Pearson Edexcel GCSE Maths · Topic S
Sampling, charts, averages, spread, cumulative frequency and histograms. 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 90 marks
26 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
A biologist is estimating the number of fish in a lake. She catches, tags and releases 40 fish. A week later she catches 50 fish and finds that 8 of them are tagged.
(a)
(2)
(b)
(1)
(Total for Question 1 is 3 marks)
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2
The frequency table shows the favourite subject of 90 students. Maths 20, English 25, Science 30, Other 15. A pie chart is to be drawn to show this information.
(a)
(2)
(b)
(1)
(Total for Question 2 is 3 marks)
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3
A rugby coach records the number of points his team scored in each of 11 matches: 12, 15, 15, 18, 20, 21, 22, 24, 25, 26, 78.
(a)
(1)
(b)
(1)
(Total for Question 3 is 2 marks)
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4
The revision time (in hours) and test mark of 8 students were recorded and plotted on a scatter graph. The points show a clear upward trend. A line of best fit is drawn; it passes through the points (2, 30) and (8, 66).
(a)
(1)
(b)
(2)
(c)
(1)
(Total for Question 4 is 4 marks)
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5
Two classes sat the same test, marked out of 100. For Class A the median mark was 62 and the range was 24. For Class B the median mark was 55 and the range was 10.
(a)
(2)
(b)
(1)
(Total for Question 5 is 3 marks)
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6
The table shows how 72 people travel to work: Car 30, Bus 18, Walk 15, Cycle 9.
(a)
(2)
(b)
(1)
(Total for Question 6 is 3 marks)
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7
A pictogram is used to show the number of emails a company receives each day. A full circle represents 10 emails, and part-circles are used for smaller amounts. On Monday the pictogram shows 3.5 circles. On Tuesday it shows 2 circles.
(a)
(1)
(b)
(1)
(c)
(2)
(Total for Question 7 is 4 marks)
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8
Here are five numbers: 5, 8, 3, 8, 6
(a)
(2)
(b)
(1)
(c)
(1)
(Total for Question 8 is 4 marks)
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9
A council wants to find out how often adults in a town exercise. A researcher asks 40 people as they leave a gym.
(2)
(Total for Question 9 is 2 marks)
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10
A factory makes 1250 components in one day. A quality inspector chooses a random starting component from the first 25 and then inspects every 25th component.
(a)
(2)
(b)
(1)
(Total for Question 10 is 3 marks)
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11
A scientist is estimating the number of ladybirds in a greenhouse. She catches, marks and releases 48 ladybirds. Later she catches 60 ladybirds, of which 12 are marked.
(a)
(2)
(b)
(2)
(c)
(1)
(Total for Question 11 is 5 marks)
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12
The travel methods used by 10 students are: bus, walk, cycle, bus, bus, walk, cycle, bus, walk, bus.
(a)
(2)
(b)
(1)
(Total for Question 12 is 3 marks)
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13
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 13 is 4 marks)
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14
The frequency distribution for the number of books read by 25 students in one month is: 0 books, frequency 4; 1 book, frequency 7; 2 books, frequency 9; 3 books, frequency 5.
(a)
(1)
(b)
(2)
(Total for Question 14 is 3 marks)
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15
The times, t minutes, taken by 38 people to complete a puzzle are grouped as follows: 0 < t ≤ 10, frequency 8; 10 < t ≤ 15, frequency 12; 15 < t ≤ 30, frequency 18.
(a)
(3)
(b)
(1)
(Total for Question 15 is 4 marks)
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16
A histogram represents the masses, m kg, of 40 parcels. For 0 < m ≤ 5 the frequency density is 2.4. For 5 < m ≤ 15 the frequency density is 1.1. The remaining parcels are in the class 15 < m ≤ 20.
(a)
(2)
(b)
(2)
(Total for Question 16 is 4 marks)
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17
A cumulative frequency graph represents 80 values. Reading from the graph gives: cumulative frequency 20 at value 18; cumulative frequency 40 at value 27; cumulative frequency 60 at value 39; cumulative frequency 80 at value 52.
(a)
(1)
(b)
(2)
(c)
(1)
(Total for Question 17 is 4 marks)
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18
The scores in a quiz have this frequency distribution: score 1, frequency 2; score 2, frequency 3; score 3, frequency 4; score 4, frequency 1.
(a)
(2)
(b)
(1)
(c)
(1)
(Total for Question 18 is 4 marks)
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19
Two groups complete the same task. For Group A the median time is 18 minutes and the interquartile range is 6 minutes. For Group B the median time is 21 minutes and the interquartile range is 11 minutes.
(2)
(Total for Question 19 is 2 marks)
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20
Six numbers have a mean of 14. Five of the numbers are 9, 11, 13, 17 and 18.
(a)
(3)
(b)
(2)
(Total for Question 20 is 5 marks)
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21
In a random sample of 50 households, 12 households do not own a car. The town has 2000 households.
(2)
(Total for Question 21 is 2 marks)
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22
The amounts, in pounds, spent by 10 customers are 22, 24, 25, 26, 27, 28, 29, 30, 31 and 180.
(a)
(1)
(b)
(2)
(c)
(1)
(Total for Question 22 is 4 marks)
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23
A random sample of 300 adults is taken from across a town. Of these adults, 180 say they prefer travelling by bus rather than by car. There are 4500 adults in the town.
(a)
(2)
(b)
(2)
(Total for Question 23 is 4 marks)
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24
For a group of homes, the data show that as the outdoor temperature increases, the amount spent on heating generally decreases.
(a)
(1)
(b)
(1)
(Total for Question 24 is 2 marks)
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25
A scatter graph compares hours of practice, x, with a performance score, y. A line of best fit passes through (4, 18) and (10, 42). The observed practice times range from 2 to 11 hours.
(a)
(2)
(b)
(2)
(Total for Question 25 is 4 marks)
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26
A scatter graph contains the points (1, 12), (2, 16), (3, 19), (4, 25), (5, 27), (6, 32) and (7, 70). A line of best fit for the first six points passes through (1, 12) and (6, 32).
(a)
(1)
(b)
(2)
(c)
(1)
(d)
(1)
(Total for Question 26 is 5 marks)
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206 questions shown as printed, 14 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 · 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 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 2F · Q7 · 5 marks
5 marks
Examiner report
There were occasions in this question where learners confused the statistical terms mean, mode, median and range, resulting in an incorrect method being used in either part (a) or more commonly in part (b). Part (a) was answered well, with many learners aware of the need to sum the ages and divide the total by 8. There were a few arithmetic errors when adding, but if the full method was shown, learners could still gain 1 mark. A variety of incorrect answers were seen, and very often these seemed to be statistics other than the mean. The most common errors seen were 10 (the mode), 11.5 (the median) and 6 (the range), all of which gained no marks. Part (b) also had many correct answers from working out the range. Sometimes either the maximum or minimum was incorrectly chosen, and as in part (a) we also saw some incorrect statistics, most often the mean. Less success was evident in part (c), with a larger than expected number of learners not being able to show the probability correctly on the scale provided. The most common incorrect response was to misinterpret the divisions shown on the scale and mark at 1 8 rather than 1 4 .
Eight ages are 14,10,10,13,15,9,15,10.
Edexcel 1MA1 · November 2024 · Paper 2F · Q21 · 3 marks
3 marks
Examiner report
This three part question centred around interpreting a given scatter diagram. Most learners were able to identify that the type of correlation was positive in (a). Common incorrect answers included ‘negative’, ‘increasing’, attempts at a description and a range of other wrong guesses but blank responses were seen less frequently. In part (b), many learners were able to draw an acceptable line of best fit and gained the mark. When the mark was not awarded, it was often due to drawing a line from the origin to the corner of the grid which was outside the range of tolerance or simply joining the points in a dot to dot fashion. Learners should be reminded regularly that a line of best fit does not need to start at the origin and that the line must be straight and not curved. Many learners reached an answer within the acceptable range in part (c), with some doing so even if their line of best fit was omitted or not fully within tolerance. For learners who drew a line of best with fit with positive gradient such as from the origin, their reading was followed through and credit given if correct for their line, even if the previous mark had not been gained. Of the learners who had gained the mark in part (b) for a suitable line, some were unable to interpret the scale correctly and didn’t recognise that each small square on the vertical axis represented a width of 0.5 m and interpreted each small square as representing either 1 m or 0.1 m leading to a frequently seen incorrect answer of 25.6.
A scatter graph has Length (m) on the x-axis from 120 to 240 and Width (m) on the y-axis from 10 to 35. The plotted crosses are at (134,20), (141,22), (149,22), (152,23), (158,24), (168,26), (177,26), (200,31), (210,30), (217,28), (222,30), (223,32) and (230,32).
Edexcel 1MA1 · November 2024 · Paper 2H · Q2 · 3 marks
3 marks
Examiner report
This question was answered well by learners. Part (a) simply asked for the type of correlation, in this case ‘positive’. Those who added further description, relating to strength for example, were still able to gain the mark. A small number of learners tried to explain the relationship between the variables. Learners should be encouraged to carefully read the demand before answering the question. Part (b) required a line of best fit to be drawn, and whilst many gained the mark, a significant number did not. Many simply joined the bottom left corner of the grid to the top right corner of the grid, which gained no credit. It was also common to see learners drawing a line of best fit that worked for the early points but not for all. Part (c) required use of the line of best fit, and those who had drawn an unsuitable line in part (b) were still able to use that and gain credit in part (c). The only real error seen in this part was from mis-reading the scale, here every 10 small squares represented a change in width of 5m. A common incorrect answer was to write 25.5 instead of 27.5
A scatter graph has Length (m) on the x-axis from 120 to 240 and Width (m) on the y-axis from 10 to 35. The plotted crosses are at (134,20), (141,22), (149,22), (152,23), (158,24), (168,26), (177,26), (200,31), (210,30), (217,28), (222,30), (223,32) and (230,32).
Edexcel 1MA1 · November 2024 · Paper 2H · Q16 · 4 marks
4 marks
Examiner report
This histogram question pulled together several different skills. Firstly, candidates had to find the frequencies for two completed bars on the histogram. They then had to use these to find the frequencies of the missing bars, then their frequency densities and finally draw the missing bars in. Those who made a successful start to the question did so by finding at least one of the missing frequencies correctly. The second mark was then gained by subtracting the frequencies from 60 and halving to find the frequency for the two missing bars. Although a good number made a single error in reading the frequency density of the given bars, they were able to still gain the next two method marks. The final method mark was for a method to find the frequency density for one of the missing bars, or for drawing one bar correctly. We did see cases of correctly drawing the first bar, but then simply drawing the second at the same height.
Histogram of 60 teachers: 0-5 has frequency 11; 10-20 frequency density 1.5; 30-50 density 0.3. Frequencies 5-10 and 20-30 equal.
Edexcel 1MA1 · November 2024 · Paper 3F · Q15 · 4 marks
4 marks
Examiner report
Part (a) saw varied success as many of this cohort were not able to gain 3 marks. For those that didn’t, it was common to see learners unable to make a correct start at all, often finding the sum of the ages column and dividing this by 5, as well as dividing 41 by 5. Some learners successfully found the sum of the products as 406 but divided by 5 instead of 41. Some learners began with the correct method and then started a different, incorrect method and pursued this to gain 0 marks. Part (b) saw more success, with a good number of learners gaining 1 mark for an acceptable example as listed in the mark scheme or something equivalent. The most common incorrect answers were those listed in the mark scheme under not acceptable examples.
The ages of 41 children are: age 8 frequency 6; age 9 frequency 7; age 10 frequency 15; age 11 frequency 11; age 12 frequency 2.
Edexcel 1MA1 · November 2024 · Paper 3F · Q17 · 2 marks
2 marks
Examiner report
This question saw 0, 1 and 2 marks awarded in almost equal measure. For those that did not gain 2 marks, there were a number of ways (detailed in the mark scheme) that learners could gain 1 mark and all were seen regularly. It should be noted that frequency polygons require points to be joined with line segments – it was often seen that learners would plot the correct points but join with a curve, gaining 1 mark, centres should encourage learners to use a ruler. It was also the case that if two errors were made this would be 0 marks, for example the learner that plotted the points at the end of the intervals (e.g. 140, 160, 180, 200, 220) and joined the first and last point directly gained 0 marks. Regularly it was seen that points were not joined together when drawn at consistent intervals and gained 0 marks. Many learners drew histograms and gained 0 marks.
Race times for 100 people are grouped: 120≤t<140: 12; 140≤t<160: 28; 160≤t<180: 30; 180≤t<200: 22; 200≤t<220: 8.
