · November 2024 · Paper 2F · Q22 · 3 marks
3 marks
Examiner report
A large range of approaches to find comparable figures were possible and seen in this best value for money involving a currency conversion question, and quite often learners lost track of what they were doing and did not complete the processes required and responses gaining full marks were rarely seen. Partial marks, commonly 1 mark, was very common for a correct starting calculation and this was most often for a process to perform a currency conversion. Despite correct use of the conversion factor, the majority of learners were not able to use direct proportion effectively or at all in order to find the cost for the same weights in both places. The most successful weight comparisons made were learners who used a unitary method to find comparative figures for either 1 gram, 100 grams or 1800 grams. Some learners attempted to convert the price and then simply double the cost in London to compare 400 grams to 360 grams but this kind of comparison was often insufficient to gain full credit. Units were not required for the final answer, but if stated they did need to be correct to gain the last mark. It should also be noted that the working for this question was often presented in a very messy and unstructured way that was often difficult to follow, particularly when a variety of approaches were shown in a single response with no clear indication as to which method the candidate wished to be marked as their final answer. In such cases, the general marking guidance is to mark each method and then award the lower number of marks. Premature rounding or truncation was also evident but was not penalised if correct to 2 significant figures.
London: 200 g Choci bar costs £3.50. Zurich: 360 g costs 7.20 Swiss francs. £1=1.25 Swiss francs.
Edexcel 1MA1 · November 2024 · Paper 2F · Q25 · 4 marks
4 marks
Examiner report
Whilst the majority attempted this question learners historically find this particular topic more challenging and this series is no different to previous series. Whilst, many learners were awarded the first mark for a suitable starting process to find one or both increases via subtraction, many also continued to use the values found incorrectly and evidence suggests that many learners are not confident in the process to calculate a percentage increase. The most commonly seen incorrect next step was simply to compare the 9 and the 1 by subtracting them from each other, dividing them or then finding 9% and 1% of the old or new prices. Although the question asked learners to compare percentage changes, alternative acceptable methods seen included working with decimal equivalents throughout. Some learners were also unsure whether to find the percentages of the old price or the new price, performing incorrect divisions such as 9 ÷ 85 or 1 ÷ 66 and so could not gain more than the first mark.
First-class stamps rose 76p to 85p; second-class rose 65p to 66p. Filip says the first percentage increase is more than 7 times the second.
Edexcel 1MA1 · November 2024 · Paper 2F · Q28 · 3 marks
3 marks
Examiner report
Although it was the last question on the paper, many learners attempted it and very few blank responses were seen. The majority were not able to calculate the volume of the cylinder correctly, with a wide variety of wrong attempts, mainly calculating the area or circumference of the circle instead, seen. However, when marks were awarded, it was often a single mark for realising the need to divide the mass by the volume, and they were able to gain the second mark for showing this even when the first mark was not awarded. Work on finding volumes of cylinders and prisms would be helpful for future exam practice. Summary Based on their performance on this paper, learners should: ensure they are well-practised in efficient use of their calculator, especially unfamiliar functions such as standard form read questions carefully, including checking whether the magnitude of an answer is sensible, units are appropriate, and the level of accuracy required is shown show every stage of working, particularly if the question specifically requests this practice questions involving percentage change practice questions requiring learners to form algebraic expressions use formal methods when working with percentages remember to cross out incorrect work or positively identify their chosen method when using a range of approaches to avoid losing marks due to choice.
A steel cylinder has radius 3 cm, height 10 cm and mass 2250 g.
Edexcel 1MA1 · November 2024 · Paper 2H · Q3 · 3 marks
3 marks
Examiner report
The first problem solving question on the paper required learners to compare the cost of a chocolate bar in two different cities. This required them to find comparable amounts by weight or per unit cost, and to use a currency exchange. The first mark was for a suitable start to the problem and could be gained by either converting one cost correctly, or by converting one item’s weight, or by finding the weight per unit cost in one city. Many learners gained this first mark, which was really pleasing to see. A very good proportion were then able to gain a second mark for the process to find comparable figures. This required the amount to be comparable as well as the currency. This was a process mark so could be awarded even if arithmetic errors had occurred, providing clear working was seen. As mentioned in the introduction, learners are continuing to improve on this front and clear annotations were often provided. The final mark was for having accurate comparable figures along with a correct conclusion. Conclusions were typically correct, except when learners working with the weight per unit cost. In this case the higher figure showed the better value and many who used this method misinterpreted this and gave London as their response.
London: 200g bar £3.50. Zurich: 360g bar 7.20 francs. £1=1.25 francs.
Edexcel 1MA1 · November 2024 · Paper 2H · Q6 · 4 marks
4 marks
Examiner report
This was the second problem solving question and required learners to compare two percentage increases. It was generally answered well by most. The first mark was a simple one for either finding a correct difference or for a correct proportion. The next two marks were for finding, or showing the process to find, one, then both, correct percentage changes. Many were able to gain one, if not both, of these marks. The errors that stopped some were either choosing the new, rather than original, value as the denominator, or for those who didn’t find the subtraction originally, for forgetting to subtract 100 from their percentage. For those who gained the 3 P marks, the C mark often followed for a correct comparison and conclusion. However, some candidates followed a correct comparison with an incorrect conclusion that Filip was wrong, muddling the interpretation of what they had found and that which they had been asked. Early rounding or truncating also could lead to losing this mark as candidates were unable to draw the correct conclusion, for example, rounding 11.84 to 12 and 1.53 to 2, and dividing these values. This meant they thought it was only 6 times greater and therefore Filip was wrong. Learners should be reminded of the risk of premature rounding.
Stamps rose 76p→85p and 65p→66p. Claim: first percentage rise exceeds seven times second.
Edexcel 1MA1 · November 2024 · Paper 2H · Q12 · 5 marks
5 marks
Examiner report
This shape problem had 4 stages, and each one was available to candidates, even with prior errors. The first step was to find the volume of the cylinder, which many struggled to do. There were various errors from finding the surface area to multiplying the radius by the height. The next mark was for using the volume and given density to find the mass. This value was then to be used to find the volume of the cube using a given density. The final step was to cube root the volume to find the length of the cube. Although many struggled with the initial volume, their working was clear enough to establish that the value they used for the next step was what they believed to be the volume. Given this was the case the second mark could be gained, and often was. As was the case with the next mark for the second use of the density formula. The final process mark for cube rooting, a bit like the first, was less often awarded. It was quite common to see candidates dividing by 3 or even 6 as a last step or square rooting.
Steel cylinder radius 3 cm, height 8 cm, density 7.86 g/cm³. Brass cube side h, density 8.5 g/cm³. Masses equal.
Edexcel 1MA1 · November 2024 · Paper 2H · Q13 · 5 marks
5 marks
Examiner report
Much like question 4, in part (a) learners often struggled to articulate themselves clearly enough to gain this mark. Learners had two real avenues for a successful response. The first, and most common, was to work with y kx and show the value of k was not constant. To do this they needed to complete at least 2 calculations, and this was often not done, meaning the mark was not awarded. A second approach was to realise that the graph of y kx should pass through the origin, and that is not the case here. Fewer learners seemed to use this approach. Part (b)(i) was a much more familiar question, and learners experienced more success. Many gaining at least one for setting up a correct equation, and then a good number using this to find the value of k, many of these then went on to gain the third mark too. The most common error seen was for learners to either just work with t, and not t , or when rearranging they worked out 140 instead of 140 . In part (b)(ii) the most common wrong graph was a direct proportion graph for a linear relationship, but various other incorrect sketches of familiar shape were seen.
Table: (x,y)=(2,0),(4,4),(6,8),(8,12). Also w∝√t and w=140 at t=64.
Edexcel 1MA1 · November 2024 · Paper 2H · Q20 · 3 marks
3 marks
Examiner report
Although there were not as many steps as we often see on a 3D trigonometry problem here, many candidates struggled to make a start to the question. The first step to find FC proved conceptually too difficult and many either didn’t attempt, or used a method that would lead to VC not FC. This could then lead to FC with a second step using Pythagoras, but this was normally missing. If learners did find FC, they then had to use the ratio to find MC along with Pythagoras to form an equation for the side length. Alternatively, they could use MC along with either the 60 or 30 angle and trigonometry. Neither were seen often, but those who got this far generally gained the accuracy mark.
Pyramid VABC has equilateral base ABC. M midpoint AB; F on MC with MF:FC=1:2; V vertically above F; VA=VB=VC; VF=8 cm; angle VCM=52°.
Edexcel 1MA1 · November 2024 · Paper 3F · Q9 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · November 2024 · Paper 3F · Q11 · 4 marks
4 marks
Examiner report
In part (a), a good number were able to gain 1 mark with a correct answer of 16. The most common incorrect answer was 15.2, presumably from misinterpreting the scale on the horizontal axis. Part (b) was not answered well with few learners gaining 3 marks. To make progress readings needed to be taken from the graph that could be used to convert 50 kilometres into miles and a variety of different ways of doing this were seen. A tolerance of one small square was allowed for the reading but it was still common to see inaccurate readings given in the workspace. Even if inaccurate readings were taken, the second method mark could still be gained if the readings were used in a complete method and this was often seen. Some learners attempted to convert 17 miles to km and go from there; this rarely led to a correct answer but it was often awarded the first M1 for an accurate reading.
A straight conversion graph has kilometres on the horizontal axis and miles on the vertical axis. It passes through the origin and approximately through (25 kilometres, 15.5 miles). Rob drives 17 miles and then 50 kilometres.
Edexcel 1MA1 · November 2024 · Paper 3F · Q13 · 4 marks
4 marks
Examiner report
This question saw the full range of marks awarded, with a small number of learners gaining 4 marks. Of those that didn’t, a variety of errors were seen such as, no/incorrect conversions (but could still gain 1 or 2 marks for the process), correctly converting the dimensions for the crate or the box and dividing the corresponding lengths but then adding the results rather than multiplying finding the volumes for both the crate and the box but dividing box by crate instead of vice versa. Learners who tried to convert units of volume after finding the volume of the crate or a box often used the incorrect conversion.
A crate measuring 3 m by 1 m by 1.5 m is completely filled with boxes measuring 20 cm by 10 cm by 75 cm.
Edexcel 1MA1 · November 2024 · Paper 3F · Q14 · 4 marks
4 marks
Examiner report
A good number of this cohort gained 4 marks on this question and a variety of processes were seen in achieving this. The most common process seen was to find the total pay for Monday to Friday and find the rate of pay per hour for the weekend and therefore total pay for Saturday and Sunday, and then add these two together. A common error seen was to incorrectly calculate 8 12 as 4, presumably coming from incorrect use of the calculation, writing 1 without using the mixed number button, or from reading it as one half of 8. Another common error was to work out the weekend rate of pay as 8 + 8 + 4 = 20. The majority of learners could find £240 for the weekdays and then were not sure how to deal with the rate of pay for Saturday and Sunday. It is also evident from this real life question that learners are not familiar with pay rates.
Harry earns £8 per hour Monday to Friday and 1.5 times this rate at weekends. He works 6 hours each weekday, 4 hours Saturday and 3 hours Sunday.
Edexcel 1MA1 · November 2024 · Paper 3F · Q21 · 5 marks
5 marks
Examiner report
This question saw the full range of marks awarded. It was rare to see a fully correct solution. That being said, it was common to see 2 or 3 marks awarded and these could be gained in a variety of ways. Those that worked with the ratio usually gained at least the first 2 marks and possibly the third mark for either the cost to buy or amount to sell for both or the profit for one item. If a learner was not able to work with ratio, the mark scheme still allowed them to gain up to 3 marks using their values of the number of pens and the number of pencils. It was rare to see learners gain the 4th P mark and it is clear this cohort needs to work on percentage profit and finding one amount as a percentage of another in general. A common error was to reach 2490 and 1710 but divide the wrong way round when attempting to find the percentage profit.
Robyn buys 240 pens and pencils in the ratio 3:5. Pens cost 9p and sell for 11p; pencils cost 6p and sell for 10p. She sells all items.
Edexcel 1MA1 · November 2024 · Paper 3F · Q26 · 3 marks
3 marks
Examiner report
A small number of learners were able to gain 3 marks for a correct answer for the value of interest after 3 years. Of those that didn’t, it was common to see 1 or 2 marks awarded. For those that gained 2 marks, it was usually for reaching 4747.4... but failed to subtract 4500 to work out the interest. Those that gained 1 mark usually found the value of the investment or interest after 1 year or worked with simple interest and gained SCB1 for 243 or 4743. A good number of the cohort gained 0 marks with a variety of incorrect methods seen.
Peter invests £4500 for 3 years at 1.8% compound interest per year.
Edexcel 1MA1 · November 2024 · Paper 3H · Q5 · 5 marks
5 marks
Examiner report
Overall, this question was fairly well answered, though many did not achieve full marks. Most learners were able to begin a correct solution through effective use of ratio to obtain the number of pens and pencils. Those who struggled to use the ratio to get going, doing 240 ÷ 3 = 80 pens and 240 ÷ 5 = 48 pencils; often benefitted from the mark scheme using square brackets, as they could still access subsequent process marks despite not having a correct start. The lack of a systematic approach to solving the problem seemed to be an issue for some as they lost their way when calculating a value for the profit or the total bought or sold. A number of students calculated the percentage profit for each item and then added the profits to get a final answer (66.6..% + 22.2..% = 88.8..%). Some learners who successfully obtained the values 1710 and 2490 struggled to find the percentage profit correctly, performing calculations such as or
240 pens/pencils ratio 3:5; pens buy/sell 9p/11p, pencils 6p/10p.
Edexcel 1MA1 · November 2024 · Paper 3H · Q10 · 2 marks
2 marks
Examiner report
Those that recognised that this was a reverse percentage question were often successful in gaining both marks. However, there were some who calculated with 75% instead of 85%, of which those who wrote 100 – 15 = 75 could gain a mark. Many incorrect methods were seen, most commonly increasing or decreasing £46.75 by 15%.
Sale prices are 15% below normal. Amina pays £46.75.
Edexcel 1MA1 · November 2024 · Paper 3H · Q12 · 6 marks
6 marks
Examiner report
In part (a), learners generally showed a good understanding of percentage multipliers and could apply these to gain the investment value after one year. Many of these could then correctly interpret the change in the percentage for year 2 and 3 and would multiply by 1.0182 to gain the correct solution. It is worth noting that marks were lost through an incorrect presentation of the answer, for example, not rounding to two decimal places. Learners would benefit on working on appropriate rounding, especially with monetary questions. Commonly seen errors included adding the percentages together in the first instance and then using this multiplier to the power of 3. Some worked with simple interest which allowed a maximum of 1 mark. The most successful solutions were when percentage multipliers were used, when they weren’t methods often fell apart when trying to find accurate percentages of amounts prior to adding. Unsurprisingly, part (b) was found to be more challenging. A correct first step of dividing 4107 by 7500 gained the first mark. Some then struggled with correctly interpreting the sequence of steps required to obtain 74% and then subtracting this from 100%, with many learners leaving their answer as 0.74.
Rudi invests £4500: 2.4% first year, 1.8% next years. Bruna's £7500 car becomes £4107 after 2 years at x% annual depreciation.
Edexcel 1MA1 · November 2024 · Paper 3H · Q18 · 4 marks
4 marks
Examiner report
In part (a), the most successful learners went straight to 11 55 x and solved this to find x. Common errors included adding the tagged and the untagged frogs, giving an answer of 84. A greater understanding of equivalent proportion in capture-recapture would benefit many candidates in this question. Of those who had some understanding but didn’t achieve a correct answer, the ratio was usually incorrectly written as 11 x for which one mark was awarded. In part (b) the most common scoring answer was an assumption that no tags fell off, closely followed by no births or deaths. A few appeared to misunderstand that the question was asking for assumptions giving answers such as ‘all the frogs were caught’ or giving numerical values from their answer in part (a).
Capture-recapture: tag 40 Saturday; catch 55 Monday, 11 tagged.
Edexcel 1MA1 · June 2024 · Paper 1F · Q2 · 1 mark
1 mark
Examiner report
The vast majority of candidates were able to write 0.3 as a percentage. Where incorrect answers were seen the most common was 3%, although a few gave an answer of 10.
Write 0.3 as a percentage.
Edexcel 1MA1 · June 2024 · Paper 1F · Q10 · 2 marks
2 marks
Examiner report
This question differentiated well between candidates. A significant proportion were able to correctly write the ratio of the number of cows to the number of sheep in its simplest form as was required. There were also many candidates who were able to write down a correct initial ratio of 24:36 but did not successfully write this in its simplest form often due to incomplete simplification leading to answers of 12:18, 8:12, 4:6 or commonly 6:9. Some candidates struggled to simplify their initial correct ratio either due to errors in the process of simplifying (not dividing by the same amount on each side) or errors in arithmetic when attempting to simplify. It was uncommon to see answers of 3:2 or 1.5:1. Where incorrect answers were seen these often demonstrated a lack of understanding of the requirement for a ratio with fractions being the most common error, but attempts at the total numbers of animals was also seen.
There are 24 cows and 36 sheep on a farm.
Edexcel 1MA1 · June 2024 · Paper 1F · Q16 · 3 marks
3 marks
Examiner report
This question on best value based on comparison of the three pack sizes of batteries was well answered by the majority of students with many able to give the correct conclusion of ‘8 pack’ together with correct supporting values. The most common approach seen was to find the cost of one battery from each of the pack sizes, but other approaches were also commonly seen with finding the cost of 12 or 24 batteries using each pack size being other popular approaches. There were also a significant number of pairwise comparisons seen which in many cases allowed candidates to conclude the best value pack, although some pairwise comparisons did not give the information needed to reach the required decision. Where candidates did not have a fully correct response this was sometimes due to errors in arithmetic or calculation process (such as attempts to divide by 3 by halving and halving again) meaning that the correct values to compare the packs were not obtained. Some candidates wrote their divisions the wrong way around and, for example, would calculate 12 divided by 6 instead of 6 divided by 12 for the value of one battery from the 12-pack. In a minority of cases, students who found the cost of one battery for each pack could not be awarded all three marks due to inconsistency of units (i.e. 0.45p, 40p and 50p). In other cases candidates only had sufficient working to be able to compare two of the packs. A common mistake was to double the cost of the 8 pack, thinking this was comparable to the 12 pack. There were also a minority of candidates who stated the pack that they considered to be the best value without supporting working, sometimes offering a worded description of why they believed that this was the best value option. Others simply multiplied each cost by the number of batteries in the pack to come to their conclusion or merely added or subtracted the costs of the different packs.
Batteries are sold in packs of 4, in packs of 8 and in packs of 12
Edexcel 1MA1 · June 2024 · Paper 1F · Q26 · 5 marks
5 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2024 · Paper 1F · Q27 · 2 marks
2 marks
Examiner report
In this question candidates needed to perform a reverse percentage change. Only a minority of candidates were able to give a fully correct answer. When candidates correctly identified that £280 was 70% of the original amount they were often able to go on to find the normal price of the TV. The most common error was to treat the reduced amount as 100%, finding 30% of this and adding this on giving an answer of 364. Other incorrect responses included reducing 280 by 30% (answer 196) or treating £280 as 30% of the normal price. It should be noted that a fair number of candidates did not consider their answers in the context of the question, obtaining a normal price for the TV that was less than the sale price or obtaining an answer that was in the thousands.
In a sale, normal prices are reduced by 30%
Edexcel 1MA1 · June 2024 · Paper 1H · Q3 · 5 marks
5 marks
Examiner report
It was pleasing to see many fully correct solutions to the problem in part (a) and the majority of students gained at least one mark. Most students divided the floor plan into two rectangles and were usually able to work out that the area is 68 m2. A few students made simple arithmetic errors but still gained the mark for a complete process to find the total area. After finding a floor area, students needed to find out whether Petra has enough paint to cover the floor. The most common approach was to work out that the 3 tins will cover an area of 75 m2. Alternatively, some students divided their area by 10 to find the number of litres needed and multiplied 3 by 2.5 to find that Petra has 7.5 litres of paint. Some students used approximation successfully, stating the area and stating that 7 litres would be sufficient and this was less than the 7.5 litres Petra had available. Whichever approach they chose, students usually went on to give the correct decision that Petra has enough paint. The majority of students did specify a “yes/no” answer and very few lost the final mark if the rest of the work was correct. Incorrect approaches included working with the perimeter or finding the product of all the given lengths. Part (b) was also well answered with many students stating that it would not affect the answer to part (a) and giving a correct reason such as she will need less paint or she will have more paint left over. Some students made a comment about Petra needing less paint but could not be awarded the mark because they did not make a decision. If figures were included in the answer to part (b) they had to be correct for the area that had been calculated in part (a). Many students correctly found that Petra would now be able to cover 82.5 m2.
A floor is an L-shape formed from a 10 m by 8 m rectangle with a 4 m by 3 m rectangular corner removed. Petra has 3 tins containing 2.5 litres each, and she thinks each litre covers 10 m^2.
Edexcel 1MA1 · June 2024 · Paper 1H · Q5 · 4 marks
4 marks
Examiner report
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.
Sophie drives a distance of 513 kilometres on a motorway in France.
Edexcel 1MA1 · June 2024 · Paper 1H · Q7 · 5 marks
5 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2024 · Paper 1H · Q9 · 1 mark
1 mark
Examiner report
A good portion of the students found the correct value of R. Those who wrote 30% rather than 30 on the answer line were awarded the mark. Common incorrect answers were 70, 0.7 and 0.3
In a sale, the normal price of a coat is reduced by R%
Edexcel 1MA1 · June 2024 · Paper 1H · Q13 · 5 marks
5 marks
Examiner report
In part (a) the students who worked out the frequency densities and used these to draw a histogram often drew five correct bars. This alone was not sufficient for full marks because the two axes needed to be correctly scaled and labelled. Some arithmetic errors such as 22 ÷ 5 = 4.5 were made when working out the frequency densities. Students should be encouraged to show the method they use to work out each frequency density so that examiners can see if incorrect values come from a correct method of dividing frequency by class width. Some students made an error drawing one of the bars but still gained two of the three marks. A few students with the correct frequency densities did not draw the bars in the correct intervals and gained one mark only. Weaker students often did not recognise the need to find frequency densities and drew a bar chart or a frequency polygon or a cumulative frequency graph. A similar proportion of students gained full marks in part (b) for working out an estimate for the fraction of the 150 people who were in the shop for between 20 minutes and 40 minutes. As this can be done by using the table or by using the histogram some students who had gained no marks in part (a) were able to give a correct fraction in part (b) by using the table. The marks were also awarded in part (b) for answers which followed through correctly from incorrect histograms. A common mistake was to give the answer as 67, not as a fraction, and this gained one mark only.
The grouped times, t minutes, for 150 people in a shop are: 0 < t ≤ 10: 20; 10 < t ≤ 30: 70; 30 < t ≤ 35: 22; 35 < t ≤ 50: 30; 50 < t ≤ 60: 8.
Edexcel 1MA1 · June 2024 · Paper 1H · Q19 · 3 marks
3 marks
Examiner report
Overall, this question was answered poorly with the majority of students unable to find an appropriate strategy to work out the ratio AB : AD. Some students made a good start by using similar triangles to form an equation involving AB, e.g. AB AB = , or an equation involving the scale factor, e.g. 4 × scale factor = 25 ÷ scale factor. Many of those who formed a correct equation were able to complete the process to find the required ratio. Most students, however, were unable to identify the need to compare the sides of the two similar triangles, ABC and DAB. Many used the ratio 4 : 21 incorrectly and answers of 4 : 25 were common. Students are advised that drawing two separate triangles and marking in lengths on the sides may help them to use the similarity of the triangles. A small number of students used Pythagoras to find the perpendicular height of the triangles and then AB. Some students assumed that Pythagoras could be applied to triangle ACD to find AC but it is not a right-angled triangle.
ABC and DAB are similar isosceles triangles. AB = AC, AD = BD, and C lies on BD. Given BC : CD = 4 : 21, find AB : AD.
Edexcel 1MA1 · June 2024 · Paper 2F · Q2 · 1 mark
1 mark
Examiner report
It was pleasing to see that many more students could successfully convert between litres and millilitres compared to previous sessions. The most common error was to divide by 100 rather than 1000.
Change 5000 millilitres to litres.
Edexcel 1MA1 · June 2024 · Paper 2F · Q9 · 4 marks
4 marks
Examiner report
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.
Anil has a job as a driver.
Edexcel 1MA1 · June 2024 · Paper 2F · Q14 · 5 marks
5 marks
Examiner report
Both parts of this question required students to use knowledge of the relationship between speed, distance and time, with many students making good use of a formula triangle and many obtaining correct answers in part (a) and partially correct answers in part (b) as a result. The majority gained both marks in part (a) and very few only gaining one mark. Students gaining no marks often multiplied instead of dividing, with many not considering the large magnitude and not realising that 108km/hr is fast for a bike ride. Only some students felt the need to work in minutes and not hours, despite no need for converting units of time. Part (b) was answered less well, with only a small proportion giving a fully correct answer. Partial marks were often awarded, with students often gaining one mark for 2.25 and most then continuing to find 5.25 to gain the second mark. The third mark was often lost for an inability to correctly convert the decimal to minutes, with 5 hours and 25 minutes along with the wrong decision being made due to this. Some successfully converted fully to minutes and then compared but this approach was rarely seen. Converting time from decimal form to hours and minutes continues to be an area of weakness for students on this tier. Ensuring students are confident with converting to and from time base 60 to decimal base 10 and developing understanding of compound measure skills involving speed distance and time with a calculator would be beneficial at all grades.
On Monday, Lizzie cycled 36 kilometres in 3 hours.
Edexcel 1MA1 · June 2024 · Paper 2F · Q15 · 2 marks
2 marks
Examiner report
Whilst there were very few blank responses seen, many failed to score both marks. It was common to see incorrect use of decimal multipliers, frequently forgetting to divide by 100 and 8750 being a commonly seen incorrect answer. It was also noted that a larger than expected number of students used compound interest instead of simple interest and this may have been more commonly attempted due to a lack of understanding of the differences and using the formulae sheet provided. Where responses included 6 × 2.5 in an attempt to find the total percentage interest, the method mark was rarely awarded, as there was often no mention of percentage or an expression in the form 6 × 0.025 and there was often confusion over what the 2.5 really was, so was not uncommon to see an answer of 2.5 × 6 = £15. Multiple examples of 3500 × 6, 3500 × 2.5 or attempts to subtract interest amounts once found were also seen. Given students had access to a calculator, a significant number chose to use a build-up method with no clear process shown. This often led to no marks being scored due to an arithmetic error. Centres should emphasise the need to show a valid process even when using a build-up approach and that ‘of’ is not an acceptable process. To improve on this skill, students need to be secure in their understanding of what a percentage is as a fraction or part of 100. Centres should also ensure students can confidently use their calculator to find basic percentages. Students would benefit with being more familiar with the difference between simple and compound interest applied in real life contexts to make it more memorable to candidates.
£3500 is invested in a bank for 6 years.
Edexcel 1MA1 · June 2024 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
Part (a) required an accurate reading from the conversion graph provided, and many students were able to give an answer within the acceptable range of 167 to 173 and those not gaining the mark often demonstrated they knew how to use the graph correctly but made an error when interpreting the grams scale. Part (b) however, was often poorly attempted in comparison. Successful students were those who used the graph wisely to extrapolate data and clearly showed what reading they were using and how this multiplied to make 1000g. Many students were either competent in using readings from the graph as a factor of 1000 or applied a build-up method of various readings. Of the students identifying the need to use a factor of 1000 and reading from the graph, most go on to get full marks. Some students only gained one of the two marks available as they were unable to interpret the scale for ounces, e.g. reading 100g = 3.5 ounces as 100g = 2.8 ounces, but could follow through and scale up correctly. Another common error that students made was to use 300 grams as part of a build-up, usually equating this to 10 ounces or more before multiplying by 3 and adding a reading for 100g. This approach gained no credit due to 300g being outside of the range of the graph. Extrapolation has always proved to be a challenging topic for students and in this series, although improvements can be seen, many of the students show insufficient working when the answer is outside of the specified range as incorrect readings need to be supported to gain credit.
A straight ounces-to-grams conversion graph passes through approximately (0 oz, 0 g) and (10 oz, 283 g).
Edexcel 1MA1 · June 2024 · Paper 2F · Q18 · 3 marks
3 marks
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.
Mrs Simpson organised a school trip for 66 children.
Edexcel 1MA1 · June 2024 · Paper 2F · Q22 · 2 marks
2 marks
Examiner report
This 2-mark question, on the whole, was answered very well with most students being able to substitute both of the values correctly and being able to find the difference to gain both marks. A common mistake was to substitute the incorrect values or not using the formula at all and dividing the number of bottles, redundant information, by the number of machines. It is therefore important for centres to ensure that students read the questions carefully and not assume that every number is to be used in the question.
The time H hours for n machines to make 5000 bottles is H = 72/n. On Monday n = 6 and on Tuesday n = 9. How much longer did Monday take?
Edexcel 1MA1 · June 2024 · Paper 2F · Q23 · 4 marks
4 marks
Examiner report
This question was a good discriminator for this cohort, with the full range of different possible scores seen. Almost all students attempted the question and very few blank responses were seen. Many were able to gain the first mark, usually by working out 1 − 0.16 and thereby showing some understanding of probability and some gained the first mark for working correctly with ratio to find the total number of discs in the bag, but this was seen less frequently. A score of 2 marks was also often seen, usually where students got as far as a probability of 0.46 but then did not know how to go further, or for working with probability and ratio separately but not knowing how to combine both skills correctly to make further progress through the problem. Of the students who understood how to approach the problem and showed a complete process, many rounded their numbers prematurely, often reaching answers like 69, 70.5 or 71 and scored all but the accuracy mark. Centres should remind students to work with accurate values fully until the end of the question and avoid premature rounding or truncating.
There are only red discs, blue discs and yellow discs in a bag.
Edexcel 1MA1 · June 2024 · Paper 2F · Q25 · 4 marks
4 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2024 · Paper 2H · Q3 · 2 marks
2 marks
Examiner report
On the whole, this small problem was answered well, but many were put off by the extra numbers in the question. The ‘5000’ was simply there to show the same number of bottles were made both days, but many tried to use this figure in the formula, often in place of 72. There were also cases where students wrote 72 ÷ 6 but then went on to use this in an incorrect calculation. This said, many did gain full credit for using the formula twice and subtracting to get an answer of 4.
The time H hours for n machines to make 5000 bottles is H = 72/n. On Monday n = 6 and on Tuesday n = 9. How much longer did Monday take?
Edexcel 1MA1 · June 2024 · Paper 2H · Q4 · 4 marks
4 marks
Examiner report
This question was the first main challenge of the paper, and it was just that for a good number. The most common successful approach was to use the number and probability of yellow to find the total number of discs, followed by dividing by the ratio to get the number of red (and often blue) discs. It was then quite straight forward to work out the number of red discs. Others did find success by working with the probability and ratio first to find the probability of red, and then with the total to get the number of red. Some lost marks after working with ratio to gain the number of red and blue but didn’t clearly identify the value for red and lost the final mark. A significant number of students prematurely rounded or truncated their probability value, often working with 0.46 or 0.47 which resulted in incorrect values of 69 or 71 for the answer. Where it was clear from working that correct processes were being followed it was still possible for all process marks to be gained.
There are only red discs, blue discs and yellow discs in a bag.
Edexcel 1MA1 · June 2024 · Paper 2H · Q6 · 4 marks
4 marks
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.
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.
Edexcel 1MA1 · June 2024 · Paper 2H · Q8 · 3 marks
3 marks
Examiner report
There were two processes in this question, a use of scale and a use of the formula for the area of a triangle. The more successful students used the scale first on RQ to get a drawing length of 8 cm. This was then used correctly with the area of the scale drawing to find PQ, which was then scaled back up to get the real length. The other method was to scale up the area first, and then use the real length of RQ to find the real length of PQ. This method was the better of the two as it seems to have less steps. However, most who attempted this method only multiplied the area by the length scale factor of 5, not the area scale factor of 52, and as a result could only gain the one mark. It was common to see a correct scaling of 8 for the length together with an incorrect scaling of 140 for the area, and this was considered to be a choice of methods.
A playground is a right-angled triangle PQR. Dan makes a scale drawing using 1 cm to represent 5 m. The area of the triangle on the drawing is 28 cm^2, and the real length QR is 40 m. Work out the real length PQ.
Edexcel 1MA1 · June 2024 · Paper 2H · Q12 · 4 marks
4 marks
Examiner report
As is often the case with inverse proportion, a significant number lost all marks as they worked with 𝑓= 𝑘𝑑2 rather than 𝑓= 𝑘 𝑑2. Those who got the format of this relationship correct typically scored 1 if not 2 marks in part (a). Some found the correct constant but didn’t state the equation correctly (including their found value of 224) and so didn’t gain the accuracy. In part (b) students had to use the equation found in part (a). The equation did not need to be fully correct, but it did have to be in the form 𝑓= 𝑘 𝑑2. Again, those who had the correct form typically scored well in part (b).
f is inversely proportional to d^2. Given f = 3.5 when d = 8: (a) find f in terms of d; (b) find the positive d when f = 10, to 3 significant figures.
Edexcel 1MA1 · June 2024 · Paper 2H · Q14 · 6 marks
6 marks
Examiner report
This question tested two topics that were new to 1MA1 and students are now scoring some good marks. In part (a) a tangent needed to be drawn and the gradient calculated. Many gained the first mark for drawing the tangent, and of those a significant number gained the second mark for a correct method to find the gradient. Unfortunately, many who did this, lost the third mark due to a missing negative sign in their answer. Weaker students read off at x = 5 and either multiplied or divided these two values, and thus scored zero. In this question, if no tangent was drawn, no marks could be scored. In part (b) a method to find the area under the curve was required and a pleasing number attempted this with trapezia. This was also seen in terms of triangle and rectangles, which was perfectly acceptable. To gain the first mark, a single correct area of a trapezium (or rectangle and triangle) was required, with a complete method needed for the second M mark. Those who used rectangles whose height was the point where the middle of the bar crossed the graph could also gain full credit here, and normally did. This method led to an answer of 78 compared to the 79 got from the other. Quite a few found the area under the tangent or had problems reading from the scale, but method marks could still be gained if this was limited to just one error.
The official velocity-time curve passes through (0,25), (2,16), (4,9), (5,6), (6,4), (8,1) and (10,0); a tangent drawn at t=5 passes approximately through (3,11) and (7,1).
Edexcel 1MA1 · June 2024 · Paper 2H · Q17 · 4 marks
4 marks
Examiner report
This question was attempted by most, but only the stronger students were able to score. The first mark was for working with the volume scale factors of L and M to find the length scale factors, and the second similarly to work with the area scale factors of M and P to find the length scale factors. Both of these processes required students to take some form of root, and it is perhaps not surprising that students were better when the square root was involved. Many of the students who were able to find the 2 separate length scale factors or ratios, were then unsure as to how to combine them and scored no further credit. Those who did know, typically scored both the 3rd and 4th marks. The A mark was ‘or equivalent’ and we saw numerous acceptable possibilities, including 9.6 : 12 : 4 which had non-integer values.
L, M and P are three similar solid cylinders made from the same material. L has mass 64 g. M has mass 125 g and total surface area 144 cm^2. P has total surface area 16 cm^2. Work out height of L : height of M : height of P.
Edexcel 1MA1 · June 2024 · Paper 3F · Q1 · 1 mark
1 mark
Examiner report
This question was answered very well with most students gaining one mark for a correct answer. The most common error was writing the answer as a decimal rather than a fraction.
Write 23% as a fraction.
Edexcel 1MA1 · June 2024 · Paper 3F · Q6 · 4 marks
4 marks
Examiner report
Part (a) was answered well with the majority of students gaining 2 marks for a correct answer of 32. Of those that didn’t, many gained 1 mark for a correct process e.g. 8 × 4 evaluated inaccurately, despite this being a calculator paper. Some students attempted a build-up process e.g. adding 8 lots of 4 but missed one out or included an extra 4, gaining 0 marks. Part (b) saw more mixed results. Again most of the cohort gained 2 marks for a correct value with accompanying units, e.g. 2.5 cm. Of those that didn’t, some were able to gain 1 mark for 2.5 without the correct units. A significant number of students were unable to show a correct process and gained 0 marks. Some students used the values from part (a) rather than part (b) or tried to multiply like in part (a) e.g. 4 × 10.
A map has a scale of 1 cm represents 4 km.
Edexcel 1MA1 · June 2024 · Paper 3F · Q15 · 3 marks
3 marks
Examiner report
The majority of students scored 3 marks on this question for reaching two comparable figures and making a correct decision. A small number of students gained 0 marks and it was evident that they found working with percentages challenging or they showed an incorrect process such as, for example, finding 115% of 88 and 120% of 62 or 85% of 88 and 80% of 62. It should be noted that 15% × 88 is not considered a mathematical process and therefore will not gain credit unless it is accompanied by the correct figure (e.g. 15% × 88 = 13.2 would gain the mark but without the 13.2 it would not). Many students used non-calculator processes that resulted in errors in arithmetic, or the full process was not shown and therefore credit could not be awarded.
Which is greater
Edexcel 1MA1 · June 2024 · Paper 3F · Q17 · 3 marks
3 marks
Examiner report
This question was answered well with most students able to gain the full 3 marks for 3 correct values. The most common method seen was to find the amount needed for 10 biscuits and then to add this to the amount needed for 20 biscuits or to multiply by 3. Very few students found a scale factor from 20 to 30 e.g. 30 ÷ 20 = 1.5 and worked from there. A variety of incorrect methods were seen including multiplying all the ingredients by 30 or adding 10 or 60 to all the ingredients.
Here are the ingredients needed to make 20 shortbread biscuits.
Edexcel 1MA1 · June 2024 · Paper 3F · Q20 · 5 marks
5 marks
Examiner report
This question was not well attempted by students. Many homed in on the statement ‘Angle BCD = 4 × angle ABC’ and multiplied 81 by 4 and went from there, gaining 0 marks. It is advisable for future cohorts to approach angles questions by taking in all the information given, including the diagram, and then working through systematically using the geometrical rules they know. For the other students, 1, 2, 3, 4 and 5 marks were all awarded, with 1 and 5 being most common; those that scored 1 mark achieved ABC = 18 but were then unable to interpret the other information correctly and made no further progress. A few students thought that angle ABD was a right angle and hence labelled angle CBD as 72 from 90 – 18. Correct 3-letter notation was rarely seen and a significant number of students lost marks as a result. Some students misinterpreted the isosceles triangle and thought that angle BAC = angle ABC. Marks were lost by students writing the angles in the incorrect positions on the diagram thus creating a contradiction where no 3-letter notation were used for the angles in the working, with the most common being 72 being placed as angle CBD on the diagram.
ABC and BCD are isosceles triangles.
Edexcel 1MA1 · June 2024 · Paper 3F · Q25 · 4 marks
4 marks
Examiner report
A majority of this cohort gained 0 or 1 mark on this ‘compound interest’ question. Many of those who gained 1 mark worked with ‘simple interest’ and therefore gained a mark for finding 6% of 25 000 or for one of the Special Cases in the mark scheme. Some students did work with ‘compound interest’ correctly and it was pleasing to see a good number of those students, once they had reached 29 775.4, understand that the answer must be an integer and give a correct answer, usually 29 775. Some students worked with both ‘simple interest’ and ‘compound interest’ figures, and chose the simple interest answer. The majority of correct answers came from using the traditional compound interest formula, marks only being lost for failing to round to a whole number. Some students arrived at the correct answer by using repeated percentage change (rather than a multiplier with power of 3), but more often than not this process led to mistakes, particularly in the last stage. A few students used the wrong multiplier e.g. 1.006 or 1.6.
A company has 25 000 workers.
Edexcel 1MA1 · June 2024 · Paper 3F · Q26 · 4 marks
4 marks
Examiner report
The majority of students were not able to make any progress on this question. Of those that did, one mark was often gained, usually for the 1st P1 600 ÷ 0.6 = 1000 or the 3rd P1 600 ÷ [volume], with [volume] usually being 700. A small number of students were able to work through the complete process correctly and gain a correct answer of 2; it should be noted that an answer of 2 without supportive working gained 0 marks. Some students used an incorrect formula for Density e.g. Mass × Volume.
Habib has two identical tins. 600 g of flour fills one tin completely, and the flour density is 0.6 g/cm^3. He puts 600 g of salt into the other tin; the unfilled space has volume 700 cm^3. Work out the density of the salt.
Edexcel 1MA1 · June 2024 · Paper 3F · Q28 · 4 marks
4 marks
Examiner report
A significant number of this cohort gained 0 marks on this question. It is clear that many did not know the formula for the volume of a cylinder. Of those that did not gain 0 marks, gaining 1 mark for [volume] ÷ 250 was often seen, with the most common incorrect volume used being 3000. Success beyond 1 mark was rarely seen and a minority of students were able to go on and gain 4 marks for a correct answer in the range 62 to 63.