Edexcel 1MA1 · November 2024 · Paper 3F · Q22 · 4 marks
4 marks
Examiner report
This question saw the full range of marks awarded. Some learners managed to gain 3 or 4 marks, usually for two correct values for median and range and at least one correct comparison. It should be noted that simply writing the value of two medians or ranges is not enough for comparison, some sort of statement relating to their sizes like the two examples in the mark scheme is required. Some learners used a method to find the median from the stem and leaf diagram but failed to extract 57 from it, leaving the 7 circled, which was not enough to gain B1.
School A scores (stem-and-leaf): 30; 41,42,44,44,45,47; 53,54,54,56,57,58,58,59; 60,68,68,69,69; 71,73,79. School B has median 56 and range 47.
Edexcel 1MA1 · November 2024 · Paper 3H · Q1 · 2 marks
2 marks
Examiner report
A standard question with the majority of learners scoring at least one mark for making at most one error in their diagram. The main single error was correct points being plotted but were either joined with a curve or the first and last point were also directly joined. Learners who did not plot the points correctly often gained a mark for plotting the points consistently at either the beginning or end of the interval and joining them with straight line segments.
Race times: 120≤t<140:12; 140≤t<160:28; 160≤t<180:30; 180≤t<200:22; 200≤t<220:8.
Edexcel 1MA1 · November 2024 · Paper 3H · Q6 · 4 marks
4 marks
Examiner report
Learners gained full marks for correctly stating the median and range for school A and making a correct comparison such as “the median for School A is greater than School B” and “School A has a greater range”. There were some who did not find the median correctly, working it out as 56 or 56.5, these learners often gained the mark for a correct comparison following through their value for the median. It should be noted that to gain the mark for a median of 57 this needed to be clearly stated, only indicating the 7 in the stem and leaf diagram through circling or crossing out was not sufficient. Similarly, when making a comparison it is not sufficient just to state the difference in the values, it needs to be clear which is greater.
School A stem-and-leaf diagram: 3 | 0 4 | 1 2 4 4 5 7 5 | 3 4 4 6 7 8 8 9 6 | 0 8 8 9 9 7 | 1 3 9 Key: 3 | 0 represents 30. For School B's 23 students, the median is 56 and the range is 47.
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 · Q7 · 4 marks
4 marks
Examiner report
In this question candidates were provided with some data and asked to draw a suitable diagram or chart for the information. A variety of different diagrams and charts were presented by candidates, the most common being a bar chart, compound bar chart or dual/comparative bar chart. Frequency polygons and pictograms were also alternative choices. A majority of candidates gave a key or suitable labels for Lena and Pavel, however candidates should be reminded that they should not use colour for differentiating between two lines or bars as scripts are marked in grey scale. Where candidates opted to draw bar chart(s) these generally included the key or labels for Lena and Pavel, suitable labels for days and often correctly showed data for at least one person or for two days. Common errors included scales that were not linear, scales that did not label grid lines and instead labelled the grid squares, or a lack of scale but the majority of candidates were not awarded the final mark due to failing to label the vertical axis. A number of candidates also did not start their linear scale from 0 which prevented the award of the C mark. A small proportion of candidates opted to add the data for Lena and Pavel and draw a chart for the total number of hours worked on each of the four days, as this lost some of the initial detail in the given information, only partial marks were available for the labels for days or linear scale and where the total hours per day were all correctly represented on the graph. Some superimposed one bar onto another, possibly in an attempt to draw a composite bar chart, so it was impossible to see unambiguously correct bars. Frequency polygons were the next most common chart type after bar charts. Candidates generally had a key for Lena and Pavel, labels for days or a linear scale and showed at least 1 person or 2 days correctly on these. A minority of candidates drew scatter graphs which were somewhat suitable given the bivariate nature of the data, but not entirely so given the small number of data points. These candidates were able to gain credit for their scale, labels for Lena and Pavel, and for plotting of the data for at least one person or 2 days correctly. Some candidates attempted to draw pie charts, but found this challenging given the values involved and the non-calculator nature of the paper, often losing accuracy in their calculations and subsequent measurement of angles. This lead to marks generally only being awarded for the labels for Lena and Pavel and/or those for the days. Some candidates opted to draw a tally chart which was a step back from the data as presented in the question and so did not get credit. Other diagrams that were not suitable included redrawing the table as provided in the question or with the total hours worked per day, and Venn diagrams where several aspects of the initial information were lost.
The table shows the number of hours that Lena and Pavel worked on each of four days
Edexcel 1MA1 · June 2024 · Paper 1F · Q15 · 4 marks
4 marks
Examiner report
In part (a) candidates were required to find the median from the stem and leaf diagram. The majority of candidates were able to do this accurately. A common incorrect answer was 67 which was the mode. Some candidates incorrectly wrote their answer as 6|4 leaving it written in the stem and leaf structure or 4 having not appreciated the meaning of the key. In part (b) candidates were required to find the range. This was also well answered with many candidates able to correctly identify the highest and lowest values from the diagram and work out the range. Some candidates were able to correctly identify the highest and lowest values, but did not perform the required subtraction accurately or left their answer as 45 to 81. Where candidates had identified 45 and 81 some incorrectly gave an answer of 44 from incorrect evaluation of 45 −81. A minority of candidates found the answer 32 having incorrectly selected 49 rather than 45 as the lowest value or gave an answer of 8 having incorrectly interpreted the values in the diagram as single digit. It was sometimes the case that the answers for (a) and (b) were reversed with candidates calculating the range in (a) and stating the median in (b). This scored no marks. In part (c) candidates needed to compare the median for the adults (found in (a)) with the median for the children. This was well answered with around half of candidates able to make an appropriate comparison of the value that they found in (a), be that correct or incorrect, with the given median for children. Common correct responses identified that the adults were faster, the children were slower or that the children took more time. Even where candidates had an incorrect answer in (a) they were often able to give a correct comparative interpretation. Some candidates attempted to include figures in their comparisons, but these needed to be correct if present, so errors in arithmetic were then an issue sometimes. A common response which did not gain credit was to give the difference between the two median values or to simply restate the median values for adults and children without any comparison. A small number of candidates erroneously stated that a high median meant the children were faster. Often responses did not clearly indicate whether it was adults or children being commented on with ambiguous references to ‘they’ being seen.
Tessa recorded the times that 15 adults took to complete a run.
Edexcel 1MA1 · June 2024 · Paper 1H · Q8 · 3 marks
3 marks
Examiner report
This question was generally answered well and there were many fully correct responses. If students knew how to get started they often went on to gain full marks. Some of the students who achieved the first mark for a method to find the total weight of the 8 parcels or the total weight of the 3 parcels made no further progress. Some did subtract 6 from 20 but gave 14 as the final answer. Many, though, did go on to show a complete process, subtracting 6 from 20 and then dividing the result by 5. If the calculations were carried out correctly, they scored full marks but some students made an arithmetic error and this meant that they did not gain the accuracy mark. Most arithmetic errors occurred when working out 14 ÷ 5. Some gave the answer 14 5 but this was not awarded the accuracy mark. A common misconception was that the weight of the three parcels should be added to the weight of the eight parcels. Some students merely subtracted 2 from 2.5 and either gave 0.5 as the answer or multiplied it by 5 and gave 2.5 as the answer. Some found the mean of 2.5 and 2. These methods could not, of course, be awarded any marks.
Len has 8 parcels.
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 2F · Q6 · 5 marks
5 marks
Examiner report
This question contained three parts and required students to use knowledge of pictograms. Part (a) was answered very well, with a very large number of students showing they could use the key to state the number of houses for a given month. Similarly, part (b) was also often answered well with most students being able to draw symbols to represent 11 houses for April to gain the mark. A variety of representations totalling 11 houses were seen, with students often using two full squares and predominantly an ‘L’ shape and, although the ‘L’ shapes were drawn freehand, the intention of the candidate to represent a value of 3 was almost always clear. Some drew internal lines to show the ‘L’ shape representing three smaller squares each of value 1 and some even added numbers indicating the value of the symbols (i.e. full squares labelled with 4). Some drew a rectangle to represent half of a large square and a separate smaller square representing one quarter of the large square. Whilst a variety of sizes in diagrams were shown, the intention was clear in the majority of responses. Full marks were most commonly awarded on the final part of this. Some students wrote 18 on the answer line without any working, while many showed working in a variety of ways. Where working was shown but a correct answer not given, this enabled them to pick up partial marks for a valid method. It was common to see the totals for each month adjacent to each row on the diagram followed by a total or an addition for the number of houses sold in the first four months and/or a subtraction from 60. Where working was shown, errors were few and far between suggesting writing down the stages of calculations was helpful. When full marks were not awarded, it was usually due to a mistake in interpreting the key and using an incorrect value for one of the months. March tended to be read as 16 and not 12 on occasion and this led to an answer of 14, but a lack of working often led to the mark for 60 – ([Jan + Feb + Mar] + 11) not being awarded and as such, centres should impress on students the value of showing their working. Some gave 42 on the answer line as they forgot to subtract this from 60. However, these types of errors were uncommon.
Ben's pictogram uses one full symbol for 4 houses: January has 2½ symbols, February 2¼ symbols and March 3 symbols.
Edexcel 1MA1 · June 2024 · Paper 2F · Q28 · 4 marks
4 marks
Examiner report
Finding the class interval containing the median in part (a) was not answered well. The most common incorrect answer was the interval in the middle of the table, giving evidence that frequencies were not considered. The working and answer for part (b) was also seen in this part which was surprising to see. Performance in part (b) when calculating an estimate for the mean was in line with previous series with a range of incorrect methods seen and blank responses being frequent as well. Students who knew what they were doing tended to score full marks or at least one mark for finding 5 products but dividing by the wrong value, often 5 (groups) or the sum of the midpoints. A small number of students correctly found products but then rounded before adding and dividing and this approach leading to the second mark not being awarded. Some students rounded the frequencies to the nearest 10 before multiplying by the midpoint, no doubt attempting to ‘estimate’ but this was given no credit. Various other approaches that scored no marks were seen such as totalling the minimum or maximum values of the intervals and dividing by five. As with previous series, choice of method was a common issue. Whilst many students correctly found products within the interval, a large number were ultimately not awarded the first mark due to using an alternative incorrect method as noted in the additional guidance on the mark scheme. Summary Based on their performance on this paper, students should: • read questions carefully, including checking whether the magnitude of an answer is sensible, units are appropriate, and the level of accuracy required is shown; • practise questions involving ratio and forming algebraic expressions; • practise using equipment such as rulers, protractors and compasses; • practise using calculator functions and negative numbers; • use formal methods when working with fractions or percentages.
The grouped weights, w grams, of 120 oranges are: 50 < w ≤ 100: 34; 100 < w ≤ 150: 29; 150 < w ≤ 200: 27; 200 < w ≤ 250: 19; 250 < w ≤ 300: 11.
Edexcel 1MA1 · June 2024 · Paper 2H · Q11 · 7 marks
7 marks
Examiner report
Cumulative frequency is another familiar topic and proved a good opportunity for students to show their data handling skills. A large proportion of students scored full marks in (a) and (b) for completing the table and drawing the diagram. We do still see some students lose a mark on the graph for either plotting on mid-points rather than endpoints or for simply not joining the points. Either curves or straight-line segments were accepted. Parts (c) and (d) required interpretation of the graph, and part (d) was typically done better. For the IQR we saw students not reading off at the correct values on the CF axis (often at 10 and 50 or 20 and 40, not 15 and 45) but this number does seem to be coming down each series. In part (d) it was not uncommon to find students reading off the graph correctly, but then failing to find the difference to 60. It is worth noting that students could score full marks in parts (c) and (d) even if the graph was incorrect. To do this their processes must be correct, and the graph must have had no negative gradient.
The grouped weights, w kg, of 60 parcels are: 0 < w ≤ 2: 7; 2 < w ≤ 4: 21; 4 < w ≤ 6: 15; 6 < w ≤ 8: 11; 8 < w ≤ 10: 6.
Edexcel 1MA1 · June 2024 · Paper 3F · Q7 · 2 marks
2 marks
Examiner report
Part (a) was answered well with most students gaining the 1 mark for correctly identifying “Bus” as the mode. Of those that didn’t, a variety of incorrect answers were seen; with either “Car” or “9” given the most often. In part (b) most were able to gain 1 mark for an answer of 5; of those that didn’t 6 and 8 were often given as the answer or some students added rather than subtracted.