A cylindrical paddling pool has radius 100 cm and depth 30 cm. It is filled from empty at 250 cm^3 per second. Work out the number of minutes needed to fill it, correct to the nearest minute.
Edexcel 1MA1 · June 2024 · Paper 3H · Q4 · 4 marks
4 marks
Examiner report
A good discriminator with most students showing understanding of working with percentages. There were, though, too many students who just used a simple interest rather than a compound interest process. A common approach was to find 6% of 25000, multiply this by 3 and often add this to the 25000 with 29500 being a very common incorrect answer. There were multiple errors in copying down the numbers, particularly missed zeros from the 25000 and using a multiplier of 1.006 instead of 1.06. A number of students also mistakenly used a multiplier of 1.03, through either a misunderstanding of the question, or a misread, this could not be credited. Those who gained just 3 of the marks usually did so because they gave the answer as 29775.4. These students were not awarded the accuracy mark as they hadn’t taken account of the context of the question, being that we cannot have 0.4 of a person.
A company has 25 000 workers.
Edexcel 1MA1 · June 2024 · Paper 3H · Q5 · 4 marks
4 marks
Examiner report
Most students realised that they needed to find the volume of the flour by dividing the mass by the density. However, many failed to appreciate that the volume of the salt was this volume subtract 700 and so did not gain the second process mark. An unexpectedly high number of students wrote 600/300 but gave the answer as 0.5 or 0.2 instead of 2, hence losing the final accuracy mark. The third process was not for a complete process and a student could gain this mark for 600 / [volume], where [volume] did not have to come from a correct process. Many students gained this mark for a calculation of 600 / 700 or 600 / 1000 but they did not get this mark for 0.857.. seen, this is because the process to arrive at this value had to be shown. Given the more common occurrence of square brackets in the mark scheme it is important that students get into a better habit of showing their method and processes so that they have a greater access to these marks.
Habib has two identical tins. 600 g of flour fills one tin completely, and the flour density is 0.6 g/cm^3. He puts 600 g of salt into the other tin; the unfilled space has volume 700 cm^3. Work out the density of the salt.
Edexcel 1MA1 · June 2024 · Paper 3H · Q7 · 4 marks
4 marks
Examiner report
This multi-step question required the use of a variety of skills being combined to solve a problem and appeared to be challenging to many students. Many students multiplied the radius by the height or finding the surface area or squaring pi instead of the radius or dividing the volume by 3 and, hence spoiling this process. The second process mark was often the only mark being awarded, usually for [volume] ÷ 250. On this occasion [volume] could be anything the student believed to be the volume provided it was not a value that was not allowed as stipulated in the mark scheme. It was unfortunate and relatively rare when students divided something labelled other than volume by 250 and hence not achieving this mark. Again, it is important that students show their method and process so that they have greater access to these marks. A number of students who had a fully correct process to find the time in seconds often stopped short of finding the time in minutes and hence only gained 2 of the 4 marks. With this question, full marks were given for an answer within the range from 62 to 63 inclusive but as the questions stipulated that ‘you must show all your working’ a correct answer with no supportive working scored no marks. It is important that students heed this instruction given on specific questions to ensure that they do not fall foul of this.
A cylindrical paddling pool has radius 100 cm and depth 30 cm. It is filled from empty at 250 cm^3 per second. Work out the number of minutes needed to fill it, correct to the nearest minute.
Edexcel 1MA1 · June 2024 · Paper 3H · Q10 · 3 marks
3 marks
Examiner report
This question was a good discriminator of students understanding of algebraic concepts and proved to be challenging for many. Those that gained all 3 marks for this question usually went down the route of finding the number of yellow counters or the total number of counters in bag A in terms of x rather than for starting to work with ratio using algebra eg 3y , 5y . Too often students incorrectly had the number of red counters as 3x instead of x and hence the number of yellow counters as 5x instead of 5 x . This incorrect method led to the total number of counters in bag B being 4x rather than the total number of counters in bag A and bag B being 4x and hence gained no marks. Another common error was for students to think that replacing x with a numerical value was an algebraic approach, as such this gained no marks in the same way that substituting in values for n when trying to prove 2 + n n is always even would gain no marks. There were a few students who lost out on gaining the C mark as rather than using fractions they worked with decimals but did not have these as recurring decimals. The variable ‘x’ was frequently lost on the total number of counters for bag B meaning marks were deducted.
There are only red counters and yellow counters in bag A.
Edexcel 1MA1 · June 2024 · Paper 3H · Q14 · 4 marks
4 marks
Examiner report
Another multi-step question that appeared to be very challenging to a large proportion of students, as many struggled with the order in which to carry out their calculations; with many adding both the 1000 and the 750 before dividing by 1.0352. Those students that carried out their calculations in an incorrect order had access to a maximum of two of the four marks. However, a good start was made by many who usually went down the numerical route of adding 1000 to the final amount of 2937.14, for which the first process mark was gained. The second mark could then be obtained from dividing an allowed value by 1.035. At this point in their process, there was obvious confusion amongst some students about reverse percentages shown by either multiplying their value by 1.035 or multiplying or dividing by 0.965. Those who were able to achieve these first two marks from a correct process and carrying out the operations in the correct order often successfully completed the calculations and gained all four marks. As with other questions in this paper, the scheme for this question had the use of square brackets and those students that wrote down their process rather than expecting the examiner to guess or assume had significantly greater access to these marks. The numerical approach was more commonly seen and generally more successful than the algebraic approach. It is important that students show clear working and take care to not miscopy numbers on these multi-step questions as very often students work was poorly organised and had evidence of misreading of values.
At the start of 2022 Kim invested some money in a savings account.
Edexcel 1MA1 · November 2023 · Paper 1F · Q6 · 3 marks
3 marks
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.
There are 3 litres of oil in a can. Jermaine uses 700 millilitres.
Edexcel 1MA1 · November 2023 · Paper 1F · Q7 · 2 marks
2 marks
Examiner report
Part (a) was answered very well with the majority gaining B1 for an answer of 15. Some students found the difference between 1 and 5 and added this to 3. Part (b) saw less success with more incorrect answers seen than in (a), the most common being 10 from dividing 20 by 2 instead of 4. There were still a good proportion of the cohort who gained B1 for an answer of 4.
In a scale diagram, 1 cm represents 5 m.
Edexcel 1MA1 · November 2023 · Paper 1F · Q10 · 3 marks
3 marks
Examiner report
It was pleasing to see the majority of students gain 3 marks on this question. The most common process seen was to divide 60 by 20 and then multiply 250 by 3 to arrive at 750. The majority of students who reached this point also gave a positive decision to gain the full 3 marks. Some students used a ‘build-down’ process starting at 900 and subtracting 250 three times to deduce there would be 150 grams left. Some students attempted to find the amount needed for one cookie and go from there but this process often led to arithmetic errors. Common incorrect processes often revolved around arithmetic errors and a small number of students reached an accurate figure to compare but gave an incorrect or no decision. Some students worked with the other ingredients too but this was ignored as long as it did not contradict their final answer. A number of students believed doubling and then doubling again went from 20 to 60 rather than 80 and therefore gained no credit.
A recipe for 20 cookies uses 250 g of peanut butter, 200 g of sugar and 2 small eggs. Derek wants to make 60 cookies. He has 900 g of peanut butter.
Edexcel 1MA1 · November 2023 · Paper 1F · Q13 · 4 marks
4 marks
Examiner report
This question saw the full range of marks awarded. Some students were able to work through the process to reach an answer of 23p or £0.23. Of those that didn’t, it was common to see 2 or 3 marks awarded, in particular for students who reached 160 or 460 but could go no further. Those that earned 3 marks gave a complete process with arithmetic errors in the process. It is encouraging to see that more students are fully demonstrating their method enabling them to gain marks despite their final answer being incorrect. Centres should continue to encourage their students to set out their working in a logical order so that they can access Method and Process marks. Some students dealt with the information and started the process incorrectly such as 100 ÷ 3 or started correctly e.g. 100 ÷ 5 but went wrong after that such as 20 + 8 and an answer of 28p. Some students incorrectly divided £3 by 5 following their process of dividing 100 by 5, resulting in an answer of 60p or 68p (after adding 8p) whereas others mixed up units within their working, e.g. 300/100 = 3g instead of 3p.
Each scrunchy uses one 8p hair band and 5 g of wool. Chloe buys 100 g of wool for £3 and makes as many scrunchies as possible.
Edexcel 1MA1 · November 2023 · Paper 1F · Q15 · 4 marks
4 marks
Examiner report
This question saw the full range of marks awarded. The majority of the cohort made a good start with a process to find 25% of 12,000. It was common to see students using the build-up method to work out percentages of amounts but this alone could not be credited with method or process marks if arithmetic errors were made and the process is not complete e.g. all steps seen such as 10% = 12,000 ÷ 10 = 1,200. Many then picked up the 2nd process mark for subtracting the deposit from 12,000 and also the 3rd for a complete process. It was common to see the accuracy mark not gained as students were unable to carry out the arithmetic for the division; 405 and 45 were commonly seen incorrect answers. Some students were not able to gain the first P mark but were able to gain the second and third P mark for a correct process using their deposit value and this was often seen. 12,000 was often misread as 1,200.
A car costs £12,000. Steve pays 25% as a deposit and pays the rest in 20 equal monthly payments.
Edexcel 1MA1 · November 2023 · Paper 1F · Q16 · 2 marks
2 marks
Examiner report
Around two thirds of this cohort were able to gain 2 marks by reaching a value to show that Shah had passed the exam, usually 42 or 75(%). Some students had a correct method but could not carry it out accurately. Others were not able to gain any marks as they set up a fraction such as 60 but were not able to go any further. Some students reached 42 or 75 but failed to interpret the results correctly, often saying that Shah did not pass the exam.
An exam is out of 60 marks. Shah needs at least 70% to pass and scores 45 marks.
Edexcel 1MA1 · November 2023 · Paper 1F · Q23 · 4 marks
4 marks
Examiner report
Very few students were able to gain full marks on this question. A small number made a positive start and gained one of the first two P marks, the equations most commonly seen were x = 2y, 2x + y = 180 and y + w = 180. Division by 3, rather than 5, of the 180° in the triangle was commonly seen. Most students understood the correct angle facts for angles in a triangle / on a straight line. Many students ignored the fact the triangle was isosceles and calculated the angles as if it was an equilateral triangle, giving 60° angles which led to 180 − 60 = 120 as the incorrect answer. Many students attempted to assign values to x and y, these values were usually incorrect but if the correct values were seen this usually led to a correct value for w as well.
ABD is an isosceles triangle with BA = BD. ABC is a straight line. The angle at A is x degrees, the interior angle at B is y degrees and x:y = 2:1. The exterior angle at B on line BC is w degrees.
Edexcel 1MA1 · November 2023 · Paper 1F · Q25 · 2 marks
2 marks
Examiner report
Those that knew the density, mass, volume formula generally scored 2 marks. Of those that did not gain 2 marks, most scored 0 for incorrect use of mass and volume, with the most common error being to multiply 27 and 10 instead of divide. Other incorrect methods involved trying a volume unit conversion, confusing units3 with 103 and dividing 27 by 1000, and being unable to choose between m/v and m × v and stating both.
A piece of glass has mass 27 g and volume 10 cm^3.
Edexcel 1MA1 · November 2023 · Paper 1H · Q6 · 4 marks
4 marks
Examiner report
Many students gained one mark for using angle facts to write an equation such as y + w = 180 or x + x + y = 180. Further progress then depended on being able to use the ratio x : y = 2 : 1 correctly. Those that could deal with the ratio usually went on to give fully correct solutions. A significant number of students, though, could not use the ratio correctly and incorrect statements such as x = 120, y = 60 or x = 90, y = 45 were very common. It was disappointing that a large proportion of the students failed to make any meaningful progress with this question.
An isosceles triangle ABD is drawn on the straight line ABC, with D above the line and C beyond B. BA = BD. Angle DAB = x°, angle DBA = y° and angle DBC = w°. Also x : y = 2 : 1.
Edexcel 1MA1 · November 2023 · Paper 1H · Q8 · 2 marks
2 marks
Examiner report
Those students who knew how to work out the normal price of the mattress were usually able to complete the arithmetic correctly and gain both marks. Many went from 60% = 660 to either 10% = 110 or 1% = 11 before finding that 100% = 1100. Many students did not recognise this as a reverse percentage question. The most common misunderstanding was to use £660 as 100% instead of 60%, with students working out 40% of £660 and adding it to £660 to get an answer of £924. Some students took £660 to be 40% of the original price and gave an answer of £1650.
The normal price of a mattress is reduced by 40% in a sale. The price of the mattress in the sale is £660
Edexcel 1MA1 · November 2023 · Paper 1H · Q13 · 3 marks
3 marks
Examiner report
This question was very poorly answered. Relatively few students showed that they understood the relationships between lengths, areas and volumes in similar figures. Those who did recognise that they should use the ratio of the heights, 2 : 5, to find the ratio of the volumes or the volume scale factor were usually able to give a complete method to find the volume of solid B. Many students worked out the scale factor as 2.5 but the majority then proceeded to use this as their volume scale factor, giving an answer of 30.
Solid A and solid B are similar. The ratio of the height of solid A to the height of solid B is 2 : 5. The volume of solid A is 12 cm³
Edexcel 1MA1 · November 2023 · Paper 1H · Q16 · 4 marks
4 marks
Examiner report
In part (a) it was clear that many students did not have a clear understanding of the notation used in the recurrence relation. However, those that did understand the notation and scored the first mark for 6 = 8 × k usually went on to give a complete and fully correct solution. The students who worked with 6 000 000 and 8 000 000 rather than with 6 and 8 tended to make more arithmetic errors. Many students simply assumed that the population decreased by 2 million each year which resulted in the very common incorrect answer of 4 million. A reasonable proportion of the students scoring marks in part (a) were able to make a correct decision in part (b) and give an acceptable reason. Students needed to justify their decision by linking the increase in the value of k to the value of k found in part (a). Some of those who made the correct decision could not give an acceptable reason for their answer and consequently did not gain the mark. Many students claimed that as the value of k increased, so did the population. This is only true in this specific case as the value of k would now exceed 1.
At the start of year n the population of a species is P_n. At the start of the following year the population of the species is given by P_(n+1) = k P_n, where k is a positive constant. The population of the species at the start of year 1 is 8 million. The population of the species at the start of year 2 is 6 million.
Edexcel 1MA1 · November 2023 · Paper 2F · Q3 · 1 mark
1 mark
Examiner report
Over two thirds of students could change between metres and centimetres. Converting between metric units still remains challenging for some students with many forgetting the conversion factor to use.
Convert metres to centimetres.
Edexcel 1MA1 · November 2023 · Paper 2F · Q6 · 2 marks
2 marks
Examiner report
The majority of students were able to score full marks for finding the amount paid per hour. The final answer was often presented in a variety of ways including £12.5, £12.50 and £12.50p, all of which gained full marks. A small number of students lost the accuracy mark by writing 12.40, 12.45 or 12.05, however these students often still scored 1 mark for showing a correct method. There were a significant number who did not show any method and potentially risked both marks had they evaluated incorrectly. The most common incorrect response was to multiply rather than divide.
Lydia works for 4 hours and is paid £50.
Edexcel 1MA1 · November 2023 · Paper 2F · Q10 · 2 marks
2 marks
Examiner report
Many correct ratios in the simplest form of 3 : 5 were seen and gained full marks. Where 2 marks were not awarded, the majority picked up the method mark for using the information given in the question to set out the ratio as 24 : 40. If the ratio was not fully simplified, students usually stopped at 6:10 and occasionally further incorrect simplifications were shown or changed to a fraction leading to the loss of the accuracy mark. When no marks were awarded it was often due to writing fractions rather than using ratio notation or writing the ratio 24:16 instead of 24:40.
There are 24 red counters and 40 blue counters.
Edexcel 1MA1 · November 2023 · Paper 2F · Q12 · 2 marks
2 marks
Examiner report
This simple speed/distance/time question produced a lot of fully correct responses, with most students demonstrating they were able to multiply the speed and time to gain the correct answer. The most common incorrect method involved dividing 37 by 3 or doing an extra step such as dividing by 2 or multiplying by 60. Sometimes, students incorrectly believed that they needed to convert one or more of the figures by multiplying or dividing by 60.
A car travels at an average speed of 37 mph for 3 hours.
Edexcel 1MA1 · November 2023 · Paper 2F · Q14 · 4 marks
4 marks
Examiner report
This question involving the use of direct proportion in a multi-step problem was answered correctly by more than half of the students which was very pleasing to note. Almost all students were able to find the cost of 1kg of flour by dividing 4.05 by 3 to get 1.35, with many then gaining the second mark for beginning to work with the cost of the sugar using a variety of methods. A larger than expected number of students misinterpreted the information with many assuming that 6kg of sugar was £11.85 and then dividing £11.85 by 6 to find the cost of 5kg sugar without considering whether their answer was feasible. Students who found 5.10 often then correctly found the cost of 5kg of sugar and stopped. Many found 6.95 as the answer but some found the separate costs (2.70 and 4.25), which were also awarded full marks. For this question involving a large number of figures to use and interpret, students may have benefitted from labelling each calculation with what the value represented, as students who showed their processes clearly and methodically were often more successful.
Three kilograms of flour cost £4.05. Five kilograms of flour and six kilograms of sugar together cost £11.85.
Edexcel 1MA1 · November 2023 · Paper 2F · Q23 · 4 marks
4 marks
Examiner report
It was pleasing to note that students were able to access this calculating the percentage profit after working with income and outgoings in this small problem, with some students successfully reaching the correct answer and a large number gaining partial marks. Responses to this question often started well, with many students gaining 1 mark for finding both the income and outgoings. A second mark was also often awarded for beginning the process to find the percentage profit, commonly by finding the difference between income and outgoings. Unfortunately, many who found the difference did not seem to know what to do next with this value, with a variety of attempts to work with it being seen. It did not seem to be clear to most in this cohort that percentage profit means percentage of outgoings. Incorrect next steps that were frequently seen were writing 10.5 or dividing 105 by 100 or by 405. Others instead worked out 300 as a percentage of 405 or attempted to add 300 to 405, meaning that there was no work with profit and only 1 mark was scored.
An event costs £100, £120 and £80. It sells 54 tickets at £7.50 each.
Edexcel 1MA1 · November 2023 · Paper 2F · Q24 · 2 marks
2 marks
Examiner report
The vast majority of students achieved 1 mark in this standard compound interest question, for finding the amount in the savings account after 1 year including interest. Some students successfully found the interest for one year or embedded this by finding simple interest for two years, showing that they could work with percentages but not all could distinguish the difference between simple and compound interest. Some students, however, found the interest for one year but did not gain the mark as they failed to add it to the starting investment amount, and a small number also failed to gain any marks as they successfully found the simple interest but then incorrectly subtracted it from 4500. A very small number of students simply multiplied or divided 4500 by 3.4 or 6.8, showing no understanding of how to calculate with percentages.
£4500 is invested for 2 years at 3.4% compound interest per year.
Edexcel 1MA1 · November 2023 · Paper 2F · Q26 · 4 marks
4 marks
Examiner report
This question was poorly answered with the vast majority of scoring students only scoring one mark for identifying and working with the given amount of £120 equating to four parts of the ratio. The ratio 90:120:60 was often seen and awarded the first mark. Of those scoring no marks, it was often due to interpreting the question as being to share £120 in the ratio of 3:4:2 rather than considering the information as being a part to whole problem, with the most popular incorrect value seen as £30. Of the students who successfully worked with the initial ratio correctly, a few continued to complete the question correctly and divide the total of the initial ratios of £270 by 10 to give one part of the new ratio as £27. Hence, obtaining the correct answer of £21 difference.
Chris, Debbie and Errol first share money in the ratio 3:4:2, with Debbie receiving £120. They then redistribute the same total in the ratio 2:5:3.
Edexcel 1MA1 · November 2023 · Paper 2F · Q28 · 4 marks
4 marks
Examiner report
This multi-step question required the use of a variety of skills being combined to solve a problem and appeared to be very challenging to a large number of students. Whilst many students knew they needed to find the volume, only a very few students were able to correctly calculate this, with many simply multiplying the radius by the height or the circumference by the height. Converting cm3 to litres or 0.47 litres to cm3 was generally only seen in fully correct responses. The final skill of working with a flow rate was often the only mark being awarded, namely for [volume] ÷ 0.47 to find the time taken. However, a large number multiplied by the flow rate rather than divided.
A cylindrical tank has radius 15 cm and height 43 cm. Liquid flows in at 0.47 litres per minute.
Edexcel 1MA1 · November 2023 · Paper 2H · Q2 · 4 marks
4 marks
Examiner report
This question required students to calculate a percentage profit. All students were able to make an attempt with almost all gaining some credit. The first mark was for finding the amount spent and earned, and then the second was for calculating the profit. Unfortunately, many students then did not know how to progress further. Many chose to divide the profit by the amount earned rather than the amount spent, and as such gained no further credit.
Karen is organising a party for a charity. She spends £100 on food, £120 on a hall and £80 on a DJ. Karen sells 54 tickets for the party. Each ticket costs £7.50
Edexcel 1MA1 · November 2023 · Paper 2H · Q3 · 2 marks
2 marks
Examiner report
A familiar compound interest question, and it was really pleasing to see so many students gaining both marks. Compared to the similar question in summer, it was notable that there were far fewer students working with simple interest. Those who did use simple interest were able to gain some credit for adding the percentage on. The mark scheme was generous as it allowed students who did not use correct money notation to gain full marks. This will not always be the case so students should ensure that when a question is dealing with money, the expectation is to give answers correct to two decimal places.
Andrew invests £4500 in a savings account for 2 years. The account pays compound interest at a rate of 3.4% per year.
Edexcel 1MA1 · November 2023 · Paper 2H · Q5 · 4 marks
4 marks
Examiner report
This ratio problem proved a real challenge to many. A good number of students were able to gain the first mark for realising that they had to work from part to whole and either found the original total or the values for Chris and Errol at the start. For many that was as far as they were able to get as they didn’t then work correctly with the new ratio and the total amount. Those that did, typically gained at least 3 marks for getting both values for Errol. Unfortunately, quite a few students lost the final mark because rather than subtracting these two values, they subtracted the value for Chris from the value for Errol.
Chris, Debbie and Errol share some money in the ratio 3 : 4 : 2. Debbie gets £120. Chris then gives some of his share to Debbie and some of his share to Errol. The money that Chris, Debbie and Errol each have is now in the ratio 2 : 5 : 3
Edexcel 1MA1 · November 2023 · Paper 2H · Q7 · 4 marks
4 marks
Examiner report
Most were able to gain some credit on this volume and flow problem. This was either for correctly working out the volume of the cylinder, or for correctly using the rate of flow. Unfortunately, very few were able to put all the steps together. Many didn’t work with the conversion at all which could have been used with either the rate of flow or the volume, and this meant in most cases the maximum they could score was 2 marks out of the 4.
An empty tank is in the shape of a cylinder. The cylinder has radius 15 cm and height 43 cm. Water flows into the tank at a rate of 0.47 litres per minute.
Edexcel 1MA1 · November 2023 · Paper 2H · Q14 · 5 marks
5 marks
Examiner report
This question required students to work with two difference types of ratios, either individually or by combining the two ratios. Many students were able to gain some marks on this which was really encouraging to see. Two marks were gained often for setting up a correct relationship and substituting to find one of the constants. Candidates then failed in most cases to gain any more marks. The next mark was for either combining the two equations, or for correctly substituting into the equation linking x and w. Unfortunately, the majority attempted the first method, and did so incorrectly, and so gained no further credit. Those who took the simpler path and substituted first, normally had more success.
y is proportional to x². y = 3 when x = 0.5. x is inversely proportional to w. x = 2 when w = 0.2
Edexcel 1MA1 · November 2023 · Paper 3F · Q1 · 1 mark
1 mark
Examiner report
A well answered first question on the paper where most candidates gained the mark. The most common mistake was to just remove the percentage sign and write 35. Occasionally it was seen as a fraction or only divided by 10 instead of 100.
Write 35% as a decimal.
Edexcel 1MA1 · November 2023 · Paper 3F · Q4 · 1 mark
1 mark
Examiner report
Mostly answered correctly, relatively few candidates chose to simplify to 2 7 and errors only arose when candidates counted the total number of squares incorrectly.
A rectangular grid has 3 rows and 7 columns. All 6 squares in the first two columns are shaded.
Edexcel 1MA1 · November 2023 · Paper 3F · Q14 · 2 marks
2 marks
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.
The five numbers are 0.56, 57%, 7/12, 0.558 and 6/11.
Edexcel 1MA1 · November 2023 · Paper 3F · Q17 · 3 marks
3 marks
Examiner report
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.
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.
Edexcel 1MA1 · November 2023 · Paper 3F · Q25 · 2 marks
2 marks
Examiner report
Many candidates did not recognise this question as inverse proportion, so there were many examples of 30 ÷ 4 = 7.5 Some candidates just worked with the numbers to see what they got, though a few reached the correct answer, explaining their logical steps. An example of this was where they reasoned that if it takes 4 machine 30 hours it will take 4 × 30 = 120 hours for 1 machine, then 120 ÷ 6 = 20 machines to take 6 hours. Candidates were usually awarded 0 or 2 for this question; it was very rare for anyone to pick up 1 mark.
Four machines take 30 hours to make an order of plates, with identical constant rates.
Edexcel 1MA1 · November 2023 · Paper 3F · Q26 · 3 marks
3 marks
Examiner report
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.
Riley travels 143 miles by car at 55 mph, then travels 5 hours 20 minutes by aeroplane.
Edexcel 1MA1 · November 2023 · Paper 3F · Q27 · 3 marks
3 marks
Examiner report
Some candidates scored 1 mark for correctly substituting the values correctly into the equation or were able to gain the mark for 144. Very few scored marks beyond this point. The most common error was to rearrange the formula into a multiplication instead of a division. Most did not substitute the values into the equation as a first step and hence missed out on the method marks. Most of the candidates showed a lack of understanding of pressure and where an object presses onto another. Once they found the area of one face, they often made no further progress as they failed to understand this was one face of the cube and not the whole cube. Several candidates divided 900 by 144 (area of one face) = 6.25 but did not then show the 6 to compare it to, failing to realise they had demonstrated that 900 cm2 was more than enough to cover 6 faces. Sometimes 3.5 was substituted as 3.52 as candidates sometimes confuse the square on the units and apply it to the numbers also. The candidates that answered successfully for full marks understood that a cube has 6 faces. 864 was the most common correct answer.
A cube exerts force 504 N on a table and pressure 3.5 N/cm^2. Pressure = force/area.
Edexcel 1MA1 · November 2023 · Paper 3H · Q6 · 2 marks
2 marks
Examiner report
There was a greater proportion of correct answers to this question testing inverse proportionality in a real life context than there has been in previous series. However, there were many students who approached the question using direct proportionality, often obtaining a time of 0.8 hours which may have been seen as unlikely had students carried out a common sense check. 45 machines was also a commonly seen incorrect response coming from 30 × 4 or equivalent.
A company orders a large number of plates from a factory. It would take 30 hours to make all the plates using 4 machines.
Edexcel 1MA1 · November 2023 · Paper 3H · Q7 · 3 marks
3 marks
Examiner report
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.
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.
Edexcel 1MA1 · November 2023 · Paper 3H · Q8 · 3 marks
3 marks
Examiner report
A high percentage of students were able to use the given formula in this question to work out area, given pressure and force. Fewer candidates realised that their result gave them the area of one face of the cube and that they would need to multiply this by the number of faces before they could compare it with a total surface area of 900 cm². Consequently, they compared 144 with 900. Nevertheless, many students were able to do this and gained full marks for their responses. Hardly any students used an accepted alternative approach, for example comparing 144 with 150.
A solid cube is placed on a horizontal table. You are given that pressure = force / area. The pressure on the table due to the cube is 3.5 newtons/cm^2. The force exerted by the cube on the table is 504 newtons.
Edexcel 1MA1 · November 2023 · Paper 3H · Q11 · 3 marks
3 marks
Examiner report
There were very few fully correct answers to this question. Lower attaining students did not appreciate the need to use 50² or 100² in one way or another to take into account area and unit conversions. These students often restricted their response to working out Hours 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Minutes 48×50 100 , resulting in the answer 24. However, examiners were able to give partial credit to the relatively small proportion of students who realised the need to use 1 m2 = 10 000 cm2, often expressed in the form of dividing by 100 twice. Very few students identified the need to use the scale factor of 2500 (or 50 × 50). Some students successfully chose dimensions for the room on the plan, for example 8 cm and 6 cm then converted these to metres before recalculating the area.
The floor plan of a house is drawn using a scale of 1:50. On the plan, a room in the house has a floor area of 48 cm^2.
Edexcel 1MA1 · November 2023 · Paper 3H · Q23 · 4 marks
4 marks
Examiner report
There was a good number of complete, clear and concise solutions to this question. The great majority of students who attempted this question started by eliminating the fractions and were given due credit for this first step. Most of the students following this approach were able to isolate terms in x and y accurately to get as far as 54y2 = 150x2 or equivalent, then went on to get 3y = 5x. A small number of students getting this far made an error when interpreting their linear relationship to get a ratio for x : y and wrote 5 : 3 as their answer. The few students who used an approach involving simultaneous equations were usually successful.
Given that (2x^2 + y^2)/(4x^2 - y^2) = 43/11, where x > 0 and y > 0,
Edexcel 1MA1 · June 2023 · Paper 1F · Q1 · 1 mark
1 mark
Examiner report
This first question was generally well answered although incorrect answers of 3.8 and 0.38% were not uncommon. A significant number failed to give their answer as a decimal and often an answer of 100 was seen.
Write 38% as a decimal.
Edexcel 1MA1 · June 2023 · Paper 1F · Q2 · 1 mark
1 mark
Examiner report
This question was usually answered correctly although answers in an incorrect form were sometimes seen, eg. 30% and 0.3 Occasional miscounting of the number of sections led to an incorrect fraction e.g., 3/9
A shape is divided into 10 equal regions, of which 3 are shaded.
Edexcel 1MA1 · June 2023 · Paper 1F · Q14 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · June 2023 · Paper 1F · Q16 · 2 marks
2 marks
Examiner report
This question was generally well answered although arithmetic errors were common. Many students wasted valuable time by working out the amount of all three ingredients required to make 60 biscuits. Most correctly found 3 lots of 250 but some did try to find the amount of flour required to make one biscuit and then multiplied by 60. The method here gained credit but rarely was a correct final answer seen because of poor division of 250 by 20. Some students misinterpreted the question and assumed that Harry already had 250g of flour and that the question was asking how much more was needed. Multiplying 250 by 4 was also a common mistake.
A recipe uses 250 g of flour for 20 biscuits.
Edexcel 1MA1 · June 2023 · Paper 1F · Q17 · 4 marks
4 marks
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.
There are 200 counters in a bag: 38 red, 52 blue, and the rest split equally between yellow and green.
Edexcel 1MA1 · June 2023 · Paper 1F · Q26 · 2 marks
2 marks
Examiner report
This was poorly answered with very many students simply finding 20% of 240 and either decreasing £240 to give £192 or increasing £240 to give £288 Those that started with 20% = £240 usually went on to work accurately leading to a correct answer. Occasionally answers of 960 or 1440 were seen and these gained one mark.
A holiday price increases by 20%, and the increase is £240.
Edexcel 1MA1 · June 2023 · Paper 1F · Q27 · 3 marks
3 marks
Examiner report
Inability to find the area of the cross-section of the cylinder prevented any chance of success in this question, rarely was1200 divided by 40 correctly, 300 being a common incorrect result but that did lead to the possibility of picking up another mark by attempting to divide it into 90. Some tried to use the formula for the volume of a cylinder in an attempt to find the radius of the circular base and then its area.
A solid cylinder has volume 1200 cm^3 and height 40 cm. It stands on its circular base and exerts a force of 90 N on the floor. Pressure = force / area.
Edexcel 1MA1 · June 2023 · Paper 1H · Q7 · 2 marks
2 marks
Examiner report
Many students were able to work out the price of the holiday before the increase. Common approaches included 240 × 5 and 10% = 120 so 100% = 1200. Some students showed a method leading to 1200 but then gave a final answer of 960 or, less frequently, 1440. These students gained one mark only. A greater number of students than expected gained no marks at all. Often this was because they misinterpreted the question and took £240 to be the price of the holiday after the 20% increase giving the answer of £200.
The price of a holiday increases by 20%. This 20% increase adds £240 to the price of the holiday.
Edexcel 1MA1 · June 2023 · Paper 1H · Q8 · 3 marks
3 marks
Examiner report
A good proportion of the students who gained the first mark for dividing 1200 by 40 then went on to show a complete process. Many gained all three marks but some students made arithmetic errors and lost the accuracy mark. Errors such as 1200 ÷ 40 = 300 and 90 ÷ 30 = 30 were quite common. After dividing 1200 by 40 some students did not realise that they had found the value they needed to use in the pressure formula and it was common to see equated πr2 equated to 30 in an attempt to find the value of r. Some carried out further incorrect work in an attempt to find the ‘area’ and some made no further progress. A common error was attempting to find the surface area of the cylinder and using this in the pressure formula. Some attempts failed at the first hurdle when students did not know how to use the volume of 1200 cm3 and the height of 40 cm.
A solid cylinder rests on a horizontal floor. The cylinder has a volume of 1200 cm³ and a height of 40 cm. The cylinder exerts a force of 90 newtons on the floor. You are given that pressure = force ÷ area.
Edexcel 1MA1 · June 2023 · Paper 1H · Q13 · 3 marks
3 marks
Examiner report
This direct proportion question was answered very well. Many of the students who gained the first mark for y = kx or 24 = 1.5x went on to give a fully correct answer. When full marks were not gained this was often because of arithmetic errors when dividing 24 by 1.5 to work out the value of k and k = 1.6 was frequently seen. A significant number of students used a non-algebraic approach and although these attempts were often successful this approach tended to be more prone to arithmetic errors which resulted in a loss of accuracy. Many who divided 5 by 1.5 lost the final accuracy mark as they rounded 3.33… to 3.3 or 3 before multiplying by 24. Some students used inverse proportion rather than direct proportion and gained no marks.
y is directly proportional to x. y = 24 when x = 1.5
Edexcel 1MA1 · June 2023 · Paper 1H · Q18 · 4 marks
4 marks
Examiner report
Many students struggled to find a strategy that would enable them to solve this problem and there were many solutions that had calculations dotted around the page making the working very difficult for examiners to follow. Many of the algebraic methods broke down at an early stage. After gaining the first mark for writing an equation such as 7c + 5t = 480 many students were unable to use the ratio 5 : 9 correctly to write down a second equation. Writing 5c = 9t instead of 9c = 5t was a common mistake and the incorrect equations 5c + 9t = 14 and c + t = 14 were frequently seen. Nevertheless, it was pleasing to see some successful solutions from students using an algebraic method. The majority of the correct answers came from students adopting a numerical approach. The most efficient of these saw students working with the ratio of total costs, finding 7 × 5 = 35 and 5 × 9 = 45, often as 35 : 45, and then dividing 480 by 80 to get 6. Multiplying 5 by 6 and 9 by 6 completed the solution. Some students worked out the total cost of the tomatoes and the total cost of the carrots and gained the first two marks but did not find the cost of 1 kg of each. Many of the incorrect strategies were based on dividing 480 by 12 or by 14.
7 kg of carrots and 5 kg of tomatoes cost a total of 480p. cost of 1 kg of carrots : cost of 1 kg of tomatoes = 5 : 9
Edexcel 1MA1 · June 2023 · Paper 2F · Q8 · 3 marks
3 marks
Examiner report
It was pleasing to see the majority of students attempt this first mini problem-solving question. Whilst there was mixed level of success, many students were able to gain full marks by reaching an answer of 96, either using the scale before or after adding the distances. When a correct answer was not given, many gained partial credit for either using the scale for one of the shorter distances or for adding both lengths to find the total distance. A significant minority of students ignored the labelling on the diagram, and attempted to work with their own measurements, typically using 12cm. Centres should encourage students to refer to diagrams, particularly noting any labels or measurements given.
On a map, service station Q is 8 cm from P and R is a further 16 cm along the same route. The scale is 1 cm = 4 km.
Edexcel 1MA1 · June 2023 · Paper 2F · Q9 · 3 marks
3 marks
Examiner report
Almost all students could continue the sequence correctly to gain the mark in part (a). Part (b) performed less successfully. Whilst many were generally able to write the correct values using ratio notation, not all continued to write their ratio in the simplest form and although many achieved the correct simplified ratio, some went on to do further incorrect simplification such as 4:9 leading to 2:3 which lost the accuracy mark. However correct simplification to 1:2.25 (1: n) did not lose the accuracy mark and was occasionally seen. When no marks were awarded, it was often due to not understanding how to write the appropriate values using ratio notation, such as simply writing as a fraction instead. Other commonly seen responses that gained no credit included choosing the incorrect terms from the sequence or selecting three terms e.g. 8:23 or 8:13:18 and a small minority attempted to find the nth term.
The first five terms of a sequence are 3, 8, 13, 18, 23.
Edexcel 1MA1 · June 2023 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
A single mark was often awarded in this question. Whilst a mark was often awarded for multiplying speed by time, frequently using minutes or an unconventionally written time, many students struggled to efficiently work with decimal time. Converting to minutes and calculating 56 ×105 was a popular start to the question, but this was often left as 5880 or divided by 100 rather than being divided by 60. Errors with decimal time were common with conversion to 145 min or 1.45 hours seen regularly. There were successful attempts by students who chose to use a partitioning approach by adding 56, 28 and 14 after splitting 56 in half and then in half again. However, a small number choosing this method then didn’t add the correct quantities together to show a complete method and gained only 1 method mark. A substantial number did not know the formula for speed, distance and time and some who drew the correct formula triangle for speed were still unable to rearrange or apply this successfully.
Paulo drives at an average speed of 56 km/h for 1 hour 45 minutes.
Edexcel 1MA1 · June 2023 · Paper 2F · Q18 · 6 marks
6 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2023 · Paper 2F · Q19 · 5 marks
5 marks
Examiner report
The majority of students gained marks on this familiar frequency tree question, with part (a) being well attempted and many gaining at least one mark. Of those who were not awarded full marks, the vast majority were able to correctly place at least one of the given values, generally for placing 150 correctly, and then could calculate at least 1 or 2 of the missing values. However, many students placed 110 incorrectly as the number of students who have a bicycle and a car, simply reading this value from the question and not realising this was the total number of people with a bicycle and making use of the final piece of information given. Careful reading should be encouraged for this type of question and it was pleasing to see students checking that the values they had placed totalled 240 and correcting as necessary if 240 was not reached. Part (b) required students to use their frequency tree to find a percentage, with a large proportion of students who were successful with the frequency tree, correctly working out the required percentage. Whilst many identified the correct value to use as a numerator, a small number of students calculated this as a percentage of the total people rather than the number of people who had a car and therefore gained no marks. The most common errors from incorrect frequency trees led to 110 and 150 being used in part (b) but could be followed through for both marks if used correctly. Other students simply stated the values from their frequency tree or as a fraction rather than converting them to a percentage or gave a subtraction e.g. 150 – 45 or even 100 – 45.
At a factory, 240 people work in total; 150 have a car; 110 have a bicycle; and 65 bicycle owners do not have a car.
Edexcel 1MA1 · June 2023 · Paper 2F · Q22 · 1 mark
1 mark
Examiner report
As with previous series and explanation questions, a variety of responses were seen. Approximately half of the cohort provided a suitable explanation with a decision of “No” that was accompanied by appropriate figures to support and justify the reasoning. The common correct approach was to correctly calculate the number of red and blue counters there actually were or reason that if the statement were correct then there would be 72 counters in the bag. Centres should discourage students from writing answers that simply restate the facts given in the question such as there is 1 red for every 2 blue, as these are unlikely to gain credit. Occasionally a decision was not provided, incorrect figures were stated or a contradiction was given which led to the mark being withheld but this was less frequent than with previous similar explanation style questions.
A bag has 48 counters in the ratio red:blue = 1:2. Helen claims there are 24 red counters because 1 is half of 2 and 24 is half of 48.