A bar chart records travel to school: Bus 9, Car 7, Cycle 3, Walk 8 and Other 1 student.
Edexcel 1MA1 · June 2024 · Paper 3F · Q13 · 3 marks
3 marks
Examiner report
This question was answered well with a majority of students able to gain the full 3 marks. Of those that didn’t, the whole range of incorrect entries was seen from 1 up to 6. Students attempting these types of questions on future papers should be encouraged to check the totals for each column and row, as this is a way to highlight any errors they have made and can therefore be corrected. It does appear that the majority of errors were caused by arithmetic errors and incorrect use of calculators.
James asks Year 10 and Year 11 students to choose French, German or Spanish as their favourite language. Complete the two-way table from these given entries: Year 10 French = 33 and Spanish = 34; Year 11 German = 45 and total = 113; Spanish total = 67; grand total = 207.
Edexcel 1MA1 · June 2024 · Paper 3F · Q14 · 3 marks
3 marks
Examiner report
Drawing pie charts is clearly an area of improvement for this cohort as a minority were able to score full marks for a correct pie chart. Some were able to gain 2 marks for all 3 angles correctly calculated or for accurately drawing one correct angle on the pie chart. Most of the cohort gained no marks and common incorrect solutions often included an incorrect or no attempt to calculate the angles and if sectors were drawn on the pie chart, the angles were the same as the frequencies (30, 10, 50) or some other incorrect values. There were indications that some students had not come equipped with a protractor and a small number of students did not use the line given or drew their angles not from the centre. A few who drew a correct pie chart forgot to label it correctly, it should be noted that labelling the sectors with the values of the angles, e.g. 120, 40, 200, is not acceptable.
The table gives information about the drinks people ordered in a cafe.
Edexcel 1MA1 · June 2024 · Paper 3H · Q11 · 5 marks
5 marks
Examiner report
In part (a) most students gained at least one mark for 3 correct values on the box plot. Those who had a good understanding gained three marks. There were a high proportion of students who did not recognise the need to find the UQ and the highest value and only gained one mark whereas some students only found and plotted one of these correctly and hence only gained two of the marks. It was very pleasing to see how the comparison of boxplots in part (b) was answered very well compared to previous series. As previously, examiners expected to see a comparison of the medians and either the ranges or the interquartile ranges with specific reference to the measure used. Students using the wrong vocabulary, using average or mean or medium instead of median and likewise spread or variation instead of range or IQR did not gain marks. Comparisons of the minimum, lower quartile, upper quartile and maximum values also gained no marks. As in previous series there were still some students merely stating values without comparing them. For example, "the median for Friday = 40 whereas the median for Sunday = 42" cannot be given any credit. It should also be noted that there is no need to give values in the comparisons but, if they are given, they must be correct. Students quite often failed to refer to the context of the question eg by referring to speed in some way and so restricted themselves to the award of only one of the two marks available. When trying to compare range and IQR in context a few students who attempted this wrongly interpreted a larger range / IQR to mean that the cars were faster rather than identifying that the speeds were less consistent. A significant number of students used incorrect days in this question; students could be encouraged to underline key information like this so that there is no ambiguity with which box plot they are referring to.
Friday speed summary: minimum 25, lower quartile 35, median 40, IQR 12 and range 37 mph. Sunday's box plot has five-number summary 22, 33, 42, 48 and 66 mph.
Edexcel 1MA1 · November 2023 · Paper 1F · Q1 · 1 mark
1 mark
Examiner report
A good number of students were able to give a correct answer of 6 but there were a significant number who did not and a wide variety of incorrect answers were given. The most common incorrect answers were 4 (from finding the median) and 5 (from finding the mean).
The numbers are 2, 4, 4, 7 and 8.
Edexcel 1MA1 · November 2023 · Paper 1F · Q8 · 6 marks
6 marks
Examiner report
Part (a) saw mixed results. A good number of students were able to find the correct frequencies for 2 marks. Many gave the correct frequencies in the tally column and something incorrect such as frequency/24 as a fraction which gained 1 mark. Some also confused the definitions of tally and frequency and put the information in the wrong column. It was encouraging to see that a number of students were crossing out items in the list as they entered their tally marks in the frequency table and were using the correct bar notation for recording the tallies. Part (b) was answered well with many gaining B1 for a correct answer; those that didn’t often gave a number for their answer instead of the correct word. Part (c) saw the full range of marks awarded with most students gaining full marks. Of those that didn’t, the most common error was an incorrect linear scale, although these students could still gain 2 marks for labelling bars and correct height bars for their scales and many did. Students often struggled to correctly scale the vertical axis, sometimes writing the numbers between the squares instead of on the gridline or using multiples of 3 or 5 which often led to errors.
Twenty-four students chose a school trip destination: museum, castle, castle, farm; farm, castle, farm, farm; castle, farm, castle, castle; castle, farm, castle, museum; museum, farm, castle, museum; museum, museum, castle, castle.
Edexcel 1MA1 · November 2023 · Paper 1F · Q21 · 4 marks
4 marks
Examiner report
Part (a) saw the full range of marks awarded. Some students completed a fully correct process to reach an answer of 3.5 or equivalent. Of those that didn’t, some reached as far as 14 ÷ 4 but could not follow the process through with 3.2 quite often seen as the result of the division; students and centres should note that 14 4 gained full marks. Some students were able to find the total length of the 5 sticks but made no further progress. There were also a good number who did not manage to make a correct first step and gained 0 marks; a common error was to calculate 4 × 7 or 4 × 4.2 rather than 5 × 4.2. Part (b) saw little success as most students gained no marks, with common incorrect responses centring around the mean increasing or the length of the other 4 sticks being reduced.
The mean length of 5 sticks is 4.2 cm. One measured stick was recorded as 7 cm.
Edexcel 1MA1 · November 2023 · Paper 1H · Q4 · 4 marks
4 marks
Examiner report
Some of the students who achieved the first mark in part (a) for a process to find the length of the 5 sticks, 4.2 × 5, made no further progress. Many, though, did go on to show a complete process, subtracting 7 from 21 and then dividing the result by 4. If the calculations were carried out correctly, they scored full marks but some students made an arithmetic error and this meant that they did not gain the accuracy mark. Sometimes 4.2 × 5 was evaluated incorrectly but most arithmetic errors occurred with 14 ÷ 4. Answers of 3.2 were quite common. In part (b) a good number of students were able to explain how the answer to part (a) would be affected. Some explanations gained no mark because they said that the mean would be higher but there were many explanations which made no mention of the answer to part (a) or the mean but simply referred to the lengths of the sticks, stating that the remaining sticks would be shorter.
The mean length of 5 sticks is 4.2 cm. Nawal measured the length of one of the sticks as 7 cm.
Edexcel 1MA1 · November 2023 · Paper 2F · Q16 · 4 marks
4 marks
Examiner report
It was pleasing to note that a good number of students used two-way tables in this unstructured problem and using this method often yielded full marks. Other successful approaches involved using a flow diagram for children and adults which again yielded a high success rate. Most students gained at least one mark for using the initial given information to find either the total number of adults or adult romance, children adventure and many then calculating the number of adult horror. Finding the number of children horror was more troublesome for many students not gaining full marks. One notable error was for the students to add the various totals together to get 116 and subtract from 160 and continuing to divide by two as they misinterpreted the part about two sections being equal. This gave an incorrect result of 22. Many students unfortunately, just had numbers written in the answer space not linked to anything specific. Students should be encouraged to approach this style of question in a systematic way such as using a table or labelling when calculating values as this may allow them to keep track of the information they have found and guide them as to which information they still need to find.
A library survey covers 160 readers: 85 children and 75 adults. Romance books total 33, of which 19 are children. Adventure books total 76, of which 34 are adults. Seven adults chose thriller, and the number of children choosing thriller equals the number of adults choosing horror.
Edexcel 1MA1 · November 2023 · Paper 2F · Q17 · 3 marks
3 marks
Examiner report
A standard question requiring students to draw an ordered stem and leaf diagram with key for given data. Almost all students attempted the question, with many scoring full marks and nearly all students gaining at least one mark. Where marks were lost it was often due to a missing or an incomplete key, not ordering the leaves, or an ordered diagram with one omission. Learners should be encouraged to count the number of digits in their answer and check that it agrees with the number of values in the initial data. Where no marks were awarded, it was often due to not demonstrating an understanding of a stem and leaf diagram, some using the number 1 as the stem, listing all numbers as leaves or trying to complete some sort of pictogram or tally chart.
The heights in centimetres are 160, 162, 168, 172, 172, 173, 177, 178, 180, 180, 183, 184, 186, 188, 191 and 197.
Edexcel 1MA1 · November 2023 · Paper 2H · Q15 · 3 marks
3 marks
Examiner report
This question, whilst relatively standard, especially parts (a) and (b), was answered very poorly by the majority of candidates. The first two parts required students to fill in a frequency table from a histogram, and then to complete the graph. Part (c) asked for an estimate of the median. In fact, students were more likely to score a mark in part (c), normally for finding at least 2 areas, but it was very rare to see any further correct working.
A histogram (drawn with frequency density against time) gives information about the times taken by 43 students to run a race. The bars are: 10 < t ≤ 12 with frequency density 2; 12 < t ≤ 16 with frequency density 2; 16 < t ≤ 20 with frequency density 4; 20 < t ≤ 22 with frequency density 6.5; 22 < t ≤ 26 with frequency density 0.5 (t in seconds).
Edexcel 1MA1 · November 2023 · Paper 3F · Q6 · 4 marks
4 marks
Examiner report
Nearly all candidates were able to draw the pictogram accurately with the vast majority getting full marks. In part (b) nearly all the candidates managed to get at least one total correct with the errors mainly associated with the partial circles. 4 instead of 3 cakes was a common error for what a quarter circle represented. Totalling the number of cakes was generally well done with few arithmetic errors. Some of these candidates then forgot to end with a statement making their choice as to which year sold more cakes and thus missed out on full marks from an otherwise excellent response.
A pictogram uses one whole symbol for 12 cakes. Chocolate has 5 symbols, vanilla has 3 1/4 symbols, lemon has 1 1/2 symbols, and the banana row is blank. Year 7 sold 24 banana cakes. Year 8 sold 150 cakes in total.
Edexcel 1MA1 · November 2023 · Paper 3F · Q22 · 4 marks
4 marks
Examiner report
In part (a) the majority of candidates were able to show they understood what the table meant. Many candidates were able to find a value within the inequalities and multiply this by the frequency. In using a variety of different methods candidates used mid-points, ends and other values. All candidates were able to pick up the two method marks if they then went on to sum their six products and divide the total by fifty to find an estimate for the mean. Those who used the correct method of using the mid-points were able to go on to achieve the correct solution and were awarded the final accuracy mark. The usual misconceptions were seen, such as adding the frequencies, adding the midpoints or summing their chosen values from within each inequality and then finding the mean of these, all of which gained no marks. In part (b) many candidates were unable to answer this question correctly and gain any credit. Many took the misconception offered and chose to agree that Seija was correct often justifying this by taking the ordered midpoints and finding the middle of these. Other common misconceptions seen included ordering the frequencies and then opting for the 15-20 inequality or selecting 17.5 (the midpoint from this).
For 50 cities, midday temperatures are grouped: 10<T<=15: 2; 15<T<=20: 8; 20<T<=25: 13; 25<T<=30: 21; 30<T<=35: 6.
Edexcel 1MA1 · November 2023 · Paper 3H · Q3 · 4 marks
4 marks
Examiner report
This question was also a good discriminator between students working at the lower end of the attainment range. Higher attaining students generally scored full marks. A good proportion of students realised that they needed to use a temperature within each interval in order to calculate an estimate of the mean temperature. Many of these students used the midpoints. However, a significant number of students used the upper boundaries or other values within the intervals. Some students just added the 5 midpoints and divided by 5 while some other students did get the products of the temperatures and frequencies and added them, but then divided by 5 instead of the total frequency, 50. A small number of students merely added the frequencies and divided by 5 thereby not taking account of the temperatures at all. Part (b) of the question was not answered as well as part (a) though there were some students who gained no credit in part (a) but who gave a correct response in part (b). There were many clear responses though a significant number of students gave an answer which was either too vague or ambiguous.