Edexcel 1MA1 · June 2023 · Paper 2F · Q25 · 3 marks
3 marks
Examiner report
Combining the skills of applying percentages and ratio in this small problem appeared to be demanding for many students, with many often only being able to work with one or the other but not both together. Calculating 57% of 800 was by far the most common first step shown but, after finding 456, it was common either to multiply or divide by 7 or 12 without using 19 in their calculations. Of those who chose to work with percentage first, this was not always done correctly by those using a build-up method rather than the calculator. When doing this, very few showed a method for the individual percentages and just stated what they thought the percentage was, so any error lost the method mark. Almost all responses that gained full marks worked through each part as an individual calculation such as dividing by 19 and then separately multiplying by 7, very few used fractions in their working. This approach proved to be the most successful and should be encouraged.
A family recycled 800 kg of waste. 57% was paper and glass, in the ratio paper:glass = 12:7.
Edexcel 1MA1 · June 2023 · Paper 2F · Q27 · 4 marks
4 marks
Examiner report
Most students scored at least one mark in this question for working out the value of either 4% of £150 000 or 1.5% of 160 000. Many continued working to gain a second mark for either using compound interest for one value or, more commonly, working with percentage increase for one year for both values. It was common for 8% and 3% to be used due to only considering simple interest. Students are reminded to read the questions carefully as the third mark could not be achieved unless compound interest was used. A very few students used the approach of using decimal multipliers, a few students used the formula from the exam aid, and those that did tended to get it correct, others listed values for each year separately. Students should be encouraged to write down all their processes when using a calculator to make their intention clear. A build-up method was commonly used and often led to an incorrect answer, and without any working out, marks could not be awarded. Unfortunately, some students used 1.4 for 4% or 1.15 for 1.5% or attempted to use the % button on their calculator which often led to only adding 0.04 or 0.015. One approach to this question was to use compound interest for only Tamsin and add one year of interest for Rachel to find valid comparable figures. This approach was seen rarely, with many that used compound interest rather than simple interest, often calculating 2 years for both Tamsin and Rachel. When compound interest was used, correct figures and a correct decision often followed. A very small number of students did not make a final decision though.
Tamsin's £150,000 house rises 4% per year. Rachel's £160,000 house rises 1.5% per year.
Edexcel 1MA1 · June 2023 · Paper 2H · Q3 · 1 mark
1 mark
Examiner report
The first reasoning question that required a written explanation and one that was typically answered well. Most recognised that the red counters represented a third of the total and not a half. As is often the case on such response questions, the clarity of candidates’ explanations sometimes led to them not being credited the mark. Some candidates gave a correct explanation but then lost the mark with the inclusion of inaccurate figures or comments which contradicted their explanation; for communication marks the statement must be fully correct. Giving students the opportunity to talk and write using correct mathematical language will benefit many. Their ability to explain varied but most were able to state that the number of red counters should be 16 rather than 24. Those who used fractions in their explanation or described that the ratio would then be 1: 1 showed a good understanding of the mistake which had been made. Another common way forward was to assume that if there were 24 red, then there would have to be 48 blue and then the total of 72 would be more than the given total of counters in the bag. Explanations often lacked clarity and did not refer to the numbers in the question. There was also some carelessness over using the correct order of numbers in division with 3 divided by 48. Some also failed to express their reasoning unambiguously, such as only mentioning the number of blue counters, rather than focusing on the red.
There are 48 counters in a bag. There are only red counters and blue counters in the bag. number of red counters : number of blue counters = 1 : 2. Helen has to work out how many red counters are in the bag. She says, "There are 24 red counters in the bag because 1 is half of 2 and 24 is half of 48".
Edexcel 1MA1 · June 2023 · Paper 2H · Q6 · 3 marks
3 marks
Examiner report
This was another problem solving question and another with good success for candidates. Many were able to gain all 3 marks for a correct answer. Those who didn’t score full marks normally scored at least one for a correct process, either finding 57% or starting to work with the ratio. It was evident though, that a lot of candidates do not have efficient calculator strategies with many using build-up methods for percentage, rather than just multiplying by 0.57 or equivalent.
Last year a family recycled 800 kg of household waste. 57% of this waste was paper and glass. weight of paper recycled : weight of glass recycled = 12 : 7
Edexcel 1MA1 · June 2023 · Paper 2H · Q8 · 4 marks
4 marks
Examiner report
Unlike with Question 6, there were fewer candidates attempting build up methods here for the percentages, which was good to see. There were still a disappointing number of candidates working with simple rather than compound interest and these were able to score a maximum of 2 of the 4 marks on offer. Overall though we saw a significant number of candidates showing efficient methods and gaining all 4 marks. Use of the formula sheet was evident in some candidates' responses.
Tamsin buys a house with a value of £150000. The value of Tamsin's house increases by 4% each year. Rachel buys a house with a value of £160000. The value of Rachel's house increases by 1.5% each year.
Edexcel 1MA1 · June 2023 · Paper 2H · Q18 · 3 marks
3 marks
Examiner report
This ratio problem proved to be one of the most challenging on the paper for candidates. A pleasing number did make a start to working with the ratio, normally working with a : c = 3 : 5 or b : c = 5 : 3. However, then next step of equating the c element of the ratios proved too challenging for many. Others tried more complex methods working with ratios that contained numbers as variables, but struggled to complete any working that was worthy of credit. The most efficient method led to a ratio of a : b : c = 9 : 25 : 15 which would have gained 2 marks, it is only a single step from there to get to 34:40 and hence 17:20.
2a : 5c = 6 : 25 and 4b : 7c = 20 : 21
Edexcel 1MA1 · June 2023 · Paper 2H · Q23 · 3 marks
3 marks
Examiner report
Many candidates were caught out but the relatively familiar figures of 1, 8 and 27, and thought they had to work with cubing numbers. However, candidates had to find the length scale factor of the 3 triangles from the given ratio as 1:3:6 to gain the first mark, whereas many worked with the 1:2:3. Once they had the correct ratio of lengths they could then work out the correct ratio of areas for the 3 triangles to get 1:9:36. From here they had to work out the ratio of the areas of the 3 shapes, 2 of which were trapezia not triangles. There were a number of excellent responses, some working as above and others working nicely with algebra. There were also a number of candidates that gave lengths to the parallel sides and perpendicular height and worked correctly with areas.
Here are three similar triangles, ABG, ACF and ADE. ABCD and AGFE are straight lines, with GB, FC and ED parallel. AB : BC : CD = 1 : 2 : 3.
Edexcel 1MA1 · June 2023 · Paper 3F · Q2 · 1 mark
1 mark
Examiner report
This was generally very well answered. Some candidates showed misunderstanding by giving a fraction out of 100. A common incorrect answer was 3.
Write 3/10 as a percentage.
Edexcel 1MA1 · June 2023 · Paper 3F · Q13 · 5 marks
5 marks
Examiner report
Both parts of (a) were generally answered well with candidates demonstrating that they were able to read the initial information from the graph, though a significant minority struggled to read the scale on the graph correctly, sometimes reading the wrong scale and giving the answer 10 in (i). Others offered nothing close to 30, with 65 and 95 not uncommon. In part (b) many candidates were able to draw a horizontal line at the correct length to indicate Daniel resting and most went on to draw a diagonal line back to the x-axis with a ruler. Candidates who did not use a ruler were not penalised provided that their line appeared straight. Those who had not drawn a horizontal line or drew a horizontal line of incorrect length were still able to understand that the diagonal line should be drawn to 1600 on the x-axis. In part (c) candidates used their correct diagonal line OR the information provided to correctly arrive at the average speed of 35 miles per hour. It was rare to see a candidate use "their" incorrect diagonal line to try and calculate the average speed, however the few candidates that were able to do this were rewarded for demonstrating this correct process. In this final part, there were some candidates who were able to write the formula, but were unable to substitute their values correctly, and others who were unable to manipulate it correctly or were confused with the concept of time and/or units.
Rowena drove from home to a beach and stopped at a cafe on the way. The official travel graph is represented below; each labelled time column is 30 minutes and each vertical step is 5 miles. Distance from home (miles) 40 | 35 | * beach 30 | / 25 | / 20 | / 15 | / 10 | *---* cafe 5 | / 0 |* +-------------------------- 12:00 12:30 13:00 13:30 Rowena stayed at the beach for 1.5 hours, then drove home without stopping and arrived at 16:00.
Edexcel 1MA1 · June 2023 · Paper 3F · Q14 · 4 marks
4 marks
Examiner report
Failing to understand what the question was asking and a lack of working both contributed to this being a poorly answered question. Many candidates started the process with quantity divided by cost, thus finding 20 boxes per £1 and 27 bags per £1. They were then unable to progress any further, usually calculating 27 – 20 to arrive at the common incorrect answer of 7p. Those who started with cost divided by quantity nearly all gained a mark for showing 0.05 or 5 for one box. For the bag, when candidates failed to show working and only gave the figure 0.03 or 0.04 their penalty was the eventual loss of an accuracy mark, at the very least. Examiners needed to be able to see where the 0.03 or 0.04 came from in order to award marks for working. Those who did show their calculations up to this stage often did not show the subtraction and struggled with using the correct units, getting no further than 0.01296, 0.013, 0.02, 2, 0.01 or 1p thus losing the accuracy mark.
120 boxes cost £6 and 270 bags cost £10. A bag is cheaper than a box.
Edexcel 1MA1 · June 2023 · Paper 3F · Q15 · 2 marks
2 marks
Examiner report
Most candidates were able to utilise the ratio and scale up the 35 to 140 with many of them then realising that they had to sum the two parts to arrive at the correct answer. Those that did sum the two parts were rewarded with the method mark and nearly all candidates were then able to secure the accuracy mark. However, not all candidates were able to do this and left their answer as 140 scoring no marks.
A bag contains only red and green beads in the ratio 1:4. There are 35 red beads.
Edexcel 1MA1 · June 2023 · Paper 3F · Q19 · 3 marks
3 marks
Examiner report
This question was attempted by most candidates, but few achieved full marks. Many candidates gained 1 mark, often by calculating 450 ÷ 6 and getting an answer of 75; or for finding ‘450 is 15% of 3000’. Unfortunately, many candidates were not able to progress past this point in their calculations and gained no further marks. Some candidates were able to take the calculation further but failed to finish the calculation giving final answers of 0.025 or 1.025. A common incorrect approach was to consider this to be a compound interest question and to use the compound interest formula.
Jenny invests £3000 for 6 years at y% simple interest per year and receives £450 total interest.
Edexcel 1MA1 · June 2023 · Paper 3F · Q21 · 5 marks
5 marks
Examiner report
A large proportion of candidates were able to secure a mark for commencing this problem by taking into consideration the two cups of coffee by doubling one of the other stated values, or by multiplying by 10.6 to take into consideration the amount of coffee required for one cup of coffee. These two steps could have been completed after working with the proportion of the 800 people (68%) that would drink coffee. In order to progress with this problem, candidates had to work with the 68% and in most cases, this was completed by working out how many people this was. Although they could use calculators for this paper, a significant number of candidates chose to compute this by demonstrating a build-up method. When this was done correctly, most went on to arrive at the correct solution of 11532.8. Where candidates did not show all stages of their working and simply stated correct and incorrect percentage values that they then added, no marks or no further marks were able to be awarded. Generally, partitioning methods frequently led to error, but those using a more direct approach, typically by multiplying by 0.68, usually went on to work the percentage out correctly. In part (b) responses of "there will not be enough coffee" or "more coffee will be needed" or similar equivalent responses were rewarded with the communication mark. Some candidates chose to recalculate the problem and chose to work out the new total of people drinking coffee or the new weight of coffee required. When they did this correctly this also secured this last mark. Candidates should be encouraged to generalise so that they do not have to complete additional unnecessary work, particularly when there was only one mark to be gained. It was encouraging to see many correct responses to this part.
Jonny is providing coffee for 800 people. Each coffee drinker has 2 cups and each cup needs 10.6 g. Jonny assumes 68% drink coffee, but the true figure is 72%.
Edexcel 1MA1 · June 2023 · Paper 3F · Q23 · 2 marks
2 marks
Examiner report
It was rare to see a fully correct answer to this question. The majority of successful answers were found by 14 × 5 = 70 and then dividing by 4. Many students did not grasp the question at all or recognise that the answer must be larger. By far the most common answer seen was 11.2, the result of 14 ÷ 5 and then multiplying by 4. Some simply added their result from 14 ÷ 5 to 14, giving 16.8. Some students tried to convert to minutes, which was rarely successful.
Five identical pumps fill a tank in 14 hours. The tank size and pump rates are unchanged.
Edexcel 1MA1 · June 2023 · Paper 3F · Q25 · 3 marks
3 marks
Examiner report
There was mixed success with this question. The majority of students successfully started this question by dividing 67205600 by 11.9 to find the number of seconds, thereby gaining P1, but were then unable to convert this to days. Few students calculated 60 × 60 × 24 separately and the minority of students who successfully went on to find the correct answer often did the conversion to days in stages. Common errors in the time conversion were to omit one or more of the numbers, or to multiply when they should have divided and vice versa. Some students saw the m3 and incorrectly surmised that they needed to cube 11.9.
Lava flows at a constant rate of 11.9 m^3/s. A total of 67,205,600 m^3 flows.
Edexcel 1MA1 · June 2023 · Paper 3F · Q27 · 2 marks
2 marks
Examiner report
A significant number of students started with the formula density = mass/volume or showed a correct formula triangle but then were unable to rearrange to make mass the subject. Of those who arrived at the correct formula, mass = density × volume, and could substitute the values required correctly, most gained full marks for 648, with very few gaining just the method mark for 72 × 9. The most common incorrect answer was 8 coming from the division 72 ÷ 9. A significant number of candidates were confused by the units cm³ and cubed the 9 and the 72. Overall, it was encouraging to see so many gaining marks in this question, so late in the paper.
A solid metal cuboid has density 9 g/cm^3 and volume 72 cm^3.
Edexcel 1MA1 · June 2023 · Paper 3F · Q28 · 4 marks
4 marks
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.
Work with standard form and ordering.
Edexcel 1MA1 · June 2023 · Paper 3H · Q2 · 5 marks
5 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2023 · Paper 3H · Q4 · 2 marks
2 marks
Examiner report
There was a disappointing proportion of correct answers to this question testing inverse proportionality in a real life context. Many students approached the question using direct proportionality and so came to the conclusion that it would take less time (11.2 hours) for 4 pumps to fill the water tank than it does if 5 pumps are used. It was perhaps surprising that few students did a common sense check on this figure which may have led them to question whether they had applied the correct processes in their working.
It takes 14 hours for 5 identical pumps to fill a water tank. How many hours would it take 4 of these pumps to fill another water tank of the same size?
Edexcel 1MA1 · June 2023 · Paper 3H · Q6 · 3 marks
3 marks
Examiner report
The majority of students made a good attempt at this problem. There were many fully correct solutions. Answers of 65 or 66 were accepted to reward students who rounded their answer to the nearest day and those who rounded up because they reasoned that in 65 days, not quite enough lava had flowed from the volcano. Students who could not be awarded full marks often scored one mark for either dividing by 11.9 or for a correct process to convert between seconds and days. The latter process is exemplified by 24 × 60 × 60 (= 86 400) or by successively dividing by 60, 60 and 24. The most common errors seen were from students who multiplied together 67, 205, 600 and 11.9 and from students who used incorrect conversion factors such as 60 × 24 or 60 × 60 × 12.
Lava flows from a volcano at a constant rate of 11.9 m^3/s. How many days does it take for 67205600 m^3 of lava to flow from the volcano? Give your answer correct to the nearest day.
Edexcel 1MA1 · June 2023 · Paper 3H · Q8 · 2 marks
2 marks
Examiner report
Most students found this question to be straightforward. However, a minority of students divided 72 by 9 or divided 9 by 72 so could not be awarded any marks.
A solid cuboid is made of metal. The metal has a density of 9 g/cm^3. The volume of the cuboid is 72 cm^3. Work out the mass of the cuboid.
Edexcel 1MA1 · June 2023 · Paper 3H · Q9 · 2 marks
2 marks
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.
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?
Edexcel 1MA1 · November 2022 · Paper 1F · Q13 · 4 marks
4 marks
Examiner report
Part (a) was answered correctly by the majority of students, reading 60 from the bar chart. Part (b) was answered less well when a certain amount of extrapolation was required from the chart. 210 was a common incorrect answer. In part (c), it was evident that many students weren’t able to accurately read data from a composite bar chart, many reading the number of men as 90, women 200 and children 280 in 2020. The method mark here was awarded for sight of 80 (children) or 200 (men + women) used in a ratio. Many gained this mark but failed to score full marks as a result of incorrect values read from the chart. As a result of not reading the questions correctly, some students wrote an answer of 80 (child) : 90 (men) : 110 (women).
A composite bar chart shows the numbers of men, women and children in a village. In 2000 there were 60 men, 70 women and 40 children. In 2010 there were 70 men, 90 women and 50 children. In 2020 there were 90 men, 110 women and 80 children.
Edexcel 1MA1 · November 2022 · Paper 1F · Q14 · 5 marks
5 marks
Examiner report
Greater success was achieved in part (a) of this question by finding the sum of the distance travelled in one hour (54 miles) and the distance travelled in half an hour (27 miles). It was pleasing however, to see many students correctly quoting the equation distance = speed × time to solve this problem, although accuracy was often lost through incorrect use of the units of time. 54 × 90(mins) or 54 × 1.30 were common errors made. In part (b), very few students were able to correctly convert from centimetres to kilometres. Many gained one mark for using the scale on the map correctly, 25 000 × 6. Credit was then given for a reasonable attempt at the conversion of 150 000 cm to km, usually just dividing by 1000. Most didn’t seem to be clear that they had found a measurement in cm by multiplying by 25 000, those who did include units were more likely to be able to convert correctly as they often spotted that they could convert cm to m then m to km.
Complete the two independent parts.
Edexcel 1MA1 · November 2022 · Paper 1F · Q17 · 5 marks
5 marks
Examiner report
Again, understanding of probability was good and many students gained the full 2 marks in part (a). One mark was awarded for sight of 100 – 30 (= 70) or a correct value for the probability of taking a blue counter. 4 was a common incorrect answer by some of the less able students, assuming there was an equal number of coloured counters. Students should be reminded that expressing a probability as a ratio is not an acceptable form for this answer. In part (b), the correct answer of 45 was the modal answer, with incorrect methods following no particular pattern. A common incorrect attempt was also to try to share 30 in the ratio 2 : 3. Part (c) followed through student’s answers in (b). Explanations were usually acceptable, such that 25 counters could not be shared equally between red and yellow. It should be noted that just saying ‘25 can’t be divided by 2’ gained no credit. Also, students should be aware that any calculations given as evidence in such questions need to be accurate.
There are only blue, green, red and yellow counters in a bag. There are 30 blue counters and 100 counters in total. Ashin takes a counter at random.
Edexcel 1MA1 · November 2022 · Paper 1F · Q18 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 1F · Q24 · 6 marks
6 marks
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.
Rizwan writes down three numbers a, b and c a : b = 1 : 3 b : c = 6 : 5
Edexcel 1MA1 · November 2022 · Paper 1F · Q25 · 2 marks
2 marks
Examiner report
This was very poorly answered. The formula and the force both being given meant there was only the need to work out the area by multiplying 4 by 2. Some students still think that when working with area, they need to square the values first before using them to divide into 10 000. Those who correctly worked out the area usually tried to divide 10 000 by 8, for one mark, but often then failed, again through poor arithmetic. Some stated the area as 6 (4 + 2) and therefore gained no credit.
pressure = force area A storage tank exerts a force of 10 000 newtons on the ground. The base of the tank in contact with the ground is a 4 m by 2 m rectangle. Work out the pressure on the ground due to the tank.
Edexcel 1MA1 · November 2022 · Paper 1H · Q6 · 6 marks
6 marks
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.
Rizwan writes down three numbers a, b and c a : b = 1 : 3 b : c = 6 : 5
Edexcel 1MA1 · November 2022 · Paper 1H · Q7 · 2 marks
2 marks
Examiner report
Many students gained the first mark for using the area of the base in the pressure formula. The accuracy mark was sometimes lost because of arithmetic errors when dividing 10 000 by 8 or because of an inability to divide 10 000 by 8. A few students used the formula incorrectly and worked out 10 000 × 8 rather than 10 000 ÷ 8. Many attempts failed at the first hurdle when students used an incorrect method to find the area of the base, e.g. 4 + 4 + 2 + 2= 12, or did not realise that they needed to find the area of the base. These students gained no marks.
pressure = force area A storage tank exerts a force of 10 000 newtons on the ground. The base of the tank in contact with the ground is a 4 m by 2 m rectangle. Work out the pressure on the ground due to the tank.
Edexcel 1MA1 · November 2022 · Paper 1H · Q13 · 3 marks
3 marks
Examiner report
This inverse proportion question was presented in an unfamiliar format but a good proportion of students managed to gain at least one mark. Many completed the table correctly, often without showing any working out. Students who wrote down the equation p = 100/t nearly always found at least one correct value. A common mistake was using direct proportion rather than inverse proportion.
p is inversely proportional to t. Complete the table: (t,p) = (100,1), (25, blank), (blank,5), (2, blank).
Edexcel 1MA1 · November 2022 · Paper 2F · Q2 · 1 mark
1 mark
Examiner report
This question was well answered, with nearly all candidates scoring this mark.
Write 37% as a fraction.
Edexcel 1MA1 · November 2022 · Paper 2F · Q4 · 1 mark
1 mark
Examiner report
In line with previous series students found this conversion question more difficult. Just over half of the cohort were able to do this simple conversion. Centres are advised to spend time on this skill as it is often required.
Change 53 centimetres to millimetres. millimetres
Edexcel 1MA1 · November 2022 · Paper 2F · Q11 · 4 marks
4 marks
Examiner report
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.
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.
Edexcel 1MA1 · November 2022 · Paper 2F · Q13 · 4 marks
4 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
Most students gained only 1 mark for an appropriate step to the process, most commonly from 12 divided by 4, but their answers broke down frequently applying direct proportion rather than inverse. It was also common to see several approaches for this question. From the scripts seen it was clear that students found this question challenging. Going forward students are advised that checking the response to see if it is sensible is a good strategy: "Do we expect a larger or smaller numerical answer?" this will assist the students in dismissing incorrect working and selecting the correct operations needed.
Four identical pipes take 12 hours to fill a lake.
Edexcel 1MA1 · November 2022 · Paper 2F · Q23 · 3 marks
3 marks
Examiner report
This question required students to calculate with compound interest and a mark was often awarded for calculating the interest for a single year but many did not add this amount on before working with the interest rate for the second year and instead used the starting value of £7000 for both rates before adding the values together. A small minority of students used the second interest rate of 1.5% for 2 years instead of one year. It was also disappointing to see some students using written calculations to find their answer and practice using a calculator to answer this type of question would be beneficial to students.
Ella invests £7000 for 2 years in an account paying compound interest. In the first year, the rate of interest is 3% In the second year, the rate of interest is 1.5% Work out the value of Ella’s investment at the end of 2 years. £
Edexcel 1MA1 · November 2022 · Paper 2F · Q26 · 2 marks
2 marks
Examiner report
Where students understood the process to calculate the original amount, they were successful in gaining both marks. Unfortunately the majority of responses saw students increase or decrease the given amount by 9%. Another common mistake was to use 0.91 as a multiplier. The best solutions came from those who identified 165680 as 109% at the outset and then proceeded to divide by the correct multiplier of 1.09. A few did recognise that 165680 was 109% but only divided by 109. In summary Based on their performance on this paper, students should • carefully read questions • practice questions involving significant figures • provide solutions to problems in a systematic manner • use a calculator for this paper.
The population of a town increased by 9% between 2018 and 2019 The population in 2019 was 165 680 Calculate the population in 2018
Edexcel 1MA1 · November 2022 · Paper 2H · Q6 · 3 marks
3 marks
Examiner report
This was another familiar style of question, the only complication being a different interest rate for each year. As is normal with this question, weaker students struggle to understand fully the compound nature of the question and work with simple interest. Those who did this normally gained 1 mark for finding 3%. Most of those who understood the question fully and worked with compound interest went on to score full marks. The few that didn't normally gave a final answer of £318.15, finding the value of the interest and not the investment.
Ella invests £7000 for 2 years in an account paying compound interest. In the first year, the rate of interest is 3% In the second year, the rate of interest is 1.5% Work out the value of Ella’s investment at the end of 2 years. £
Edexcel 1MA1 · November 2022 · Paper 2H · Q8 · 3 marks
3 marks
Examiner report
This AO1 question required learners to be able to find a percentage increase. On the whole it was answered quite well, with many learners able to gain at least 1 mark for finding the profit, or for finding the new value as a percentage or decimal of the original. However, a significant number couldn't complete the method, either by finding the profit as a percentage of the original, or by subtracting 100 or 1 from their value, and thus didn’t gain the 2nd mark. A common error was to divide the profit by the selling price rather than the purchase price.
Chanda buys a necklace for £120 She sells the necklace for £135 Work out her percentage profit.
Edexcel 1MA1 · November 2022 · Paper 2H · Q10 · 3 marks
3 marks
Examiner report
This problem combined reverse percentages with repeated percentage change, and proved a challenge to many, but primarily in relation to the reverse percentage aspect. It was very common to see candidates using multipliers of 1.19 and 1.23 rather than dividing by 0.81 and 0.77. This led to no marks being awarded. Of those who understood the reverse percentage, most then went on to complete the process and gain both P marks, and then normally the accuracy mark also.
Aaliyah bought a car. In the first year after she bought the car, its value depreciated at a rate of 23% per annum. In the second year after she bought the car, its value depreciated at a rate of 19% per annum. At the end of the second year the car was worth £10 914.75 What was the value of the car when Aaliyah bought it? £
Edexcel 1MA1 · November 2022 · Paper 2H · Q12 · 3 marks
3 marks
Examiner report
Part (a) proved a real challenge to candidates and it is clear that many didn’t really understand iterative processes or how to use an iterative formula. Most tried to multiply 1.13 by the number of years, rather than raising to a power, and thus the majority of candidates scored no marks. The limited number of candidates who used the formula correctly were split into two groups, those who gained 1 mark for using the formula correctly once, and those who went on to gain both marks as they fully understood. In both these groups there were candidates who dealt with the constant alone, and looked to see when this became greater than 2, and candidates who chose a starting value (often 100) and worked till this value doubled. Both approaches were acceptable and seen as regularly as each other. The communication aspect of part (b) was approached well by many, with certainly more success than part (a). Many candidates correctly realised that by increasing the value of k would decrease the time taken.
The number of insects in a population at the start of the year n is Pn The number of insects in the population at the start of year (n + 1) is Pn+1 where Pn+1 = kPn Given that k has a constant value of 1.13
Edexcel 1MA1 · November 2022 · Paper 2H · Q15 · 4 marks
4 marks
Examiner report
This is again a common style of question and one we have seen in recent series. With that in mind it was again unfortunate to see so many candidates with no real idea of how to approach this Peterson Capture Recapture question. A good number scored a single mark for a suitable fraction given, but just as many scored zero. This was normally due to them working with differences rather than ratios. Many were close to scoring the second mark, but often set up the two fractions as a product rather than an equation. Most of those who gained the second, went on to gain the third mark also. Some students gained 2 marks only for setting up a correct equation, but could not then rearrange to gain a correct answer, in particular when their unknown value was the denominator of a fraction. In part (b), candidates had much greater success. A significant proportion realised that the population must be greater than 50 as Albie had already caught 55. Some of the wrong responses focused on tags falling off, or on the 40 who were tagged.
Faiza is studying the population of rabbits in a park. She wants to estimate the number of rabbits in the park. On Monday she catches a random sample of 20 rabbits in the park, marks each rabbit with a tag and releases them back into the park. On Tuesday she catches a random sample of 42 rabbits in the park. 12 of the rabbits are marked with a tag.
Edexcel 1MA1 · November 2022 · Paper 2H · Q21 · 4 marks
4 marks
Examiner report
Well into the Grade 8 questions on the paper and it is not surprising that fewer candidates are now scoring marks. For part (a), failure to draw a tangent at t = 17.5 meant that no marks could be scored at all. It was very common to just see 10.5 17.5 which came from reading the volume at t = 17.5, and this scored zero. Those who drew a suitable tangent often then went on to score full marks for an answer in range. However, some were unable to use the scale correctly and then lost marks for their method to find the gradient. Part (b) showed improvements on previous series, and there were many suitable descriptions of what the gradient represented although students still relate this answer to a correlation type response. ‘Acceleration’ was a commonly seen incorrect answer.
A smooth graph gives the volume V, in litres, of water in a container t seconds after filling starts. Approximate plotted readings are (0,0), (2.5,0.8), (5,1.8), (7.5,3.0), (10,4.5), (12.5,6.3), (15,8.2), (17.5,10.6), (20,13.5), (22.5,17.3) and (25,23.0).
Edexcel 1MA1 · November 2022 · Paper 2H · Q23 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 3F · Q12 · 2 marks
2 marks
Examiner report
This was answered well by most candidates, many of whom obtained 2 marks by stating the ratio 1: 6 : 3 or an equivalent ratio. Frequently 1 mark was given for finding one correct pairing of ratios. Few candidates went down the algebraic route, but those who did often picked up at least 1 mark. Those who simply wrote down three acceptable numbers without using ratio notation could only gain 1 mark.
Amol, Gemma and Harry each have a number of sweets. The number of sweets that Gemma has is 6 times the number of sweets that Amol has. The number of sweets that Harry has is half the number of sweets that Gemma has. Write down the ratio the number of sweets : the number of sweets : the number of sweets that Amol has that Gemma has that Harry has
Edexcel 1MA1 · November 2022 · Paper 3F · Q14 · 3 marks
3 marks
Examiner report
In part (a), the answer of 30 was most often correct. But in part (b) many candidates were unprepared for the requirements for reading from the graph and scaling their reading. There were very few who chose the most appropriate value of 20 to scale to 80, and many who took inaccurate readings from the axis. This question highlighted that candidates need more practice with this topic of the curriculum.
A straight conversion graph for ounces and grams passes through (10 ounces, 300 grams) and (35 ounces, 1000 grams). Use the graph for the conversions below.
Edexcel 1MA1 · November 2022 · Paper 3F · Q15 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 3F · Q19 · 4 marks
4 marks
Examiner report
The axes scaling proved challenging for some candidates in this question and thus they were unable to correctly read off values from the graph. Though the majority of candidates gave the correct answer of 15 for part (a), a significant number gave the incorrect answer of 20 instead. In part (b) the majority of candidates gave a value within the acceptable range. The most common answer was 4.5 and the most common incorrect answer was 7. Candidates who drew guidelines on the graph had greater success. In part (c) candidates were less successful and a multitude of errors were seen stopping many candidates from scoring all or some of the marks. These included not knowing or being able to substitute correctly into the speed/distance/time formula, being unable to convert minutes into hours or even reading the correct values from the graph. It was common to see answers of 5 and 0.2 from 20 ÷ 4 (no marks) and 4 ÷ 20 (1 mark). It was rare to see a correct answer of 12, but when it was seen it was often due to a scaled approach to this question rather than 20 minutes being converted to a fraction of an hour or attempting to convert 0.2km per minute.
Carly cycles to her friend’s house, stays there, then cycles home. Her travel graph joins the points (08:00, 0 km), (08:20, 4 km), (08:30, 7 km), (08:45, 7 km) and (09:00, 0 km) with straight line segments.
Edexcel 1MA1 · November 2022 · Paper 3F · Q20 · 4 marks
4 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 3F · Q22 · 1 mark
1 mark
Examiner report
This question was answered well by a large proportion of candidates, who identified that Rob should have added the ratios before dividing. Comments such as “add the ratios and then divide by 120” were accepted as simply being poorly worded. Some candidates spoilt an otherwise good answer suggesting that after adding the ratios, they should multiply 40 and 24 by 8, which was an incorrect statement. Often candidates showed full correct working for sharing 120 in the ratio 3:5 which was an alternative way of answering the question.
Rob has been asked to divide 120 in the ratio 3 : 5 Here is his working. 120 ÷ 3 = 40 120 ÷ 5 = 24 Rob’s working is not correct. Describe what Rob has done wrong.
Edexcel 1MA1 · November 2022 · Paper 3F · Q24 · 4 marks
4 marks
Examiner report
Nearly all responses scored zero marks. Responses that scored all 4 marks were very rare. Very few candidates used the correct formula for the area of the cross-section or for the whole cylinder, many using the diameter rather than the radius. Most candidates failed to find a volume, but simply found the area of a rectangle by multiplying 80 by 160 and worked with 12800 as if it was the volume of one cylinder. The most common way of scoring a mark was for finding the amount of fertiliser for each tank. Where marks were gained this was generally for the process of working out the volume of a single tank or for a process to find the volume of water per tank. A small minority of candidates got 1 mark for showing 8000 in their working. The ratio of 100:1 equalling 101 parts evaded nearly all candidates, resulting in minimal full mark answers.
Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm. 160 cm 80 cm The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1 : 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.
Edexcel 1MA1 · November 2022 · Paper 3F · Q27 · 4 marks
4 marks
Examiner report
Part (a) was poorly answered; it was rare to see a correct answer with 80, 800, 0.8, 0.08 all appearing more regularly than the correct answer of 0.008 In part (b) conversion between km and m remains a weakness; in too many cases candidates showed a division operation instead of multiplication, even worse with 100 instead of 1000. The proportional factor of 1000 was almost always correct. Conversion between hours and minutes was, perhaps predictably, less effectively completed overall with many attempts dividing by 60 once rather than by 60 × 60.
Complete all parts of this question.
Edexcel 1MA1 · November 2022 · Paper 3H · Q2 · 1 mark
1 mark
Examiner report
Candidates taking this paper could usually identify and describe what Rob had done wrong with sufficient clarity to score the available mark. It was enough for a candidate to say that Rob should have added the 3 and 5 together as a first step instead of dividing the 120 by the 3 and 5 separately. The small proportion of candidates who did not secure a mark here either did not appreciate just what was being asked and merely went ahead and divided 120 into the ratio 3:5 without explaining what Rob had done wrong or they gave an answer which was too vague to gain credit. Examiners noted that many candidates wrote that 8 needed to be divided by 120 and though this did not necessarily affect whether the mark was awarded or not, centres might like to address this error with candidates.
Rob has been asked to divide 120 in the ratio 3 : 5 Here is his working. 120 ÷ 3 = 40 120 ÷ 5 = 24 Rob’s working is not correct. Describe what Rob has done wrong.
Edexcel 1MA1 · November 2022 · Paper 3H · Q4 · 4 marks
4 marks
Examiner report
A good discriminator, most candidates were able to score at least 2 marks for showing how to get the total volume of 4 tanks. Only the lowest attaining candidates failed to use a correct formula for the volume of a tank. A few candidates used the diameter instead of the radius to work out the volume, in effect working out the value of πd²h or sometimes πdh instead of πr²h. Some candidates who left their volumes as a multiple of π, for example 256000π, then lost the π in the next step of their working. Correct attempts to use the ratio 1 : 100 were usually restricted to answers from higher attaining candidates and many candidates used 100 where they should have used 101 in their calculations. There was a wide range of possible approaches to answering the question and responses seen were very varied. The most common successful approach was to compare the volume of the 4 tanks with the amount of mixture that could be made with the available fertilizer.
Karina has 4 tanks on her tractor. Each tank is a cylinder with diameter 80 cm and height 160 cm. 160 cm 80 cm The 4 tanks are to be filled completely with a mixture of fertiliser and water. The fertiliser has to be mixed with water in the ratio 1 : 100 by volume. Karina has 32 litres of fertiliser. 1 litre = 1000 cm³ Has Karina enough fertiliser for the 4 tanks? You must show how you get your answer.
Edexcel 1MA1 · November 2022 · Paper 3H · Q7 · 4 marks
4 marks
Examiner report
This question, involving change of units, was poorly answered by those candidates at which it was targetted. In particular, part (a) rarely attracted a correct answer. Attempts at part (b) were often more successful with the majority of candidates gaining at least one of the three marks available. Where both marks were not awarded for part (b) a good proportion of candidates scored one mark, usually for multiplying by 1000 and showing their conversion from kilometres to metres. A good number of candidates lost marks because they used 360 for 60 × 60 or because they divided by 60 instead of by 3600. Some other candidates multiplied by 3600 instead of dividing by it.
Complete all parts of this question.
Edexcel 1MA1 · November 2022 · Paper 3H · Q17 · 4 marks
4 marks
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.
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.
Edexcel 1MA1 · November 2022 · Paper 3H · Q19 · 3 marks
3 marks
Examiner report
A small proportion of lower attaining candidates merely added the three numbers 0.4, 7 and 8 given in the question and tried to work with this. In general, however, the question was quite well answered. When it was not completed successfully, examiners could usually award some credit to a candidate for showing a correct process to find the probability that a counter was red or green, (1 − 0.4 or 0.6). Many candidates went on to find the correct probability for picking a green counter (0.32), thus showing an understanding of how to apply the ratio, but were then unable to make the final link to multiply this by the number of trials (50).
There are only blue counters, red counters and green counters in a box. The probability that a counter taken at random from the box will be blue is 0.4 The ratio of the number of red counters to the number of green counters is 7 : 8 Sameena takes at random a counter from the box. She records its colour and puts the counter back in the box. Sameena does this a total of 50 times. Work out an estimate for the number of times she takes a green counter.
Edexcel 1MA1 · November 2022 · Paper 3H · Q25 · 5 marks
5 marks
Examiner report
Many candidates could make a successful start on the question by using a correct process to find the volume of the top part of the pyramid and so scored the first mark available. This was often the limit to any credit which examiners could give candidates. A common mistake was for candidates to use the average density in a misguided attempt to work out the volume of the bottom part of the pyramid. This was, by design, a challenging question and so, as expected there were only a small number of completely successful solutions seen.
The pyramid P is formed from two parts made of different materials. top bottom The top part of P has a mass of 92.8 g and is made from material with a density of 2.9 g/cm³ The bottom part of P has a mass of 972.8 g The average density of P is 4.7 g/cm³ Calculate the volume of the top part of P as a percentage of the total volume of P. Give your answer correct to 1 decimal place. You must show all your working.
Edexcel 1MA1 · June 2022 · Paper 1F · Q1 · 1 mark
1 mark
Examiner report
For the first question on the paper, this question was not well answered. Many students were clearly unaware of the conversion factor of centimetres into millimetres. The most common errors were using a factor of 100 to give an answer of 4000 or using a factor of 10 to divide rather than multiply with 40 being often given.
Change 40 centimetres into millimetres.
Edexcel 1MA1 · June 2022 · Paper 1F · Q16 · 4 marks
4 marks
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.
Savio leaves at 07:30 and drives 50 miles at an average 40 mph.
Edexcel 1MA1 · June 2022 · Paper 1F · Q18 · 2 marks
2 marks
Examiner report
The most popular method in answering this question was by working out the amount of sugar required to make 20 and then 5 scones. Some did simply work out 40 × 2.5 In the former method, loss of marks was a result of not explicitly identifying the number of scones that were being considered. or finding the amount of sugar required for 20 scones accurately but then simply adding 5 more grams for the 5 extra scones. A significant number just multiplied by 25, thinking the ingredients given were for one scone. Some students wasted considerable time by working out the amount of each ingredient in making 25 scones.
For 10 scones, 40 g sugar is needed. Mia makes 25 scones.
Edexcel 1MA1 · June 2022 · Paper 1F · Q19 · 3 marks
3 marks
Examiner report
Finding 20% of 240 was the more common starting point here although many methods to do this were incomplete or flawed. It was not uncommon to see 10% = 24 and then a second 10% equal to half or a tenth of 24. Poor arithmetic was often the reason for loss of marks. Even those who found 48 often couldn’t get to 288. A significant number went on to subtract 20% from the 240 rather than adding it or did not realise they needed to add it on resulting in a common final answer of 48.
Increase 240 by 20%.
Edexcel 1MA1 · June 2022 · Paper 1F · Q25 · 5 marks
5 marks
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.
There are 160 vehicles with cars:vans=3:7. Of the cars, 1/8 use electricity and 25% use diesel; the rest use petrol.
Edexcel 1MA1 · June 2022 · Paper 1F · Q29 · 3 marks
3 marks
Examiner report
Only the more able students, appreciating the need to find the volumes of the given cubes, made any progress in this question. Some multiplied the mass by the volume and then tried to simplify their ratio. Some did divide the masses by the volumes but left the un-simplified ratio 27 : The most common error was to divide the masses by the length of an edge, leaving a ratio of 27:32. Also common was to multiply the 81 and 128 by 3 and 4 to get 243:512
Cube A has side 3 cm and mass 81 g. Cube B has side 4 cm and mass 128 g.
Edexcel 1MA1 · June 2022 · Paper 1H · Q3 · 5 marks
5 marks
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.
There are 160 vehicles with cars:vans=3:7. Of the cars, 1/8 use electricity and 25% use diesel; the rest use petrol.
Edexcel 1MA1 · June 2022 · Paper 1H · Q7 · 3 marks
3 marks
Examiner report
The majority of students gained the first mark for a process to find a volume and many went on to give a correct answer. The final mark was sometimes lost because of arithmetic errors, these occurred most often when dividing 81 by 27 or dividing 128 by 64. Having found the volume of each cube some students gained no more marks because they were unable to use density = mass ÷ volume. It was common to see mass × volume and volume ÷ mass being used. Some students did not realise that it was necessary to find the volume of each cube and scored no marks at all. Often these students simply used the figures in the question, dividing 81 by 3 and dividing 128 by 4 or multiplying 81 by 3 and 128 by 4. There were also some students who calculated the surface area of the cubes and attempted to divide the mass by the surface area and gained no credit. Some students included units in their final answer but they were not penalised.
Cube A has side 3 cm and mass 81 g. Cube B has side 4 cm and mass 128 g.
Edexcel 1MA1 · June 2022 · Paper 1H · Q11 · 3 marks
3 marks
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 .
Lime:strawberry:orange sweets = 9:4:x and P(lime)=3/7.
Edexcel 1MA1 · June 2022 · Paper 1H · Q14 · 4 marks
4 marks
Examiner report
Where tangents were drawn they were generally accurate and students often went on to gain all three marks for working out an estimate of the gradient that was within the acceptable range. Some answers were given in the form a/b and the final mark was lost when a and b were not integers. Errors were often the result of reading the scales incorrectly although some students divided the change in x by the change in y. A significant number of students drew a tangent, thus gaining the first method mark, but could not then complete the method to find the gradient. Many students used the coordinates of the point on the curve at t = 2 and simply divided 2.8 by 2. Some of these students had already drawn a tangent to the curve at t = 2. In part (b) many students knew that the area under the graph represents the distance travelled. Incorrect answers often referred to acceleration or to time. Some students gave the answer as velocity or speed.
A smooth speed-time curve rises from (0,0) through about (2,2.8), peaks near (4.5,4), and falls to (9,0).
Edexcel 1MA1 · June 2022 · Paper 1H · Q17 · 4 marks
4 marks
Examiner report
Many students were able to set up an equation with a constant term and they often wrote down both y k t = and t = k/x3. Most then went on to gain the second mark for substituting values in at least one equation. The values found for the constants were usually correct although 8 = k/8 did sometimes lead to k = 1. Having found the values of the constants many students did not use them to write down the two equations y t = and t = 𝑥3 . Centres should encourage students to clearly show the equations as doing so would have gained the third mark and it might also have helped them to find a formula for y in terms of x. Many simply stopped after finding the values of the constants and went no further. Those who did continue and gave x y = as the final answer were not awarded the accuracy mark because the question required the answer to be given in its simplest form. Simplifying x to x was quite a common mistake. Students should ensure that they read the question carefully as a significant proportion failed to recognise “root”, “inversely” and “cube”. Notation when attempting to find the constants was often poor and some students omitted the constant from their initial equation.
y is directly proportional to √t, with y=15 when t=9. t is inversely proportional to x³, with t=8 when x=2.
Edexcel 1MA1 · June 2022 · Paper 2F · Q5 · 1 mark
1 mark
Examiner report
This question was answered correctly by over 80% of the cohort. The common incorrect answer was to give 4% as the final answer.
Write 0.4 as a percentage.
Edexcel 1MA1 · June 2022 · Paper 2F · Q9 · 3 marks
3 marks
Examiner report
Whilst almost two thirds of the cohort could read off the scale correctly for part (a) this means that one third could not. This is a basic skill which students should practise. In part (b) the vast majority of students scored at least one mark for clearly identifying either 10 or 56. The upper value of 56 was sometimes incorrect as students misread the scale of the graph or some students lost the final mark for expressing the numbers not as a ratio but as a fraction. The other common error seen was to simply subtract the two values to give an answer of 46. Any incorrect simplification of a correct answer was not penalised as this was not required by the question.
A graph of monthly house sales shows January 10, February 23 and June 56.
Edexcel 1MA1 · June 2022 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
This use of scale question was accessible with many pleasingly being awarded the 3 marks available. Students generally answered this question well with many using the correct process to find the scale factor between the two corresponding lengths and then continuing to multiply correctly by the width of the scale drawing. When full marks were not awarded, it was often due to converting the figures and getting confused, such as working with a scale factor of 500, having commonly converted 62 metres into centimetres. This approach occasionally caused confusion when units were not changed consistently. A small minority tried to find area; careful reading of the question is always recommended. Centres could encourage students to show all steps of their method as there were some answers that may have come from a partially correct method but with little or no working shown credit could not be given. Students could also be reminded that when answering questions involving scale they could draw a diagram to help them.
On a scale drawing, a building is 12.4 cm by 9.4 cm. Real length is 62 m.
Edexcel 1MA1 · June 2022 · Paper 2F · Q18 · 3 marks
3 marks
Examiner report
A range of marks were awarded for this question which tested students’ ability to convert between different time units and to calculate the mean. Many were able to convert 25.3 hours to minutes by multiplying by 60. Where this was unsuccessful it was often the case that students converted the 25 hours correctly but could not deal with the decimal part. Often 0.3 was incorrectly converted to 20 or 30 minutes, this meant that the mark for time conversion could not be awarded. However, students were able to gain a mark for working with the mean when they divided what they thought the time was, in minutes, by 115. Students who started with 25.3÷115=0.22 often failed to go any further and incorrectly interpreted this as 22 minutes. A significant number of students attempted to divide the number of appointments by the total time.
115 missed appointments totalled 25.3 hours.
Edexcel 1MA1 · June 2022 · Paper 2F · Q19 · 5 marks
5 marks
Examiner report
The majority of students gained marks on this question. Many gained three marks for finding the number of bags as 20 and the percentage increase as £23.76. Unfortunately, most students were unable to go onto the next stage of 23.76 ÷ 20 = 1.188 and then round to £1.19. Of those students that managed this calculation, some gave the final answer as £1.18 but many seemed unable to do the final division and so started to ‘guess’ possible answers and multiplied up in a trial and improvement method; this method was rarely successful. A common error was to attempt the build up method for the percentage calculation, by finding 10% and then 5% and adding appropriate multiples to get to 35%. There were many responses where the intermediate figures, often inaccurate, were stated without giving the process they came from given, this does not score marks as no process is available to mark. Students should be encouraged to use calculators for this type of question on a calculator paper. Only a small minority attempted the alternative method to start working with the price of the small bag first before working with percentage and most who did stopped when they reached £0.88.
Nimra buys 3 kg sweets for £17.60, packs 150 g per bag and wants at least 35% profit.
Edexcel 1MA1 · June 2022 · Paper 2F · Q24 · 5 marks
5 marks
Examiner report
It was pleasing to see that the many students were able to at least begin this multi-step problem involving area and proportion, with many gaining marks on this question. Most students were able to work out the area of the field at festival B and score the first mark, with many then continuing to use proportion correctly. Two or three marks were often awarded to students who were able to find the available area per person for each field, with many then continuing to complete the solution and gain full marks. However, a larger than expected number of students were unable to progress any further once they had found the area available at Festival B, with common mistakes being to subtract or divide the two areas rather than using proportionality. The final mark was occasionally lost due to arithmetic errors but the amount of working shown was pleasing to see. Part (b) of this question was demanding for most students. This type of question is a specification requirement and, as with previous years, the conversion of units of area proved not to be well known. For this example some students did have the notion that the squared term was involved but mistakenly wanted to square the 3 as well giving the popular incorrect value of 90000 or 9. Others said that you had to use 100 ×100 but said this was to multiply by 1000. This is a contradiction and as such so no marks were awarded. Students should be encouraged to check for contradictions in their explanations.
Festival A area 80,000 m² for 425 people. Festival B is 700 m by 2000 m for 6750 people.
Edexcel 1MA1 · June 2022 · Paper 2F · Q25 · 4 marks
4 marks
Examiner report
This was another question that was not well answered. The majority of students did not understand the need to work out distances using the coordinates given in the question. Both positive and negative values were accepted for these distances. There were many students who gave the answer of (11,17) implying that the differences of 7 and 8 were correctly calculated and added on to (4,9). However, in most of these responses, there was no working shown. When working was shown, students often tried to draw axes and plot points. The use of a diagram did allow some students to progress though this question and there were a small number of students who managed to find the y-coordinate.
L=(−3,1), M=(4,9), and LM:MN=2:3 on a straight line.
Edexcel 1MA1 · June 2022 · Paper 2F · Q26 · 3 marks
3 marks
Examiner report
Most students scored at least one mark in this question for working out the value of 4% of £679. Some used 12% and only considered simple interest, students are reminded to read the questions carefully as the second mark could not be achieved unless compound interest was used. A very few students used the approach of 679 × 0.963, others listed each the value for each year. Students should be encouraged to write down all their processes when using a calculator to make their intention clear as some inaccuracies or rounding can occur during working. Unfortunately, some students typed 679 - 4% into their calculator, to give 678.96. It was also common to see students find 4% and add on or use the formula with a decimal multiplier for increasing.
A £679 phone depreciates 4% per year for 3 years.
Edexcel 1MA1 · June 2022 · Paper 2F · Q27 · 4 marks
4 marks
Examiner report
It is very pleasing to see that the modal score for this question was 4 marks. This question involved two conversions, the use of proportionality, and a conclusion. For those students who did not score full marks it was pleasing to note that many could correctly convert both the monetary and the fuel terms correct. This gained two of the marks available. However, they then failed to use the proportionality element which often meant doubling one commodity or halving or to find comparable unit prices. Of the many different approaches to answer this question, comparing the cost of 8 gallons in pounds with the cost of 8 gallons in euros and cost of 18 litres in pounds to the given value of 18 litres in euros were the most popular and most successful. The most common error was connected with incorrect use of currency conversion with many attempting to divide by 0.85 rather than multiply by 0.85 when converting euros to pounds. To improve outcomes students need exposure to different conversions in a variety of situations and need to think more about the units presented to them. Students would also benefit from improving their presentation of their calculations when answering these types of question. Systematic approaches were often always successful and when students split their working into two sections, one for Spain and one for Wales, they were often able to complete the processes required and often gained at least 3 or 4 marks, depending upon arithmetic accuracy and the final decision.
Spain: €27 for 18 L. Wales: £40.80 for 8 gallons. €1=£0.85; 4.5 L=1 gallon.
Edexcel 1MA1 · June 2022 · Paper 2H · Q4 · 5 marks
5 marks
Examiner report
Part (a) was the first problem question on the paper and was looking for students to compare the people per unit area at two festivals. To be able to do so students had to first find the area at one of the festivals. However, students could gain the second and third marks even if they were unsuccessful in finding this area. These two marks were for finding the area per person at one or both festivals. Part (b) required students to understand the mistake made in the unit conversion. To gain the mark students needed to explain that, for the conversion from cm2 to m2, the conversion factor is 10000 or 1002. This was done with varying degrees of success with a good number able to work with the correct conversion factor, often showing the correct conversion for 3m2 to cm2 or 300cm2 to m2. The most common incorrect answer was to show that 300 × 300 = 90,000.
Festival A area 80,000 m² for 425 people. Festival B is 700 m by 2000 m for 6750 people.
Edexcel 1MA1 · June 2022 · Paper 2H · Q5 · 4 marks
4 marks
Examiner report
This problem required students to work with coordinates and a ratio to determine the coordinates of another point. A good number of students were able to gain credit on this question, with many gaining all 4 marks. Those who didn’t score fully often only went as far as finding the vertical and horizontal distances, but then didn’t add these onto the coordinates of L or M. Another common error was to use the ratio incorrectly, typically dividing by 3 and multiplying by 2, as was finding the equation of the line LMN, which could still gain P1 for the values of 8 and 7 within the gradient.
L=(−3,1), M=(4,9), and LM:MN=2:3 on a straight line.
Edexcel 1MA1 · June 2022 · Paper 2H · Q6 · 3 marks
3 marks
Examiner report
This is a standard depreciation question and was generally answered well by most students. Common errors were students working with simple interest, which normally meant they were able to score the first mark for finding the decrease for one year. The other common error was to divide by 1.04 rather than multiply by 0.96. In this case they were not able to gain any credit at all. Those who had a correct method and gained 2 marks almost always gained the 3rd mark. The minority who didn’t failed to gain this mark because they didn’t use correct money notation of 2 decimal places or used the ‘long way round’ method by subtracting 4% year after year and so lost accuracy.
A £679 phone depreciates 4% per year for 3 years.
Edexcel 1MA1 · June 2022 · Paper 2H · Q7 · 4 marks
4 marks
Examiner report
This problem question required students to compare different volumes of petrol in different currencies. There are many approaches that could be used to answer this question. Most students were able to score some marks. The most commonly awarded marks were those for converting volumes and for converting currency. It was often the third mark to get to the comparable figures that students struggled to gain. One common error was confusion with the currency conversion e.g. 27 ÷ 0.85 instead of 27 × 0.85.
Spain: €27 for 18 L. Wales: £40.80 for 8 gallons. €1=£0.85; 4.5 L=1 gallon.
Edexcel 1MA1 · June 2022 · Paper 2H · Q9 · 3 marks
3 marks
Examiner report
This problem required students to use the given pressure formula to first find the area and then subsequently the length of the base of a cuboid. Most students were able to gain the first mark for substituting the force and pressure correctly into the formula. Unfortunately, many were then unable to rearrange the formula correctly to find the area. This meant that although they then divided by the width they couldn’t gain the second mark as the process to find the area was incorrect. That said, there was still a high proportion of students who were able to complete the process correctly and gain an answer of 0.8 for 3 marks.
A box exerts force 180 N and pressure 187.5 N/m². Contact face is 1.2 m by x m; pressure=force/area.
Edexcel 1MA1 · June 2022 · Paper 2H · Q11 · 3 marks
3 marks
Examiner report
Inverse proportion is a topic that many students find difficult. The students who understood that this was inverse proportion rather than direct proportion, typically did well and gained all three marks. The remaining students struggled to gain any marks, normally dividing 14.5 by 13 or 6 as a first step, and were then unable to get any further. Another common error was to try a ‘build up’ method, e.g. recognise that if 6 workers take 14 2 days then 12 workers will take 7 4 days but they were unable to get to the time taken for 13 workers.
Six workers take 14.5 days. Kieron has 13 workers.
Edexcel 1MA1 · June 2022 · Paper 2H · Q14 · 3 marks
3 marks
Examiner report
Petersen’s Capture-Recapture method is one that is becoming familiar to students and as such most were able to start this problem by providing a suitable ratio for one mark. Many though were unable to form this into a correct equation, with most getting one of the fractions upside down, or struggling to manipulate the equation to correctly find the estimated number of fish. That said, a good number of students were able to correctly rearrange the equation to gain an answer of 1220 for three marks. Students should refrain from rounding numbers to 1sf, simply because they see ‘estimate’.
Capture-recapture: 180 fish tagged Friday; Saturday catch 305, including 45 tagged.
Edexcel 1MA1 · June 2022 · Paper 2H · Q15 · 4 marks
4 marks
Examiner report
Many students struggled to start this problem. There were 2 main methods to solving this problem. The first method was to use the 2 ratios to form an equation, which could then be solved. This is the method that most tried to attempt but struggled to combine the different parts. The second more efficient method was to compare 12 : 10 with 13 : 11 and realise this means the £1.50 is worth one part of this ratio. Students looking to earn the higher grades need to practice more with using equating ratios to form equations.
Marta:Khalid hourly pay=6:5. Both rise £1.50; new ratio=13:11.
Edexcel 1MA1 · June 2022 · Paper 3F · Q1 · 1 mark
1 mark
Examiner report
Most responses were correct for this question with the most common answer of 35 100 . The simplified version of 7 20 sometimes followed or was the only answer given.
Write 35% as a fraction.
Edexcel 1MA1 · June 2022 · Paper 3F · Q12 · 2 marks
2 marks
Examiner report
This was well done by the majority of students who gained 2 marks. They knew how to write 60 as a fraction of 1000 and then correctly simplified the fraction. Those that did not fully simplify were able to gain one mark for 100. A few students did not use fraction form giving their answers in ratio or decimal form but as long as they wrote 100 as the starting point they were awarded the method mark. Students should be encouraged to always show the first step from the information given in the question.
Write 60 m as a fraction of 1000 m, simplest form.
Edexcel 1MA1 · June 2022 · Paper 3F · Q13 · 4 marks
4 marks
Examiner report
Part (a) was well attempted by most students who were able to measure accurately and convert to metres. It was pleasing to see that most showed the calculations required for the conversion. The majority of these went on to gain full marks correctly, adding the appropriate two distances and subtracting the other to find the difference in the overall total. There were a few who used their measurements to calculate the difference of 2 and then multiply by 150 which is a very efficient method. Those that did not measure accurately often went on to gain one mark for showing clear working for conversion and then the difference between the distances, but it was disappointing to find students using measurements that were more than 2 cm different to the diagram, leading to the suspicion that they either did not have a ruler, or did not know how to use it accurately. In part (b) the vast majority were unable to tackle this bearings question. Of those who did attempt this question it was common to see the bearing of C from A given. There were very few correct answers in the range with quite a few answers of 285 seen, which was just out of range.
Text-complete scale-map adaptation: on a coordinate grid measured in centimetres, plot C=(0,0), A=(−6.66,2.16) and B=(−3.58,−1.78), with north in the positive y-direction. Use scale 1 cm=150 m. Join A to B, B to C, and A to C.
Edexcel 1MA1 · June 2022 · Paper 3F · Q19 · 4 marks
4 marks
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.
400 counters are red/yellow/green. 3/8 are red and 82 are yellow.
Edexcel 1MA1 · June 2022 · Paper 3F · Q24 · 5 marks
5 marks
Examiner report
In this question many students were able to find the number of counters each person would get. There were two main routes to these values: algebraic and numeric. Weaker students started by dividing 54 by 3 but were then unsure of where to go from there. Students who adopted a clear algebraic approach often went on to solve the question completely. However, students occasionally ended up with 4x – 6 = 54 rather than 5x – 6 = 54, due to not understanding that Tony had six less counters than Selma rather than Rick. Most students adopted a numeric approach, and most were successful in arriving at the three numbers 12, 24 and 18 scoring three marks. Students were less successful in converting the counters each had into a ratio between Rick and Tony. Where students managed this, they usually then went on to gain the full marks for p = 1.5 but those who did not recognise this unitary ratio expression were sometimes put off from writing their ratio of Rick to Tony.
Rick has r counters, Selma twice as many, Tony 6 fewer than Selma; total 54. Rick:Tony=1:p.
Edexcel 1MA1 · June 2022 · Paper 3F · Q25 · 4 marks
4 marks
Examiner report
Despite being later in the paper it was pleasing to find many students gained full marks on this question with the vast majority able to gain at least 1 mark. There were various methods used but the most popular was to find the cost of 15 rolls for each shop. It was common to find the values £180 and £184.80 clearly stated with the correct conclusion of Chic being the cheapest. The next popular method was to work it out for 5 rolls each. Those that did not gain full marks generally made an error in calculating the percentage discount for Style Papers because they used the breakdown method with the common error of showing 2% as 0.14 rather than 1.4; a correct method to calculate an appropriate percentage was essential to proceed through this question.
15 rolls: Chic Decor 3 for £36. Style Papers packs of 5, normal £70, 12% off.
Edexcel 1MA1 · June 2022 · Paper 3F · Q27 · 4 marks
4 marks
Examiner report
The most common method for this question was to find the distance of 7.5 by working out the two parts of the journey and adding them together. The difficulty came when trying to find the average speed for Amy and using the time converted to a decimal. Other students used the other method to get to the final answer of 10 by doing 450 ÷ 45 but this was not as common. Students who were successful in following this question through, often worked in minutes using 15, 40 and 45 which gave the correct answer without having to convert them first. Very few students converted the times into hours and when they did, a common issue was the use of 0.6 for 60. A good proportion of students scored full marks for this question though many students just found the average of the two speeds.
Jessica runs 15 min at 6 mph then 40 min at 9 mph. Amy covers same total distance in 45 min.
Edexcel 1MA1 · June 2022 · Paper 3F · Q29 · 2 marks
2 marks
Examiner report
Most found this question challenging. Many students just offered the wrong answer of 3000 or 30000 or 300 on the answer line. One of the most common errors was converting metres to km by multiplying by 1000. A significant proportion divided by 1000, correctly, to convert metres to kilometres and thought they had finished. The majority of the marks given were for seeing 0.03 or 108000.
Change 30 metres per second to kilometres per hour.
Edexcel 1MA1 · June 2022 · Paper 3F · Q30 · 2 marks
2 marks
Examiner report
Most of the students did not recognise that this was a reverse percentage question so just found 15% of 13600 and added it on. This is a very common misconception. Those who were awarded full marks mostly used the method 85% = 13600, 1% = 160, 100% = 16000 Those who used the multiplier of 0.85 often incorrectly used it to multiply rather than divide. Even when students correctly identified that they had 85%, they did not understand that they needed to divide by 85 and multiply by 100 to get back to 100%. Summary: Based on their performance on this paper, students should: • ensure that their written work is legible. Figures taken from the question, and taken from student’s own work, need to be transcribed accurately. • avoid rounding or truncating answers to calculations and use the most accurate values where possible. • practise algebraic manipulation and derivation, application of ratios, scaling and rates, and time. • learn to use their calculators for working with percentages, rather than always using a break-down / partitioned approach. • include working out to support answers. • be confident in their use of measuring equipment in drawing and in measuring.
A car's value decreased 15% to £13,600.
Edexcel 1MA1 · June 2022 · Paper 3H · Q3 · 5 marks
5 marks
Examiner report
A majority of students scored full marks on this question. Many students in this higher tier paper used an algebraic approach, formulating and solving an equation, then using the solution to find a ratio and the value of p. Students usually worked accurately, but there were a number of students who wrote down a correct equation but collected terms in x to get 4x instead of the correct 5x. Other students, having got the correct equation, 5x − 6 = 54, then made an error in the first step to solve it, writing 5x = 48. A significant proportion of students adopted a purely numerical approach, finding, by trial and improvement, three numbers which satisfied the criteria given in the question, then using them to form a ratio. Some students found the number of counters for Rick and for Tony but did not form a ratio. There were also some other students who did form a ratio but did not write it in the ratio 1 : p.
Rick has r counters, Selma twice as many, Tony 6 fewer than Selma; total 54. Rick:Tony=1:p.
Edexcel 1MA1 · June 2022 · Paper 3H · Q4 · 4 marks
4 marks
Examiner report
A good discriminator between lower attaining students, this question attracted many fully correct solutions. Despite there being a number of possible routes that students could take, there were also many incorrect or incomplete solutions. The most common approach was to find the cost of 15 rolls of wallpaper at each of the shops, though credit was given for comparing any number of rolls, for example 1 roll or 5 rolls. A high proportion of students compared £180 with £184.80 and reached a correct conclusion to score all 4 marks. However, some students worked out the discount and took that to be the cost of the wallpaper at Style Papers. A common error seen was, for students who did not appear to have access to a calculator, to use a build-up method to find 12%, for example by writing down 10%, 1% and 1%. Students who did this often made an error with the arithmetic and lost marks because they did not show the calculation, for example the addition of the three percentages or how they worked out the 10% or 1%. Students are reminded that when showing their calculation of a percentage, they should show a full method, so for example instead of writing 12% of £70 = £8.40, they should write 100 × 70 = 8.40 or 0.12 × 70 = 8.40. This is so that in the event of an incorrect answer, marks for a correct method can be awarded.
15 rolls: Chic Decor 3 for £36. Style Papers packs of 5, normal £70, 12% off.
Edexcel 1MA1 · June 2022 · Paper 3H · Q6 · 4 marks
4 marks
Examiner report
The majority of students made a good attempt at this problem on distance, time and average speed. Many students produced a concise, accurate and complete solution. Lower attaining students sometimes lost accuracy in their working because they used 0.6, 0.66 or another decimal approximation when coverting 40 minutes to hours. These students were still able to be given 3 of the 4 marks available if they had used and shown correct processes in their solutions. A significant number of students appeared to ignore the units in the question and were very fortunate to get a correct answer because the nature of the problem depended on the ratio of the times taken, rather than the times themselves. Of those students who answered the question incorrectly, many did so because they did not know the formula and divided the speed by the time, instead of multiplying them.
Jessica runs 15 min at 6 mph then 40 min at 9 mph. Amy covers same total distance in 45 min.
Edexcel 1MA1 · June 2022 · Paper 3H · Q8 · 3 marks
3 marks
Examiner report
Many students found this question to be straightforward. They often used a triangle where readings were easy to take and gave a value for the gradient of the graph within the accepted range, more often than not 0.14. For some other students who drew a small triangle on the line getting an accurate answer was less likely. However, if the value given for the gradient was outside the range 0.135 to 0.145, examiners awarded both marks in part (a) provided a correct method was clearly shown. A small number of students used “increase in x ÷ increase in y” or counted squares rather than using the scales on the axes. These students could not be credited with any marks in part (a). Part (b) was answered less well and many incorrect or ambiguous statements were seen. An answer equivalent to “cost per unit of electricity” was expected but many students merely described what the graph, not the gradient, showed and statements such as “cost of how many units used” were often seen.
A straight-line electricity cost graph passes through (0 units, £0) and (100 units, £14).
Edexcel 1MA1 · June 2022 · Paper 3H · Q10 · 3 marks
3 marks
Examiner report
This question was not well done. Too many students showed the misunderstanding that, to reverse a 10% decrease, they had to increase the value of the car by 10%, so they multiplied by 1.1 rather than using the correct method of dividing by 0.9. It was relatively unusual to award 1 or 2 marks for responses. Students usually either showed a good understanding or no understanding of the processes required to solve the problem.
A car depreciates 12.5% in year 1 then 10% in each of years 2 and 3; final value £17,010.
Edexcel 1MA1 · June 2022 · Paper 3H · Q18 · 5 marks
5 marks
Examiner report
It is encouraging to report that the majority of students gained some credit for their attempt at this question. The length of TC was often found successfully and a good proportion of students were also able to find the length of at least one of SD and TD. Only the higher attaining students were able to identify the angle which was required and put everything together in order to find the size of this angle, that is the size of angle DTS. Errors commonly seen included, substituting 12 and 14 incorrectly into the formula for the area of the cross section and making an error in the use of Pythagoras’ rule to find the length of DT.
Prism base ABCD is a 14 cm square. T lies on BC with BT:TC=4:3. Cross-section SRCD is a trapezium of area 147 cm² with CR=12 cm. ST rises from base point T to S above D.
Edexcel 1MA1 · June 2022 · Paper 3H · Q20 · 4 marks
4 marks
Examiner report
Though a significant number of students did not attempt this question, many of those students who did attempt it scored full marks for a complete and correct solution. The most common error seen was for students to write down a correct equation, 29 600 = 24 000a + 800 but then make an error in solving the equation. It was not unusual for students to divide 29600 by 24800 as a first step, then subtract 800. Some students who found a correct value for “a” went on to use the iterative relationship correctly but only went as far as finding the profit made by the shop in the year 2020.
Pn+1=aPn+800. Profit was £24,000 in 2018 and £29,600 in 2019.
Edexcel 1MA1 · November 2021 · Paper 1F · Q1 · 1 mark
1 mark
Examiner report
Very few failed to earn the mark here. Those with incorrect answers usually wrote 3%.
Write 3/10 as a percentage.
Edexcel 1MA1 · November 2021 · Paper 1F · Q12 · 3 marks
3 marks
Examiner report
This question was not well answered with only a few understanding what was being asked in the question. Many did not realise that they had to find the ratio of boys to girls for each of the two drama groups. A common approach was to find ଷ and in some cases ସ of 84 (36 + 48) concluding that there were 36 boys and 48 girls also in the second group and therefore Ann must be correct. This was not enough to get full marks without ratios (or fractions) being considered. Very few wrote ଷ ൊ ସ for the second group, 3 : 7 frequently appearing. Those that did usually went on to gain full marks. A common error when considering fractions was to express the boys in group one as ଷ ସ଼ rather than ଷ଼ ସ . Those students who set up two columns and worked separately on the two groups had the greater chance of success.
There are two drama groups. In one group there are 36 boys and 48 girls. In the other group, 3/7 of the students are boys and the rest are girls. Ann says, 'The ratio of boys to girls is the same for both groups.'
Edexcel 1MA1 · November 2021 · Paper 1F · Q14 · 4 marks
4 marks
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.
3 kg of carrots cost £1.80. 2 kg of carrots and 5 kg of potatoes cost £3.45 in total.
Edexcel 1MA1 · November 2021 · Paper 1F · Q17 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · November 2021 · Paper 1F · Q19 · 3 marks
3 marks
Examiner report
Most students gained at least one mark for correctly calculating the actual loss of £24 but very many were unable to represent this as a percentage of the cost price of the watch. 24% was the most common incorrect answer seen. Some students correctly quoted £80 = 100% but were unable to use this to answer the question.
Robin buys a watch for £80 and sells it for £56.
Edexcel 1MA1 · November 2021 · Paper 1F · Q23 · 4 marks
4 marks
Examiner report
Whilst some students were able to fully complete a solution for this problem, many were unable to find 20% or 30% of the required value, often getting confused with the numbers of ‘zeros’ involved. It was not uncommon to see 10% of 220 000 given as 2200 or 220. A great many students lost marks because they did not show a mathematical method, simply writing “20% of 220000” gains no marks whereas 100 × 220 000 gets the method mark. Many students found the correct decrease or increase of £44 000 and £48 000 respectively and went no further. The fact that one was an increase in value and one a decrease in value was often missed. Again, students must read the questions carefully. Of those who did gain the correct values many failed to say which was the larger amount, thus failing to gain the final mark.
At the end of 2017, Tamara's house was worth £220,000 and Rahim's house was worth £160,000. By the end of 2019, Tamara's value had decreased by 20% and Rahim's had increased by 30%.
Edexcel 1MA1 · November 2021 · Paper 1F · Q24 · 3 marks
3 marks
Examiner report
Many students found the sum of the ratios (26) perhaps thinking that they were required to share an amount with the given ratio. Some ignored the 24 and simply subtracted 4 from 15 for their answer. Marks were available for build-up methods of finding equivalent ratios, but 12 (:21) : 45 was required for both method marks.
Rosie, Matilda and Ibrahim have stickers in the ratio 4:7:15. Ibrahim has 24 more stickers than Matilda.
Edexcel 1MA1 · November 2021 · Paper 1H · Q4 · 4 marks
4 marks
Examiner report
It was pleasing that a great many students were able to gain at least three of the four marks by working out the value of either Tamara’s house or Rahim’s house at the end of 2019. Many students worked out both values correctly and stated that Rahim’s house had the greater value and they were awarded full marks. Too many responses, though, were spoilt by careless errors. Some students used the multipliers 0.8 and 1.3 to work out the new values but it was more common to see students start by working out 20% of 220 000 and 30% of 160 000. Build up methods for finding percentages were quite popular but incorrect statements such as 10% of 220 000 = 2200 and 10% of 160 000 = 1600 with no method shown gained no credit. Students should be advised that the method needs to be clear. When finding 10%, for example, they should show that they intend to divide by 10. Errors were frequently made in the final part of the process. Subtracting 44 000 from 220 000 was a problem for some students; sometimes the result of this calculation was greater than 220 000. Some students correctly found 30% of 160 000 but then subtracted this from 160 000 instead of adding. A few students only worked out 20% of 220 000 as 44 000 and 30% of 160 000 as 48 000 and stated that Rahim’s house had the greater value. They were awarded the first mark only.
At the end of 2017 Tamara's house was worth £220,000 and Rahim's £160,000. By the end of 2019 Tamara's value had decreased 20% and Rahim's had increased 30%.
Edexcel 1MA1 · November 2021 · Paper 1H · Q5 · 3 marks
3 marks
Examiner report
Although some students gained only the first mark, usually for 15 – 7 = 8 or for 24 ÷ 3 = 8, the majority of students gained either full marks or no marks. Those that made a correct start frequently went on to gain all three marks but many students were not able to find a suitable strategy to solve this ratio problem. Incorrect processes were often the result of adding the three numbers in the ratio, 4 + 7 + 15 = 26, as a first step.
Rosie, Matilda and Ibrahim have stickers in the ratio 4:7:15. Ibrahim has 24 more than Matilda.
Edexcel 1MA1 · November 2021 · Paper 1H · Q18 · 5 marks
5 marks
Examiner report
This proved to be a challenging question and finding the length of AB proved to be beyond most students. Some of those who attempted the question identified that they need to find the perpendicular height of the trapezium and gained the first mark for writing a correct trigonometric statement such as sin30 = h/6. Some students could not recall the value of sin30 and did not complete the process to find the height. After finding the height many students struggled to make any further progress, failing to realise that they should use the formula for the area of a trapezium. It was common to see the trapezium split into two triangles and a rectangle and attempts at using Pythagoras. A good proportion of those that did substitute correctly into the formula went on to show a complete process to find the length of AB. A small number of students gave 5 as the final answer and lost the accuracy mark.
ABCD is a trapezium with parallel sides AB and CD. A sloping side of length 6 cm makes a 30° angle with a parallel side. Area=66 cm^2 and AB:CD=2:3.
Edexcel 1MA1 · November 2021 · Paper 2F · Q1 · 1 mark
1 mark
Examiner report
This question was very well answered with the vast majority of answers being correct. A few incorrect answers were seen with 3 10 being one of the incorrect answers given.
Write 31% as a fraction.
Edexcel 1MA1 · November 2021 · Paper 2F · Q2 · 1 mark
1 mark
Examiner report
Students do find conversions difficult and even at this simple level approximately a third of the students gave an incorrect answer, with 3000 being a popular incorrect answer.
Change 3 metres into centimetres.
Edexcel 1MA1 · November 2021 · Paper 2F · Q5 · 2 marks
2 marks
Examiner report
This question was well answered, with most students scoring the 2 marks available. The most common incorrect responses were either to draw a 6cm by 3cm rectangle, seemingly from counting the grid lines rather than the squares, or to draw either a 5cm by 1cm rectangle or a 5cm by 5cm square. When full marks were not awarded, a mark was often achieved for engaging with the scale given by either drawing a diagram with one dimension correct or by calculating both dimensions correctly.
A rectangle is 35 m by 20 m.
Edexcel 1MA1 · November 2021 · Paper 2F · Q10 · 1 mark
1 mark
Examiner report
Three quarters of the cohort gave a correct answer to this question. The common incorrect answer was to just write down a decimal answer.
Write 17 as a fraction of 30.
Edexcel 1MA1 · November 2021 · Paper 2F · Q14 · 3 marks
3 marks
Examiner report
The vast majority of students answered both parts of this question correctly, demonstrating a good understanding of the skills being assessed. In part (a) many did gain the first mark by stating an answer within the range of 14 to 16. A common error seen was to read off the value of 75 for 5 hours but not make the adjustment to a payment for one hour or not being able to interpret the divisions on the scale correctly as £2 per square, with £10.60 being seen frequently. A very small number of students added together readings for 1, 2, 3, 4 and 5 hours. The most common and successful approach to part (b) was to use their hourly rate found in part (a) and multiply by 36. A build up method using one or more readings from the graph was less common and less successful, particularly as many using this method only found the pay for 35 hours by using the reading at 5 hours and not adding an extra hour of pay to show a complete build-up.
A straight-line pay graph passes through (0 hours, £0), (1, £15), (2, £30), (3, £45), (4, £60) and (5, £75).
Edexcel 1MA1 · November 2021 · Paper 2F · Q17 · 5 marks
5 marks
Examiner report
It was common to award 2 marks or full marks for this question. Students often correctly placed 38 or 15 for the first mark and therefore went on to calculate or place 22 or 7 for the second mark. Many students then failed to attempt to find 60% of 60 but when they did they often went on to correctly complete the rest of the question. The most common error was to find 60% of the wrong value (usually 38). Some students gained a third mark by simply showing that the total number of texts was 36 but not using it in the diagram, this skill in working with percentages was enough for the third mark. Some responses had the correct numbers misplaced in the tree diagram and students should be encouraged to check their answers thoroughly. These students did gain some marks for working but could not gain communication and accuracy marks.
60 people are asked whether they prefer texting or emailing. 38 are women and the rest are men. 15 men prefer email. 60% of all the people prefer text.
Edexcel 1MA1 · November 2021 · Paper 2F · Q23 · 5 marks
5 marks
Examiner report
Part (a) of this question was not often correctly answered. Many students were able to correctly identify that they needed to divide distance by time to arrive at the answer but very few went on to convert minutes into hours. Common incorrect responses were often 1.3 or 20. Those students that obtained the correct answer of 80 often did so by scaling ie multiplying 20 by 4. It would be beneficial for centres to ensure students are confident answering questions involving compound measures. Part (b) was often awarded part marks with only a few students scoring all the marks for a fully correct graph. Those who scored one mark often did so by drawing the correct horizontal line for the stop in Sam’s journey. A few students scored two marks for drawing a line representing the correct distance travelled in the last 20 minutes but forgot to show the stopping time on the graph. Rarely was 25 seen as part of calculations and a common error seen was for students to continue their line to (1050,50).
A travel graph shows Sam travelling 20 km from 10:00 to 10:15. At 10:15 he stops for 10 minutes, then drives for 20 minutes at 75 km/h.
Edexcel 1MA1 · November 2021 · Paper 2F · Q28 · 2 marks
2 marks
Examiner report
As the last question on the paper it was not surprising to see that students found this question challenging. The overwhelming number of responses to this question was £312800, coming from a variety of methods to find 115% of £272000. Occasionally 85% of £272000 was seen, usually from £272000 – (15% of £272000). The fact that what was required was 100% when the given figure was actually 85% was rare. Those who did recognise this usually went on to gain full marks. Summary Based on their performance on this paper, students should • carefully read questions • practice questions involving negative numbers • give succinct explanations • use a calculator.
In a sale, a boat's normal price is reduced by 15%. The sale price is £272,000.
Edexcel 1MA1 · November 2021 · Paper 2H · Q3 · 5 marks
5 marks
Examiner report
In both parts of this question it was evident that many students did not have a secure understanding of time and calculations involving time. In part (a) students typically scored either two marks as they understood the question, or no marks as they incorrectly worked in minutes rather than hours. Part (b) allowed students who struggled with time to score at least one mark for the horizontal line segment to represent the stationary part of the journey. Those who calculated the time correctly and gained a method mark then normally gained the communication mark for the correct sloping section to the graph. A note to students is that 3 is not equal to 0.3
A travel graph shows Sam travelling 20 km from 10:00 to 10:15. He then stops 10 minutes and drives 20 minutes at 75 km/h.
Edexcel 1MA1 · November 2021 · Paper 2H · Q7 · 3 marks
3 marks
Examiner report
A fully correct response was not seen in the majority of cases, and in fact it was evident that students did not properly know the formula linking density, mass and volume. Of those who were able to score a mark the most common score was one mark for finding either an individual mass, or the total mass (192). At this point most didn’t know to use total volume to calculate the density of C, and often divided by 3.
Liquid A density=1.8 g/cm^3, liquid B density=1.2 g/cm^3. 80 cm^3 A and 40 cm^3 B make 120 cm^3 C.
Edexcel 1MA1 · November 2021 · Paper 2H · Q10 · 4 marks
4 marks
Examiner report
The problem nature of this question proved a challenge for a good number of students, with many being unable to work backwards to find the initial investment. It was very common to see a multiplier of 0.975 rather than 1.025 being used. However, of those who struggled with the first part, and therefore to access the first two marks, many were then able to gain the third mark as they knew the required processes to calculate compound interest.
Louise and Sadiq each invest £x for 3 years. Louise earns 2.5% compound annually and ends with £344,605. Sadiq earns 2% for each of the first two years and 3.5% for the third.
Edexcel 1MA1 · November 2021 · Paper 2H · Q11 · 5 marks
5 marks
Examiner report
Part (a) was not well answered, with most students not understanding the ratio and how to apply it to the coordinates. It was rare to award both marks, with some students able to find one coordinate (typically the x value) or for getting as far as 4.5 when working with the y-coordinate. Part (b) was a more common type of question and it showed that students have completed work on gradients and, compared to previous questions, a good number showed knowledge of gradients of perpendicular lines. The first mark was awarded in equal numbers for a correct process to find the gradient of L or for an equation in the form y = mx + 3. Those who correctly (or incorrectly) found a gradient for L, were still able to gain the second mark for a correct process to find the gradient of the perpendicular line, and this mark was awarded nearly as frequently as the first. Few gained full marks, either due to an error in finding the first gradient or for an incorrect y intercept, despite this being given in the question.
Line L passes through P(-6,0) and Q(0,3). R is on the same straight line beyond Q and PQ:QR=2:3.