Seija works at a weather station. The table gives information about the temperature, T °C, at midday for each of 50 cities in the UK on Tuesday. Temperature (T °C) Frequency 10 < T <= 15 2 15 < T <= 20 8 20 < T <= 25 13 25 < T <= 30 21 30 < T <= 35 6
Edexcel 1MA1 · June 2023 · Paper 1F · Q12 · 2 marks
2 marks
Examiner report
The majority of students understood the concept of the mean of a set of numbers and divided the sum of the six numbers by 6. Arithmetic errors here were plentiful, both in the addition and division stages. Many students tried to find the median by ordering the list of numbers and selecting a number between 5 and 8. Fortunately a correct answer of 7 from this incorrect approach was rarely seen. The range of 10 was a common answer for weaker candidates.
Here are six numbers: 13, 5, 4, 9, 3, 8.
Edexcel 1MA1 · June 2023 · Paper 1F · Q23 · 2 marks
2 marks
Examiner report
It was pleasing to see many students plotting the required points consistently within the given intervals although many did not use the mid-interval values; upper limits were commonly used. Accuracy of plotting was generally good, but students must realise that a polygon has straight sides, not curves. Many mistakenly joined the first and last point. Many drew histograms, which are acceptable in finding the specific points, but single points must be identified and joined with line segments.
Daily rainfall over 60 days is grouped as follows: 0 <= R < 5: 8 days; 5 <= R < 10: 24; 10 <= R < 15: 13; 15 <= R < 20: 11; 20 <= R < 25: 4.
Edexcel 1MA1 · June 2023 · Paper 1F · Q25 · 3 marks
3 marks
Examiner report
Descriptions of the relationship between age and weight were usually acceptable in part (a) where an increase in age related to an increase in weight. Some answers were vague quoting babies being “bigger” or “as babies grow”. Some students were drawn into talking about the development of babies in the first 12 months without actually answering the question. Positive correlation was accepted as a description of the relationship but “positive” alone was not. Direct proportion was another common answer that gained no marks. In part (b), a correct answer in the given range was often seen (gaining full marks) although often the evidence shown on the graph was less convincing. Some read from the graph from 5.8kg but then approximated their readings to 2 months (outside of the range). Finding 5.8 on the axis was poorly executed. Very few candidates drew a line of best fit and if they did, it was often not in the correct place.
A scatter graph plots baby age in months against weight in kg. The approximate plotted crosses are (0.4,3.4), (1,4.4), (1,3.0), (2,4.6), (2.5,4.1), (2.5,5.4), (2.8,6.4), (4,7.1), (4,4.9), (4.5,6.3), (5,7.6), (5,9.2), (6,8.0), (6,6.8), (7,9.5), (7,8.3), (7.5,7.3), (8,9.0), (8.5,10.0), (8.5,8.3), (9,10.6), (10,11.2), (10,9.6), (11,10.9), (11,9.7).
Edexcel 1MA1 · June 2023 · Paper 2F · Q17 · 4 marks
4 marks
Examiner report
Most students managed to score the first mark for a start to the process, typically for a correct starting process of adding the number of seats in cinemas A and B (250+350). However, many failed to know how to progress from there with many dividing 600 by 2 or 3 and very few knowing they needed to calculate 3 × 380 to find the total number of seats in all three cinemas, which was also a valid start. A lot of students worked with an embedded correct answer, showing their understanding of calculating the mean as adding then dividing, but the value 540 remained embedded with another number (e.g. 1140 or 380) given as the final answer. This scored 3 marks. A significant number of students attempted to try various values added and divided by 3 to give the desired mean but then gave up. Some had success with this approach, but students need to be reminded that where a trial and improvement method is used, all or no marks can be awarded. Another common incorrect approach was to see the numbers as a sequence leading to an answer of 150 or even 450. Use of algebra was very rarely seen. Often it could be seen that students understood what the mean is but do not know how to work in reverse in this question. Therefore, it would be useful for centres to ensure more exposure and practice of worded reverse mean problems.
There are three cinemas A, B and C. The mean number of seats is 380. A has 350 seats and B has 250.
Edexcel 1MA1 · June 2023 · Paper 3F · Q9 · 6 marks
6 marks
Examiner report
In part (a) the majority of candidates ordered the numbers successfully and went on to find the median correctly. A number of candidates calculated the mean instead. Part (b) was well answered. Part (c) was also well answered. Candidates were able to correctly scale the y-axis and then plot four bars, at the correct height, as well as label them. Those that did not gain full marks tended to lose a mark for an incorrect scale or missing bar labels or another mistake, such as misplacing the linear scale within the square, rather than on the grid lines, which sometimes led to confusion in drawing their own bars. Some candidates used the values from the table to label the axis, i.e 1, 5, 7, 9 without the appropriate scaling.
The numbers of books read in a month are Ximena 7, Martha 9, Kezia 1 and Tabby 5.
Edexcel 1MA1 · June 2023 · Paper 3F · Q12 · 4 marks
4 marks
Examiner report
In part (a) most candidates answered correctly. A common error was for candidates to write the size of the angle, 150 degrees, instead of merit and some candidates wrote no response here. In part (b) the most common approach was to work out the angle for one student and then divide each angle separately, summing the results. Of those who didn't score full marks the method was usually correct and so an incorrect answer was due to an arithmetic error. Some found 2, 5 and 10 but added these to get 15 instead of 7, losing 2 marks. The more efficient approach of a single calculation 360 105 was rarely seen. A common incorrect expression was 360 ÷ 4. Occasionally candidates found the percentage for each sector but rounded too early, leading to the loss of the accuracy mark.
A guitar-exam pie chart has sector angles: Fail 30 degrees, Distinction 105 degrees, Pass 75 degrees and Merit 150 degrees. Seven students got Distinction.
Edexcel 1MA1 · November 2022 · Paper 1F · Q7 · 3 marks
3 marks
Examiner report
Part (a) was answered well, the vast majority clearly understanding the concept of mode. In part (b) also, understanding of probability scales and probability in general was good. In (ii), some simply added a cross to the probability scale, failing to quote the actual numerical probability; this gained no marks. Some students are still using terms such as unlikely in terms of describing probability.
Here is a list of 8 letters. B C A A A A B A
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 1H · Q5 · 2 marks
2 marks
Examiner report
Students who showed a correct method to work out how many model B cars the factory should make generally went on to give the correct answer. Some, however, made an arithmetical error when working out 40000 ÷ 80 × 15 and gained one mark only. A common incorrect method was 40 000 ÷ 15. Some students attempted to find 15% of 40 000 leading to an incorrect answer of 6000.
A car factory asks 80 people which model they are most likely to buy. The results are: A, 23 people; B, 15; C, 30; D, 12. The factory is going to make 40 000 cars next year. Work out how many model B cars it should make.
Edexcel 1MA1 · November 2022 · Paper 1H · Q14 · 3 marks
3 marks
Examiner report
The students who worked out frequency densities and used these to draw a histogram often gained all three marks. Some students drew the first three bars correctly but then made an error drawing the bar representing the interval 90 < w ≤ 110 and 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. Some students used the midpoints of the class intervals and the frequencies to get values which they then used to draw a frequency polygon.
The potato weights are grouped as follows: 50 < w ≤ 70: 20 potatoes; 70 < w ≤ 80: 50; 80 < w ≤ 90: 60; 90 < w ≤ 110: 30.
Edexcel 1MA1 · November 2022 · Paper 2F · Q9 · 3 marks
3 marks
Examiner report
Most students were awarded full marks. Of those not scoring full marks, a common error was with the linear scale. Many chose an appropriate linear scale of one square to one unit, although there were some candidates who labelled the spaces rather than the lines and others who did not start their scale at zero which often resulted in the 3 bar being only 2 squares high. Other errors with linear scale included using a scale of 3 to a square or 5 to a square, which caused issues when drawing their bars as it was difficult to clearly represent all of the frequencies. Centres should give students practice in identifying an appropriate scale when drawing graphs
The table shows the number of students who arrived late at school on each day of one week: Monday 9, Tuesday 10, Wednesday 8, Thursday 6, Friday 3. Draw a bar chart for this information.
Edexcel 1MA1 · November 2022 · Paper 2F · Q15 · 5 marks
5 marks
Examiner report
The marks for this question were well distributed over the full range available. For part (a) when full marks were not scored the main issues were with the key, omission of a figure, or uncertainty around how to place '103'. Some students were unsure on how to represent this number with some choosing to use 1 in the stem instead of 10 or 100, and/or writing stem as 03. Secondly, some students were unsure of the notation needed to explain the key, with some writing in words and others using various symbols as a separator between the tens and units. Practice of examination questions and emphasise the importance of crossing out the numbers as they place them in the diagram, completing an unordered diagram first, then ordering it allowing them to order fewer integers at once. Students should always check that they have the same number of values in their diagram as there are in the original question, this is an easy way to avoid losing marks. For part (b), if pupils understood the median, they were generally successful in gaining 1 or 2 marks. A significant number of students disregarded the stem and leaf diagram and re-wrote the list, not appreciating that the median could be read from their diagram, this method did produce many correct answers but would have been more time consuming. There were common incorrect responses for example calculating the mode, range or mean.
Hetvi’s friends have these numbers of stickers: 77, 86, 94, 87, 71, 98, 74, 103, 71, 85, 82, 84, 97, 91, 88, 89, 75.
Edexcel 1MA1 · November 2022 · Paper 2F · Q17 · 3 marks
3 marks
Examiner report
This question was not answered well with all the usual misconceptions seen. A common approach was to find the mid-points of the intervals (usually successfully), add them together and divide by the frequency. Responses where fx was seen frequently broke down by division by 5 rather than 80. For those students who do calculate frequency multiplied by the midpoint, it is helpful when working is shown so that credit can be given where the answer is incorrect from arithmetic error. Understanding and checking their answer is sensible would be of benefit to candidates to avoid lots of responses being outside the range of data.
The table shows the heights of 80 teenagers: 150 < h ≤ 160, frequency 8; 160 < h ≤ 170, frequency 14; 170 < h ≤ 180, frequency 24; 180 < h ≤ 190, frequency 30; 190 < h ≤ 200, frequency 4. Work out an estimate for the mean height of the teenagers, in cm.
Edexcel 1MA1 · November 2022 · Paper 2F · Q18 · 4 marks
4 marks
Examiner report
Part (a) was answered well, with the majority correctly identifying the coordinates of the outlier. When the mark was not awarded, it was often due to either selecting (6, 1) as the outlier or for writing the coordinates incorrectly as (1, 2) but this was seen rarely. Part (b) required learners to describe the relationship shown by the scatter graph and many students were able to correctly describe that as one variable increased, the other variable decreased. Stating negative correlation was also sufficient to gain the mark but of the students who did not describe the relationship in words, some just stated negative or negative gradient and did not use the word correlation. The other popular incorrect answer was to say there was a positive correlation. In part (c) whilst some fully correct answers within the given range were seen, a large number of students were not able to use the graph correctly. It was common to see an incorrect line of fit being used and a few instances of a line of best fit being drawn from the origin and showing a positive gradient were also seen. Some lines were drawn across from 7 but students did not seem to know how to use this to read off an accurate figure. Centres should ensure students have access to questions involving negative correlation.
The scatter graph plots (rainfall in mm, hours of sunshine) for ten English towns: (1, 9.4), (1.6, 11), (2, 7.4), (3, 8), (3.4, 6), (4.4, 4), (5, 7.4), (5.4, 5), (6, 1) and (2, 1). One point is an outlier.
Edexcel 1MA1 · November 2022 · Paper 2H · Q1 · 4 marks
4 marks
Examiner report
This scatter diagram question gives students a familiar starting point. Part (a) required them to identify the outlier on the diagram. The vast majority of students identified the correct point, but some were unable to correctly identify the coordinates, with (1, 2) being a reasonably common incorrect answer. In part (b) we were looking for the relationship between the two variables, and again this was answered well with suitable descriptions relating to one variable increasing as the other decreases. It was common to see a description of correlation, which was acceptable providing the word ‘correlation’ was used. ‘Negative’ alone did not gain the mark as the question was not asking them to describe the correlation. Part (c) was the standard question asking students to use the graph to interpolate the rainfall for a given number of hours of sunshine. It was surprising to see so few candidates drawing a line of best fit, although this was not needed to gain full marks. Many were able to get both marks by giving an answer in the range 3-4. Those who did use a line of best fit often gained only 1 or no marks as they were drawing their line too low and gaining an answer outside the given range.
The scatter graph plots (rainfall in mm, hours of sunshine) for ten English towns: (1, 9.4), (1.6, 11), (2, 7.4), (3, 8), (3.4, 6), (4.4, 4), (5, 7.4), (5.4, 5), (6, 1) and (2, 1). One point is an outlier.