Edexcel 1MA1 · November 2021 · Paper 2H · Q19 · 3 marks
3 marks
Examiner report
This ratio problem required students to work with scale factors and ratios between 3 spheres. The most common error was to work with the 27 and the ratio 1 : 2 and arrive at 54. The first mark was for the ability to cube root to find 5 and 3, and at this stage the values did not need to be given in a ratio. Many students who succeeded this far then got confused and failed to work with the value of 3 and the ratio 1 : 2. Of those who got to the values of 3 and 6, many then failed to link the 6 from sphere C and the 5 from sphere A. Even fewer then knew to square to find the ratio of surface areas. Quite a few saw the question as having to find the radius for the sphere and had difficulty rearranging the correct formula or even trying to use an incorrect formula.
Spheres A,B have volumes 125 and 27 cm^3. Radius B:radius C=1:2.
Edexcel 1MA1 · November 2021 · Paper 3F · Q1 · 1 mark
1 mark
Examiner report
A well answered first question on the paper where most students gained the mark.
Write 45% as a decimal.
Edexcel 1MA1 · November 2021 · Paper 3F · Q11 · 3 marks
3 marks
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.
Complete a time conversion and an average-speed expression.
Edexcel 1MA1 · November 2021 · Paper 3F · Q12 · 4 marks
4 marks
Examiner report
In part (a) there were, surprisingly, too many instances of students incorrectly measuring the distance between Shelton and Trilby. Failure to indicate where their measurements came from resulted in lost marks for many. For example, those who just estimated (or prematurely rounded) their distance to 3 cm but did not indicate this was the distance between Shelton and Trilby could not be credited any marks. This was not uncommon. Some measured accurately and then failed to use the scale correctly. Common incorrect answers were 35 × 2 = 70, or doing 2 × 20 then adding on 0.5 = 40.5 There were far fewer correct answers to part (b). When 1 mark was awarded, it was usually for finding 6000 but failing to convert to metres. Knowledge of unit conversion remains a weakness.
On a map, Shelton and Trilby are 2.5 cm apart. The scale is 1 cm represents 20 km.
Edexcel 1MA1 · November 2021 · Paper 3F · Q13 · 4 marks
4 marks
Examiner report
In part (a) the most common incorrect answer was obtained by writing 2 : 3 as 66%. Students using equivalent ratios and recognising they needed ଶ ହ or 20% did much better. Part (b) was answered better than part (a), with many students able to link the percentage to the ratio. It is evidence that a number of students incorrectly carried forward information from part (a). The majority of correct answers were given as 1 : 4 or 2 : 8. One mark was awarded to those students who did not get this far, but did show sufficient understanding to get to 80.
In the Northern hemisphere, land area : water area = 2:3. In the Southern hemisphere, 20% of the area is land.
Edexcel 1MA1 · November 2021 · Paper 3F · Q18 · 1 mark
1 mark
Examiner report
Probably the worse answered question on the paper. Lots of 100 and 1000, with the correct answer of 10 000 very rare.
Change 1 m^2 into cm^2.
Edexcel 1MA1 · November 2021 · Paper 3F · Q22 · 4 marks
4 marks
Examiner report
The majority of the students were only able to gain 1 mark. This was for adding the parts of the ratio or for noting that the weight of the cheese would be 1000g. Some got no further than this although they did produce a large amount of spurious working out. Many divided 6000 by 175 or multiplied 600 by 2.25 not having realised that they needed to calculate the weight of cheese required first. Again, premature rounding played a part in some incorrect calculations.
Potato cakes use potato:cheese:onion in the ratio 9:2:1. Natalie needs 6000 g. Cheese costs £2.25 per 175 g.
Edexcel 1MA1 · November 2021 · Paper 3F · Q24 · 4 marks
4 marks
Examiner report
Many students made a correct first step of 2400 ÷ 8 = 300 but then misunderstood the subsequent value as 300 minutes rather than 300 lots of 1 minute and 40 seconds. Conversions involving time caused problems for the majority of students who went on to multiply 300 by 1.4 rather than multiplying by 1.666666 to reach the value of 500. A few struggled to work with 2.2 gallons, even on calculator paper. A significant number multiplied 4.54 by 2 (instead of 2.2), some then trying to adjust their answers by adding on values such as 0.2, but by this stage marks were lost. Use of 2 rather than 2.2 was incorrect processing as this figure was given in the question. The different types of units involved within the question often overwhelmed students who were then unsure of the resultant units they were dealing with. Solutions to this problem were often very disorganised; examiners found it quite difficult to follow the working whist searching to see if credit could be given.
A 2400-litre tank is empty. Company A supplies 8 litres in 1 minute 40 seconds. Company B supplies 2.2 gallons per minute. 1 gallon = 4.54 litres. Company A takes longer.
Edexcel 1MA1 · November 2021 · Paper 3H · Q2 · 4 marks
4 marks
Examiner report
This question was a good discriminator between lower attaining students taking this paper. Most students realized the need to work with the ratio 9 : 2 : 1 in order to calculate the weight of cheese in 6000g of potato cakes and scored at least one mark finding the total of 9, 2 and 1. However, a surprising number of students misguidedly divided 6000g (of potato cakes) by 175g (of cheese) as their first calculation. These students rarely realized their error and so could score no marks for their attempts to answer this question. On the other hand a considerable proportion of students scored full marks for a fully correct answer. Some students assumed that the cheese was sold in 175g packets and so rounded up the 5.71…lots of 175g to 6. These students were awarded full marks for an answer of £13.50. Nearly all students gave answers rounded to the nearest penny.
Potato cakes use potato, cheese and onion in the ratio 9:2:1. Natalie needs 6000 g of potato cakes. Cheese costs £2.25 per 175 g.
Edexcel 1MA1 · November 2021 · Paper 3H · Q4 · 4 marks
4 marks
Examiner report
A good discriminator, this question attracted many fully correct solutions but also many attempts which were awarded each of the marks available. There were a number of possible routes that students could take to solve the problem. By far the most common route taken was for students to work in litres and so to start off by working out the number of 8 litres in 2400 litres. Most students then showed the intention to work out the time for company A to fill the tank by multiplying 300 by 1 minute 40 seconds. These students usually scored at least 2 marks for their working. However, a significant number of students did not change their 1 minute 40 seconds accurately to minutes and examiners saw figures such as 1.6 and 1.40 used frequently. This inevitably led to otherwise successfully completed answers scoring 3 of the 4 marks available. About one third of students obtained full marks for their solution to this question.
A 2400-litre tank is empty. Company A supplies 8 litres in 1 minute 40 seconds. Company B supplies 2.2 gallons per minute. One gallon is 4.54 litres. Company A takes longer.
Edexcel 1MA1 · November 2021 · Paper 3H · Q8 · 2 marks
2 marks
Examiner report
In this question the great majority of students sketched a straight line from the origin to score the mark available in part (a). Part (b) was less well answered with many students drawing another straight line but this time with a negative gradient. This did relay the idea that as the value of x increases then the value of y decreases. However, it did not accurately represent the inverse relationship and could not be awarded the mark available.
On separate positive x-y axes, sketch graphs representing two proportional relationships.
Edexcel 1MA1 · November 2021 · Paper 3H · Q9 · 3 marks
3 marks
Examiner report
For part (a) it was disappointing to see so many students use a directly proportional relationship and give an answer of 6.25 hours thereby implying that it would take 15 people longer than it would take 12 people to clean the same number of cars. There was little evidence of students applying a common sense check to their answers followed by a review of the processes applied to get their answer. Part (b) was not generally answered well with examiners accepting any statement which might reflect that the time might change and which did not contain any contradiction. Further reasoning was not always required in order to access this mark. So, for example, “the time might increase” was accepted whereas it might have been preferred to have seen “if people worked at a slower rate, the time would increase”. However, examiners did not accept definite statements such as “the time will increase” without further qualification, so “the time will increase if they work at a slower rate” was accepted. Too many students had not properly understood the question and compared the amount of time taken by 15 people with the time taken by 12 people. This could not be accepted for the award of the mark.
On Monday, 12 people took 5 hours to clean a number of cars. On Tuesday, 15 people cleaned the same number of cars.
Edexcel 1MA1 · November 2021 · Paper 3H · Q14 · 4 marks
4 marks
Examiner report
Most students could make some progress with this question and gained a mark for finding the sum of the parts of each of the given ratios, 2 : 3 (=5) and 9 : 1 (=10). However, far fewer students could get any further. Students often tried to apply the fact that Olivia and Jessica had half as many sweets as Fran and Gary but then doubled the numbers relating to the wrong pair. Examiners were surprised that not more students assigned a given total number of sweets to one of the pairs, for example 100 sweets to be shared between Fran and Gary. Students could then have worked with this to find the number of sweets each student gets before writing them as a ratio in its simplest form. Very few students attempted the question using algebra and where they did, they seemed to get confused because they used the initial letters of the names in their working.
Olivia and Jessica have in total half as many sweets as Fran and Gary. Fran and Gary share theirs in the ratio 2:3; Olivia and Jessica share theirs in the ratio 9:1. Fran, Gary, Olivia and Jessica receive w, x, y and z sweets respectively.
Edexcel 1MA1 · November 2021 · Paper 3H · Q15 · 3 marks
3 marks
Examiner report
Higher attaining students often scored full marks for their answers to this question. Where tangents were drawn they were generally accurate and allowed them to be used to get a good estimate of the gradient. However there was a significant number of students who used the coordinates of the point on the curve at t = 12 and who simply divided the y coordinate by the x coordinate (17 ÷ 12) to get the gradient. Some of these students had already drawn a tangent to the curve at t = 12.
A smooth decreasing graph gives water volume V litres against time t seconds. Approximate readings from the official curve are (0,40), (5,29), (10,22), (15,16), (20,12), (30,7), (40,4) and (50,2.5).
Edexcel 1MA1 · November 2021 · Paper 3H · Q17 · 4 marks
4 marks
Examiner report
It was relatively rare to see a fully correct solution to this question together with the award of 4 marks. However, many more students were able to access some marks for expressing the proportionalities between x and y and between y and z using symbols, by substituting the 2 given values in their equations and in some cases for getting as far as writing down an equation which would enable them to find the constant of proportionality for the relationship between z and x. Nearly all students used the same constant of proportionality for the relationship between x and y as they did for the relationship between y and z. This was condoned as far as it could be though students should be advised to use different constants in cases like this.
x is directly proportional to y^2. y is directly proportional to z^3. Also z=2 when x=32.
Edexcel 1MA1 · November 2021 · Paper 3H · Q19 · 3 marks
3 marks
Examiner report
This question was often not attempted though there were some excellent responses from higher attaining students taking this paper. However, it was clear that most students did not have a clear understanding of the notation used. Many students who did have some understanding used the incorrect relationship 3610 = k × 4000 and examiners were left wondering whether these students had thought they were dealing with successive years and not times which were 2 years apart. Examiners were generally unable to award these students any marks.
At the start of year n a population is P_n, and P_(n+1)=kP_n. The population was 4000 at the start of 2017 and 3610 at the start of 2019.
Edexcel 1MA1 · November 2020 · Paper 1F · Q9 · 3 marks
3 marks
A bag contains red counters and blue counters only. number of red counters : number of blue counters = 3 : 4 Write down the fraction of the counters that are red.
Edexcel 1MA1 · November 2020 · Paper 1F · Q13 · 4 marks
4 marks
On an accurately drawn map, B is 4.53 cm north and 2.11 cm east of A. The map scale is 1:25 000.
Edexcel 1MA1 · November 2020 · Paper 1F · Q15 · 3 marks
3 marks
Jamil makes a drink by mixing 1 part of orange squash with 9 parts of water. He uses 750 millilitres of orange squash. Jamil is going to put the drink he has mixed into 1 litre bottles. Work out the greatest number of 1 litre bottles that Jamil can completely fill.
Edexcel 1MA1 · November 2020 · Paper 1F · Q17 · 5 marks
5 marks
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.
Edexcel 1MA1 · November 2020 · Paper 1F · Q24 · 3 marks
3 marks
Sean pays GBP 10 for 24 chocolate bars. He sells all 24 chocolate bars for 50p each. Work out Seans percentage profit. ....................................................... %
Edexcel 1MA1 · November 2020 · Paper 1F · Q27 · 3 marks
3 marks
A prism of height 3 m stands on a horizontal floor. Its volume is 18 m^3 and the pressure it exerts on the floor is 75 N/m^2. Use pressure = force/area.
Edexcel 1MA1 · November 2020 · Paper 1F · Q29 · 3 marks
3 marks
Edexcel 1MA1 · November 2020 · Paper 1H · Q5 · 3 marks
3 marks
Sean pays GBP 10 for 24 chocolate bars. He sells all 24 chocolate bars for 50p each. Work out Seans percentage profit. ....................................................... %
Edexcel 1MA1 · November 2020 · Paper 1H · Q8 · 3 marks
3 marks
A prism of height 3 m stands on a horizontal floor. Its volume is 18 m^3 and the pressure it exerts on the floor is 75 N/m^2. Use pressure = force/area.
Edexcel 1MA1 · November 2020 · Paper 1H · Q10 · 3 marks
3 marks
Edexcel 1MA1 · November 2020 · Paper 1H · Q13 · 3 marks
3 marks
Liquid A and liquid B are mixed to make liquid C. Liquid A has a density of 70 kg/m3 Liquid A has a mass of 1400 kg Liquid B has a density of 280 kg/m3 Liquid B has a volume of 30 m3 Work out the density of liquid C. ....................................................... kg/m3
Edexcel 1MA1 · November 2020 · Paper 1H · Q16 · 4 marks
4 marks
Shirley wants to find an estimate for the number of bees in her hive. On Monday she catches 90 of the bees. She puts a mark on each bee and returns them to her hive. On Tuesday she catches 120 of the bees. She finds that 20 of these bees have been marked.
Edexcel 1MA1 · November 2020 · Paper 1H · Q18 · 3 marks
3 marks
x is proportional to sqrt(y), where y > 0. The value of y is increased by 44%. Work out the percentage increase in x.
Edexcel 1MA1 · November 2020 · Paper 1H · Q23 · 3 marks
3 marks
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.
Edexcel 1MA1 · November 2020 · Paper 2F · Q4 · 1 mark
1 mark
Edexcel 1MA1 · November 2020 · Paper 2F · Q9 · 4 marks
4 marks
A conversion scale shows 40 kilometres as approximately 25 miles. An approximate rule says: divide kilometres by 10, then multiply by 6.
Edexcel 1MA1 · November 2020 · Paper 2F · Q16 · 4 marks
4 marks
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?
Edexcel 1MA1 · November 2020 · Paper 2F · Q17 · 5 marks
5 marks
There are 24 oranges in each box and 30 oranges make 2 litres of juice. Scott needs enough oranges for 8 litres. He also buys 1260 apples and 280 bananas.
Edexcel 1MA1 · November 2020 · Paper 2F · Q20 · 4 marks
4 marks
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 .......................................................
Edexcel 1MA1 · November 2020 · Paper 2F · Q23 · 5 marks
5 marks
Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box. Carlo puts a total of 3000 tins into the boxes so that number of tins in small boxes : number of tins in large boxes = 2 : 3 Carlo says that less than 30% of the boxes filled with tins are large boxes. Is Carlo correct? You must show all your working.
Edexcel 1MA1 · November 2020 · Paper 2H · Q3 · 5 marks
5 marks
Carlo puts tins into small boxes and into large boxes. He puts 6 tins into each small box. He puts 20 tins into each large box. Carlo puts a total of 3000 tins into the boxes so that number of tins in small boxes : number of tins in large boxes = 2 : 3 Carlo says that less than 30% of the boxes filled with tins are large boxes. Is Carlo correct? You must show all your working.
Edexcel 1MA1 · November 2020 · Paper 2H · Q8 · 5 marks
5 marks
Tariq pays GBP 551 after a 5% discount. Joan separately invests GBP 6000 at 2.4% compound interest for year 1 and 1.7% for each later year.
Edexcel 1MA1 · November 2020 · Paper 2H · Q12 · 3 marks
3 marks
A straight-line graph of petrol volume v litres against distance d kilometres passes through (d, v) = (0, 27) and (300, 0).
Edexcel 1MA1 · November 2020 · Paper 2H · Q19 · 4 marks
4 marks
A hot air balloon is descending. The height of the balloon n minutes after it starts to descend is hn metres. The height of the balloon (n +1) minutes after it starts to descend, hn + 1 metres, is given by hn + 1 = K x hn + 20 where K is a constant. The balloon starts to descend from a height of 1200 metres at 09 15 At 09 16 the height of the balloon is 1040 metres. Work out the height of the balloon at 09 18 ....................................................... m
Edexcel 1MA1 · November 2020 · Paper 3F · Q1 · 1 mark
1 mark
Change 300 centimetres into metres. ................................................ metres
Edexcel 1MA1 · November 2020 · Paper 3F · Q3 · 1 mark
1 mark
Edexcel 1MA1 · November 2020 · Paper 3F · Q7 · 2 marks
2 marks
A shape is divided into 16 equal squares, of which 12 are shaded.
Edexcel 1MA1 · November 2020 · Paper 3F · Q15 · 5 marks
5 marks
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.
Edexcel 1MA1 · November 2020 · Paper 3F · Q18 · 3 marks
3 marks
A currency-conversion graph is a straight line through the origin and the point (GBP 50, USD 65). Rosie paid 345 US dollars.
Edexcel 1MA1 · November 2020 · Paper 3F · Q19 · 4 marks
4 marks
Here are the types of sandwiches sold in a cafe last week. Sandwiches Tuna Cheese Chicken Egg 56 tuna sandwiches were sold. This was 40% of the total number of sandwiches sold.
Edexcel 1MA1 · November 2020 · Paper 3F · Q24 · 3 marks
3 marks
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
Edexcel 1MA1 · November 2020 · Paper 3F · Q26 · 5 marks
5 marks
Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9 m. Grass seed is sold in 2 kg boxes. Maisie wants to make a rectangular lawn 10 m by 14 m. She has 5 boxes of grass seed.
Edexcel 1MA1 · November 2020 · Paper 3F · Q29 · 3 marks
3 marks
A solid triangular prism has a right-triangular cross-section with perpendicular sides 4 cm and 6 cm, length 10 cm, and density 0.8 g/cm^3.
Edexcel 1MA1 · November 2020 · Paper 3H · Q2 · 3 marks
3 marks
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
Edexcel 1MA1 · November 2020 · Paper 3H · Q4 · 5 marks
5 marks
Maisie knows that she needs 3 kg of grass seed to make a rectangular lawn 5 m by 9 m. Grass seed is sold in 2 kg boxes. Maisie wants to make a rectangular lawn 10 m by 14 m. She has 5 boxes of grass seed.
Edexcel 1MA1 · November 2020 · Paper 3H · Q16 · 4 marks
4 marks
A car's speed-time graph is a smooth concave-down curve from (0, 0) to a maximum of about (75, 13.5), then back to (150, 0). During the first 30 seconds the graph gives approximate speeds 0, 3.4, 6.4 and 8.8 m/s at 0, 10, 20 and 30 seconds.
Edexcel 1MA1 · November 2020 · Paper 3H · Q19 · 4 marks
4 marks
ABCDEF is a regular hexagon with side length x. It is enlarged, centre F, by scale factor p to give regular hexagon FGHIJK. The shaded region is the part of the enlarged hexagon outside ABCDEF.
Edexcel 1MA1 · November 2020 · Paper 3H · Q21 · 5 marks
5 marks
Given 5c + d = c + 4d, and separately 6x^2 = 7xy + 20y^2 with x>0 and y>0.
Edexcel 1MA1 · November 2019 · Paper 1F · Q5 · 1 mark
1 mark
Examiner report
Nearly all students answered this question correctly though a few students gave incorrect answers such as 1.5 and ଵହ ଵ.
Write 15% as a decimal.
Edexcel 1MA1 · November 2019 · Paper 1F · Q16 · 3 marks
3 marks
Examiner report
About three quarters of students gave a correct answer to part (a) of this question. A fully correct answer to part (b) was seen much more infrequently. However, a fair proportion of students could score at least one mark for either an attempt to find the gradient of the line representing Steve’s journey home or for using the speed, distance, time formula correctly. Students often scored a mark for ଶହ ଷ but could then not convert this to a speed in km/h. Those students who did give the correct answer, 50, had usually argued that 25 km in half an hour was equivalent to an average speed of 50 km/h. Other common errors included multiplying 25 by 30 and dividing 25 by 2 instead of by ଵ ଶ.
A travel graph shows Steve 25 km from home from 12:45 until 13:30, then travelling home from 13:30 to 14:00.
Edexcel 1MA1 · November 2019 · Paper 1F · Q21 · 4 marks
4 marks
Examiner report
This question was quite well attempted by most students sitting this paper, with a high proportion of students being awarded at least two of the four marks available for finding that there were 10 men and 20 children in the choir. Some students stopped at this point, giving 20 as their final answer. However, many students did go on to write down a correct ratio and simplified it to .2 : 1. Examiners allowed 2 : 1 for full marks though the question did in fact ask for only the value of n.
There are 60 people in a choir. Half of the people in the choir are women. The number of women in the choir is 3 times the number of men in the choir. The rest of the people in the choir are children. the number of children in the choir : the number of men in the choir = n : 1 Work out the value of n. You must show how you get your answer. n .......................................................
Edexcel 1MA1 · November 2019 · Paper 1F · Q24 · 4 marks
4 marks
Examiner report
This multi-step question was not answered well. Many students mistakenly used the result that “angles on a straight line sum to 180̊” with angles ABC, BDC and BAC to get an answer of 54̊ for the size of angle BDC. Of those students who did make a correct first step to find that angle BCA was 54°, few went on to split the angle correctly in the ratio 2 : 1 and then to complete the problem successfully.
In triangle ABC, D lies on AB between A and B, so A, D and B are collinear in that order. Angle BAC=75 degrees and angle ABC=51 degrees. The internal line CD splits angle ACB so that angle DCB : angle ACD = 2 : 1.
Edexcel 1MA1 · November 2019 · Paper 1F · Q27 · 5 marks
5 marks
Examiner report
Fully correct answers to this question were hardly ever seen. Only about one third of students were able to get at least one mark for drawing a correct bearing and/or for calculating the distance travelled by the boat and using the scale of the diagram. Examiners were able to award three marks to students who plotted the position of Q accurately on the diagram. Those who did plot Q correctly were often able to use the scale to give an accurate distance from L to Q but were unable to measure the bearing, often giving the angle measured anticlockwise from the north line. Weaker students often started their working by multiplying 90 by 12 but seemingly with little purpose evident. There was a disappointing number of students who measured the length of one or more of the north lines on the diagram.
A scale drawing uses 1 cm to represent 4 km. On it, lighthouse L is 7.5 cm east and 2.7 cm south of port P. Aleena sails from P on a bearing of 070 degrees for 1.5 hours at 12 km/h, arriving at port Q.
Edexcel 1MA1 · November 2019 · Paper 1H · Q2 · 4 marks
4 marks
Examiner report
Only a few students failed to determine that there were 10 men and 20 children in the choir. The correct value for n (2) or a correct ratio of 2:1 was often seen but many misread the question thinking that n was the number of children and an answer of 20 was a common error. An answer of 2:1 was awarded full marks. It was common to see students do 60/3 =20 and give 20 as the number of men and then 10 as the number of children meaning their answer of 2 but came from incorrect working and so could not be credited.
There are 60 people in a choir. Half of the people in the choir are women. The number of women in the choir is 3 times the number of men in the choir. The rest of the people in the choir are children. the number of children in the choir : the number of men in the choir = n : 1 Work out the value of n. You must show how you get your answer. n .......................................................
Edexcel 1MA1 · November 2019 · Paper 1H · Q5 · 4 marks
4 marks
Examiner report
180 – 75 – 51 = 54 was the common first step seen but many saw this as a method to find the required angle BDC incorrectly using ‘angles on a straight line’. Some correctly found angle ACB = 54o but could go no further and for those that did arithmetic errors were often seen preventing a complete and correct solution. Some students were unable to deal with the ratio and often 54 was simply halved. Others assumed that angle ADC or BDC was 90 degrees.
In triangle ABC, D lies on AB between A and B, so A, D and B are collinear in that order. Angle BAC=75 degrees and angle ABC=51 degrees. The internal line CD splits angle ACB so that angle DCB : angle ACD = 2 : 1.
Edexcel 1MA1 · November 2019 · Paper 1H · Q8 · 5 marks
5 marks
Examiner report
It was rare to see a fully correct solution to this question. Bearings remains a topic which many students find difficult to understand. Those students able to correctly draw a bearing of 070o usually went on to score well. The ability to use distance = speed × time did enable many students to gain at least one mark for a distance of 18 km and often an additional mark for correct use of scale. When a correct position for Q was found, the distance from L was usually correct but the bearing of Q from L, a reflex angle, was usually not correct.
A scale drawing uses 1 cm to represent 4 km. On it, lighthouse L is 7.5 cm east and 2.7 cm south of port P. Aleena sails from P on a bearing of 070 degrees for 1.5 hours at 12 km/h, arriving at port Q.
Edexcel 1MA1 · November 2019 · Paper 1H · Q9 · 4 marks
4 marks
Examiner report
Distance = speed × time was usually applied in part (a) gaining the majority of students at least one mark. Misuse of units however was very common. 72 × 18 (= 1296) and 72 × 0.18 were the usual errors seen. Partitioning methods were usually incomplete and therefore gained no credit. Part (b) was less well done again largely through the use of incorrect conversions. 1 km = 100 metres was a common mistake. Some students showed that the two speeds were the same but failed to answer the question posed.
A car travels for 18 minutes at an average speed of 72 km/h. David separately says that 72 km/h is faster than 20 m/s.
Edexcel 1MA1 · November 2019 · Paper 1H · Q11 · 2 marks
2 marks
Examiner report
Those students who understood the concepts involved usually gave a correct solution. An incorrect answer of 60 (12 ×5) was common, as was 30 – 5 + 12 = 37.
There are p counters in a bag. 12 of the counters are yellow. Shafiq takes at random 30 counters from the bag. 5 of these 30 counters are yellow. Work out an estimate for the value of p.
Edexcel 1MA1 · November 2019 · Paper 1H · Q17 · 4 marks
4 marks
Examiner report
This question was very poorly answered, many simply using a scale factor of 2.25 (9 ÷ 4) in an attempt to make progress. Some looked as though they wanted to use the formulae for surface area and volume of a cylinder, but never really made any meaningful start. A few students correctly found the ratio of lengths but could go no further.
A and B are two similar cylindrical containers. A B the surface area of container A : the surface area of container B = 4 : 9 Tyler fills container A with water. She then pours all the water into container B. Tyler repeats this and stops when container B is full of water. Work out the number of times that Tyler fills container A with water. You must show all your working.
Edexcel 1MA1 · November 2019 · Paper 2F · Q3 · 1 mark
1 mark
Examiner report
Most students were able to write 0.23 as a percentage.
Write 0.23 as a percentage.
Edexcel 1MA1 · November 2019 · Paper 2F · Q7 · 2 marks
2 marks
Examiner report
After working out 20 – 7 = 13 to find the number of sweets that Harry had left most students gave the correct fraction 13/20. Some students gave the answer in decimal form and lost the accuracy mark. A few students gave the answer as 7/20, the fraction of the sweets that Nadia had, and were awarded one mark. Those that made an arithmetic error could be awarded the method mark if 20 – 7 was shown but an incorrect answer such as 14/20 with no working meant that no mark could be awarded.
Harry has 20 sweets. He gives 7 of the sweets to Nadia.
Edexcel 1MA1 · November 2019 · Paper 2F · Q10 · 3 marks
3 marks
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.
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.
Edexcel 1MA1 · November 2019 · Paper 2F · Q11 · 3 marks
3 marks
Examiner report
In part (a) some students did not read the graph with sufficient care when changing 3 stones to kilograms. Answers such as 10.9 or 20 were quite common. The most common approach seen to change 80 kilograms to stones in part (b) was reading from the graph at a factor of 80, which was often 40, and scaling up to 80. A few students used two values that sum to 80. The scale on the horizontal axis was often not read correctly and statements such as 40 kg = 6.1 stones or 10 kg = 1.3 stones were common. An answer outside the range 12.4 to 12.8 was awarded full marks if it came from a complete method that included a correct reading from the graph. Some students, for example, read from the graph to find 1 stone = 6 kg and then divided 80 by 6 to complete the method. Too many students gave an answer with little or no working out. When the answer was not in the range 12.4 to 12.8 marks could only be awarded if a complete method was shown. Students should be encouraged to show a clear method on the graph as, without this, incorrect conversions can be given no marks. Attempts at answering the question by extending the graph were usually unsuccessful.
A straight conversion graph passes through (0 stones, 0 kilograms), (3 stones, 19 kilograms) and approximately (10 stones, 63.5 kilograms).
Edexcel 1MA1 · November 2019 · Paper 2F · Q14 · 3 marks
3 marks
Examiner report
Students that interpreted the two offers correctly were frequently able to find comparable values on which to base a decision. Many students found the cost of the same amount of compost for each offer, most often for 120 litres or for 40 litres. It was much less common to see students working out the cost per litre or the number of litres per £ for each offer. Having found comparable values students were usually able to make the correct decision. Those who worked with the number of litres per £ sometimes made the wrong decision. Some students interpreted the two offers correctly, for example 40 litres = £3.50 and 120 litres = £9, but gained only one mark because they did not find comparable values to support their decision. The offers were often not interpreted correctly. The first offer, for example, was often interpreted as 20 litres for £3.50 or 20 litres for £7. Some students simply worked out the cost of one bag for each offer and did not take the volume into account. Students should be encouraged to set out working clearly for questions like this one as it will be helpful to them if they can follow their own calculations and working when making their conclusion.
A shop sells compost in 20-litre and 40-litre bags. Offer 1 is two 20-litre bags for £3.50. Offer 2 is three 40-litre bags for £9.
Edexcel 1MA1 · November 2019 · Paper 2F · Q15 · 3 marks
3 marks
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.
The length of a plane is 19.2 metres. A scale model is made at a scale of 1:24.
Edexcel 1MA1 · November 2019 · Paper 2F · Q16 · 2 marks
2 marks
Examiner report
For those that understood simple interest a common first step was to work out 1.8% of 4500. It was surprising to see some students using an inefficient build up method to work out 1.8% of 4500 on this calculator paper. They were often not successful. Some students took the 3 years into account at the start and worked out 5.4% of 4500. Having used a complete method to get 243 some students were not awarded the accuracy mark because they gave the final answer as 4743 or 4257. A common incorrect first step was to divide 4500 by 3 and assume that Maria invested £1500 each year. Many students treated this as a compound interest question rather than as a simple interest question and they could score at most one mark for a calculation of the form 4500 × 1.018n. This was usually 4500 × 1.018 or 4500 × 1.0183. Incorrect multipliers such as 1.8 or 1.18 were quite common. A significant number of students gave answers which were large compared to the initial amount invested. Students should be encouraged to consider whether their answers are reasonable in the context of the question.
Maria invests £4500 in a savings account for 3 years. The account pays simple interest at 1.8% per year.
Edexcel 1MA1 · November 2019 · Paper 2F · Q19 · 3 marks
3 marks
Examiner report
Many students were able to make progress with this question and gain at least one mark. This was awarded for finding the maximum number of batches of 16 biscuits for one ingredient or the amount of one ingredient needed for one biscuit or for doubling the quantities in the recipe in the first stage of a build-up method, e.g. 350 g butter, 150 g sugar, 500 g flour. Many students went on to gain the second mark for showing a process to find the maximum number of biscuits for one ingredient or for an answer of 32. Students should be aware that it is possible to make a non-integer number of batches unless the question states otherwise. Some of the students that used a unitary method of solution and showed a complete process rounded or truncated intermediate values and lost the accuracy mark. A common incorrect start to the process was to add together quantities of the different ingredients. The presentation of work on this question was often poor with calculations spread all over the working space.
To make 16 biscuits requires 175 g butter, 75 g sugar and 250 g flour. Anna has 500 g butter, 300 g sugar and 625 g flour.
Edexcel 1MA1 · November 2019 · Paper 2F · Q20 · 4 marks
4 marks
Examiner report
Most of the students that substituted f = 110 into the formula obtained 452 and were awarded the first two marks. Many students, however, were not able to complete the solution by showing that the difference between 452 and the real height is less than 5% of the real height. Some made no attempt to do so. Others did make an attempt but could not show a complete method. Some found the difference of 10 but did not work with percentages whereas others found 5% of 442 but not the difference of 10. A common mistake was to find 5% of 452 instead of 5% of the real height. A significant number of students did not use the formula correctly and gained no marks. Attempts at solving an equation such as 442 = 4f + 12 or 110 = 4f + 12 were quite common. Some students thought that they needed to round values because of the word ‘estimate’.
The height H metres of a building is estimated using H = 4f + 12, where f is its number of floors. A building is 110 floors high and its real height is 442 m.
Edexcel 1MA1 · November 2019 · Paper 2F · Q23 · 4 marks
4 marks
Examiner report
Many students successfully started by using the ratio 3 : 7 to find the number of stamps that Tom and Adam each had before Tom bought some stamps from Adam. There were some students who divided 240 by 3 and by 7 instead of by 10 but most used a correct process and found that Tom started with 72 stamps and Adam with 168 stamps. Those who then used the ratio 3 : 5 correctly to find that Tom finished with 90 stamps and Adam with 150 stamps usually went on to give the correct answer. There were many students, however, who did not use the ratio 3 : 5 correctly. Instead of working out 240 ÷ 8 = 30 they used 24 (from 240 ÷ 10). It was common to see 7 – 5 = 2 followed by 2 × 24 and a final answer of 48.
Tom and Adam have 240 stamps in the ratio Tom:Adam = 3:7. Tom buys some stamps from Adam, after which the ratio Tom:Adam is 3:5.
Edexcel 1MA1 · November 2019 · Paper 2F · Q24 · 3 marks
3 marks
Examiner report
Part (i) was answered quite well with many students able to work out how many sports bags Stan should order. Those who showed a correct process usually gave the correct answer. Students were far less successful in part (ii) where they were asked to write down an assumption they had made. Acceptable statements were based on the assumption that Stan’s sample is representative. Although some students explained how this could have affected their answer this was not required for the mark to be awarded. Many students gave a criticism of Stan’s sampling rather than an assumption they had made. Some simply described the calculation they had carried out in part (i).
Stan samples 50 people from a fitness club about which free gift they want. The results are: sports bag 17, gym towel 7, headphones 11, voucher 15. There are 700 people in the club.
Edexcel 1MA1 · November 2019 · Paper 2F · Q28 · 3 marks
3 marks
Examiner report
This question was generally answered quite well and it was pleasing that many students were able to gain the first mark for finding the number of workers used each day by Ali’s company or by Hayley’s company. Most went on to give a fully correct solution. Having found the two correct values (18 and 24) a few students did not complete the process by subtracting 18 from 24. Some students could not use the formula correctly and a common error was to work out 720 × 40 and 720 × 30.
The number of days d needed to build a house is d = 720/n, where n is the number of workers used each day. Ali's company takes 40 days and Hayley's company takes 30 days.
Edexcel 1MA1 · November 2019 · Paper 2H · Q3 · 4 marks
4 marks
Examiner report
The majority of students gained full marks. Where this was not the case, many students gained two marks for finding 168 and 72 using the first ratio, but then carried on using 24 with the second ratio, using 48, rather than starting again with 240. On a rare occasion a student would gain the correct values to make a decision but subtracted the wrong numbers. Other common errors included dividing by the individual numbers in the ratio, not the sum, or multiplying 240 × 10 and 240 × 8.
Tom and Adam have 240 stamps in ratio 3:7. Tom buys stamps from Adam, making the ratio 3:5.
Edexcel 1MA1 · November 2019 · Paper 2H · Q8 · 3 marks
3 marks
Examiner report
This was a well-answered question. Some incorrect answers showed all numbers multiplied together resulting in nonsensically large answers. The few students that did this thought nothing of giving an answer in thousands suggesting the context of the question had been missed. A common answer was to show 720 × 40 – 720 × 30 (leading to 7200).
The days d to build a house satisfy d = 720/n, where n is daily workers. Ali's company takes 40 days and Hayley's 30 days.
Edexcel 1MA1 · November 2019 · Paper 2H · Q13 · 3 marks
3 marks
Examiner report
A common response was 3550 × 1.0262 which gained both process marks. Some left it there, but a minority finished it off by writing 2.2 Premature rounding was all too prevalent in this question which frequently led to an answer outside the range allowed for the final mark. Weaker students used an incorrect multiplier which meant no marks could be awarded for example using 1.26 or 0.026 or even 10.26 Some trial and improvement methods were seen in this question, particularly when trying to find the final answer.
Sakira invests £3550 for 3 years. Interest is 2.6% compound for each of the first 2 years and R% for year 3. Final balance is £3819.21.
Edexcel 1MA1 · November 2019 · Paper 2H · Q22 · 4 marks
4 marks
Examiner report
Part (a) was poorly attempted, but there were some who gained full marks. Those who understood that 200 should be substituted generally gained at least the first mark leading to 190. It was unfortunate that some calculated 163.6 but failed to associate this with whole rabbits. Part (b) was poorly answered, with many students either assuming that the number of rabbits got bigger, irrespective of their answer to part (a).
Rabbit numbers satisfy P_(n+1) = 1.2P_n - 50. At end of March P = 200.
Edexcel 1MA1 · November 2019 · Paper 3F · Q5 · 1 mark
1 mark
Examiner report
In this question students were required to convert metric units, in this case kilometres to metres. Generally speaking, the students performed well, but there was evidence of students not fully understanding their conversion and either dividing by 1000 rather than multiplying or multiplying by 10 or 100.
Change 4 kilometres into metres.
Edexcel 1MA1 · November 2019 · Paper 3F · Q6 · 1 mark
1 mark
Examiner report
Students were required to extract a ratio from a diagram of the shaded to unshaded squares. The question was answered well with most of those who actually worked with ratio able to do so successfully. However, some students got confused and tried to work with fractions: ଷ ହ, ଷ଼, ହ ଷ and ହ଼ being commonly seen or worked with ‘the whole’ eg 3:8.
A grid has 3 shaded squares and 5 unshaded squares.
Edexcel 1MA1 · November 2019 · Paper 3F · Q15 · 4 marks
4 marks
Examiner report
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.
A school has 800 students. 31% have packed lunches; 55% are boys; 60% of boys have school dinners.
Edexcel 1MA1 · November 2019 · Paper 3F · Q16 · 4 marks
4 marks
Examiner report
The fundamental part of this question was the first step, where students had to equate the sum of the probabilities to 1. Without using this, students were unable to gain credit for later processes. Once students had found that the sum of the probabilities for blue and green is 0.35, they had to divide this value in the ratio 3 : 4. This was done with varying degrees of success, many dividing by 3 and 4 separately rather than dividing by (3 + 4). Students were able to work in any suitable form (fractions, decimals and percentages) and those who worked in percentages were able to gain process marks with a missing % symbol. However, it did need to be present to gain the final accuracy mark.
A bag contains only red, blue, green, yellow counters. P(red)=0.4, P(yellow)=0.25, and blue:green counts=3:4.
Edexcel 1MA1 · November 2019 · Paper 3F · Q21 · 3 marks
3 marks
Examiner report
This was a question that students generally struggled with. Most were able to make a start and gain the first mark for finding the profit. At that point many students did not know how to progress further to find the percentage profit. Students generally knew division was necessary part of this calculation, but often this was seen as profit ÷ new rather than profit ÷ original and as a result no further marks were awarded. It is evident that percentage change and percentage profit is an area that foundation students need to work on further. Trial and improvement methods were seen and were usually unsuccessful in finding a correct solution; this method should be discouraged.
Franco buys a house for £146500 and sells it for £158220.
Edexcel 1MA1 · November 2019 · Paper 3F · Q26 · 1 mark
1 mark
Examiner report
Conversion of metric units of volume is clearly something that students at this level find difficult. Various powers of 10 were used, most commonly 10 and 100 rather than 1000.
Write 37 cm^3 in mm^3.
Edexcel 1MA1 · November 2019 · Paper 3F · Q27 · 4 marks
4 marks
Examiner report
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.
At 13:30 Nimer is 65 miles from a hotel. He arrives at 14:48.
Edexcel 1MA1 · November 2019 · Paper 3H · Q5 · 1 mark
1 mark
Edexcel 1MA1 · November 2019 · Paper 3H · Q6 · 4 marks
4 marks
At 13:30 Nimer is 65 miles from a hotel; he arrives 14:48.
Edexcel 1MA1 · November 2019 · Paper 3H · Q13 · 4 marks
4 marks
Liquids A:B are mixed 2:13 by volume. Densities are 1.21 and 1.02 g/cm^3. A cylinder of mixture has radius 3 cm and height 25 cm.