Edexcel 1MA1 · November 2022 · Paper 2H · Q11 · 3 marks
3 marks
Examiner report
This boxplot question required learners to be able to use a Cumulative Frequency curve to find the median and upper and lower quartiles. To gain all 3 marks, they had to draw a fully correct box-plot. 2 marks were awarded for drawing a box-plot with at least 3 correct values plotted. For those who were unable to plot a boxplot candidates could gain 1 mark for identifying one of the LQ, Median or UQ. A significant number of candidates gained some credit on this question, but it was disappointing to see that so many had no idea how to use the CF graph. There were a number of candidates who knew what a box plot was, but couldn't find the values from the graph and hence scored zero marks.
In an experiment, 60 students each completed a puzzle. The cumulative-frequency curve includes the readings (24 s, 0), (42 s, 15), (54 s, 30), (64 s, 45) and (96 s, 60). The least time was 24 seconds and the greatest was 96 seconds. Draw a box plot for the distribution.
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 3F · Q6 · 2 marks
2 marks
Examiner report
In part (a), 6 was the most common answer, but some candidates mis-counted and gave either 5 or 7 as their answer. Part (b) was well answered, though a small number of candidates read off April instead of May.
The graph shows the average monthly temperature in Amman: Jan 8°C, Feb 9°C, Mar 11°C, Apr 16°C, May 20°C, Jun 23°C, Jul 25°C, Aug 24°C, Sep 21°C, Oct 20°C, Nov 14°C, Dec 10°C.
Edexcel 1MA1 · November 2022 · Paper 3F · Q8 · 3 marks
3 marks
Examiner report
Part (a) was a well answered question. In part (b) many candidates gained both marks. Common errors included attempting the question by summing the numbers, but not always summing all of them, or by dividing by 2, 3 or 5. A few candidates found the range or median. Some candidates lost marks because they did not extract the correct numbers from the table.
Four students play a game. Their points are: Ali 143, Barbara 121, Calliope 45 and Danesh 19. Barbara has more points than Danesh.
Edexcel 1MA1 · November 2022 · Paper 3F · Q16 · 2 marks
2 marks
Examiner report
Stating the need for labelling was the successful answer most often given. Only occasionally was the second mark achieved. Many candidates identified that the number of potatoes added up to 300, but rarely showed an understanding that scaling to 360° was required. Very few candidates actually worked out the correct angles of 108°, 126°, 126° to illustrate the incorrect pie chart.
There are three types of potato in a box: 90 Jersey Royal, 105 Charlotte and 105 Maris Piper. Salim draws an unlabelled pie chart headed only ‘Box of potatoes’; its three sectors are drawn as approximately 90°, 135° and 135°. Write down two different things that are wrong or misleading with the pie chart.
Edexcel 1MA1 · November 2022 · Paper 3F · Q23 · 3 marks
3 marks
Examiner report
Candidates who used a 2-way table for this question were significantly more likely to score full marks than those who chose a series of written calculations. The majority of candidates did not use words to describe the answers to their working out, so they frequently got themselves lost in a page full of numbers. Most candidates scored one mark on this question, with the majority opting for a process to find girls choosing French (44) or total number of girls (110). Of the candidates that were able to progress past a first step, most were able to go on and score full marks, however there were a number of responses seen that did not identify the correct answer from their working or table and often placed a wrong total on the answer line.
200 students chose one language to study. Each student chose one language from French or Spanish or German. Of the 200 students, 90 are boys and the rest of the students are girls 70 chose Spanish 60 of the 104 students who chose French are boys 18 girls chose German. Work out how many boys chose Spanish.
Edexcel 1MA1 · November 2022 · Paper 3F · Q28 · 3 marks
3 marks
Examiner report
Only a few candidates were able to gain marks on this question. Those who did were only able to gain one mark for either finding the total mean height 50 × 167.6 (=8380) or the mean height for the 20 men (=3640). The most common mistake was to add both given mean heights (167.6 and 182), halve the sum, then multiply the result by 30. Candidates found it challenging to find the sum of the data when given the mean. Some candidates calculated both totals but then didn’t know what to do with the results. A lot of answers simply wouldn’t have made any sense if the candidates had actually thought about it needing to be a height.
There are 30 women and 20 men at a gym. The mean height of all 50 people is 167.6 cm The mean height of the 20 men is 182 cm Work out the mean height of the 30 women. cm
Edexcel 1MA1 · November 2022 · Paper 3H · Q3 · 3 marks
3 marks
Examiner report
A good discriminator between lower attaining candidates, this question attracted many fully correct solutions. However, there were also many errors made. The most common approach was to use a 2-way table. A frequency tree diagram approach was also seen quite often. These more structured approaches were generally more successful than attempts where candidates tried to work with the figures without a table or diagram. A few candidates who used a two-way table completed it correctly but then transferred the wrong entry to the answer line. Lower attaining candidates often limited themselves to earning one mark for working out the number of girls (choosing one language to study). This question did sometimes seem to attract working written randomly around the working space and without any indication of what it was for. This made it difficult for examiners to track the processes a candidate had followed.
200 students chose one language to study. Each student chose one language from French or Spanish or German. Of the 200 students, 90 are boys and the rest of the students are girls 70 chose Spanish 60 of the 104 students who chose French are boys 18 girls chose German. Work out how many boys chose Spanish.
Edexcel 1MA1 · November 2022 · Paper 3H · Q8 · 3 marks
3 marks
Examiner report
Many candidates found this question to be straightforward and they scored all 3 marks. There were, however, a considerable proportion of candidates who could not be awarded any credit for their answers. Many of these candidates took the mean of all 50 people to be the mean of the women’s mean and men’s mean and wrote down the equation 182+𝑥 = 167.6 thereby assuming there were equal numbers of men and women. Some other candidates tried to work with the difference between 182 and 167.6. This was invariably unsuccessful. Candidates who did gain some but not all of the marks available usually worked out the total of the weights for the 20 men and/or for all 50 people but got no further.
There are 30 women and 20 men at a gym. The mean height of all 50 people is 167.6 cm The mean height of the 20 men is 182 cm Work out the mean height of the 30 women. cm
Edexcel 1MA1 · November 2022 · Paper 3H · Q13 · 2 marks
2 marks
Examiner report
This question was quite well answered and descriptions of the mistakes made when the cumulative frequency graph was drawn were generally clearly described. There were two mistakes to identify, one mark for each. The mark for the missing label on the x-axis was awarded more frequently than the mark related to the error in plotting midpoints rather than upper boundaries. Many statements made by candidates were too vague. For example, “the graph is not labelled properly” and “the points are not plotted correctly” were often seen and could not be accepted. Reference to the x-axis or time axis and midpoints/endpoints was needed.
For 90 calls, cumulative frequencies are: 0 < t ≤ 10: 4; 0 < t ≤ 20: 25; 0 < t ≤ 30: 70; 0 < t ≤ 40: 88; 0 < t ≤ 50: 90. Chen plots these at t = 5, 10, 15, 20 and 25 and omits the horizontal-axis label.
Edexcel 1MA1 · June 2022 · Paper 1F · Q6 · 1 mark
1 mark
Examiner report
Very well answered with few errors. Errors tended to be either giving the number of sunshine hours on Sunday or the sum of the two day’s values.
A pictogram shows 4 sun symbols for Saturday; each sun represents 2 hours of sunshine.
Edexcel 1MA1 · June 2022 · Paper 1F · Q8 · 3 marks
3 marks
Examiner report
In part (a), the modal mark was 2 for a fully correct bar chart. Sometimes just one bar was drawn correctly gaining one mark. Failure to score any marks was more often than not because the student left the whole diagram blank. Part (b) was a little more demanding. Many realised why Rupa was incorrect but could not always express their reasons clearly. The marking was sympathetic and credit was given if explanations implied some understanding. Some confused January’s results with February’s, resulting in contradictory information given in their response. A common misunderstanding was that only whole numbers could be used, or that rainfall could not be measured in part cm. Some students found it difficult to find the half-way point between 15 and 20. Many read from the graph and stated that the amount of rainfall was 17 or 18 cm. This question exposed many mis-conceptions regarding decimal and whole numbers, discrete and continuous data. Some students contradicted the question and asserted that Rupa was correct.
A rainfall bar chart has Jan 12 cm, Feb 17.5 cm, Mar 32 cm and Apr 40 cm; the vertical scale runs in 5 cm intervals. May was 35 cm and June was 20 cm.
Edexcel 1MA1 · June 2022 · Paper 1F · Q21 · 3 marks
3 marks
Examiner report
Those students who understood the concept of a stem and leaf diagram usually scored well, losing marks generally through carelessness by omitting a value or giving an unordered diagram or an incomplete key. Some errors in the key including ‘people’ when the figures were ages. Pictograms and tally charts were quite often seen.
The ages are 19,28,29,33,27,27,37,25,27,37,17,45,47,25,26.
Edexcel 1MA1 · June 2022 · Paper 1H · Q8 · 3 marks
3 marks
Examiner report
It was surprising to see this familiar type of question answered so poorly with many students not knowing how to work out an estimate for the mean. When students did understand what to do it was most common to see two or three marks awarded. Many who scored the first two marks didn't gain the third mark due to arithmetic errors, typically when finding the sum of the five products. Some students did not use the mid-values of the intervals but were still able to gain two marks for using values from within the intervals and dividing the sum of their products by 30. Having found the sum of their products some students made the common error of dividing the total by 5 and gained one mark only for attempting to find correct products. Students should be encouraged to check the reasonableness of their answers; 114 cm is clearly not a sensible answer when the table shows that no day had more than 50 cm of snow. Many students appeared to not understand estimating the mean at all and made no attempt to find fx. Some simply added the frequencies, or the mid-values, and divided the total by 5. A common error was to multiply all the frequencies by 10 before adding them.
The amounts of snow in 30 days are grouped: [0,10):8, [10,20):10, [20,30):7, [30,40):2, [40,50):3.
Edexcel 1MA1 · June 2022 · Paper 1H · Q10 · 6 marks
6 marks
Examiner report
The cumulative frequency table was usually completed correctly with addition errors relatively infrequent. Those who completed the table correctly generally plotted the points and joined them with a curve or with line segments. A common error was for the points (100, 25) and (250, 85) to be plotted at (100, 30) and (250, 90) respectively because students misread the scale on the vertical axis. Lines of best fit were quite common and there were some students who made no attempt to join the points. Graphs drawn with the points plotted at the midpoints of the intervals were awarded one mark if the points were joined but these were seen less often than in previous series. Some graphs were ‘squashed’ into the region from x = 25 to x = 150 because students plotted at the midpoints of the intervals in the cumulative frequency table and these graphs gained no marks. Histograms were often drawn and gained no marks unless 5 or 6 of the points were identified and plotted correctly. In part (c) many students gained the mark for reading a value from the graph at Profit = 125. Part (d) was answered quite well with many students able to find an estimate for the interquartile range. Some marks were lost through reading incorrect values from the graph or from not interpreting the scale correctly. Centres should encourage students to show a clear method on the graph as, without this, answers just outside the required range cannot be awarded any marks. Instead of reading across from cf = 25 and cf = 75 some students read from cf = 30 and cf = 70 and some found 25% of 300 = 75 and 75% of 300 = 225 and read up from these values on the profit axis.
Profit over 100 days is grouped: [0,50):10, [50,100):15, [100,150):25, [150,200):30, [200,250):5, [250,300):15.
Edexcel 1MA1 · June 2022 · Paper 2F · Q3 · 1 mark
1 mark
Examiner report
Over 80% of the cohort was able to give the correct answer. Others often gave a different statistical measure.
The numbers are 3,3,3,3,4,4,5,7,8.
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 · Q13 · 3 marks
3 marks
Examiner report
Completing the two-way table was well done by the students with the vast majority scoring 2 or 3 marks. The main errors were a failure to give the final total as 198. Students should be encouraged to tick off values in the question as they are used. Some students placed one of the initial given values in the wrong box or made arithmetic errors. As with most questions on this paper, student outcomes would be improved by making use of their calculator instead of relying on written methods on calculator papers. It is also important to reinforce the importance of checking answers. In this question, students should be encouraged to check if the total column and row of the two-way table add up and if they do not then they should be encouraged to try again.
198 beds: 59 without mattress; 45 double; 17 single without mattress; 83 king size, of which 67 with mattress.
Edexcel 1MA1 · June 2022 · Paper 2F · Q15 · 4 marks
4 marks
Examiner report
Part (a) was accurately answered by about half the cohort. Several students made an arithmetic error, writing 3 × 0 = 3. This gave an answer of 777 which gained one mark. Where this question was not well answered, common misconceptions were the addition of the frequency column leading to 300 or the addition of the social media accounts column leading to an answer of 10. Both these responses show a lack of understanding of the meaning of the frequency column in the table. Centres should practice using frequency tables in a variety of ways. Students found the second part of this question more challenging. There were some correct answers seen from correct methods but efficient methods were not always seen. Some students wrote out ALL of the data and then found the median from a very long list. A few students used the method of 300 ÷ 2 = 150 to identify the 150th item as the median and then stated 3 as the answer. There were many incorrect methods used for example many students ordered the number of social media accounts and found the median of those i.e. 0, 1, 2, 3, 4 with a median of 2. Others ordered the frequencies and found the median of those i.e. 3, 57, 75, 81, 84 with a median of 75, with a few also achieving a final answer of 3 incorrectly from equating their 75 to the number of social media accounts. Another common incorrect method which sometimes led to a correct answer was the calculation of the mean using 772 ÷ 300 = 2.58 and rounding to 3, this was clearly the wrong method and gained no credit. A small number of students identified the mode instead of the median. Students need to be familiar with all the different types of averages they can be asked to find and be able to distinguish between them, using a variety of tables as well as a list of numbers.
For 300 students, number of accounts/frequency: 0/3, 1/57, 2/84, 3/75, 4/81.
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 2H · Q10 · 5 marks
5 marks
Examiner report
This three-part question challenged students understanding of box plots. Part (a) dealt with the proportionality of box plots and like with many response questions, students often struggled to articulate themselves. To gain the mark in this question students had to explain that the difference between the quartiles represents 50% not just LQ = 4 and UQ = Part (b) required students to draw a box plot. Students performed very well, the vast majority gaining 2 marks. In part (c) a comparison of distributions was required. This is again a familiar question and most students were able to get at least one mark for a correct comparison of either the median or the spread. Most students continue to struggle to gain both marks as they are unable to contextualise these comparisons, misunderstanding what the median and range/IQR actually tell us. Other errors included the word ‘average’ used instead of ‘median’ and values being stated without comparison. Other incorrect answers saw students comparing the quartiles or the highest and lowest values.
Online-store box plot five-number summary: minimum 60, lower quartile 160, median 200, upper quartile 350, maximum 420 (£000s). Shop summary: 30,80,170,260,350.
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 3F · Q14 · 4 marks
4 marks
Examiner report
Part (a) was well answered. A minority gave the answer 7,7 without realising that only one 7 was required highlighting the misconception for how to calculate the median. Part (b) was also well answered. Some lost the mark because, although 9 – 4 was seen, it was evaluated incorrectly. For both parts (a) and (b) some students answered incorrectly, giving values for the mean (6.8) and the mode (8). In part (c) most students attempted an answer. Marks were credited for comparisons using the words median and range (or the acceptable alternatives) but many students did not know that this was the required approach, instead using the words shoe size, feet or distribution. Some simply described the data, listing it or using ‘whereas’ rather than using a comparison word such as larger, smaller.
Boys' shoe sizes: 4,5,6,6,6,7,7,8,8,8,8,9. Girls: median 6, range 3.
Edexcel 1MA1 · June 2022 · Paper 3F · Q26 · 2 marks
2 marks
![Edexcel 1MA1 · June 2022 · Paper 3F · Q26 · 2 marks — Grouped string lengths have frequencies 15,20,50,25,5 for intervals (0,10],(10,20],(20,30],(30,40],(40,50]. Amos's polygon uses midpoints except the last point (50,5), and the frequency axis labels om…](/api/paper-crops/1ma1/2022-06/foundation-paper-3/q26/question-r1-9928f44b.webp)
Examiner report
Most students gained at least one mark, either spotting that the 40 was missing from the frequency scale or that the last point was plotted incorrectly. Clear statements were often given which made the marking more straight forward. Common incorrect statements included that the first and last points should be joined to make a polygon, the graph should start at 0 or that a line of best fit would be better.
Grouped string lengths have frequencies 15,20,50,25,5 for intervals (0,10],(10,20],(20,30],(30,40],(40,50]. Amos's polygon uses midpoints except the last point (50,5), and the frequency axis labels omit 40 between 30 and 50.
Edexcel 1MA1 · June 2022 · Paper 3H · Q5 · 2 marks
2 marks
![Edexcel 1MA1 · June 2022 · Paper 3H · Q5 · 2 marks — Grouped string lengths have frequencies 15,20,50,25,5 for intervals (0,10],(10,20],(20,30],(30,40],(40,50]. Amos's polygon uses midpoints except the last point (50,5), and the frequency axis labels om…](/api/paper-crops/1ma1/2022-06/higher-paper-3/q05/question-r1-0af0caab.webp)
Examiner report
This question was quite well answered and descriptions of the mistakes made when the frequency polygon was drawn were generally clearly described. There were two mistakes to identify and students needed to describe them both to score the full 2 marks. Examiners were surprised that more students gained the mark for stating that the point plotted at (50, 5) should have been plotted at (45, 5) than gained the mark for stating that 40 had been omitted from the scale on the frequency axis. Any statement equivalent to one of these, and which was unambiguously stated, earned a mark. The most commonly seen unacceptable statements included not joining the polygon to (0, 0) and not joining the ends of the polygon.
Grouped string lengths have frequencies 15,20,50,25,5 for intervals (0,10],(10,20],(20,30],(30,40],(40,50]. Amos's polygon uses midpoints except the last point (50,5), and the frequency axis labels omit 40 between 30 and 50.
Edexcel 1MA1 · June 2022 · Paper 3H · Q17 · 5 marks
5 marks
![Edexcel 1MA1 · June 2022 · Paper 3H · Q17 · 5 marks — Year 10 distances/frequencies: (0,1]:90,(1,1.5]:48,(1.5,2]:22,(2,3]:8,(3,5]:12. A Year 11 histogram has density-height ratio for 1–2 miles to 3–5 miles of 5:1.](/api/paper-crops/1ma1/2022-06/higher-paper-3/q17/question-r1-5a99bd0a.webp)
Examiner report
In part (a) of this question, lower attaining students often drew a bar chart and did not recognise the need to find and use frequency densities. Some students used the midpoints of the class intervals erroneously together with the frequencies to get values which they then used to draw a diagram. Having said that, there was a good proportion of students who did successfully calculate frequency densities and use these to draw a histogram. It was interesting to note that a significant number of students drew the first four bars correctly but then made an error drawing the bar representing the interval 3.0 < 𝑑 ≤ 5.0 Part (b) of the question was less well done with only a small proportion of students able to use the ratio of the areas of the two bars concerned to find a correct expression. Examiners did award one mark to a significant number of students who showed that they needed to compare the heights, widths and areas of the two bars concerned.
Year 10 distances/frequencies: (0,1]:90,(1,1.5]:48,(1.5,2]:22,(2,3]:8,(3,5]:12. A Year 11 histogram has density-height ratio for 1–2 miles to 3–5 miles of 5:1.
Edexcel 1MA1 · November 2021 · Paper 1F · Q8 · 1 mark
1 mark
Examiner report
The great majority of students spotted the error in the bar chart. Quantifying their response was not required. Common incorrect responses included: ‘no title on the bar chart’, ‘the x and y axes are not labelled’ and ‘the frequency axis should not go up in 2s’.
A frequency table gives eye colours blue 10, brown 15 and green 4. A bar chart shows bars of heights 10, 16 and 4 respectively.
Edexcel 1MA1 · November 2021 · Paper 1F · Q11 · 6 marks
6 marks
Examiner report
The vast majority of students answered part (a) correctly and thus showed clear understanding of the key. Part (b) was not as well answered, many students were happy to count the complete symbol as 8 but then thought that the smaller squares represented1 video game, giving 19 and 9 for Tuesday and Wednesday respectively. Many students were able to find the 22 or the 10 but not both or gave the answer 6 from 22 -16, the difference between Monday and Tuesday In part (c), there were very many correct solutions. Some reversed their diagrams for Thursday and Friday, some simply shared the 32 video games equally between the two days. Mistakes were also common in the division of (or inability to divide) 32 by 4.
A pictogram records video games sold. One full symbol represents 8 games. Monday has 2 symbols, Tuesday has 2 3/4 symbols and Wednesday has 1 1/4 symbols. Thursday and Friday are blank.
Edexcel 1MA1 · November 2021 · Paper 1H · Q12 · 3 marks
3 marks
Examiner report
This very familiar type of question was not answered as well as might have been expected. Many students did plot the points correctly and joined them with a curve or with line segments and gained both marks. A few students did not join the points and some attempts at a line of best fit were seen. Some graphs were drawn with the points plotted at the midpoints of the intervals and these were awarded one mark if the points were plotted at the correct heights and joined. Some students plotted at the midpoints of the intervals in the cumulative frequency table and this resulted in graphs that were ‘squashed’ into the region from h = 2.5 to 15. These graphs gained no marks. Histograms were often drawn and these gained no marks unless at least 5 or 6 of the points were identified and plotted correctly. In part (b) many students gained one mark for finding the median. Some errors were made when reading from the graph, most often with the scale on the horizontal axis. A surprising number of students used the graph incorrectly or made no attempt to use the graph.
For 40 plant heights, cumulative frequencies at upper boundaries 5,10,15,20,25,30 cm are 4,11,24,34,38,40.
Edexcel 1MA1 · November 2021 · Paper 2F · Q8 · 3 marks
3 marks
Examiner report
A high proportion of students added the correct heights to give 35 and many went on to gain full marks by dividing by five. A few divided by six, so only gained one mark, and there were some arithmetic errors and misreading of the y-axis, causing the accuracy mark to be lost. There were also some students who used both the frequencies and the numbers on x-axis adding a mixture of both or adding all together whilst others incorrectly multiplied the number on the dice by the frequency. All these methods were incorrect and did not score any marks.
Five students each throw a die the same number of times. A vertical line graph shows frequencies 6, 4, 5, 8, 7 and 5 for die scores 1, 2, 3, 4, 5 and 6 respectively.
Edexcel 1MA1 · November 2021 · Paper 2F · Q16 · 5 marks
5 marks
Examiner report
This question required students to interpret a pie chart, firstly to find the number of cars being represented in a sector followed by calculating a probability, with many finding both parts of the question challenging. A range of approaches using either knowledge of the number of degrees in a pie chart or using proportionality could gain credit, with the most successful approach appearing to be to use an appropriate method to find the number of degrees per car or per 10 cars. However, many deducted the number of degrees difference for the two sectors from the number of black cars arriving at the incorrect answer of 125 or dividing by 10 rather than 9 when working with proportionality. Very few identified that the whole pie chart represented 540 cars and used this to work out the number represented by 80 degrees. Students were required to combine knowledge of probability with interpretation of the pie chart in part (b). Whilst many gained a mark for using 50 as the numerator in a fraction, the majority were unable to also give a correct denominator. Common incorrect denominators included 100, presumably using percentage, or 360 from using the total number of degrees in a circle. A small minority of students are still expressing a probability as a ratio rather than a fraction, decimal or percentage. Centres are encouraged to promote the use of fractions for probability in this type of problem.
A pie chart for car colours has a 90° black sector and an 80° white sector. There are 135 black cars. There are 50 grey cars.
Edexcel 1MA1 · November 2021 · Paper 2F · Q18 · 3 marks
3 marks
Examiner report
This problem presented students with a slightly different approach to testing frequency tables and the question was well answered by many. When partial marks were awarded it was often for finding the total length of the planks represented in the table, continuing to subtract from 92 to find that the 2m lengths equated to 26m and then losing the final mark due to either forgetting to divide by 2 or because of arithmetic errors. Common incorrect approaches seen included adding the frequencies and subtracting this from 92, giving an answer of 55 or using a combination of adding both columns of the table. Less commonly seen incorrect approaches included looking for a pattern or sequence from the frequencies provided, usually arriving at 11, or giving an answer of 20 due to assuming that if 10 planks represented the 1 metre lengths then 20 planks must represent the 2 metre lengths.
Ben has planks: 5 of length 3 m, 8 of length 2.5 m, an unknown number of length 2 m, 14 of length 1.5 m and 10 of length 1 m. Their total length is 92 m.
Edexcel 1MA1 · November 2021 · Paper 2H · Q8 · 1 mark
1 mark
Examiner report
The first question requiring a written response and it was pleasing to see a good proportion of students were able to identify the error in the lower bounds. This was expressed in various ways, but the most common type of response related to the starting value should be zero for all intervals.