Edexcel 1MA1 · November 2019 · Paper 3H · Q14 · 4 marks
4 marks
People choose soup or prawns and lasagne or curry. Soup:prawns=2:3. For soup, lasagne:curry=5:3. For prawns, lasagne:curry=1:5.
Edexcel 1MA1 · November 2019 · Paper 3H · Q16 · 3 marks
3 marks
y is inversely proportional to x^2. y=8 when x=2.5.
Edexcel 1MA1 · November 2019 · Paper 3H · Q19 · 3 marks
3 marks
A distance-time graph for part of a cyclist's journey has time in seconds on the horizontal axis (0 to 9) and distance travelled in metres on the vertical axis (0 to 20). The graph is a smooth increasing curve, concave upwards, starting at (0,0) and passing approximately through (1,0.2), (2,1.0), (3,2.4), (4,4.4), (5,6.9), (6,9.8), (7,13.8), (8,18.2), reaching 20 m at about 8.4 s.
Edexcel 1MA1 · November 2019 · Paper 3H · Q24 · 5 marks
5 marks
OXYZ is a parallelogram with vector OX = a and vector OY = b. P lies on OX with OP:PX = 1:2. R lies on OY with OR:RY = 1:3.
Edexcel 1MA1 · June 2019 · Paper 1F · Q2 · 1 mark
1 mark
Examiner report
This question was also well answered with very few errors seen.
Write 0.73 as a percentage.
Edexcel 1MA1 · June 2019 · Paper 1F · Q9 · 4 marks
4 marks
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.
Ruth walks from 9:00 to 10:30 at 4 mph, stays 50 min, then takes 1.25 h to walk home.
Edexcel 1MA1 · June 2019 · Paper 1F · Q20 · 3 marks
3 marks
Examiner report
There were very few correct answers of 12.5% seen. Many students did not attempt this question at all. Success came most commonly from a diagrammatic approach. Successful students drew examples of square A inside square B and recognised that the area of A was in fact a quarter of the area of B and therefore the area of the triangle was 1/8 of the area of B. This helped students to visually see the relationship between the 2 shapes. A few students were unable to convert 1/8 into a percentage. Even here arithmetic errors were made with 25 ÷ 2 = 13 seen. Some students assigned lengths to the squares in order to find areas but only a small number of those went on to actually calculate an area. The most common incorrect answer seen was 25% from halving 50%.
Square A side is 50% of square B side. In A, a diagonal halves the square and one half is shaded.
Edexcel 1MA1 · June 2019 · Paper 1F · Q23 · 5 marks
5 marks
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.
50 g sugar makes 15 biscuits; flour is 3× sugar and butter 2× sugar. Deon makes 60 biscuits; butter packs are 250 g.
Edexcel 1MA1 · June 2019 · Paper 1F · Q27 · 4 marks
4 marks
Examiner report
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.
Packs contain black2, red5, green6 pens. Packs sold ratio black:red:green=7:3:4; total pens 212.
Edexcel 1MA1 · June 2019 · Paper 1H · Q2 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · June 2019 · Paper 1H · Q6 · 4 marks
4 marks
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.
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.
Edexcel 1MA1 · June 2019 · Paper 1H · Q12 · 3 marks
3 marks
Examiner report
There was generally a poor understanding of how to tackle this question. A common approach was to assign a value to the volume of P and use it to work out the volumes of Q and R, for example P =100, Q = 150, R = 225. These values were often written on the spheres in the diagram. This was one of the most successful approaches as many students went on to write down an appropriate fraction. Some students made a mistake with the volume of R, writing 100, 150, 200 for example, and gained only the first mark. A different approach was to work out that the multiplier from P to R is 1.5 × 1.5. Whichever method was used the final hurdle for students was to write the volume of P as a fraction of the volume of R. For some this was their downfall. Fractions such as 1/2.25 that contained a decimal were common. These were not awarded the accuracy mark unless they were the result of simplifying a correct fraction. Some students gave an inverted fraction such as 9/4 and there were others who could not complete their method by giving any fraction at all. A common misconception was to assume that the volume of Q is 50% less than the volume of R and the volume of P is 50% less than the volume of Q (writing for example R =100, Q = 50, P = 25 or P = 1/2Q and Q = 1/2R) and give an answer of 1/4.
Sphere Q has 50% more volume than sphere P. Sphere R has 50% more volume than sphere Q.
Edexcel 1MA1 · June 2019 · Paper 1H · Q17 · 4 marks
4 marks
Examiner report
Many of the students who used the given statement, x2 : (3x + 5) = 1 : 2, to form a correct equation were able to give fully correct solutions. Marks were sometimes lost through factorising 2x2 – 3x – 5 = 0 incorrectly. Some students gained only the first mark because they could not write their equation (which was often 2x2 = 3x +5) in a suitable form ready for solution. Many students scored no marks at although some of these students had attempted to form an equation. Common incorrect equations were x2 = 2(3x + 5) and x2 + 3x + 5 = 3 and some students used x2 = 1 and 3x + 5 = 2. Many students, though, simply substituted different values of x into the given statement. This approach sometimes resulted in an answer of x = –1 but gained no marks because two values of x are needed.
Given x^2:(3x+5)=1:2, find the possible values of x.
Edexcel 1MA1 · June 2019 · Paper 1H · Q20 · 4 marks
4 marks
Examiner report
Many students were able to set up at least one correct proportional relationship and often wrote down both h 1/p and p t . At this stage a few students used direct proportion instead of inverse proportion and vice versa. Students who introduced a constant k and wrote h = k/p or p = k t were usually able to substitute correctly and find the value of the constant. However, a correct substitution did not always lead to a correct value with 6 = k × 144 sometimes leading to k = 2, for example. Some students found the value of one constant and used it incorrectly in their second equation. Having found k = 60 from 10 = k/6 they then wrote p = 60 × 144 followed by p = 720. Another error was to use k as the constant of proportionality in both relationships and to assume that it had the same value in both equations. The use of two different symbols reduced the potential for error. Some students did not write down an equation involving k and statements such as 6 12 were quite common. Many of the students who found the values of both constants failed to use them in their original equations and did not write down h = 60/p and t p 5.0 . Those that did gained the third mark and frequently went on to find a formula for h in terms of t. Many students found the values of the two constants but then continued with incorrect further working. Some simply stopped and went no further.
h is inversely proportional to p. p is directly proportional to √t. Given h=10 and t=144 when p=6.
Edexcel 1MA1 · June 2019 · Paper 2F · Q4 · 1 mark
1 mark
Examiner report
The correct answer was by far the modal response although some students did try to round or truncate 1.756 This was acceptable provided the correct answer had been seen in the working. A number of students carried out division by 100 giving 17.56
Change 1756 grams to kilograms.
Edexcel 1MA1 · June 2019 · Paper 2F · Q9 · 5 marks
5 marks
Examiner report
Both questions in part (a) were usually correctly answered. In part (b), a great many students failed to use the ratio of the numbers of records sold on Wednesday to the number of records sold on Thursday. The most common approach was to divide 36 by 8 (= 4.5) leading to an incorrect pictogram. Some students identified 4 and 32 but only in their attempt to find the number of 8s in 36. This gained no credit; the 4 and 32 had to be clearly seen as a result of dividing 36 in the ratio 1 : 8. It was common to see pictograms with the correct symbols reversed for Wednesday and Thursday, indicating that some students had not read the question carefully enough. Very few students followed an algebraic approach and equations such as x + 8x = 36 were rarely seen.
A pictogram uses one full symbol for 8 vinyl records. Monday shows 3 symbols; Tuesday shows 2¼ symbols. Wednesday and Thursday total 36 records, with Thursday selling 8 times Wednesday.
Edexcel 1MA1 · June 2019 · Paper 2F · Q14 · 1 mark
1 mark
Examiner report
This was a very poorly answered question. Many students were able to write a ratio equivalent to 4.5 : 2.25 but rarely in the required form.
Write 4.5:2.25 in the form n:1.
Edexcel 1MA1 · June 2019 · Paper 2F · Q17 · 4 marks
4 marks
Examiner report
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.
Banana has 84 calories per 100 g; yogurt has 87 calories per 100 g. Priti eats 60 g banana and 150 g yogurt.
Edexcel 1MA1 · June 2019 · Paper 2F · Q18 · 4 marks
4 marks
Examiner report
It was pleasing to see so many students gaining at least two marks for working out the number of parts produced by either of the machines; machine B (520) being the more successful. Many then went on to gain full marks. Simply converting hours into minutes was not seen as a sufficient start in solving the problem and no credit was given just for this. The most efficient process for each machine was to work out the number of parts made each hour, 36 for machine A and 52 for machine B, students working along these lines usually went on to give a fully correct solution. Mistakes were made by many when working out the number of parts made per minute or the time taken to make one part. Some students, failing to carefully read the question, mixed up the values and therefore were unable to gain any credit. Many students were happy saying there were 4 lots of 15 minutes in an hour and successfully getting 52 for machine B, but did not apply the same reasoning for lots of 10 minutes in an hour for machine A. 60 × 12 = 720 was a common incorrect answer for machine A.
Machine A makes 6 parts every 10 minutes and runs 12 hours. Machine B makes 13 parts every 15 minutes and runs 10 hours.
Edexcel 1MA1 · June 2019 · Paper 2F · Q19 · 4 marks
4 marks
Examiner report
The vast majority of students did not understand how to draw the locus of points a given distance from a point and so it was rare to see attempts at arcs drawn with point A as the centre. Often points were marked at a distance of 6 cm from A. This gained no marks other than the M1 for using the scale (180 ÷ 30) correctly. This was the only mark gained by many students who failed to draw any loci on the diagram. Clearly a lot of students had no concept of loci either not attempting the question or simply shading an area with no defined boundaries. However, many students were able to score at least two marks for a correct line segment drawn 5 cm from the line BC. Sometimes this was achieved by drawing a ‘table’ with one side 5 cm from BC. Many students shaded a small rectangular table in the middle of the region.
A kitchen plan is the interior of rectangle ABCD, with A at the top left, B at the top right, C at the bottom right and D at the bottom left. It is drawn at scale 1:30. A table must be more than 180 cm from A and more than 150 cm from the side BC.
Edexcel 1MA1 · June 2019 · Paper 2F · Q22 · 3 marks
3 marks
Examiner report
Part (i) was answered well with many students correctly finding one third of 195. Some used ‘build up’ methods but too often this stopped at an answer of 60 out of 180. Many weaker students simply subtracted 30 from 195 showing a lack of understanding of the concepts involved. Some students recognised that a third of the students had chosen the Theme Park, but then used 0.3 or 0.33. The marking of the second part of this question was eased and credit was given to any sensible assumption that could have been made. The accepted assumption needed to be based upon the sample being representative of all 195 students. Many students simply explained their method by which they worked out their answer to part (i).
From 195 students, Hannah samples 30: Theme Park 10, Theatre 5, Sports Centre 8, Seaside 7.
Edexcel 1MA1 · June 2019 · Paper 2F · Q26 · 4 marks
4 marks
Examiner report
This question was poorly answered with the majority of students starting their solution by dividing £360 into the ratio 2 : 7 No marks were available after this initial error. Trial and improvement methods sometimes lead to a correct solution but those working with the correct ratio of 2 : 7 : 3 : 3 usually found the correct answer of £168. A common misconception led to a ratio of 2 : 7 : 3.5 : 3.5 where 1.5 had been added rather than been used as a scale factor. Algebraic approaches were rarely seen and were often error strewn when attempted. A few students used 6 as a total ratio for C and D and incorrectly got the ‘correct’ answer by using 1 and 5 or 5 and 1 instead of 3 and 3. This gained NO marks.
£360 is shared among Abby, Ben, Chloe and Denesh. Abby:Ben=2:7. Chloe and Denesh each receive 1.5 times Abby's amount.
Edexcel 1MA1 · June 2019 · Paper 2H · Q4 · 4 marks
4 marks
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.
A 30 cm by 6 cm by 19 cm cuboid container is 2/3 full of water. Each cup holds 275 ml.
Edexcel 1MA1 · June 2019 · Paper 2H · Q7 · 4 marks
4 marks
Examiner report
This question required students to find two parts of a four-part ratio using a multiplicative relationship. A good number of students were unable to do this and, as a result, failed to score on this question. Typically, those who were able to find the values for C and D in the ratio went on to score well. Most scored four marks, and of those who didn’t, many scored three marks, only dropping the last mark as they calculated all four values and either identified the wrong one as the answer, or didn’t identify one at all. With questions that involve dividing in a ratio, where only one value is required, students need to be clear of the need to identify which is the value required by the question. The most common incorrect method seen was to divide 360 by 9, which led to zero marks.
£360 is shared among Abby, Ben, Chloe and Denesh. Abby:Ben=2:7. Chloe and Denesh each receive 1.5 times Abby's amount.
Edexcel 1MA1 · June 2019 · Paper 2H · Q9 · 4 marks
4 marks
Examiner report
Part (a) posed a challenge to many, including some of the highest achieving students. It goes to show that students still sometimes struggle to apply skills such as the relationship between length and area scale factors to unfamiliar situations. Most successful students started with a suitable ratio of the two circumferences, for example, 1 : 0.9 or more commonly 10 : 9. From here students had to square the values to achieve the ratio for areas, commonly seen as 100 : 81. The question didn’t state that the ratio had to be in its simplest form so any equivalent ratio was acceptable for the accuracy mark. Much like part (a), part (b) also caused problems. This time the first step was to write down a ratio of the two areas. Students struggled more with this first step than in part (a). Often 0.44 or 0.56 was used and no credit was given. Many students did not have the ratios the correct way round. Many appeared to think that f2 was in fact greater than e2. As in the previous part, once this first ratio was set up, the second mark was gained by applying knowledge of scale factors, in this case taking the square root to gain the ratio of lengths.
Circle B's circumference is 90% of circle A's. Square E has side e cm and area 44% greater than square F, whose side is f cm.
Edexcel 1MA1 · June 2019 · Paper 2H · Q14 · 7 marks
7 marks
Examiner report
This new topic was a challenge to many students. A large number failed to draw a tangent, often simply dividing the speed at t = 15 by 15, and so scored zero marks. Those who did draw a tangent then often scored all three marks. Some students took little care over the reading of the scales and therefore had an incorrect method for their gradient. It is important to realise that these questions need to have a tangent drawn. Several students gave an answer within the acceptable range, but they scored no marks as their answer clearly came from an incorrect method. Part (ii) proved more challenging than the earlier one. This is a new topic and many students do not fully understand that gradients represent the instantaneous rate of change. In this context that being acceleration. Part (b) brought in another new topic and students appeared better prepared than in previous series. However, the method for finding the area under the curve was often crude. Many students attempted to use rectangles, and whilst this does give an estimate, it is not a very good one. These students were able to score two marks typically for the processes, but their answer was usually outside the range given in the mark scheme. Students should be encouraged to use trapezia to find a better estimate. Many responses showed attempts to estimate distance using distance = speed × time. Many forgot to divide the triangle product for the first strip by two.
A car moves from rest. Its speed-time graph has time t in seconds on the horizontal axis (0 to 40) and speed v in m/s on the vertical axis (0 to 25). The source graph is a smooth curve passing approximately through (0,0), (5,4), (10,12), (15,18), (20,20), (22,20), (25,19.8), (30,18), (35,14.5), (40,12.7).
Edexcel 1MA1 · June 2019 · Paper 2H · Q17 · 4 marks
4 marks
Examiner report
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.
A bag contains small/large cubes, each red/yellow. Small:large=4:7 and red:yellow=3:5. All small cubes are yellow.
Edexcel 1MA1 · June 2019 · Paper 2H · Q19 · 4 marks
4 marks
Examiner report
3D trigonometry always poses a problem for all but the most able students, but again, it was good to see the majority of students attempting the problem, with most able to score at least one mark for either splitting DA in the correct ratio, or for using tan correctly to find BE. However, it is apparent that many students did not even know which angle they were trying to calculate. Also, several found AE which is not in the required triangle and so, on its own, was not enough for a mark. An impressive number of students were able to take the next step and have a correct process to find either MB or ME and gain two marks. It was at this stage that the vast majority of students struggled to get further, with many pupils incorrectly identifying and finding EMA. The final process mark was for a correct trigonometric statement involving angle EMB, which could be gained from numerous routes through the diagram.
A triangular prism has square base ABCD of side 15 cm. ABE and CBE are right angles, angle EAB=35°. M lies on DA with DM:MA=2:3.
Edexcel 1MA1 · June 2019 · Paper 3F · Q3 · 1 mark
1 mark
Examiner report
This was not answered well. 150, 15 or 1.5 were the most common incorrect responses, with about 2/3 giving the correct answer.
Change 1.5 kilometres to metres.
Edexcel 1MA1 · June 2019 · Paper 3F · Q5 · 1 mark
1 mark
Examiner report
This was very well answered with few failing to gain the mark.
Write 19% as a fraction.
Edexcel 1MA1 · June 2019 · Paper 3F · Q10 · 3 marks
3 marks
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.
Bill has 400 counters. He gives 35 to Sameena, 50 to Henry and 75 to Lucas.
Edexcel 1MA1 · June 2019 · Paper 3F · Q12 · 2 marks
2 marks
Examiner report
This was well done by the majority, giving 9/25 as the final answer. A few students added 6, 9 and 10 incorrectly but were still able to gain the method mark. The final mark was sometimes lost when the student failed to give the final answer as a fraction. Common incorrect answers included 25/9 and 9/100.
Ali, Ben and Cathy share an amount of money in the ratio 6:9:10.
Edexcel 1MA1 · June 2019 · Paper 3F · Q17 · 2 marks
2 marks
Examiner report
Students found this question difficult. Instead of using the given width of the box (1.5 metres) and measurement (1.8 cm) some measured the height of the box instead and used that measurement. Common incorrect methods included multiplying 10.8 by 1.5 or dividing 10.8 by 1.5. Others chose to just measure the pole and give that as their answer. Some gave their scaling factor as the final answer. But those who realised that they could use the length of the box to divide up the mast into between 5.5 and 6.5 sections and then multiply this by the real length of 1.5 scored full marks.
An accurate scale diagram shows a telephone mast and a box on the same baseline. On the diagram, the mast is 60 equal scale-units high and the box is 10 equal scale-units wide. The box has a real width of 1.5 metres.
Edexcel 1MA1 · June 2019 · Paper 3F · Q22 · 4 marks
4 marks
Examiner report
This was a question where students were very happy rounding and truncating figures, sometimes at every stage of their calculations, sometimes inducing a level of inaccuracy that left their final answer well away from what was expected. There was also evidence of mis-copying either the figures in the question, or their own figures from a calculation. The most common method was to find the number of gallons (560 ÷ 34.5) followed by conversion of gallons to litres (16.23 × 4.55); most then multiplied by 1.08 to find the cost, but some just gave their litres conversion as the final answer. The most common error after scoring the first two process marks was to divide by 1.08 instead of multiplying. Many gained process marks, but it was important that their working was clear and unambiguous. There were some good attempts at this question, which is evidence of the increased work that centres are doing on proportion and rates.
In October Sally drove 560 miles. Her car travelled 34.5 miles per gallon. Petrol cost £1.08 per litre. One gallon is 4.55 litres.
Edexcel 1MA1 · June 2019 · Paper 3F · Q23 · 5 marks
5 marks
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.
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.
Edexcel 1MA1 · June 2019 · Paper 3F · Q25 · 3 marks
3 marks
Examiner report
Most students showed some understanding of working with percentages, but there was considerable confusion about the necessary processes attached to compound interest. Firstly, there were errors in copying down the numbers, particularly missed zeros. Then the issue as to what to do with 1.5%. Some used this as 15%, others 0.15%. Some remembered something to do with multipliers and used 1.05, 1.005 or 1.15. But the main issue was simply that they had no notion of compound interest. The most common approach was to find a percentage of 200000 and multiply this by 4; 12000 was a very common answer. Those who tried to remember a formula approach usually inserted an incorrect multiplier, 200000 × 1.54 being common. Those students who made the most in-roads into the process were those who worked it out year by year, but premature rounding was in evidence again here, so the accuracy mark was rarely gained. And finally, those who could get to the end frequently gave the answer as 212272.71 (the amount rather than the interest). So overall too many errors in what is a standard process; the most successful approach being one year at a time and using accurate figures from the calculator.
Katy invests £200,000 for 4 years at compound interest of 1.5% per annum.
Edexcel 1MA1 · June 2019 · Paper 3F · Q28 · 4 marks
4 marks
Examiner report
Very few marks were gained in this question. The most common approach was to consider the angle BCF, and giving this as 63 earned a mark, but they could rarely proceed beyond this point. Some earned a mark by working with the total angles of a polygon, but again regularly failed to proceed beyond the point at which this figure was found. Most incorrectly used 360 as the total angles in a hexagon or pentagon; many were unable to label angles correctly, which was particularly disappointing when BCD and CDE were found, but written the wrong way around.
ABCDEF is a hexagon with one line of symmetry. AB is the top side and ED the bottom side; symmetry pairs A with B, F with C and E with D. EF = FA and BC = CD. Angle ABC = 117°. Angle BCD is twice angle CDE.
Edexcel 1MA1 · June 2019 · Paper 3H · Q2 · 3 marks
3 marks
Examiner report
This question was a good discriminator. About one third of students entered for the examination scored full marks for their responses to this question testing compound interest. Students generally used a multiplier approach though students frequently used an incorrect multiplier, for example 1.15 A very common error was for students to give 212272.71 as their answer, the total value of the savings after 4 years and not the interest earned over the period. This answer was awarded two of the three marks available. A great majority of students got at least one mark for the interest earned in the first year. Very few students lost the accuracy mark for not using correct money notation, that is for giving an answer to more than 2 decimal places.
Katy invests £200 000 in a savings account for 4 years. The account pays compound interest at a rate of 1.5 % per annum. Calculate the total amount of interest Katy will get at the end of 4 years. £
Edexcel 1MA1 · June 2019 · Paper 3H · Q9 · 3 marks
3 marks
Examiner report
This question was not well answered in general though there were many clear and concise responses which earned full marks. Many students were able to make a start by stating that 54 (6 × 9) machine days were needed to make all the boxes. A much smaller proportion of students could make further progress. The most common strategy used by students who successfully solved the problem was to identify that 42 machine days were needed in addition to the first 3 days and then that 42 machine days is equivalent to 7 days with all the machines working. A small number of students who used this approach gave 7 as their final answer instead of the correct 10 days (3 + 7). The most able students were able to identify that 6 machine days were lost in the first 3 days so one extra day in addition to the 9 days would be needed to make all the boxes.
A company has to make a large number of boxes. The company has 6 machines. All the machines work at the same rate. When all the machines are working, they can make all the boxes in 9 days. The table gives the number of machines working each day. day 1 day 2 day 3 all other days Number of machines working 3 4 5 6 Work out the total number of days taken to make all the boxes.
Edexcel 1MA1 · June 2019 · Paper 3H · Q10 · 3 marks
3 marks
Examiner report
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.
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. %
Edexcel 1MA1 · June 2019 · Paper 3H · Q11 · 3 marks
3 marks
Examiner report
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.
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.
Edexcel 1MA1 · June 2019 · Paper 3H · Q13 · 4 marks
4 marks
Examiner report
This question was successfully answered by about a half of all students. About two thirds of all students realised the need to multiply the measures of density and volume of both ethanol and propylene and so accessed the first two marks for these processes. Some students changed litres to millilitres before doing this. About a half of all students were able to move on from there to complete the calculation of the density of the antifreeze. The most common error seen by examiners was for students to use division rather than multiplication to work out 188 ÷ ቀ ଵ.ଽ+ ଵଶ଼ .ଽቁ or equivalent. The answer given, 1.005, was in the range of acceptable values but could not be awarded any credit.
The density of ethanol is 1.09 g/cm3 The density of propylene is 0.97 g/cm3 60 litres of ethanol are mixed with 128 litres of propylene to make 188 litres of antifreeze. Work out the density of the antifreeze. Give your answer correct to 2 decimal places. g/cm3
Edexcel 1MA1 · June 2019 · Paper 3H · Q14 · 4 marks
4 marks
Examiner report
A small minority of students scored full marks for their responses to this question. Weaker students often showed little or no working and if they did show working, it was often characterised by assuming that the triangles were right angled and using trigonometry to fit such a situation. More able students often did realise that references to area in the question together with the diagram showing non right angled triangles suggested use of the formula ଵ ଶ absinC. However, some of these students tried to find the length of AE instead of using the ratio AB : AE to express AE as an unknown variable, for example 3x. Students who used AB = x and AE = 3x scored at least one mark and often went on to write down and solve an equation using the given fact that the sum of the areas of the triangles was equal to the area of the rectangle. Examiners were surprised at the number of students who equated the area of one triangle to the area of the rectangle which led to the incorrect final answer of 18.
ABDE is a rectangle. Congruent triangles AFE and BCD are attached to the two sides of the rectangle. AF = BC = 24 cm, angle FAE = angle CBD = 30 degrees, and the area of rectangle ABDE equals the total area of the two triangles. Also AB : AE = 1 : 3.
Edexcel 1MA1 · June 2019 · Paper 3H · Q17 · 2 marks
2 marks
Examiner report
Matching the functions to the graphs in this question produced a good spread of marks with about a third of all students scoring each of the marks available. The graph of a trigonometrical function was identified correctly more frequently than the other graphs and the graphs showing one form of proportionality or another were the least well known.
Four graphs are labelled A to D. Graph A crosses the x-axis at a negative x-value, falls to a minimum in quadrant III, passes through the origin, rises to a maximum in quadrant I, and returns to the positive x-axis. Graph B has two branches, one in quadrant I and one in quadrant III, with the coordinate axes as asymptotes. Graph C starts at the origin and increases in quadrant I with decreasing gradient. Graph D is positive and increasing, crosses the y-axis above the origin, and approaches the x-axis for negative x-values.
Edexcel 1MA1 · November 2018 · Paper 1F · Q2 · 1 mark
1 mark
Examiner report
Nearly all students correctly wrote that 0.6 is 60%. The most common error seen was to write 6%.
Write 0.6 as a percentage. %
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Edexcel 1MA1 · November 2018 · Paper 1F · Q12 · 3 marks
3 marks
Examiner report
There were many fully successful answers to this question though a good proportion of students could not relate the idea of a “fixed charge” to the graph and there were some students who gave £40 as their answer to part (b) this being the delivery cost corresponding to a distance of 20 miles instead of the difference between two delivery costs. Some students interpreted the vertical scale on the graph incorrectly and used 2 mm to represent £1.
A delivery-cost graph is a straight line through (0 miles, GBP 10) and (60 miles, GBP 100).
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1F · Q13 · 2 marks
2 marks
Examiner report
This question, testing multiplicative relationships and ratio notation proved to be a good discriminator. Many students gave the correct ratio 4 : 1 : 2 or an equivalent ratio as their answer. Examiners did not expect the ratio to be written in its simplest form. Of those students who did not score full marks, many either gave a partially correct ratio for which examiners awarded one mark or they expressed the scores algebraically, for example 4x, x, and 2x. Some students re-ordered the ratio into alphabetical (or size) order on the answer line. This was acceptable provided the “parts” were clearly linked correctly to Azmol, Kim and Ryan..
Azmol, Ryan and Kim each played a game. Azmol’s score was four times Ryan’s score. Kim’s score was half of Azmol’s score. Write down the ratio of Azmol’s score to Ryan’s score to Kim’s score.
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Edexcel 1MA1 · November 2018 · Paper 1F · Q15 · 4 marks
4 marks
Examiner report
Very few students successfully completed this question. However, in part (a), a large proportion of students were able to make a start to the process by dividing 300 by 5 or by dividing 200 by 2. These students were awarded one mark. They often went on to add 60 and 100 to give the incorrect answer, 160 ml. Weaker students frequently gave an answer of 1900 (from 2 × 200 + 5 × 300). Part (b) was also poorly answered with some students suggesting that less fizzy drink could be made because there was 40 ml less lemonade. Some other students answered “yes” to part (b) because they did not appreciate that the amount of orange juice was the limiting factor.
A fizzy drink is made by mixing orange juice and lemonade in the ratio 5:2.
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Edexcel 1MA1 · November 2018 · Paper 1F · Q18 · 4 marks
4 marks
Examiner report
Students often scored well on this question, with the majority of students scoring at least 2 marks for finding the reduced price of a box of cereal bought at “Food Mart” together with the total number of grams in a box of cereal bought at “Jan’s Store”. It is encouraging to report that more students are now showing a full method when finding percentages, not merely using a build up method stating “10% =…” etc. In order to compare value for money at the two shops, most students opted to find the number of grams bought per pound. Arithmetic errors were quite often seen when students tried to divide 520 by 5. Despite the instruction in the question that “you must show all your working”, many students wrote their conclusion without citing comparative values and so could not be awarded full marks. A few students scored 3 marks out of 4 because they chose the wrong conclusion after obtaining correct comparable values.
Food Mart and Jan's Store sell the same cereal. Food Mart offers a 400 g box at 20% off its normal GBP 5 price. Jan's Store offers a GBP 5 box containing 400 g plus 30% extra.
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Edexcel 1MA1 · November 2018 · Paper 1F · Q22 · 5 marks
5 marks
Examiner report
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.
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.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1F · Q23 · 3 marks
3 marks
Examiner report
One of the least well attempted questions on the paper, the most common answer seen was 72 minutes. This was obtained by students mistakenly making the assumption that the time taken to fill the pool would be directly proportional to the number of taps used. It seems disappointing that more students did not appear to question the fact that it might take only 24 minutes for 1 tap to fill the pool or that they had found that fewer taps would take less time to fill the pool. Some students who made this error then went on to state, in part (b), that they had assumed that the pool would take longer to fill with fewer taps. Examiners expected a statement in part (b) equivalent to saying that water flowed out of each tap at the same rate, an assumption which could lead to a solution of the problem. Many students resorted to a commentary on their method, for example “I divided by 5 then multiplied by 3” or as mentioned previously the vague statement that less taps would mean it takes longer to fill the pool.
It would take 120 minutes to fill a swimming pool using water from 5 taps.
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Edexcel 1MA1 · November 2018 · Paper 1F · Q24 · 4 marks
4 marks
Examiner report
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
A plane is travelling at 213 miles per hour.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1H · Q3 · 5 marks
5 marks
Examiner report
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.
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.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1H · Q4 · 3 marks
3 marks
Examiner report
Part (a) was poorly answered with many students thinking that each tap took (120 ÷ 5) minutes to fill the pool. 72 minutes was the modal incorrect answer. Having found this answer, many realised that the answer should be greater than 120 minutes and so simply added the 120 to give an incorrect answer of 192 minutes. In part (b), many students correctly stated that their assumption was that all taps were working at the same rate of flow.
It would take 120 minutes to fill a swimming pool using water from 5 taps.
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Edexcel 1MA1 · November 2018 · Paper 1H · Q5 · 4 marks
4 marks
Examiner report
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.
A plane travels at a speed of 213 miles per hour.
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Edexcel 1MA1 · November 2018 · Paper 1H · Q11 · 3 marks
3 marks
Examiner report
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%.
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? %
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1H · Q15 · 4 marks
4 marks
Examiner report
Only the most able of students achieved full marks here. A mark of 2 was common, however, with ratios of 2:5 and 3:4 or their equivalences seen. Many weaker students unsuccessfully tried to combine the pairs of ratios given. It was pleasing to see some students drawing diagrams to help visualise the problem.
Three solid shapes A, B and C are similar. The surface area of shape A is 4 cm2 The surface area of shape B is 25 cm2 The ratio of the volume of shape B to the volume of shape C is 27 : 64 Work out the ratio of the height of shape A to the height of shape C. Give your answer in its simplest form.
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Edexcel 1MA1 · November 2018 · Paper 2F · Q3 · 2 marks
2 marks
Examiner report
Although many students changed 4560 g into 4.56 kg in part (a) answers of 45.6 and 456 were very common. Slightly fewer students were able to change 7.3 m into 7300 mm in part (b). The most common incorrect answers were 730, 73 and 0.73.
(a) Change 4560 g into kg. kg (1) (b) Change 7.3 m into mm. mm (1)
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Edexcel 1MA1 · November 2018 · Paper 2F · Q8 · 2 marks
2 marks
Examiner report
This question was generally answered well with many students multiplying 18.8 by 14 to find the real distance between Manchester and London. A few went on to multiply by 100 or by 1000 and lost the accuracy mark. A surprising number of students split the multiplication into two parts and first worked out 18 × 14. At this stage the method mark could be awarded. Unfortunately many could not complete the method and attempts to work out 0.8 of 14 were often unsuccessful. Some students could not use the scale correctly and divided 18.8 by 14 and there were others who did not use the scale at all and multiplied 18.8 by a power of 10.
A map has a scale of 1 cm to 14 km. On the map, the distance between Manchester and London is 18.8 cm. What is the real distance, in km, between Manchester and London? km
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Edexcel 1MA1 · November 2018 · Paper 2F · Q11 · 3 marks
3 marks
Examiner report
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.
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 · Q15 · 3 marks
3 marks
Examiner report
Many students gained the first mark for making a correct start. Most often this was dividing 75 by 5 to work out that Remi received £15 interest each year. Multiplying 600 by 5 was also a common first step. Some students were able to complete the method by working out that 15 is 2.5% of 600 and a few got as far as 0.025 and scored 2 marks. Many more were either unable to continue and gave 15 as the answer or continued with incorrect working. Some students started by working out that 75 is 12.5% of 600 but often did not complete the method. A common incorrect first step was to divide 600 by 5 and assume that Remi invested £120 each year. Some students divided 600 by 15.
Remi invests £600 for 5 years in a savings account. By the end of the 5 years he has received a total of £75 simple interest. Work out the annual rate of simple interest. %
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Edexcel 1MA1 · November 2018 · Paper 2F · Q18 · 2 marks
2 marks
Examiner report
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.
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 · Q23 · 5 marks
5 marks
Examiner report
Most students treated part (a) as a simple interest question rather than as a compound interest question and could score at most 1 mark. Those that did work with compound interest often chose to work out each year individually and made the question more ‘labour intensive’ than it needed to be. There was a lot of premature rounding of values with this approach which led to inaccurate answers. Calculations such as 2000 × 1.0253 and 1600 × 1.0353 were not as widely used as might have been expected. Students do need to ensure that they use the correct multiplier; a mistake made by some was using 1.25 instead of 1.025. Many of the students who did show a complete compound interest calculation for both accounts then gave an incorrect conclusion because they based their decision on the total amount in each account instead of on the total interest that each person received. Students who had concluded in part (a) that Ben will get the most interest were in a position to answer part (b) without any further calculation. Quite a few students did make a statement such as “No, Ben already gets the most so he will get even more” and scored 1 mark. When calculations were carried out in part (b) these were usually simple interest calculations and no credit could be given.
Ali invests GBP 2000 at 2.5% compound interest per year for 3 years. Ben invests GBP 1600 at 3.5% compound interest per year for 3 years.
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Edexcel 1MA1 · November 2018 · Paper 2F · Q24 · 5 marks
5 marks
Examiner report
Although there were relatively few fully correct solutions to this multi-step problem many students did gain at least one mark. Many students could not find the area of a trapezium correctly but even so they were still able to access three of the process marks. After finding a floor area, a common approach was to work out that each tin covers an area of 10 m2 and divide their area by 10 to find the number of tins needed. Some students divided their area by 2 to find the number of litres needed and then divided by 5 to find the number of tins needed. A common mistake was to divide by 2 or by 5 but not by both. It was disappointing to note that a small number of students used a divisor of 4 instead of 2 for paint coverage because they misunderstood the notation 2m2. After a process to find the number of tins students often went on to multiply £16.99 by a non-integer value and lost a process mark. Some students showed incorrect working to find the total cost based on finding the cost of 1 litre of paint. A small number of students used a different approach, starting with the £160 John has to spend and working out the floor area that can be covered with the tins he can buy. Many responses had little or no structure to the working with calculations scattered over the page. Students who worked logically and structured their answer generally scored better.
A trapezium-shaped area has parallel sides 10 m and 16 m and perpendicular height 7 m. Paint covers 2 square metres per litre and is sold in 5-litre tins costing GBP 16.99 each. The budget is GBP 160.
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Edexcel 1MA1 · November 2018 · Paper 2H · Q4 · 5 marks
5 marks
Examiner report
Though some students treated this as a simple interest question, the most common error for those who understood the principle of compound interest was to use an incorrect multiplier, including 1.25 and 1.35. Those who used a partitioning method regularly made arithmetic errors. Of those who worked through the problem correctly, some failed to notice that the question required a comparison of the interest amounts, rather than the total amounts, thereby losing the final mark. In part (b) many again attempted a comparison of the total amounts rather than the interest, though those who had worked out the interest in part (a) usually went on to gain the mark in part (b). Where recalculation was done the mark was frequently gained though not for those who recalculated using the 4% across the 3 years.
Ali invests GBP 2000 at 2.5% compound interest per year for 3 years. Ben invests GBP 1600 at 3.5% compound interest per year for 3 years.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 2H · Q5 · 5 marks
5 marks
Examiner report
The area of the trapezium was incorrectly calculated by many. The following step of working (that of division by 2, 5 or 10) were usually done well, but many students failed to round up the number of tins to a whole number. Some assumed you could buy the paint by the litre, and not in 5 litre tins. Those who worked through all stages ended with a comparison of 90 and 91. This was the most successful method, but other methods were credited that resulted in a comparison of the number of tins, or even the number of litres needed.
A floor is a trapezium with parallel sides 10 m and 16 m and perpendicular height 7 m. Each 5-litre tin of paint costs GBP 16.99. One litre covers 2 m^2. John has GBP 160.
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Edexcel 1MA1 · November 2018 · Paper 2H · Q10 · 5 marks
5 marks
Examiner report
Very few students managed the percentage calculation, usually trying to combine the wrong set of numbers, having little idea of how to work out a percentage change. But the first three marks were readily available to many students. Working with 20 and 30 litres was the usual start to the solution, from this working out the number of tins required and then the cost, with 248 being shown. From this the cost of 50 litres could be found, with both 248 and 334.8 being shown to achieve 3 marks. Weaker students started with the 20 and 30 but did not know what to do with these figures.
Robert makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 2 : 3 Yellow paint is sold in 5 litre tins. Each tin of yellow paint costs £26 Blue paint is sold in 10 litre tins. Each tin of blue paint costs £48 Robert sells all the green paint he makes in 10 litre tins. He sells each tin of green paint for £66.96 Work out Robert’s percentage profit on each tin of green paint he sells. %
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Edexcel 1MA1 · November 2018 · Paper 2H · Q17 · 5 marks
5 marks
Examiner report
From this point on through to the end of the paper there were many students who made few attempts at the remaining questions. In this question students sometimes gained the first mark for associating algebraic representations with the correct ratio. Beyond this step few knew what to do with their expressions. More able students went on to form simultaneous equations to solve.
p and q are numbers with p > q. Subtracting 5 from each gives (p - 5):(q - 5) = 5:1. Adding 20 to each gives (p + 20):(q + 20) = 5:2.
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Edexcel 1MA1 · November 2018 · Paper 2H · Q20 · 5 marks
5 marks
Examiner report
It was disappointing to find how few students were able to use given formulae and perform a simple substitution into them. Use of the diameter rather than the radius was seen too often, or not halving the diameter for the top half of the cone, or even not halving to find the volume of a hemisphere. Surprisingly it was not uncommon to find students who changed the 1/3 to ½ for the volume of the cone. In dealing with the densities, there was a lot of adding since students did not realise that each one applied to each part of the shape.
A solid is made by joining a frustum to a solid hemisphere of radius 3.6 cm. The frustum is formed from a cone of radius 3.6 cm and height 6.4 cm by removing a similar cone of radius 1.8 cm and height 3.2 cm. The frustum has density 2.4 g/cm^3 and the hemisphere has density 4.8 g/cm^3. Use volume of a sphere = (4/3)pi r^3 and volume of a cone = (1/3)pi r^2 h.
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Edexcel 1MA1 · November 2018 · Paper 3F · Q2 · 1 mark
1 mark
Examiner report
Another very well answered question with the vast majority of students able to correctly write 3% as a fraction. A few students incorrectly had 10 as their denominator rather than 100, but this was only a very small minority.
Write 3% as a fraction.
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Edexcel 1MA1 · November 2018 · Paper 3F · Q7 · 2 marks
2 marks
Examiner report
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.
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
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.
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
Examiner report
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%.
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 · Q16 · 2 marks
2 marks
Examiner report
Another familiar type question, and one in which most students gained at least one mark for writing the correct unsimplified ratio. It is clear however, that many students do not know how to simplify ratios and as a result they came up with a variety of incorrect ratios, or they didn’t simplify fully, often resulting in answers like 90 : 3.