A grouped table has intervals 0<t<=10,10<t<=20,... with frequencies 5,8,12,15,7,3. Brian's cumulative table keeps these same disjoint interval labels beside totals 5,13,25,40,47,50.
Edexcel 1MA1 · November 2021 · Paper 2H · Q9 · 4 marks
4 marks
Examiner report
Part (a) was not well answered with students showing they either didn’t understand a very standard higher tier topic or that they couldn’t accurately read the scale on an axis. It was the former that was most common, but many didn’t know the difference between range and interquartile range, or simply had no idea. Of those who did know, many were unable to read the upper quartile from the diagram. Part (b) proved a challenge for many. The mark was for understanding the proportional representation of a box plot and that 50% of waiting times will be up to the median. Part (c) was answered better with the most common response relating the median wait time being higher on Monday than Tuesday. Reference to measures of spread were not able to gain credit in part (c), and this was costly for some.
Monday waiting times have five-number summary: min 20, Q1 50, median 120, Q3 188, max 200 minutes. Tuesday: 20,50,100,140,210.
Edexcel 1MA1 · November 2021 · Paper 2H · Q17 · 4 marks
4 marks
Examiner report
This histogram question was pleasing to mark, with a surprising number of students gaining some credit. Many were able to gain the first mark for one (or more) correct frequencies, and of these, a significant number going on to gain three marks for the correct process to find the total and then find 20%. The last mark proved extremely challenging but gaining 3 marks at this level showed good performance for a number of students. It was interesting to see that almost all worked with frequencies rather than areas, which shows a good understanding of histograms and frequency density.
A histogram has score intervals 0-5,5-15,15-25,25-40 with frequency densities 0.8,1.6,2.2,1.2. The top 20% qualify.
Edexcel 1MA1 · November 2021 · Paper 3F · Q9 · 3 marks
3 marks
Examiner report
There were many fully correct answers. Nearly all students gained at least 1 mark for placing the given values in the correct cells of the table. Early errors in calculations meant that these errors continued, and students failed to adjust their errors to match the given numbers. Weaker students gained 1 mark for either the first column or the total row or column.
Vadim has 56 clocks, each red, blue or black. 32 are plastic. Of 14 blue clocks, 5 are plastic. Of 12 red clocks, 8 are not plastic.
Edexcel 1MA1 · November 2021 · Paper 3F · Q20 · 3 marks
3 marks
Examiner report
This question was answered well, though performance was poor compared to previous years. Many lost a mark due to the omission of a number or failed to order the leaves correctly. The key was often missing, or incomplete.
The heights in cm of 15 plants are 15, 20, 25, 33, 17, 22, 25, 18, 22, 19, 32, 35, 24, 28, 19.
Edexcel 1MA1 · November 2021 · Paper 3F · Q21 · 4 marks
4 marks
Examiner report
In part (a) most students identified (100,18) as the outlier. A significant minority incorrectly gave (18,100) as the point. Part (b) was less well answered than in previous years. Those who drew a line of best fit usually gained both marks as they went on to give an answer in the required range. But more often students relied on a guess, placing points near to the given points, or made some attempt to read off from 370. These approaches were far less successful and usually resulted in an answer outside the required range, such as 12 or 15. Part (c) was answered well for a response type question, but students need to be reminded to state “yes” or “no”. Many students gave a reason which recognised the outlier could be ignored when commenting on correlation.
A scatter graph plots traffic volume against carbon-monoxide level for 22 days. Approximate plotted points are (50,2), (60,3.2), (100,4.1), (110,9.1), (120,4.3), (150,9.2), (170,9.9), (200,12), (225,11.2), (240,12), (250,8), (275,11.8), (300,10.8), (300,12), (300,12.8), (320,14), (325,12), (350,10), (400,15), (450,15.6), (500,16.8), and (100,18).
Edexcel 1MA1 · November 2021 · Paper 3H · Q1 · 4 marks
4 marks
Examiner report
Most students found this to be a good start to the paper and scored at least 3 of the 4 marks available. Nearly all students gained some credit for their answers. For part (a), it was unusual to see an incorrect response but where the answer was wrong it was usually because a student had written (18, 100) instead of (100, 18). Part (b) of the question was answered less well but nevertheless the majority of students gained the 2 marks available for giving an answer in the range of values accepted. Where this was not the case students usually scored a mark for either drawing a line of best fit or for drawing a vertical line from 370 on the horizontal axis. In part (c) students could usually make a correct decision, that is “no” and give an acceptable reason. The most common accepted reasons were equivalent to stating that the outlier was an anomaly or that there was positive correlation when the outlier was ignored.
A scatter graph shows carbon monoxide level against traffic volume for 22 days. The approximate plotted points are (50,2), (60,3.2), (100,4.1), (110,9.1), (120,4.3), (150,9.2), (170,9.9), (200,12), (225,11.2), (240,12), (250,8), (275,11.8), (300,10.8), (300,12), (300,12.8), (320,14), (325,12), (350,10), (400,15), (450,15.6), (500,16.8), and (100,18).
Edexcel 1MA1 · November 2020 · Paper 1F · Q7 · 4 marks
4 marks
An incomplete pictogram records eggs sold on Monday, Tuesday and Wednesday. The Monday row already contains 1.5 identical egg symbols. The Tuesday and Wednesday rows and the key are blank. The shop sold 18 eggs on Monday, 24 eggs on Tuesday and 27 eggs on Wednesday.
Edexcel 1MA1 · November 2020 · Paper 1F · Q14 · 3 marks
3 marks
Ishmael asked 30 students at college to tell him the sport they each like the best from cricket or tennis or swimming. 11 of the 20 female students said swimming. 2 of the male students said tennis. 5 students said cricket. The number of male students who said cricket was the same as the number of male students who said swimming. Complete the two-way table. Cricket Tennis Swimming Total Male students Female students Total
Edexcel 1MA1 · November 2020 · Paper 1F · Q16 · 2 marks
2 marks
For 16 students, the frequencies for 0, 1, 2, 3 and 4 points are 1, 3, 5, 4 and 3 respectively.
Edexcel 1MA1 · November 2020 · Paper 1F · Q26 · 3 marks
3 marks
For a group of Year 9 girls, the least height is 150 cm, the median height is 165 cm and the greatest height is 170 cm. The heights of 15 Year 9 boys are shown by this stem-and-leaf data (key: 15|8 means 158 cm): 15|8 9 9; 16|4 5 7 7 8; 17|0 3 4 4 7; 18|0 2.
Edexcel 1MA1 · November 2020 · Paper 1H · Q7 · 3 marks
3 marks
For a group of Year 9 girls, the least height is 150 cm, the median height is 165 cm and the greatest height is 170 cm. The heights of 15 Year 9 boys are shown by this stem-and-leaf data (key: 15|8 means 158 cm): 15|8 9 9; 16|4 5 7 7 8; 17|0 3 4 4 7; 18|0 2.
Edexcel 1MA1 · November 2020 · Paper 1H · Q12 · 6 marks
6 marks
The weekly wages of 80 people are grouped as follows: GBP 200 < w <= 250: 5; 250 < w <= 300: 10; 300 < w <= 350: 20; 350 < w <= 400: 20; 400 < w <= 450: 15; 450 < w <= 500: 10.
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 2F · Q7 · 2 marks
2 marks
Farhad, George and Tom scored 74, 77 and 72 marks respectively. George drew a bar chart whose vertical axis is labelled 0 at the baseline and then 71, 72, ..., 78 at equal intervals. The Farhad and George bars are one grid square wide, but the Tom bar is two grid squares wide.
Edexcel 1MA1 · November 2020 · Paper 2F · Q14 · 3 marks
3 marks
City scored 50 goals, Rovers scored 45 goals and United scored 25 goals.
Edexcel 1MA1 · November 2020 · Paper 2H · Q9 · 2 marks
2 marks
For a data set, the least value is 142, the lower quartile is 154, the median is 162, the interquartile range is 17 and the range is 40. A proposed box plot uses endpoints 142 and 182, lower quartile 154, median 161 and upper quartile 172.
Edexcel 1MA1 · November 2020 · Paper 3F · Q6 · 2 marks
2 marks
A graph gives UK car production (millions) over years 1 to 8: 1.22, 1.27, 1.34, 1.45, 1.50, 1.50, 1.58, 1.70 respectively.
Edexcel 1MA1 · November 2020 · Paper 3F · Q20 · 4 marks
4 marks
Akhtar, Ben and Carl each have some money. Akhtar has GBP 65 Ben has GBP 100 Carl has three GBP 5 notes, one GBP 20 note and some GBP 10 notes. The mean amount of money per person is GBP 80 How many GBP 10 notes does Carl have?
Edexcel 1MA1 · November 2020 · Paper 3H · Q7 · 3 marks
3 marks
There is a total of 45 boys and girls in a choir. The mean age of the 18 boys is 16.2 years. The mean age of the 27 girls is 16.7 years. Calculate the mean age of all 45 boys and girls. ................................................ years
Edexcel 1MA1 · November 2020 · Paper 3H · Q17 · 4 marks
4 marks
A histogram for 80 long jumps has these class intervals and frequency densities: 6.4 <= d < 7.2: 10; 7.2 <= d < 7.6: 50; 7.6 <= d < 8.0: 100; 8.0 <= d < 8.2: 60.
Edexcel 1MA1 · November 2019 · Paper 1F · Q6 · 4 marks
4 marks
Examiner report
This question was generally answered well. Nearly all students could use the representation to write down the number of pictures sold in January in part (a) of the question. In part (b) a similarly high proportion of students could represent the number of pictures sold in April on the diagram. Most students could also score the two marks available in part (c) though a significant proportion of responses contained mistakes in arithmetic, usually in one of the totals for a particular day. These responses normally got one mark for adding the four totals 24, 28, 20 and 12, three of which were correct.
A pictogram uses one complete symbol to represent 8 pictures. January has 3 symbols, February has 3.5 symbols, March has 2.5 symbols, and the April row is blank.
Edexcel 1MA1 · November 2019 · Paper 1F · Q18 · 4 marks
4 marks
Examiner report
Marks gained for responses to this question were usually restricted to one or two marks for either finding the value of x in the pie chart for school A and/or for finding the number of students at school B who had tigers as their favourite animal. It was relatively rare to see a student complete the question successfully. Many students seem to get confused between the angles which represented the proportions of students and the numbers of students themselves.
The pie charts show information about the favourite animal of each student at school A and of each student at school B. School A School B monkeys lions tigers 60 degrees x degrees x degrees monkeys lions tigers 160 degrees 110 degrees There are 480 students at school A. There are 760 students at school B. Henry says, The same number of students at each school have tigers as their favourite animal. Is Henry correct? You must show how you get your answer.
Edexcel 1MA1 · November 2019 · Paper 1F · Q25 · 3 marks
3 marks
Examiner report
Relatively few students took into account that there was more than one red brick and more than one blue brick. Many students’ responses consisted of the calculation (5 + 9 + 6) ÷ 10 or (5 + 9 + 6) ÷ 3. These could not be given any marks. Some students started to find the total weight of the red bricks or of the blue bricks and scored 1 mark for doing this. Only about ten per cent of students gained two or more marks for getting as far as calculating a value which could be used to evaluate the statement that “The mean weight of the 10 bricks is less than 7 kg.” A few students calculated the total weight of the bricks but did not calculate the mean. If they compared this with a stated value of 70 they could gain full marks.
4 red bricks have a mean weight of 5 kg. 5 blue bricks have a mean weight of 9 kg. 1 green brick has a weight of 6 kg. Donna says, The mean weight of the 10 bricks is less than 7 kg. Is Donna correct? You must show how you get your answer.
Edexcel 1MA1 · November 2019 · Paper 1H · Q6 · 3 marks
3 marks
Examiner report
This question was poorly answered with the majority of students simply attempting to find the mean of the weights 5, 9 and 6. Their resulting conclusion did relate to the question asked but no credit was given unless a correct process was applied. A number of students found the mean to be 7.1 kg but then failed to conclude that Donna was incorrect in her assertion, thus only gaining two marks. A number of students worked out the total weights correctly but then added them together with the 6 in the tens column leading to an answer of 125 instead of 71.
4 red bricks have a mean weight of 5 kg. 5 blue bricks have a mean weight of 9 kg. 1 green brick has a weight of 6 kg. Donna says, The mean weight of the 10 bricks is less than 7 kg. Is Donna correct? You must show how you get your answer.