Write down the ratio of 450 grams to 15 grams. Give your answer in its simplest form.
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Edexcel 1MA1 · November 2018 · Paper 3F · Q18 · 4 marks
4 marks
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.
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. £
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Edexcel 1MA1 · November 2018 · Paper 3F · Q21 · 3 marks
3 marks
Examiner report
This problem was a difficult one to access, with most unable to gain more than one mark. This was normally for finding the difference of 638 or for dividing 883 by 245. With either of these methods, most students then struggled to know what to do, with it being common to see them trying to turn 638 into a percentage by dividing by 10 or 100. It is possible students are not used to seeing percentage changes of more than 100%.
Last year Jo paid £245 for her car insurance. This year she has to pay £883 for her car insurance. Work out the percentage increase in the cost of her car insurance. %
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Edexcel 1MA1 · November 2018 · Paper 3F · Q24 · 4 marks
4 marks
Examiner report
Many students struggled to deal with speed in any correct way, normally seen by incorrect operations using distance and time. The mark scheme did allow flexibility, until the final mark, with how students dealt with the conversion between minutes and seconds. It was apparent from working seen that many students didn’t really know what values they had and what values they were trying to calculate, on top of which, when the formula was stated, it was often wrong. In part (b) however, many students realised that an increase in speed meant a decrease in time. It was the clarity of their answers that sometimes let them down. To gain the mark it had to be clear that students were talking about time rather than a change in speed.
Lara completes a 475 m ski race in 1 minute 54 seconds. She initially assumes her average speed is the same for each race.
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Edexcel 1MA1 · November 2018 · Paper 3F · Q25 · 4 marks
4 marks
Examiner report
This question proved to be a significant challenge to the vast majority of students. The only mark that was accessed with any regularity was the first mark for dealing with the ratio to find the missing angles. From that point on, only a very few students were able to correctly apply trigonometry to further their solution.
ABC is a right-angled triangle. B A C 14 cm AC = 14 cm. Angle C = 90 size of angle B : size of angle A = 3 : 2 Work out the length of AB. Give your answer correct to 3 significant figures. cm
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Edexcel 1MA1 · November 2018 · Paper 3H · Q2 · 3 marks
3 marks
Examiner report
Most students began this question and gained one mark. The initial calculation to find the increase in cost was fine but then they did not know how to find this as a percentage increase, often doing 638 ÷ 883 × 100. Many students calculated the overall increase by doing 883 ÷ 245 × 100 stopping there to give 360.4 as a popular incorrect answer rather than continuing to find the actual percentage increase. The answer of a percentage greater than 100% did challenge some students, and some, who even though they arrived at the correct answer in the working then just wrote 26% or even 2.6% as their final answer. Centres are advised to ensure that students know that it is possible to get percentages greater than 100% when finding percentage increases.
Last year Jo paid £245 for her car insurance. This year she has to pay £883 for her car insurance. Work out the percentage increase in the cost of her car insurance. %
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Edexcel 1MA1 · November 2018 · Paper 3H · Q4 · 6 marks
6 marks
Examiner report
The first part of this question was well answered. Most students were able to find the appropriate percentage. The most common incorrect answer seen was 2.5% from 100÷40. Many fully correct answers were seen in part b, full working was required as this was a ‘show that’ question. However, a common error was to read off the vertical scale incorrectly sometimes using 10.8 instead of 11. Students should always look at the context of the question to see if their answers are sensible. As this is about the number of students buying books 10.8 is not a sensible number. In general most students received marks on this question for either the correct frequencies or the correct mid values.
A grouped bar chart records the numbers of books bought by 40 students: 0-4 books has frequency 11; 5-9 has frequency 8; 10-14 has frequency 13; 15-19 has frequency 6; 20-24 has frequency 2.
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Edexcel 1MA1 · November 2018 · Paper 3H · Q5 · 4 marks
4 marks
Examiner report
For this question most students scored at least one or two marks. Credit was given for the understanding the principles of speed is distance divided by time. This meant that the students who were unable to convert 1minute 54 seconds correctly could still get credit for using this concept. Incorrect conversions of time included 1.54 (minutes), 154 (seconds), and 104 (seconds). For those who arrived at an answer of 2.8 hours there were a significant number who could not convert this successfully into minutes and seconds. Students continue to struggle using the fact that there are 60 seconds in a minute. Part (b) required an explanation and many students were able to interpret the change in speed and the affect this would have on the time taken for the race.
Lara completes a 475 m ski race in 1 minute 54 seconds. She initially assumes her average speed is the same for each race.
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Edexcel 1MA1 · November 2018 · Paper 3H · Q6 · 4 marks
4 marks
Examiner report
The initial ratio part at the beginning of this question allowed many students to achieve one mark on this question. For those who could not find the angle correctly there was another opportunity to achieve marks by using ‘their’ value for angle A or angle B in a correct equation using trigonometry. Many students continue to make the use of trigonometry in a right-angled triangle more difficult than is necessary, by trying to use the cosine rule or sine rule but often misquoted incorrectly. Whilst this approach is acceptable and can lead to the correct answer few students are able to apply these rules correctly. The use of a trigonometry in a right-angled triangle is usually a more successful approach. However, the most common error seen in this method was for the student to correctly write sin 54 = 14 ÷ AB but then to rearrange incorrectly to AB = 14 sin 54.
ABC is a right-angled triangle. B A C 14 cm AC = 14 cm. Angle C = 90 size of angle B : size of angle A = 3 : 2 Work out the length of AB. Give your answer correct to 3 significant figures. cm
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Edexcel 1MA1 · November 2018 · Paper 3H · Q13 · 2 marks
2 marks
Examiner report
Some students gained a mark for using the 400 correctly as 1.01 × 400 on its own or as part of a larger calculation. The final mark was often lost where students did not interpret the question and gave the answer as 408.04, or used the wrong number of years, frequently giving the number for the start of year 4.
The population at the start of year t is P_t. At the start of year 1, P_1 = 400. The recurrence relation is P_(t+1) = 1.01 P_t.
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Edexcel 1MA1 · November 2018 · Paper 3H · Q14 · 3 marks
3 marks
Examiner report
This question was not well answered by the majority of students. The main error seen would appear to be a lack of knowledge of inverse proportionality and how to express it algebraically. Of the students that did gain marks the modal mark was 2 marks. They often starting by writing down a correct equation but were then unable to substitute the given values correctly. However, the main error then seen was to evaluate (2a)3 incorrectly, often giving this as 8a, thus not gaining the final mark.
y is inversely proportional to x^3, and y = 44 when x = a.
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Edexcel 1MA1 · November 2018 · Paper 3H · Q18 · 5 marks
5 marks
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.
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 · Q3 · 1 mark
1 mark
Examiner report
The majority of students gave a correct fraction for 20%. The most common correct answers given were .
Write 20% as a fraction.
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Edexcel 1MA1 · June 2018 · Paper 1F · Q8 · 2 marks
2 marks
Examiner report
About 70% of students correctly carried out this simple calculation; it was disappointing to see so many unable to divide 54 by 3 correctly. Many students thought that halving 54 and then halving again to get 13.5 was the equivalent of dividing 54 by 3 to get the cost of 1 kg of meat. £27, £40.50 and £34 (from 54 ÷ 3 = 17 instead of 18) were the most common incorrect answers.
Three kilograms of meat cost GBP54. Nina buys 2 kg.
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Edexcel 1MA1 · June 2018 · Paper 1F · Q14 · 4 marks
4 marks
Examiner report
Most students gained at least one mark here for a correct process to work with the . However, many simply converted this to 75% claiming that this was the proportion saved by Harry. Many students found difficulty in dealing with the ratio 3 : 7 where was a common incorrect fraction when finding the savings for Isabel. Conversion to comparative percentages was the most common approach although many introduced a value for their salaries and worked with this. The value chosen was often not a sensible one and created issues when trying to calculate 28% of its value. Only a few students failed to answer the question with a final statement.
Gavin saves 28% of his salary. Harry spends 3/4 and saves the rest. Isabel saves and spends in ratio 3:7.
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Edexcel 1MA1 · June 2018 · Paper 1F · Q17 · 2 marks
2 marks
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.
There are some chocolates in a box. One quarter contain nuts and the rest do not contain nuts.
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Edexcel 1MA1 · June 2018 · Paper 1F · Q20 · 3 marks
3 marks
Examiner report
Just over half of students found the demand of this question too great. Some students were able to correctly work with the ratio 8 : 5 resulting in 80 flats but could not correctly link this with the ratio 7 : 4 to find the number of houses; an incorrect answer of 70 was very common indeed. Some students used diagrams to help understand the question with some pleasing success. Very few students tried to convert the two ratios to a triple ratio and a ratio such as 14 : 8 : 5 was a rarity.
In a village the number of houses and the number of flats are in the ratio 7 : 4 the number of flats and the number of bungalows are in the ratio 8 : 5 There are 50 bungalows in the village. How many houses are there in the village?
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Edexcel 1MA1 · June 2018 · Paper 1F · Q21 · 4 marks
4 marks
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.
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.
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Edexcel 1MA1 · June 2018 · Paper 1F · Q22 · 4 marks
4 marks
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.
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 · Q2 · 3 marks
3 marks
Examiner report
This ratio question was well answered. In order to make progress students needed to associate corresponding parts from the two ratios. Those that wrote down the ratios 14 : 8 and 8 : 5 or the ratio 14 : 8 : 5 were often able to go on and work out the number of houses. A few students obtained the ratio 56 : 32 : 20 and arrived at the answer by using 2.5 × 56. Many students started with a process to find the number of flats, e.g. 50 ÷ 5 × 8 = 80. Sometimes the number of flats was shown in the ratio 80 : 50. A common error was to write the ratio 7 : 4 as 70 : 40 and state that there are 70 houses. Having found that there are 80 flats some students were able to complete the process to find the number of houses, e.g. 80 ÷ 4 × 7 = 140. If the final answer was given as 270 (the total number of houses, flats and bungalows) students were not penalised if 140 was clearly identified as the number of houses in the working. The ratios 7 : 4 and 8 : 5 were sometimes combined incorrectly to give 7 : 12 : 5 or, less frequently, 7 : 32 : 5. Some students started by adding the numbers in the ratios, working out 7 + 4 = 11 and 8 + 5 = 13, but were often unable to make any further meaningful progress.
In a village the number of houses and the number of flats are in the ratio 7 : 4 the number of flats and the number of bungalows are in the ratio 8 : 5 There are 50 bungalows in the village. How many houses are there in the village?
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Edexcel 1MA1 · June 2018 · Paper 1H · Q3 · 4 marks
4 marks
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.
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.
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Edexcel 1MA1 · June 2018 · Paper 1H · Q4 · 4 marks
4 marks
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).
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 · Q8 · 4 marks
4 marks
Examiner report
This question was generally answered very well with most students able to find the lengths of the sides of the triangle by dividing 72 in the ratio 3 : 4 : 5. A common error was to divide 72 by 3 and by 4 and by 5. Few students used the alternative method of scaling up ratios to find the lengths of the sides. Having found the lengths of the sides most students went on to identify the correct two sides for the area calculation and use a correct method to find the area of the triangle. A few students used 18 cm and 30 cm instead of 18 cm and 24 cm and some forgot to divide by 2 when finding the area. The accuracy mark was often lost because of arithmetic errors, particularly in the area calculation. Some students sensibly reduced ½ ×18×24 to 9×24 or to 12×18 but others correctly wrote ½×18×24 but then halved both 18 and 24 before multiplying. The majority chose to multiply 18 by 24 and then divide by 2. Very few students used the method of scaling area.
The perimeter of a right-angled triangle is 72 cm. The side lengths are in the ratio 3:4:5. Work out its area.
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Edexcel 1MA1 · June 2018 · Paper 1H · Q14 · 5 marks
5 marks
Examiner report
Many students were able to set up at least one correct proportional relationship and often wrote down both y 1/d2 and d x2. At this stage a common error was to use direct proportion instead of inverse proportion and vice versa. Students who used the constant k and wrote y = k/d2 or d = kx2 were usually able to substitute and find the value of the constant although the rearrangement of the equation to make k the subject sometimes went wrong. Some students did not write down an equation involving k and statements such as 24 22 were common. Many of the students who found the values of the constants were not able to use y = 400/d2 and d = 6x2 to find a formula for y in terms of x. Many simply stopped and went no further. Those who did continue sometimes wrote y = 400/6x2 rather than y = 400/(6x2)2. The question required the answer to be given in its simplest form so students who gave the answer as y = 400/36x4 were not awarded the accuracy mark. Some students could not simplify y = 400/(6x2)2 which appeared to be due to issues squaring 6x2.
y is inversely proportional to d^2, with d=10 when y=4. Also d is directly proportional to x^2, with d=24 when x=2.
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Edexcel 1MA1 · June 2018 · Paper 1H · Q16 · 3 marks
3 marks
Examiner report
Once students had identified a suitable strategy to use they were often able to work out the probability that Sam takes a red counter, though there were many errors in arithmetic. Successful solutions often started with students working out that the probability of taking a red counter or a blue counter is 0.8 and then finding 3/20 of 0.8. Division of 0.8 by 20 often lead to arithmetic errors. Some students worked out that if 20 red counters and blue counters represent 80% of the total number of counters then the total number of counters must be 25, often using an argument such as “80% = 20, 20% = 5”. Those that attempted to divide 20 by 0.8 often got into difficulties. A common error was for students to work out that the total number of counters is 24, e.g. 80% = 20, 20% of 20 = 4, 20 + 4 = 24. Some students assumed that there are 100 counters altogether and were able to work out that there are 12 red counters. Many students failed to find a successful strategy and in these cases the working out was often messy and difficult for examiners to follow. There were quite a few attempts at representing the information in tree diagrams and in ratios. These were generally unhelpful.
There are only red, blue and purple counters in a bag. The ratio red:blue is 3:17. The probability of taking a purple counter is 0.2.
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Edexcel 1MA1 · June 2018 · Paper 2F · Q1 · 1 mark
1 mark
Examiner report
There were a significant number of blank responses to this question.
Write 4/50 as a percentage.
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Edexcel 1MA1 · June 2018 · Paper 2F · Q5 · 3 marks
3 marks
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.
Convert the measurements.
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Edexcel 1MA1 · June 2018 · Paper 2F · Q9 · 4 marks
4 marks
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.
Emily drives 186 miles in 3 hours. Sarah drives at 58 mph for 4 hours.
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Edexcel 1MA1 · June 2018 · Paper 2F · Q17 · 3 marks
3 marks
Examiner report
There were a variety of approaches that students could use to answer this question, with many choosing to calculate the maximum number of batches that could be made with the amount of ingredients available, some rounded to whole batches whilst others used exact figures, both were acceptable. The majority of students were able to identify the ingredient that provided the limiting factor, with many successfully continuing to show a fully correct method to test all ingredients and conclude that 90 was the most biscuits that could be made. However, some students chose to work with just one ingredient often the butter and gave an incorrect answer of 120 biscuits. Others worked out all the batches but then failed to multiply by 30 and so did not have a complete method for the number of biscuits possible. Another common error was to find the correct number but then add up how many biscuits could be made with each ingredient to give an impossible total from these ingredients. Students who chose to use a unitary method were often unsuccessful in calculating accurately to reach the correct final answer, sometimes through arithmetic errors, other times through rounding prematurely. Although the question stated clearly that working must be shown, a significant number of responses arrived at the correct answer but failed to gain full credit due to not showing any justification involving all ingredients to support their final answer.
Here is the list of ingredients for making 30 biscuits. Ingredients for 30 biscuits 225 g butter 110 g caster sugar 275 g plain flour 75 g chocolate chips Lucas has the following ingredients. 900 g butter 1000 g caster sugar 1000 g plain flour 225 g chocolate chips What is the greatest number of biscuits Lucas can make? You must show your working.
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Edexcel 1MA1 · June 2018 · Paper 2F · Q23 · 5 marks
5 marks
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.
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 2F · Q25 · 3 marks
3 marks
Examiner report
The majority of students were able to calculate either the original pressure or the new pressure or both but most failed to engage with the percentage. There was often confusion between cm squared and squaring leading to some students clearly showing and calculating 70 ÷ 202 instead of 70 ÷ 20. Those students that did find comparative values, usually made the correct decision but it was common for students to make a decision without having found values that could be compared. A few students made the wrong decision despite having correct values.
Pressure changes from 70 N over 20 cm^2 to 80 N over 30 cm^2. Helen claims the decrease is under 20%.
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Edexcel 1MA1 · June 2018 · Paper 2H · Q4 · 5 marks
5 marks
Examiner report
The first of the problem solving questions was answered well in general. Most successful students followed the processes in the order set out in the mark scheme. It is a little disappointing to see students making arithmetic errors on questions such as this, especially as they have access to a calculator. Typically, students were able to gain the first three marks for finding 10200, 6375 and 3825. A few thought 10% of 8500 was 85, and many didn’t realise they had to add VAT on and subtracted 6375 from 8500. At this point it was split, some were unable to form a suitable ratio, 10200 was frequently part of an incorrect ratio. Many had a correct starting ratio ie 3825 : 6375, but very often students were unable to fully simplify it, often ending with 51 : 85, and thus failing to gain the final accuracy mark.
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 · Q6 · 3 marks
3 marks
Examiner report
Another problem solving question, and one that was answered well by many students. Almost every student was able to gain the first mark for finding either the original or new pressure. There were lots of methods that were suitable to answer this problem, and the most common are seen in the mark scheme. One of the most popular was to decrease the 3.5 by 20% (and get 2.8) and then realise that the pressure had dropped further. However, some students misinterpreted this value and stated that “as 2.6 is less than 2.8 Helen was right”.
Pressure changes from 70 N over 20 cm^2 to 80 N over 30 cm^2. Helen claims the decrease is under 20%.
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Edexcel 1MA1 · June 2018 · Paper 2H · Q9 · 4 marks
4 marks
Examiner report
This question differentiated well. Most students were able to access the first mark for getting the multiplier for year 1 (1.028). The weaker students then halved this value as the multiplier for year 2 and thus scored only 1 mark. More able students were able to extract the 2.8% from the multiplier and then half this to gain the interest rate for year 2. Many who got this far were then able to gain the third mark for a complete process. Some who calculated 1.4% used 1.14 as the multiplier not understanding that this equated to 114%.
Jean invests GBP12000. After year 1 it is GBP12336 at x% interest. In year 2 the rate is x/2%.
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Edexcel 1MA1 · June 2018 · Paper 2H · Q12 · 2 marks
2 marks
Examiner report
Many students were typically able to gain one mark, usually for recognising the linear and quadratic graphs. However there were a significant number who mixed up all the functions. Pleasingly, over half of all students scored both marks.
Graph A is an increasing concave-down curve from the origin. Graph B is a straight line through the origin. Graph C is a decreasing curve asymptotic to both positive axes. Graph D is an increasing concave-up curve from the origin.
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Edexcel 1MA1 · June 2018 · Paper 2H · Q14 · 3 marks
3 marks
Examiner report
This is the first time in this specification that this topic has been assessed. Commonly students read off the distance at time = 5 (28) and then worked out 28 ÷ 5. This obviously gained zero marks. Those who failed to recognise the need to draw a tangent were unable to gain any credit. Typically, those who drew a tangent went on to gain all three marks. Some work needs to be done in centres to recognise when a tangent is needed and when it is appropriate to find the area under a curve.
A tangent to the official distance-time curve at t=5 seconds passes approximately through (3 seconds, 0 metres) and (7 seconds, 60 metres).
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Edexcel 1MA1 · June 2018 · Paper 2H · Q21 · 5 marks
5 marks
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.
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 · Q2 · 1 mark
1 mark
Examiner report
Just over three quarters of students were able to give the correct percentage. The most common incorrect answers included 3 % or 0.3 %, or giving the answer as a fraction
Write 0.3 as a percentage.
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Edexcel 1MA1 · June 2018 · Paper 3F · Q10 · 3 marks
3 marks
Examiner report
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.
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 · Q11 · 2 marks
2 marks
Examiner report
The most common first step to this question was to find the increase of £40; this gained one of the two marks unless it was replaced by an alternative set of working that led to the answer on the answer line. It was not unusual see 40 written as the numerator of the answer, but with an incorrect denominator such as the final price (or 100) instead of the original price. Of those who started by looking at 600/560, this was often converted to a percentage without going on to find the increase as a fraction as specified in the question.
A season ticket increased from GBP560 to GBP600.
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Edexcel 1MA1 · June 2018 · Paper 3F · Q12 · 5 marks
5 marks
Examiner report
This question assessed a number of key aspects where it was possible for students to pick up some marks. It was, however, disappointing that about half the candidature failed to gain any marks in this question. The lengths were measured accurately by most who had a ruler and many students were able to find the perimeter from their lengths. Use of the scale or conversion to metres was the step most likely to be missed, leading to the award of only three of the five available marks. This might have been because they thought the value in centimetres for the perimeter was in fact already in meters. A small number of students believed the side lengths to have values of 1 and 200. Some had trouble distinguishing between perimeter and area and subsequently multiplied the lengths they had measured which gained no further marks. There were a number of blank scripts which could have been from the lack of a ruler, or not realising that a single measurement in the accepted range would have scored. On completing a multi-step question students should be encouraged to re-read the question to check they have met all the requirements.
A scale drawing of a rectangular tennis court measures 11.5 cm by 5.8 cm at scale 1:200.
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Edexcel 1MA1 · June 2018 · Paper 3H · Q9 · 4 marks
4 marks
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.
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 · Q11 · 3 marks
3 marks
Examiner report
Reverse percentage problems prove to be straightforward to those students who have a good understanding of the use of a scale factor approach in this topic area. Students who had such an understanding and used the scale factors 1.20 and 0.90 usually solved this problem efficiently and accurately. Those with only a partial grasp of the scale factor approach often used the scale factors 1.20 and 1.10 and, for example, multiplied the value of the house in 2012 (£162,000) by 1.10 to find its value in 2007 instead of the correct method of dividing by 0.9. This incorrect approach could not be given any credit. Weaker students did not use a scale factor approach and merely added 10% onto £162,000 then subtracted 20% off their answer to find a value for the house in 2003.
Jerry sold a house to Mia at a 20% profit. Mia later sold it for GBP162000 at a 10% loss.
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Edexcel 1MA1 · June 2018 · Paper 3H · Q12 · 4 marks
4 marks
Examiner report
There were many good answers to this question. Most students used the scales correctly to find the gradient of the straight line instead of counting squares though some students gave the gradient as “1.5x” or divided the increase in x values by the increase in y values. Good explanations were often seen in responses to parts (b) and (c) of the question. Examiners expected to see explanations in context so statements such as “the gradient represents the slope of the line” and “the value of y when x = 0” were not acceptable for the award of marks. Instead, in part (b), it was expected that students would describe, in some way, that the gradient represents the rate of flow of liquid into the container. The statement “litres per second” alone was not accepted nor was “as time increases volume increases”. A good proportion of the unacceptable answers seen were equivalent to the second of these two statements. In part (c) statements equivalent to “there were 4 litres of liquid in the container at the start” were expected.
A straight-line volume-time graph passes through (t,L)=(0,4) and (8,16), where t is time in seconds and L is volume in litres.
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Edexcel 1MA1 · June 2018 · Paper 3H · Q13 · 3 marks
3 marks
Examiner report
A small minority of students scored full marks for their responses to this question and when the question was completed correctly, answers were usually accurate and within the range of acceptable values. Some students could write down the ratio of lengths or linear scale factor to score the first available mark but could not make any further progress with the question. Weak students merely worked out ଷ ସ of 10 and gave their answer as 7.5 or cubed 3 and 4 to get the ratio of the volumes, thereby failing to realise the need to find the ratio of lengths first. Some very able students worked in exact terms to express the ratio of volumes as 3√3 : 8 before successfully working out the volume of shape A. Students who worked with approximations to scale factors, expressing them in decimal form, usually retained enough accuracy to obtain an answer within the acceptable range of values.
Similar solids A and B have surface-area ratio A:B = 3:4. Volume of B is 10 cm^3.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q1 · 2 marks
2 marks
Examiner report
This question was accessible to students. In part (a) some students wrote 36500 as the answer and others did not convert to just metres. With m on the answer line a final answer of 3.65 was expected. For part (b) many students used their knowledge of 1000g = 1kg but the common misconception seen was that there are just 100 grams in a kilogram.
(a) Change 365 cm into metres. (b) Change 2.7 kg into grams.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q11 · 3 marks
3 marks
Examiner report
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.
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 · Q15 · 2 marks
2 marks
Examiner report
A good number of students were able to gain full marks for this question and if not full marks then M1 for 9 was often awarded. A few students tried to do 20 ÷ 9 and some others added the ratio parts incorrectly; 22 was frequently seen but this was not helpful in finding the percentage they required. A small number of students found the percentage of the wrong colour, generally red buttons as this was the first part of the ratio; a full method for a colour other than orange was awarded M1, but students should be reminded to read questions carefully to maximise their potential to gain marks.
There are only red buttons, yellow buttons and orange buttons in a jar. The number of red buttons, the number of yellow buttons and the number of orange buttons are in the ratio 7 : 4 : 9 Work out what percentage of the buttons in the jar are orange.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q16 · 5 marks
5 marks
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.
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 · Q18 · 2 marks
2 marks
Examiner report
This question was well answered with many correct methods leading to the calculation of Kelan’s share of £450 seen. Most involved summing the ratio parts, dividing into 450 and multiplying by 3. A few students made errors multiplying 45 by 3. Some were only able to identify Regan’s share since this was 5 of 450. The most common incorrect attempts involved dividing 450 by the 3 shares leading to the incorrect answer of 150 or obtaining one part (45) and then dividing this by 3.
Harry, Regan and Kelan share GBP450 in the ratio 2 : 5 : 3 How much money does Kelan get? GBP
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Edexcel 1MA1 · November 2017 · Paper 1F · Q19 · 3 marks
3 marks
Examiner report
This question was well answered by students, with many gaining full marks. The most successful approach was to find the amounts for 8 people and add this on to the amounts for 16 people. On the whole non-calculator methods were shown clearly although the workings of a minority of candidates were somewhat messy and scattered making their methods difficult to decipher. Common errors seen were 24 – 16 = 8 and then adding this value onto the ingredients to get 128g, 148g etc, multiplying the given ingredients by 2 or 24 – 16 = 8 and then multiplying by 8. Of the candidates who attempted the question but didn’t gain full marks, many managed 1 mark for an initial step or 2 marks for a correct method to find the amount of ingredients required for one of the items given in grams.
Here is a list of ingredients for making 16 flapjacks. Ingredients for 16 flapjacks 120 g butter 140 g brown sugar 250 g oats 2 tablespoons syrup Jenny wants to make 24 flapjacks. Work out how much of each of the ingredients she needs. butter g brown sugar g oats g syrup tablespoons
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Edexcel 1MA1 · November 2017 · Paper 1F · Q24 · 4 marks
4 marks
Examiner report
Some students tried to use algebra to solve this problem but the majority of attempts seen were based on a trial and improvement approach, normally in a non-systematic way, trying to find 3 ages that fitted the relationship requirements in the question, and summed to 77. Those that worked systematically were more successful than those that did not. Some candidates were able to find sets of numbers eg 1, 8 and 16 that fitted the relationships, but did not sum to 77, this start was given 1 mark. Those who used algebra often failed to use a single variable to base the relationship on. Students who identified Jay as being 14 then usually correctly found the age of the other two people. A few did not express this as a ratio as was required by the question. Provided the order of the ratios was made clear, variations on the correct order of ages was allowed for full marks, as was an equivalent ratio.
Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q26 · 4 marks
4 marks
Examiner report
This question was not well answered. A high proportion of students did not attempt the question at all. Many of the answers seen tried to compare only the radii whilst another common response was to say, incorrectly, that ‘one circle out of 3 is shaded so 1 is shaded’ with no further explanation offered. Also comments such as ‘Daisy is correct there are 3 sections to the logo and one is shaded’ were very common Few students used the area of a circle formula and of those that did, it was exceedingly rare that pi was cancelled in any comparison or working. Where marks were gained, it was for calculating the area of one circle, usually using the radius of 10. Centres should discuss with students that if a question appears to require multiple calculations with pi on a non-calculator paper that an alternative method is likely to be available. The thought process required for this question did appear to be beyond the majority of students entered at this level in this November session.
A logo is three concentric circles: inner radius 4 cm, shaded annulus from radius 4 cm to 7 cm, and outer radius 10 cm. Daisy says exactly 1/3 is shaded. Is she correct? Show working.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q30 · 2 marks
2 marks
Examiner report
Most students attempted this question but many did not recognise the question as a reverse percentage and for those that did, they were often unable to find a complete method for the question. The most common incorrect approach was to increase £2.80 by 30%. The value of 4 was also seen from obviously incorrect working and so using the marking principles no marks could be awarded in this case. Summary Based on their performance in this paper, students should: learn metric conversions, E.g. 1 kg = 1000 g ensure that their basic arithmetic is sound memorise standard formulae for this new specification practice working through ‘explain’ and ‘give reason’ type questions read each question carefully to ensure that the final answer does answer the set question
In a sale, the normal price of a book is reduced by 30%. The sale price of the book is GBP2.80 Work out the normal price of the book. GBP
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Edexcel 1MA1 · November 2017 · Paper 1H · Q2 · 4 marks
4 marks
Examiner report
The most successful approach to this first problem question on the paper was to form an equation based on the ages of three friends, solve to find the ages, and then write the ages as a ratio. Most students attempted an algebraic approach, but often only managing a single mark for two correct expressions. Once expressions had been formed some students were then able to sum and equate to 77 to gain the second mark. Those who managed to form an equation, were normally able to gain the 3rd mark for isolating their terms, or more commonly for actually solving to get 14. Of those who got this far many found all three ages and formed a suitable ratio. However, there were quite a number who forgot the demand of the question and lost a mark as they did not present their final answer as a ratio.
Kiaria is 7 years older than Jay. Martha is twice as old as Kiaria. The sum of their three ages is 77 Find the ratio of Jay's age to Kiaria's age to Martha's age.
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Edexcel 1MA1 · November 2017 · Paper 1H · Q4 · 4 marks
4 marks
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 .
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.
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Edexcel 1MA1 · November 2017 · Paper 1H · Q9 · 5 marks
5 marks
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.
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 · Q13 · 4 marks
4 marks
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).
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 · Q14 · 3 marks
3 marks
Examiner report
Students typically tried to start with the solution here and work backwards and as a result scored no marks at all. Very few students started with a correct statement, eg = k. Those who did very often had sufficient skill in manipulation to gain full marks.
(y+x):(y-x) is equivalent to k:1. Show that y=x(k+1)/(k-1).
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Edexcel 1MA1 · November 2017 · Paper 1H · Q16 · 3 marks
3 marks
Examiner report
Most students did not know how to structure their response to this fairly standard question, with a significant number being unable to form a suitable equation. Those who did were then troubled significantly by the fraction 7 and struggled to be able to divide this by 3 8 . It was pleasing, however, to see students showing their working and as such, those who showed they needed to complete this division were able to score 2 of the 3 marks.
y is directly proportional to the cube root of x. y=7/6 when x=8. Find y when x=64.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q5 · 6 marks
6 marks
Examiner report
Students had a good success rate with part (a), most giving 33 as their answer, but some did simplify. The most common error was giving the probability of those that DID walk. Some failed to read the 60 in the question and added the total incorrectly. In part (b) it was disappointing to see so little working shown, which would have gained many students an additional mark. There was evidence that students did not have a protractor, particularly when they showed the angles, but were unable to draw any angles accurately. Most students did show a pie chart with at least 2 angles drawn accurately.
Of 60 students, 15 travel by bus, 27 walk, 12 travel by car and 6 cycle. (a) Find the fraction who do not walk. (b) Complete a pie chart for the data.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q6 · 2 marks
2 marks
Examiner report
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).
(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.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q9 · 3 marks
3 marks
Examiner report
Part (a) was done well, with the most common answer being 2.75. Most showed 5.5 × 0.5; there was some evidence that students did not have a ruler, and were guessing the length. There were a few students who, having shown 5.5 × 0.5, then gave their answer as 3. Students should be encouraged to write their accurate answer and not round it. In part (b) some students appeared confused as to which angle they were giving the bearing for. But even when it was clear the correct angle was being found, the protractor was being read wrong (eg 130). There was also some evidence that students were estimating the angle (perhaps because they did not have a protractor).
An accurately drawn map joins Backley to Cremford. The measured road is 5.3-5.7 cm and the scale is 1 cm to 0.5 km. Its clockwise bearing from north at Backley is 128-132 degrees. Find the distance and bearing.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q11 · 3 marks
3 marks
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”.
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
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.
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.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q15 · 5 marks
5 marks
Examiner report
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.
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 · Q17 · 3 marks
3 marks
Examiner report
Responses to this question started well. Most were able to calculate the profit on either one bottle or 12 bottles. The £0.36 profit was often seen. A significant number of students stopped there, sometimes giving 0.36 as their answer. Many students erroneously took the base for comparison as their selling price, £6 rather than £5.64 cost price. Some appeared to get as far as 1.063 but then rounded to 1.1
Emily buys a pack of 12 bottles of water. The pack costs GBP5.64 Emily sells all 12 bottles for 50p each. Work out Emily's percentage profit. Give your answer correct to 1 decimal place.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q19 · 3 marks
3 marks
Examiner report
When students worked with numbers of cubes initially they were more successful. Some students began by incorrectly writing the ratio of Y:B the wrong way around; another common mistake was to interpret the green cubes as 4 × yellow (instead of 4 × blue). Some algebraic attempts were seen but these were rare and lead to many mistakes in calculating G. The most successful methods tended to use possible numbers of each colour, eg 4, 2, 16. It was not uncommon for students to use their own chosen values to represent the ratios which could also lead to the correct answer. Some marks were lost when working was not clear, or was sometimes contradictory when multiple methods were presented.
There are only blue cubes, yellow cubes and green cubes in a bag. There are twice as many blue cubes as yellow cubes and four times as many green cubes as blue cubes. Hannah takes at random a cube from the bag. Work out the probability that Hannah takes a yellow cube.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q2 · 3 marks
3 marks
Examiner report
Students almost always earned some credit for a correct start to the processes needed by either finding how much Emily paid for one bottle of water or how much she got for selling all twelve bottles of water. Finding the percentage profit proved a greater challenge to most students, a common error being to use .ଷ or ହ.ସ instead of .ଷ ହ.ସ or ହ.ସ. A number of the students who did use a correct fraction and got 1.0638 or 106.38 were unable to interpret this as a 6.38% percentage profit.
A pack of 12 bottles costs GBP5.64 and all 12 sell for 50p each. Find the percentage profit to 1 decimal place.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q4 · 3 marks
3 marks
Examiner report
This question discriminated well between students of different abilities. The weakest students merely rephrased the question, for example by writing B = 2Y. Students going no further than this could not be awarded any marks. Most students did gain some credit for their attempts for writing down a ratio linking the number of cubes for at least two of the three colours. More able students wrote down a correct ratio linking all three colours. A common error was the use of the incorrect ratio Y : B : G = 1 : 2 : 4 leading to the incorrect answer, ଵ . An alternative strategy used by many students was to assign particular numbers of cubes to satisfy the conditions given and work from these. ଶ ଶଶ was a commonly seen acceptable answer as an alternative for the correct probability in its simplest form, ଵ ଵଵ . The general marking guidance given in the mark scheme states that probabilities given correct to at least 2 decimal places are also acceptable, so 0.09 was also accepted as a final answer.
Blue:yellow=2:1 and green:blue=4:1. Find the probability of yellow.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q9 · 3 marks
3 marks
Examiner report
Fully successful solutions to this question involving inverse proportion were not common. Most of the students who did score full marks found the total number of hours needed for the 5 cleaners to clean all the rooms in the hotel (5 × 4.5), then divided by 3 to find the number of hours needed by each of the 3 cleaners. Of those students who successfully calculated the 7.5 hours, most of them correctly rounded this to 8 before calculating what each cleaner was paid. However, a significant minority of students calculated 7.5 × £8.20 and scored 2 of the 3 marks available. Weaker students often used direct proportion and did not question why 3 cleaners would take less time than 5 cleaners to clean all the rooms in the hotel.
Five cleaners take 4.5 hours. Today three equal-rate cleaners do the same work. Each is paid GBP8.20 for each hour or part-hour. Find each cleaner's pay.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q10 · 3 marks
3 marks
Examiner report
This question discriminated well between students. Many students could state the time interval when the speed was greatest and a good proportion of those students were able to explain why, usually referring to the gradient of the lines. However a significant number of students misunderstood what the question required in part (a). The question asked for “two times” between which the speed was greatest. Some students interpreted this as a request for two answers and gave the two time intervals 0 - 20 and 20 - 60. Students who scored the marks in part (a) were often successful with part (b) of the question. However, answers to part (b) were often marred by errors made in reading accurately from the graph with many students using “380” instead of “360”.
A distance-time graph passes through (0,0),(20,360),(60,600),(80,600). (a) Find the interval of greatest speed and explain. (b) Find that speed.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q11 · 3 marks
3 marks
Examiner report
There were very few fully correct answers to the problem posed by this question. A significant minority of students realized that the sector angle was needed and some students started to work with the areas of the circles. One mark was awarded for this.
Two pie charts show town populations. Adley's chart radius is 5 units and Bridford's is 4, so population ratio is 25:16. Adley's 0-19 sector is 70 degrees. Find the proportion of both towns who live in Adley and are aged 0-19, to 3 s.f.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q13 · 5 marks
5 marks
Examiner report
Part (a) was a straight forward application of compound growth. It was well answered by a good proportion of students but a surprising number of students did the calculation long-hand by calculating eight separate increases of 2%. Of those students who used the more concise method of using a multiplier, some used 1.2 instead of 1.02 A significant number of students did not give their final answer correct to the nearest £100. The most common error in this part of the question was to treat the problem as a simple interest calculation. Part (b) of the question was found to be more demanding and only a small minority of students were able to set up the problem correctly, for example by writing down an equation such as 250 000 ൈ y6 ൌ 325 000. Rather than dividing 325 000 by 250 000 to find a multiplier for the 6 year period, students often starting by working out the difference (75 000) in these amounts and then could make no further progress. A significant number of those students who did follow a correct method to find the correct multiplier for one year (1.045) did not then go on to interpret this in terms of a yearly percentage increase (4.5%). Trial and error approaches were sometimes successful but often lead to poor accuracy in the final answer.
(a) A company worth GBP50,000 at the start of 2009 grows 2% yearly. Find its value at the start of 2017, nearest GBP100. (b) Another rises GBP250,000 to GBP325,000 in 6 years at x% yearly. Find x to 2 s.f.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q18 · 1 mark
1 mark
Examiner report
The value of k required in this question involving an iterative process was 0.98 “98%” was not an acceptable answer. Some students did more than was expected and used the iterative process to calculate the value of V1.
A tank loses 2% of its water each hour. If V_(t+1)=kV_t, state k.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q5 · 3 marks
3 marks
Examiner report
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.
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?
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Edexcel 1MA1 · November 2017 · Paper 3F · Q8 · 2 marks
2 marks
Examiner report
30m was the modal correct answer for this question, where the height of the building was estimated at two and a half bus lengths. Many students however used the height of the bus for comparison with the height of the building and made many errors. It was not enough for the award of the method mark to simply say that there were about 6 to 7 bus heights equivalent to the height of the building. Students had first to make a sensible comparison between the length of the bus and its height, possibly using the scale of 2cm = 12m.
12 m The picture shows a bus next to a building. The bus has a length of 12 m. The bus and the building are drawn to the same scale. Work out an estimate for the height, in metres, of the building.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q11 · 3 marks
3 marks
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.
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.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q12 · 2 marks
2 marks
Examiner report
Attempts to find the cost of 1 kg (or 0.5 kg) of apples were usually accurate and usually lead to the correct answer. The most common error was to find one and a half lots of £3.60 and £5.40 was the modal incorrect answer. Some candidates simply added £1 to £3.60 assuming that the difference was the ‘same’ as that between 2.5kg and 3.5kg. A few candidates tried to find the weight of apples that could be bought for £1. This approach only gained any credit when a complete method was used but this was very rare.
2.5 kg of apples cost GBP3.60 Work out the cost of 3.5 kg of apples. GBP
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Edexcel 1MA1 · November 2017 · Paper 3F · Q15 · 3 marks
3 marks
Examiner report
Most students gained at least one mark for a correct entry in the table in the ‘cotton fabric’ row, usually the first entry of £18; many then incorrectly completed this line as an arithmetic progression. Fewer students were able to deal with the ratio in order to gain any success for values in the ‘silk fibre’ row. Very few gained full marks on this question. It was rare to see working in this question; students should be reminded to show all working no matter how trivial.
Cotton:silk cost per metre is 2:5. Cotton costs GBP6 for 2 m. Complete both rows for 2,6,8,9 m.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q16 · 5 marks
5 marks
Examiner report
Both parts of this question were poorly answered. Confusion with the conversion between metres and centimetres prevented very many students completing a solution. Many found the volumes and but then divided the volume of a box by the volume of the van. A significant number of students correctly attempted to find the maximum number of boxes by finding the correct numbers, (6, 5 and 4), fitting in each dimension of the van. Unfortunately, many simply added these numbers (to get 15) or selected the lowest value and divided by 3 to find the time. Many students calculated the time by dividing the least number (in this case 4) by 3. Some students calculated surface areas rather than volumes. In part (b), very few students answered the question given. A correct response described how the time might change (greater or less) together with a coherent reason. Many students simply said that the time will change, without reason, or argued that there will be less boxes or it will be more difficult to fill the van without ever mentioning the time implication. Centres are advised to give their students more guidance on how to fully answer this type of questions.
Chloe has a van. She is going to use the van to deliver boxes. Each box is a cuboid, 40 cm by 30 cm by 35 cm. 35 cm 30 cm 40 cm The space for boxes in the van has maximum length 2.4 m maximum width 1.5 m maximum height 1.4 m The space for boxes is empty. Chloe wants to put as many boxes as possible into the van. She can put 3 boxes into the van in one minute. Assume that the space for boxes is in the shape of a cuboid. (a) Work out how many minutes it should take Chloe to put as many boxes as possible into the van. The space for boxes might not be in the shape of a cuboid. (b) Explain how this could affect the time it would take Chloe to put as many boxes as possible into the van.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q20 · 3 marks
3 marks
Examiner report
Many students at this level found the demands of this question too great. Often students were able to make a start at a solution by quoting one correct conversion, usually 1.089 × 3.785 or 2.83 ÷ 1.46, but very few went further. Many students incorrectly converted 108.9p to pounds with values of 1.89 being the most common error or simply £108.9 A great many did give New York as the most economical city for petrol but very few gave two correct comparable values. The failure to find two comparable values was very much linked to the fact that pupils didn’t really know what values they were finding when they were dividing or multiplying numbers, students should be encouraged to write their units with their calculations to help make sense of their answers.
In London, 1 litre of petrol costs 108.9p In New York, 1 US gallon of petrol costs $2.83 1 US gallon = 3.785 litres GBP1 = $1.46 In which city is petrol better value for money, London or New York? You must show your working.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q21 · 3 marks
3 marks
Examiner report
This question was very poorly answered with few students knowing the formula Volume = Mass/Density. The great majority either multiplied the mass by the density or divided density by the mass. Again conversion between units was poor, many not knowing that 1kg = 1000g.
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.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q22 · 3 marks
3 marks
Examiner report
Only a very few students understood the need to compare both ratios with a common element representing the green pens. Triple ratios of 2 : 9 : 1 or 2 : 5 : 1 or 2 : 4 : 1 were common errors followed by divisions of 100 by 12, 9 or 7 Many students tried to use the two given ratios independently. Some candidates found a number of equivalent ratios, but didn’t stop once they had found a pair that would work.
There are only blue pens, green pens and red pens in a box. The ratio of the number of blue pens to the number of green pens is 2 : 5 The ratio of the number of green pens to the number of red pens is 4 : 1 There are less than 100 pens in the box. What is the greatest possible number of red pens in the box?
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Edexcel 1MA1 · November 2017 · Paper 3H · Q2 · 3 marks
3 marks
Examiner report
Many students did make some headway on this question and it was attempted in a variety of ways. Some students used one of the given costs to find a comparative value, eg changing 108.9p per litre into $6.01 per gallon which could then be compared with the cost in New York. Other students used both given costs to find comparative values, eg changing 108.9p per litre into £4.12 per gallon and changing $2.83 per gallon into £1.94 per gallon. Mistakes were often made with the conversions, eg dividing by 1.46 instead of multiplying by 1.46, and some students wrote 108.9p as £1.89. Students attempting to work out the cost (in $) per litre in New York often did the division the wrong way round. It might help students to clarify their thinking if they included units with their values, eg $2.83 per gallon, not just 2.83. Those students that did find comparative values usually made the correct decision but it was common for students to make a decision without having found values that could be compared. A few students made the wrong decision despite having correct values. Students had to deal with two conversion factors and they did not always present a clear picture of what they were trying to do.
In London, 1 litre of petrol costs 108.9p In New York, 1 US gallon of petrol costs $2.83 1 US gallon = 3.785 litres GBP1 = $1.46 In which city is petrol better value for money, London or New York? You must show your working.
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Edexcel 1MA1 · November 2017 · Paper 3H · Q3 · 3 marks
3 marks
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.
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.
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Edexcel 1MA1 · November 2017 · Paper 3H · Q4 · 3 marks
3 marks
Examiner report
Students found this question challenging. In order to make progress they needed to associate corresponding parts from the two ratios in a way that would help them. Some students did write down a ratio equivalent to 2 : 5 and a ratio equivalent to 4 : 1 but often the components for green pens were not the same. Those that did write down the ratios 8 : 20 and 20 : 5 or the ratio 8 : 20 : 5 were often able to go on and work out the greatest possible number of red pens. Some students went from 8 : 20 : 5 to 16 : 40 : 10 and finally to 24 : 60 : 15, the last figure being the number required, and a few went from 8 : 20 : 5 to calculate 5 × 100. Some partially correct ratios such as 8 : 20 : 4 were seen but these gained no credit. A very common error was for students to start the problem by adding the numbers in the ratios, working out 2 + 5 = 7 and 4 + 1 = 5.
There are only blue pens, green pens and red pens in a box. The ratio of the number of blue pens to the number of green pens is 2 : 5 The ratio of the number of green pens to the number of red pens is 4 : 1 There are less than 100 pens in the box. What is the greatest possible number of red pens in the box?
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Edexcel 1MA1 · November 2017 · Paper 3H · Q9 · 5 marks
5 marks
Examiner report
Part (a) was answered quite well. Students were often able to substitute at least one value of n into 12 500 × (0.85)n and gain the first mark. For some students this was just substituting n = 1 to get 10625. Some of those that showed enough correct further substitutions to answer the question chose the wrong number of years. Some used parts of a year, giving an answer such as 4.27, and could be awarded only one mark. A number of students just found 50% of 12500 (= 6250) and scored no marks. Students were much less successful in part (b). Those who recognised that 79.20 = 60% of the interest before tax were sometimes able to work out the interest before tax. A common mistake was to work out 40% of 79.20 and then add the result to 79.20. Some students worked out the interest before tax as £132 but then stopped. Those that did attempt to work out 132 as a percentage of 5500 did not always complete the final step, giving an answer of 1.024 or 0.024 rather than 2.4. Some students started the question by working out 40% of 5500 as 3300. Although a small number of these students went on to give complete solutions most failed to make any further progress. Many students did not know how to start the question.
Jack bought a new boat for GBP12 500 The value, GBPV, of Jack's boat at the end of n years is given by the formula V = 12 500 x (0.85)n (a) At the end of how many years was the value of Jack's boat first less than 50% of the value of the boat when it was new? A savings account pays interest at a rate of R% per year. Jack invests GBP5500 in the account for one year. At the end of the year, Jack pays tax on the interest at a rate of 40%. After paying tax, he gets GBP79.20 (b) Work out the value of R.
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Edexcel 1MA1 · November 2017 · Paper 3H · Q14 · 3 marks
3 marks
Examiner report
Relatively few students showed that they understood the relationships between lengths, areas and volumes in similar figures. Those who did recognise that they should use the ratio of the volumes, 27 : 8, to find the ratio of the lengths or the length scale factor were usually able to give a complete method to show that the surface area of cone B is 132 cm2. Many students assumed the result they were given instead of proving it.
Cone A and cone B are mathematically similar. The ratio of the volume of cone A to the volume of cone B is 27 : 8 The surface area of cone A is 297 cm2 Show that the surface area of cone B is 132 cm2
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Edexcel 1MA1 · November 2017 · Paper 3H · Q16 · 3 marks
3 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q4 · 1 mark
1 mark
Examiner report
Generally a well answered question. Those who had success normally worked through equivalent fractions such as ଼ଵ or ଼ ଵ to achieve the correct answer. Most wrong answers, such as 90, 75, 20, came with no working.
Write 4/5 as a percentage.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q9 · 4 marks
4 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q10 · 2 marks
2 marks
Examiner report
A twist on a traditional question which threw lots of students who simply started with the values in the question, eg 6 : 20, and scored zero. A good number, however, realised the need to multiply 6 by 20 to get the total number of eggs and were then able to set up a suitable starting ratio of 12 : 120. Students do continue to struggle to simplify ratios, especially as this involved a relatively large number, and either went wrong with their division or stopped too soon. 3 : 30 was a common answer seen, and only scored one out of the two available marks.
A farmer has 20 boxes of eggs. There are 6 eggs in each box. Write, as a ratio, the number of eggs in two boxes to the total number of eggs. Give your answer in its simplest form.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q13 · 3 marks
3 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q20 · 2 marks
2 marks
Examiner report
This was a standard percentage increase question that allowed a lot of students to gain some success. Again, students were let down by their arithmetic (eg 1% shown as 1.5 rather than 15) and a lack of method shown. Weaker students struggled to find 3%, and even those who knew how, didn’t normally show the steps of their method and made calculation errors. Many who were able to find 3%, forgot to add this onto the original amount or erroneously subtracted their 3% from the original amount.
Azmol is paid GBP1500 per month. He is going to get a 3% increase in the amount of money he is paid. Work out how much money Azmol will be paid per month after the increase. GBP
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Edexcel 1MA1 · June 2017 · Paper 1F · Q25 · 5 marks
5 marks
Examiner report
Another problem solving question and again many students were able to gain some credit. The less able students tended to gain just one mark for multiplying lengths by 1.5. The more able realised the need to use Pythagoras’s theorem and most who did, did so successfully. Although a good number were able to get full marks a large number of those who showed the correct processes were again let down by their arithmetic skills, or by failing to multiply the diagonal by 1.5
This rectangular frame is made from 5 straight pieces of metal. 5 m 12 m The weight of the metal is 1.5 kg per metre. Work out the total weight of the metal in the frame.
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Edexcel 1MA1 · June 2017 · Paper 1H · Q5 · 5 marks
5 marks
Examiner report
A significant minority of candidates found the area of the rectangle and then multiplied this by the 1.5, gaining no marks. However the majority who used Pythagoras’s theorem were successful in at least gaining the marks for a Pythagorean approach; some were unable to state the square root of 169. Many were able to go on and complete the question, though there were arithmetic errors, whether candidates found individual masses and added, or added the lengths first and multiplied by 1.5. When applying the latter method those finding it as 47+ 23.5 were more successful than those attempting to multiply 47 by 1.5. Some divided by 1.5 instead of multiplying while others included the diagonal twice, but overall this question was very well answered. Candidates need to read the question carefully; for example, an error for some was not appreciating that this was a rectangular frame as attempts to find the area were seen.
This rectangular frame is made from 5 straight pieces of metal. 5 m 12 m The weight of the metal is 1.5 kg per metre. Work out the total weight of the metal in the frame.
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Edexcel 1MA1 · June 2017 · Paper 1H · Q9 · 2 marks
2 marks
Examiner report
The most common misunderstanding was to use £600 as 100% instead of 120%, with many candidates working out 20% of 600 and subtracting to get £480. Some thought that as £600 was 120% they had to find 80% of £600 to get back to the original value. These candidates also got £480 as their answer. Quite a few candidates found 1% (from 600 ÷ 120), then 10% as £50, then subtracted it from 600 to get £550. Other candidates lacked the skills to work out 600 ÷ 1.2 (600 ÷ 1.2 = 600 ÷ 12 = 50 was seen). Good candidates checked their work. If they first of all got £480, they found 20% as £96 and realised that it didn’t work (480 + 96 ≠ 600 or 600 – 96 ≠ 480). They then corrected themselves and checked again, just to make sure. It was the good practice of checking the working by taking their answer and adding 20% that saved them two marks.
Jules buys a washing machine. 20% VAT is added to the price of the washing machine. Jules then has to pay a total of GBP600 What is the price of the washing machine with no VAT added? GBP
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Edexcel 1MA1 · June 2017 · Paper 1H · Q13 · 4 marks
4 marks
Examiner report
The major errors made on part (a) were to get the wrong proportional formula. y=kx2, k y x , k y x were all seen. Occasionally the proportional symbol, was not replaced by =, and occasionally y x was seen with no reference made to a constant. Several candidates gave their final answer as k y x but, if they gave their value for k elsewhere, they were still able to get full marks in part (a) for this question. A small number of times candidates gave an equation for x (or x2) in terms of y on the answer line, forfeiting a mark. Having got full marks in part (a), the most common problem in part (b) was not being able to solve 16 = x . x = 12 was a popular answer from x= 16 9 A few left their answer in square root form, typically x = 16 9 . Others tried to work out 9 ÷ 16 (or even 16 ÷ 9) before finding the square root which inevitably led to problems.
The values (x,y) are (1,9), (2,9/4), (3,1), (4,9/16). y is inversely proportional to x^2. (a) Find y in terms of x. (b) Find positive x when y=16.
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Edexcel 1MA1 · June 2017 · Paper 1H · Q14 · 4 marks
4 marks
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
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.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q10 · 4 marks
4 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q11 · 4 marks
4 marks
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.
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?
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Edexcel 1MA1 · June 2017 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
The use of the construction of a circle centered on A and the perpendicular bisector of BC was not often seen and this inevitably reduced the number of students being able to accurately locate at least one of the two possible positions for T. More students drew a suitable circle than drew a perpendicular bisector but there were also many answers, some successful in showing the position of T accurately, where there was no evidence of either. The mark awarded for drawing at least part of a circle radius 2.5 cm or for showing a point 2.5 cm from point A was accessed by a high proportion of students but examiners did not award the mark for T being equidistant from point B and point C as frequently.
On a map, 1 cm represents 100 m. Point T is 250 m from A and equidistant from B and C. Construct one possible position for T.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q18 · 5 marks
5 marks
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
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.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q20 · 5 marks
5 marks
Examiner report
There were very few fully complete and correct solutions to this question due to most students not appreciating the need to find the total distance between Liverpool and Sheffield and the total time taken. Many students instead tried to find the average of the average speeds for the two stages of the journey. It was unusual to award more than two marks for finding the total distance from Liverpool to Sheffield and/or for a correct process to find the time taken to travel between Liver pool and Manchester. Students’ understanding of conversion to change units of time was exposed in this question. For example 0.8 hours = 80 minutes was often seen. Examiners rarely awarded the mark available in part (b) of this question. When attempts were made to answer this part, they usually consisted of statements suggesting that the distances, speeds or average speeds involved in the two stages of the journey would have to be the same.
Olly drove 56 km from Liverpool to Manchester. He then drove 61 km from Manchester to Sheffield. Olly's average speed from Liverpool to Manchester was 70 km/h. Olly took 75 minutes to drive from Manchester to Sheffield. (a) Work out Olly's average speed for his total drive from Liverpool to Sheffield. Janie drove from Barnsley to York. Janie's average speed from Barnsley to Leeds was 80 km/h. Her average speed from Leeds to York was 60 km/h. Janie says that the average speed from Barnsley to York can be found by working out the mean of 80 km/h and 60 km/h. (b) If Janie is correct, what does this tell you about the two parts of Janie's journey?
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Edexcel 1MA1 · June 2017 · Paper 2F · Q21 · 4 marks
4 marks
Examiner report
Students taking this paper seemed unfamiliar with the techniques needed to solve problems such as this involving similar triangles. It was rare to see an attempt involving the use of scale factors or ratios. Instead many students mistakenly thought they could apply Pythagoras’s theorem to one of the triangles despite there being no indication they were right angled. A sizeable proportion of students merely subtracted lengths to find AE, for example, 8.1 − 2.6 = 5.5. 2.6 was quoted as the length of AE by some students and examiners wondered whether they had confused the arrows on sides EA and DB with the notation used for showing lengths are equal. Students may have found it helpful to redraw the diagram as two separate similar triangles
A B C E D ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. AC = 6.15 cm. (b) Work out the length of AB.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q22 · 3 marks
3 marks
Examiner report
This question on compound interest was one of the better attempted questions towards the end of the paper. Most students were able to score at least one mark by showing a correct process to work out either 2% of 25 000 or 102% of 25 000. Of students who successfully found the interest gained over 3 years most were successful when dealing with Personal Bank with fewer successful attempts for Secure Bank. This was often due to students using 1.09 as the multiplier for an increase of 0.9%. 1.43 was also frequently seen as the multiplier for an increase of 4.3%. A significant number of less able students added the interest rates and increased 25 000 by 6% for the Personal Bank and by 6.1% at Secure Bank. Examiners were unable to give these students any credit. Most students stated in words which bank gave more interest but there were still some students who merely underlined or circled to indicate which interest was most or which bank gave most interest. These students were not awarded the final communication mark.
Anil wants to invest GBP25000 for 3 years in a bank. Personal Bank Secure Bank Compound Interest Compound Interest 2% for each year 4.3% for the first year 0.9% for each extra year Which bank will give Anil the most interest at the end of 3 years? You must show all your working.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q2 · 5 marks
5 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q3 · 4 marks
4 marks
Examiner report
The front elevation of a trapezium was usually correctly drawn even when shown in a 3D configuration. The side elevation however was very poorly done; a 2cm by 1cm rectangle or a 5cm by 2cm rectangle were the most common errors seen. Even when a correct 4cm by 2cm rectangle was drawn the 2 cm line, 1cm above the base, was often omitted. The students who drew the diagrams side by side had a better success rate as they seemed to have a better sense that they should be the same height. Unfortunately, many students still fail to include the horizontal line in the side elevation. Some students drew nets of the prism and rarely gained any credit.
A prism has trapezium front cross-section with base 2 m, parallel vertical sides 0.5 m and 2 m, and length 1 m. Draw front and side elevations at scale 2 cm to 1 m.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q4 · 5 marks
5 marks
Examiner report
The most common error made in part (a) of this question was by those students who assumed that average speed was found by finding the mean of two speeds and calculated, unnecessarily, the speed from Manchester to Sheffield. Conversion between hours and minutes was poor; often 0.8 hours was written as 80 minutes and 75 minutes as 1.15 hours and 123 minutes as 2.03 hours. Students who chose to work in minutes (117 ÷ 123) often lost the last mark due to not being able to convert it to km/h. In part (b), very few students recognised that the time taken for both parts of the journey had to be equal for the given statement to be correct. The most common mistake was to assume that the distances had to be equal. Some students commonly misread the question and tried to justify if she was right or not.
Olly drove 56 km from Liverpool to Manchester. He then drove 61 km from Manchester to Sheffield. Olly's average speed from Liverpool to Manchester was 70 km/h. Olly took 75 minutes to drive from Manchester to Sheffield. (a) Work out Olly's average speed for his total drive from Liverpool to Sheffield. Janie drove from Barnsley to York. Janie's average speed from Barnsley to Leeds was 80 km/h. Her average speed from Leeds to York was 60 km/h. Janie says that the average speed from Barnsley to York can be found by working out the mean of 80 km/h and 60 km/h. (b) If Janie is correct, what does this tell you about the two parts of Janie's journey?
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Edexcel 1MA1 · June 2017 · Paper 2H · Q5 · 4 marks
4 marks
Examiner report
This question was poorly answered even by many of the more able students. In part (a), many incorrectly used a ratio 2 : 1 (5.4 : 2.7) and many assumed the triangles to be right-angled at A and B and tried to apply Pythagoras’s theorem or trigonometric methods. In part (b), the most common error for those students gaining any credit was simply to divide 6.15 by the correct ratio 1.5 and then leave their answer as 4.1 without ever trying to find the length of AB.
A B C E D ABC and EDC are straight lines. EA is parallel to DB. EC = 8.1 cm. DC = 5.4 cm. DB = 2.6 cm. (a) Work out the length of AE. AC = 6.15 cm. (b) Work out the length of AB.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q6 · 3 marks
3 marks
Examiner report
This question was very well answered and most students gained at least two marks for the correct application of compound interest methods to one of the banks, usually the Personal Bank. In working out the value of the investment at the Secure Bank, many used a multiplying factor of 1.09 or 1.9 instead of 1.009, or 1.43 instead of 1.043 for Personal Bank. It is pleasing, however, to note that the majority of students adopted a method using multiplying factors rather than building up the values year by year. A small but significant number of students subtracted the interest rather than adding it on. Using £2500 instead of £25000 was a common error and lost the accuracy marks. Students often struggled to work with changing interest rates for Secure Bank, especially 0.09%, many also started again with £25000 following the calculation for the first year with 4.3%. A small minority made the standard mistake of finding simple interest. Again a few students failed to explicitly identify the bank giving the greater interest. Some circled the box of information for their choice of bank. This gained no credit.
Anil wants to invest GBP25000 for 3 years in a bank. Personal Bank Secure Bank Compound Interest Compound Interest 2% for each year 4.3% for the first year 0.9% for each extra year Which bank will give Anil the most interest at the end of 3 years? You must show all your working.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q13 · 3 marks
3 marks
Examiner report
Many students had no idea that frequency could be found by multiplying the frequency density by the class interval and so gained no credit. Of those that did, many used incorrect class intervals of 5 and/or 15 instead of 10 and 30. Inaccurate reading of the scale on the frequency density axis was condoned when awarding method marks if it was clear to which height the reading related. It was not uncommon for students to correctly find the number of members over 50 years of age (35) and then fail to even try to find 20%. Some just found 20% of 134. Students must read questions carefully and answer what is being asked. Only a few students tried to count squares; this was not a particularly successful approach.
The histogram shows some information about the ages of the 134 members of a sports club. 3.0 2.5 2.0 Frequency density 1.5 1.0 0.5 0 0 20 40 60 80 100 Age in years 20% of the members of the sports club who are over 50 years of age are female. Work out an estimate for the number of female members who are over 50 years of age.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q17 · 5 marks
5 marks
Examiner report
It was pleasing to see many students give fully correct solutions to this question. However, many did not and errors included; failure to recognise an angle of 60o in an equilateral triangle, taking 7 cm as the height of the triangle of base 7 cm when finding its area, using an incorrect formula, eg. 2 (a +b) sin C, using 5.5 cm or 7 cm as the radius of the sector OQN and some students found the length of the arc rather than area of the sector. The cosine rule was sometimes used unnecessarily to find angle AOB and the height of the triangle was often found using Pythagoras’s Theorem. Some found the area of the triangle as a percentage of the whole sector. Quite a number of students found the area of the whole circle but did not find the area of the sector. In this question, premature rounding prevented the award of full marks on many occasions.
ONQ is a 60-degree sector of a circle with centre O and radius 11 cm. A lies on ON and B on OQ such that triangle AOB is equilateral with side 7 cm. Find the shaded area (sector minus triangle) as a percentage of the sector area, to 1 decimal place.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q5 · 3 marks
3 marks
Examiner report
Most students were able to give a ratio as the answer in part (a). Many of these ratios were either 1 : 3 (the correct answer) or 1 : 4 (the most common incorrect answer). Ratios equivalent to 1 : 3 such as 25 : 75, 14 : 42 and 1 3 : 4 4 were acceptable and were seen often. Part (b) was answered well. Many of the students who did not give a correct ratio in part (a) were still able to answer this part correctly. Many students started with 56 ÷ 4 = 14 followed by either 14 × 3 or by 56 – 14. A common mistake was to give 14, the number of white tiles, as the final answer. Only a few students followed through from an incorrect answer in part (a) and generally they gained full marks.
One quarter of tiles are white. (a) Give the ratio white:grey. (b) There are 56 tiles; find the number of grey tiles.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q10 · 3 marks
3 marks
Examiner report
Those students who started by dividing 90 by 6 generally went on multiply the result by 5 and write down a final answer of 75. Some of those that got to 75 in their working then wrote a different answer, such as 15, on the answer line and scored two of the three marks. The mistake made by many students was to divide 90 by 5 and then multiply the result by 4, giving a common incorrect answer of 72. Very few students used the diagram to support their thinking.
ABC is a straight line. A B C The length AB is five times the length BC. AC = 90 cm. Work out the length AB.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q18 · 5 marks
5 marks
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
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.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q20 · 4 marks
4 marks
Examiner report
Many students were able to use volume × density to find the mass of at least one of the ingredients. Most went on to find the masses of all three ingredients and add these to find the mass of the drink. Rather surprisingly, many students stopped at this point and gave 324.45 as the final answer. Those who showed a complete process to find the density of the drink usually gave a correct answer. A common mistake in this question was to divide volume by density in an attempt to find mass. Some students simply added the three volumes and added the three densities and attempted to do something with their results. Even when they had written the “density triangle” in the working space some students did not know how to proceed.
The density of apple juice is 1.05 grams per cm3. The density of fruit syrup is 1.4 grams per cm3. The density of carbonated water is 0.99 grams per cm3. 25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3. Work out the density of the drink. Give your answer correct to 2 decimal places.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q23 · 4 marks
4 marks
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
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
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Edexcel 1MA1 · June 2017 · Paper 3H · Q4 · 5 marks
5 marks
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.
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.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q6 · 4 marks
4 marks
Examiner report
The question was well answered. Most students successfully worked out the total mass of the drink. This gained two marks. Some students stopped at this point, hence explaining why two marks was a common score on this question. Those students that carried on with the problem usually successfully completed it. Centres are advised to remind students to check they have answered the question asked fully. A small number of students calculated the total mass incorrectly by inverting the density formula. This was the main misconception seen.
The density of apple juice is 1.05 grams per cm3. The density of fruit syrup is 1.4 grams per cm3. The density of carbonated water is 0.99 grams per cm3. 25 cm3 of apple juice are mixed with 15 cm3 of fruit syrup and 280 cm3 of carbonated water to make a drink with a volume of 320 cm3. Work out the density of the drink. Give your answer correct to 2 decimal places.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q10 · 3 marks
3 marks
Examiner report
Generally this was a well answered question with many students gaining at least two marks for an answer of 1.06 or 1.0599. The failure to subtract 1 and give the correct answer lost them the final mark. A common error was to subtract £6000 from £8029.35 and then try to deal with this resulting value by either diving by 5 or finding the fifth root of the difference. Some students did try to use a simple interest approach to this question. The difference between simple and compound interest should be emphasised by centres. Trial and improvement was often seen but this can only be awarded marks if accurate figures are obtained. An understanding of compound interest and reverse percentage calculations are a better approach. Some students only wrote down the answer, this is not a good approach as any error immediately means the student scores zero.
Naoby invests GBP6000 for 5 years. The investment gets compound interest of x% per annum. At the end of 5 years the investment is worth GBP8029.35 Work out the value of x.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q12 · 3 marks
3 marks
Examiner report
A good minority of students scored full marks on this question. Many were unable to start this question. However, by drawing a diagram some did identify the multiplier of 3 by using 18 parts on their diagram. Students often stopped at this point and showed no more meaningful work. Of the methods that were seen, the use of fractions and writing all the ratios over 18 was quite successful as was the idea of equivalent ratios written under a diagram. A less often seen method was to introduce an algebraic variable but where this was seen it was often successful. The most common errors seen were to multiply 1 : 5 by 7 and 7 : 11 by 5 and do nothing else or to find 18 and 6 and then add these to work with 24 Centres are advised that there is a need to practice questions of this nature and that a diagrammatic approach may be the most successful for the majority of students.
A,B,C,D lie in order on a line. AB:BD=1:5 and AC:CD=7:11. Find AB:BC:CD.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q17 · 5 marks
5 marks
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.
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).
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Edexcel 1MA1 · sample · Paper 1F · Q7 · 2 marks
2 marks
One day Sally earned £60
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Edexcel 1MA1 · sample · Paper 1F · Q15 · 3 marks
3 marks
Carpet tiles are going to be used to cover a floor.
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Edexcel 1MA1 · sample · Paper 1F · Q20 · 2 marks
2 marks
In a sale, normal prices are reduced by 20%.
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Edexcel 1MA1 · sample · Paper 1F · Q24 · 4 marks
4 marks
Gary drove from London to Sheffield. It took him 3 hours at an average speed of 80km/h. Lyn drove from London to Sheffield. She took 5 hours. Assuming that Lyn drove along the same roads as Gary and did not take a break,
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Edexcel 1MA1 · sample · Paper 1F · Q25 · 4 marks
4 marks
In a company, the ratio of the number of men to the number of women is 3:2
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Edexcel 1MA1 · sample · Paper 1H · Q4 · 4 marks
4 marks
Gary drove from London to Sheffield. It took him 3 hours at an average speed of 80km/h. Lyn drove from London to Sheffield. She took 5 hours. Assuming that Lyn drove along the same roads as Gary and did not take a break,
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Edexcel 1MA1 · sample · Paper 1H · Q5 · 4 marks
4 marks
In a company, the ratio of the number of men to the number of women is 3:2
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Edexcel 1MA1 · sample · Paper 1H · Q12 · 2 marks
2 marks
Pressure = force ÷ area.
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Edexcel 1MA1 · sample · Paper 1H · Q15 · 2 marks
2 marks
In a shop, all normal prices are reduced by 20% to give the sale price.
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Edexcel 1MA1 · sample · Paper 1H · Q18 · 3 marks
3 marks
Solid A and solid B are mathematically similar.
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Edexcel 1MA1 · sample · Paper 2F · Q7 · 2 marks
2 marks
ABCD is a square.
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Edexcel 1MA1 · sample · Paper 2F · Q12 · 5 marks
5 marks
You can use the information in the table to convert between kilometres and miles. miles 0 5 20 40 kilometres 0 8 32 64
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Edexcel 1MA1 · sample · Paper 2F · Q14 · 5 marks
5 marks
A cuboid tank is full of oil; an empty cuboid container will receive the unspilled oil.
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Edexcel 1MA1 · sample · Paper 2F · Q15 · 2 marks
2 marks
Two towns are marked on an accurately drawn scale map.
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Edexcel 1MA1 · sample · Paper 2F · Q17 · 3 marks
3 marks
Soap powder is sold in three sizes of box.
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Edexcel 1MA1 · sample · Paper 2F · Q19 · 3 marks
3 marks
Jane made some almond biscuits which she sold at a fete.
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Edexcel 1MA1 · sample · Paper 2F · Q23 · 3 marks
3 marks
Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7
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Edexcel 1MA1 · sample · Paper 2F · Q26 · 3 marks
3 marks
Axel and Lethna are driving along a motorway.
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Edexcel 1MA1 · sample · Paper 2H · Q1 · 3 marks
3 marks
Frank, Mary and Seth shared some sweets in the ratio 4 : 5 : 7
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Edexcel 1MA1 · sample · Paper 2H · Q4 · 3 marks
3 marks
A motorway sign gives a distance and average journey time.
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Edexcel 1MA1 · sample · Paper 2H · Q8 · 2 marks
2 marks
In a box of pens, there are
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Edexcel 1MA1 · sample · Paper 2H · Q10 · 6 marks
6 marks
Katy invests £2000 in a savings account for 3 years. The account pays compound interest at an annual rate of 2.5% for the first year x% for the second year x% for the third year There is a total amount of £2124.46 in the savings account at the end of 3 years.
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Edexcel 1MA1 · sample · Paper 2H · Q13 · 3 marks
3 marks
d is inversely proportional to c
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Edexcel 1MA1 · sample · Paper 2H · Q22 · 5 marks
5 marks
A glass frustum is formed by removing a small cone from a similar large cone.
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Edexcel 1MA1 · sample · Paper 3F · Q6 · 5 marks
5 marks
At Trowton School, the Year 11 class counts are: 11A has 14 boys and 15 girls; 11B has 12 boys and 11 girls; 11C has 8 boys and 7 girls; 11D has 4 boys and 5 girls.
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Edexcel 1MA1 · sample · Paper 3F · Q8 · 3 marks
3 marks
1 yard is 36 inches.
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Edexcel 1MA1 · sample · Paper 3F · Q9 · 2 marks
2 marks
Work out 234% of 150
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Edexcel 1MA1 · sample · Paper 3F · Q12 · 2 marks
2 marks
Here is a star shape.
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Edexcel 1MA1 · sample · Paper 3F · Q16 · 3 marks
3 marks
Change 72 km/h into m/s.
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Edexcel 1MA1 · sample · Paper 3F · Q19 · 5 marks
5 marks
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 3F · Q21 · 4 marks
4 marks
A scatter diagram shows outside temperature against electricity used for heating for ten homes. A reasonable line of best fit passes approximately through (0, 85) and (20, 35).
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Edexcel 1MA1 · sample · Paper 3F · Q22 · 5 marks
5 marks
Henry is thinking of having a water meter.
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Edexcel 1MA1 · sample · Paper 3F · Q23 · 5 marks
5 marks
A and B are two companies. The table shows some information about the sales of each company and the number of workers for each company in 2004 and in 2014 Company A Company B Sales Number of Sales Number of (£ millions) workers (£ millions) workers 2004 320 2960 48 605 2014 388 3200 57 640
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Edexcel 1MA1 · sample · Paper 3H · Q4 · 4 marks
4 marks
A scatter diagram shows outside temperature against electricity used for heating for ten homes. A reasonable line of best fit passes approximately through (0, 85) and (20, 35).
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Edexcel 1MA1 · sample · Paper 3H · Q5 · 5 marks
5 marks
Henry is thinking of having a water meter.
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Edexcel 1MA1 · sample · Paper 3H · Q17 · 5 marks
5 marks
Louis and Robert are investigating the growth in the population of a type of bacteria. They have two flasks A and B. At the start of day 1, there are 1000 bacteria in flask A. The population of bacteria grows exponentially at the rate of 50% per day.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q1 · 1 mark
1 mark
Find 10% of £320.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q2 · 1 mark
1 mark
Write 0.8 as a percentage.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q6 · 3 marks
3 marks
A drink is made by adding 100 ml of juice to every 2 litres of water. Dev uses 5 litres of water.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q8 · 2 marks
2 marks
Eight identical pens cost £12.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q12 · 4 marks
4 marks
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
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 · Q14 · 6 marks
6 marks
Survey results: swimming—male 2, female 8; cycling—male 6, female 5; running—male 4, female 5. There are 30 people in total.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q17 · 3 marks
3 marks
Irena sells 80 ice creams one day and 108 the next day.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q20 · 5 marks
5 marks
A square has perimeter 16 cm, so side length 4 cm. A shaded quadrilateral has vertices at the square's bottom-left corner, a point on the top edge 3 cm left of the top-right corner, the top-right corner, and a point on the right edge 2 cm below the top-right corner.
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Edexcel 1MA1 · specimen2 · Paper 1F · Q23 · 4 marks
4 marks
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 · Q2 · 5 marks
5 marks
A square has perimeter 16 cm, so side length 4 cm. A shaded quadrilateral has vertices at the square's bottom-left corner, a point on the top edge 3 cm left of the top-right corner, the top-right corner, and a point on the right edge 2 cm below the top-right corner.
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Edexcel 1MA1 · specimen2 · Paper 1H · Q7 · 4 marks
4 marks
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 · Q10 · 3 marks
3 marks
y is inversely proportional to x. When x=1.5, y=36.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q8 · 4 marks
4 marks
Rachel's fruit survey of 10: apple 2, banana 5, orange 3. Pete's pie chart of 30 has the banana sector less than 180°.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q13 · 3 marks
3 marks
Abi invests £500 for 4 years at 2.3% simple interest yearly.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q14 · 2 marks
2 marks
Mobile cost graph has fixed rental £20 and rises to £35 at 500 minutes.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q15 · 4 marks
4 marks
A mousse recipe for 2 people needs 40 g of sugar, 110 g of chocolate, 2 eggs and 1/4 teaspoon of lemon juice. Ellie has 250 g of sugar and 550 g of chocolate.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q16 · 1 mark
1 mark
Sprinter runs 200 m in 25 s.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q18 · 3 marks
3 marks
There are 64 cards, with red cards and black cards in the ratio 1:1. Eight red cards are removed.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q20 · 2 marks
2 marks
Flow 20 gallons/min; 1 gallon=4.55 L.
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Edexcel 1MA1 · specimen2 · Paper 2F · Q27 · 3 marks
3 marks
On a farm, the ratio of cows to sheep is 6:5 and the ratio of sheep to pigs is 2:1. There are 189 animals altogether.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q6 · 3 marks
3 marks
On a farm, the ratio of cows to sheep is 6:5 and the ratio of sheep to pigs is 2:1. There are 189 animals altogether.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q10 · 6 marks
6 marks
The population of a city at the start of 2015 is 1,560,000. Assume that the population increases by 5.2% each year.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q13 · 3 marks
3 marks
A sequence is defined by p₀ = 100 and pₜ₊₁ = 1.06pₜ.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q14 · 1 mark
1 mark
D is directly proportional to n³. Mary says that doubling n multiplies D by 6.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q15 · 6 marks
6 marks
A smooth speed–time curve describes Karol's motion. With time in seconds and speed in m/s, it passes approximately through (0, 0), (2, 4.5), (4, 7.8), (6, 9.5), (7, 9.8), (8, 9.6) and (10, 8).
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 2H · Q21 · 5 marks
5 marks
The ratio equation is (2x − 1):(x − 4) = (16x + 1):(2x − 1).
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Edexcel 1MA1 · specimen2 · Paper 3F · Q5 · 1 mark
1 mark
Write 3/5 as a percentage.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q8 · 2 marks
2 marks
A model plane is 17 cm long at scale 1:200.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q11 · 2 marks
2 marks
A conversion graph shows that 30 litres is approximately 6.6 gallons (and 6 gallons is approximately 27 litres).
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Edexcel 1MA1 · specimen2 · Paper 3F · Q15 · 3 marks
3 marks
There are 35 pens. Fifteen are green and the rest are red.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q17 · 3 marks
3 marks
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 · Q22 · 3 marks
3 marks
The ratio of the number of boys to the number of girls in a school is 4:5. There are 95 girls in the school.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q27 · 4 marks
4 marks
At a depth of x metres, the temperature of the water in an ocean is T °C. At depths below 900 metres, T is inversely proportional to x and is given by T = 4500/x. Four candidate graphs are shown: A is an increasing straight line, B is a decreasing straight line, C is an increasing curve, and D is a decreasing reciprocal curve approaching both axes.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q29 · 6 marks
6 marks
An empty oil tank is a prism with a trapezium cross-section. The parallel sides of the trapezium are 3 m and 1.4 m, its perpendicular height is 2.4 m, and the prism is 2.5 m long. The tank must be filled to 85% of its capacity. After one minute, 300 litres of oil are in the tank; assume oil continues to flow at this rate. Use 1 m³ = 1000 litres.
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Edexcel 1MA1 · specimen2 · Paper 3H · Q1 · 3 marks
3 marks
The ratio of boys to girls in a school is 4:5. There are 95 girls.
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Edexcel 1MA1 · specimen2 · Paper 3H · Q6 · 4 marks
4 marks
At a depth of x metres, the temperature of the water in an ocean is T °C. At depths below 900 metres, T is inversely proportional to x and is given by T = 4500/x. Four candidate graphs are shown: A is an increasing straight line, B is a decreasing straight line, C is an increasing curve, and D is a decreasing reciprocal curve approaching both axes.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 3H · Q8 · 6 marks
6 marks
An empty oil tank is a prism with a trapezium cross-section. The parallel sides of the trapezium are 3 m and 1.4 m, its perpendicular height is 2.4 m, and the prism is 2.5 m long. The tank must be filled to 85% of its capacity. After one minute, 300 litres of oil are in the tank; assume oil continues to flow at this rate. Use 1 m³ = 1000 litres.
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Edexcel 1MA1 · specimen2 · Paper 3H · Q9 · 5 marks
5 marks
Ibrar bought a house for £145,000. Its value depreciated by 4% in the first year and by 2.5% in the second year. In the third year its value increased by x%, giving a value of £140,000 at the end of that year.
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Edexcel 1MA1 · specimen2 · Paper 3H · Q10 · 3 marks
3 marks
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 · Q12 · 4 marks
4 marks
Zahra mixes 150 g of metal A and 150 g of metal B to make 300 g of an alloy. Metal A has density 19.3 g/cm³ and metal B has density 8.9 g/cm³.
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References open the specific Pearson question paper when it is available. Missing, login-only or unverified question-paper sources are labelled on the affected row.
Question extracts are shown for study alongside a link to the original Pearson paper. Reference-only rows carry series, paper, question number and marks.
Everything here stays free. If ratio proportion and rates of change is where the marks keep going, I teach it one to one from the mark schemes. Free intro call, then a free first lesson.