Edexcel 1MA1 · November 2019 · Paper 1H · Q10 · 6 marks
6 marks
Examiner report
This question was poorly answered by this cohort of students. Any marks gained were usually in part (a) for correct plotting of the given values. However, it was common to see the points plotted in parts of the intervals other than at the ends. Often seen were plots at time values of 30, 40, 50, 60 and 70 minutes; this gained no credit and prevented any success in part (c). Many students drew histograms. A lack of understanding of quartiles and interquartile range was evident in part (b), 30 – 10 = 20 was a common error. In part (c), correct readings from time = 50 and 90 were often found but then either just stated or added together gaining no credit. Many students struggled with the scale on the horizontal axis and often misread the required values.
Cumulative frequencies for puzzle-completion time are: up to 40 min: 5; up to 60: 25; up to 80: 35; up to 100: 38; up to 120: 40.
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 2F · Q9 · 6 marks
6 marks
Examiner report
In part (a) the majority of students knew that the median was the middle number even if they tried to find the median without ordering the list. Those who gave the answer as 8.5 (middle of the unordered list) gained one mark. Most students did order the numbers with many then able to give the correct answer. Some attempts at ordering the list omitted one of the numbers, often one of the two 4s. A common error was to identify the two middle numbers as 4 and 6 and give an answer of 4 or 6 or 4, 6 or carry out an incorrect calculation such as 6 – 4 with the two numbers. Some students confused the averages and worked out the mean or the mode. A few found the range. Part (b) was answered very well. Those who did not give the correct probability often gained one mark for a fraction with either the correct numerator or the correct denominator. A few students used incorrect notation for probability such as 2 : 6 and were awarded the method mark only. A common incorrect answer was 1/2. There were relatively few students who gave a likelihood rather than a probability as the answer. In part (c) many students were able to use the information about the mode to identify one of the hidden numbers as 3 and gain the first mark. They then often went on to give the correct answer. Some students showed 3 + 3 + 8 + 5 + 6 = 25 and 25 ÷ 5 = 5 in the working space but then gave 3, 5 as the answer and gained one mark only. It was common to see 3 on the answer line with a number other than 6 and no working out shown. Some students gained the first mark for working with the mean but did not use the mode to complete the solution.
Here is a list of six numbers: 6, 4, 8, 9, 4, 3. Aisha picks at random one of these numbers. Clara has five cards showing 3, ?, 8, 5, ?. The mode of Clara's five numbers is 3 and their mean is 5.
Edexcel 1MA1 · November 2019 · Paper 2F · Q21 · 2 marks
2 marks
Examiner report
It was pleasing that many students were able to identify at least one of the things wrong with the frequency polygon. Often this was the missing frequency label on the vertical axis or the fact that the first point has been plotted incorrectly but some students identified the line joining the first and last points. Statements were often too general or incomplete. A statement such as ‘the points have been joined up wrong’ does not identify what is wrong in the way the points have been joined up. Similarly ‘the points have not all been plotted correctly’ is not sufficient as it does not specify that it is the first point that has been plotted incorrectly. A common incorrect answer was that the scale on the horizontal axis should start at 0, not at 10. Some students suggested that the points should not be joined at all or that the points should have been joined with a curve. A number of students incorrectly referred to lines of best fit.
A grouped table for 50 potatoes gives frequencies 6, 21, 13, 7, 3 for the intervals 10 < w <= 20, 20 < w <= 30, 30 < w <= 40, 40 < w <= 50, 50 < w <= 60. A frequency polygon has no frequency label on the vertical axis; it plots (15,8), (25,21), (35,13), (45,7), (55,3), and joins the last point back to the first.
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 2H · Q1 · 2 marks
2 marks
Examiner report
This was generally well answered, with many gaining the two marks. Marks were usually lost for statements that were vague or ambiguous like “points incorrectly plotted” or “should not join all the dots up”. There were a few who thought that they should not have used midpoints for plotting.
A grouped table for 50 potatoes gives frequencies 6, 21, 13, 7, 3 for 10 < w <= 20, 20 < w <= 30, 30 < w <= 40, 40 < w <= 50, 50 < w <= 60. A frequency polygon has no frequency label; it plots (15,8), (25,21), (35,13), (45,7), (55,3), and joins last to first.
Edexcel 1MA1 · November 2019 · Paper 2H · Q4 · 3 marks
3 marks
Examiner report
This question was well answered. Those who lost marks in part (i) usually made an error in the calculation, or just failed to perform the correct calculation. In part (ii) there were many good answers which made reference to “representative”, “proportional”, or the “same ratio”. The most common error was to explain the working in part (i), stating “others may not want that as a gift” or made reference to things that were of no relevance to the question.
Stan samples 50 fitness-club members about free gifts: sports bag 17, gym towel 7, headphones 11, voucher 15. The club has 700 members.
Edexcel 1MA1 · November 2019 · Paper 2H · Q11 · 3 marks
3 marks
Examiner report
Students need to be made aware that just using the term “average” within the context of statistics is not enough; throughout correct statistical terms were needed such as “median” or “IQR”. Equally if figures were used, they had to be correct. In part (a) those that recognised “half of” was associated with the median generally got the mark. Many responses quoted incorrect values or identified the incorrect parts of the box plot and a common misconception was that the box plot represented frequencies, so they would identify a "total" for the number of potatoes and then use it to try and find where the middle value was. In part (b) a number of students did not understand what was being asked for or had not realised they needed to compare the median and (interquartile) range. Common was listing the values of each without a comparison or making an arithmetic error in calculation. Students often selected the wrong vocabulary, using mean instead of median and distribution or spread instead of the range. The IQR and range were often transposed. Students need to be reminded that they need to put their responses like this in context.
Box plots show Megan's potato weights (median 57 g, range 49 g, IQR 26 g) and Amy's (median 42 g, range 47 g, IQR 16 g). Megan says half her potatoes weigh less than 50 g.
Edexcel 1MA1 · November 2019 · Paper 2H · Q18 · 3 marks
3 marks
Examiner report
Only a few gained marks on this question. Some were able to find at least one frequency but then failed to proceed. In general, those who got to 32 were able to draw the bar at 3.2 Incorrect answers came from just adding the heights of the bars or misreading the scales when drawing the bar.
An incomplete height histogram has bars: 0-2.5 m density 1.2; 2.5-5 m density 2; 5-10 m density 2.8; 12.5-25 m density 0.8. Also 20% of trees are 10-12.5 m and none exceed 25 m.
Edexcel 1MA1 · November 2019 · Paper 3F · Q9 · 6 marks
6 marks
Examiner report
Part (a) required students to tally data and complete a frequency column. This was generally answered very well. However, there were a number of students who completed frequencies in the tally column and then wrote probabilities (out of 18) in the frequency column and thus lost a mark. A small number of students wrote cumulative frequencies in the frequency column but often showed correct frequencies in the tally column. Part (b) required students to draw a bar chart to represent this data, and again this was completed well, although the most common mark was two out of three marks. This was because most students made a mistake in some way. The most common of these mistakes was to miss the frequency label from the vertical axis or to have a non-linear vertical scale. Part (c) was for recognising the most popular pet. The only students who dropped this mark were ones who left the response blank.
Pet responses from 18 children are: dog,rabbit,cat,dog,dog,hamster; cat,dog,rabbit,hamster,cat,cat; dog,dog,cat,dog,rabbit,dog.
Edexcel 1MA1 · November 2019 · Paper 3F · Q13 · 2 marks
2 marks
Examiner report
A very well answered question. A large number of students were able to extract the correct two values from the stem and leaf diagram and find the difference for two marks. It was not uncommon for students to write the answer as a range of values, such as 31 – 74, rather than subtract, and in this case one mark was awarded. Of those who were not awarded the marks, it was often due to finding the median and on occasion, some found the mean.
A stem-and-leaf diagram contains ages 31,34,35; 40,42,42,45,46; 50,51,57,57,58,59; 63,64,65,69; 70,74.
Edexcel 1MA1 · November 2019 · Paper 3F · Q24 · 2 marks
2 marks
Examiner report
Another familiar style of question and again answered well. Most students gained two marks for a correct answer in range. Of those who didn’t it was surprising to see many failing to draw in a line of best fit, which students should be encouraged to do. Some students were able to gain a mark for taking a reading from x = 34
The scatter graph has Science test mark on the horizontal axis and Maths test mark on the vertical axis, both from 0 to 60. Its plotted points (Science, Maths) are (8,21), (14,21), (23,24), (25,28), (27,38), (28,36), (37,43), (39,47), (42,42), (45,48), (50,53), (54,55). Jamie got a mark of 34 in the Science test.
Edexcel 1MA1 · November 2019 · Paper 3F · Q25 · 3 marks
3 marks
Examiner report
Finding an estimated mean is another question that students should be well prepared for. It was common for students to fail to gain the second method mark as they divided by 4 rather than 18. The final mark was then only gained by those students who had correctly used the midpoint values and had a complete correct method.
Race times for 18 students: 5<t<=10 frequency1; 10<t<=15 frequency2; 15<t<=20 frequency7; 20<t<=25 frequency8.
Edexcel 1MA1 · November 2019 · Paper 3H · Q3 · 2 marks
2 marks
The scatter graph has Science test mark on the horizontal axis and Maths test mark on the vertical axis, both from 0 to 60. Its plotted points (Science, Maths) are (8,21), (14,21), (23,24), (25,28), (27,38), (28,36), (37,43), (39,47), (42,42), (45,48), (50,53), (54,55). Jamie got a mark of 34 in the Science test.
Edexcel 1MA1 · November 2019 · Paper 3H · Q4 · 3 marks
3 marks
Race times: 5<t<=10 frequency1; 10<t<=15 frequency2; 15<t<=20 frequency7; 20<t<=25 frequency8.
Edexcel 1MA1 · November 2019 · Paper 3H · Q12 · 3 marks
3 marks
Sunflower heights (cm): 173,174,179,186,188,188,190,190,191,194,196,197,198,201,204,207,207,209,209,214,218,218,219.
Edexcel 1MA1 · June 2019 · Paper 1F · Q7 · 3 marks
3 marks
Examiner report
Part (a) was well answered with many students gaining two marks. Common errors for those who only gained one mark included arithmetic errors or misreading the height of the yellow flowers. Part (b) was not as well answered as part (a) but many correct responses were seen. The most common incorrect response was 10 instead of white.
A flower chart shows red 8, white 10, yellow 5; flowers are only red,white,yellow,blue and total 30.
Edexcel 1MA1 · June 2019 · Paper 1F · Q21 · 4 marks
4 marks
Examiner report
Many students were able to gain some marks on this question. With many able to gain at least one mark either for finding a total of 18 boys or the number of girls who got the bus. However, those who wrote down a mass of figures with no indication what these represented rarely scored any marks unless the final answer was correct; it is imperative the students do show clearly their route through a problem like this. The most successful approach was to use a two-way table or a frequency tree, but others were also able to gain full marks. It was common for students not to have a logical approach and to see numbers spread across the page without any indication of what the numbers represented. Students should realise that writing words or descriptions would help their own reasoning and also enable them to be awarded method marks, as the method is clearly indicated. Although there were different paths through the problem, a popular method was to find the number of boys that walked and add it to the number of girls that walked. Those who used a two-way table or a frequency diagram got this correct more often than those that just tried working logically through the problem. A common mistake with a frequency diagram was to miss off the girls that cycle or boys that walk and only place the figures already given in the diagram whereas with a two-way table it was more obvious which ‘gaps’ had to be filled. If a diagrammatic approach is to be used it is worth reminding students to draw the diagrams big enough to fill in, some frequency trees were very difficult to read. A different approach was to try to find the total that didn't walk and subtract from the overall total, this was not so accurately done as the girls that cycled were often missed. A common misconception seen was to just add all the numbers given and subtract from the total.
40 students walk,cycle,bus. 22 girls; 9 girls walk; 7 boys cycle; of 10 bus users 6 are boys.
Edexcel 1MA1 · June 2019 · Paper 1H · Q11 · 4 marks
4 marks
Examiner report
Part (a) was attempted well by the majority of students, with many finding all three values accurately. The lower quartile and/or the upper quartile being incorrect was the main cause of lost marks. Students appeared to be more successful in providing accurate values when they made use of the data given in the question, usually by crossing out in a systematic way. Responses to part (b) were mixed. Students who were not awarded the mark either selected the wrong statistical values to compare, often the greatest and least values but sometimes the values of one or both pairs of quartiles, or stated the median values but failed to provide a comparison between them. Occasionally an incorrect decision, often with a valid comparison was made. Similarly, responses to part (c) were often incomplete due to students not providing a comparison of the ranges or interquartile ranges of each coach. Some arithmetic errors when calculating the interquartile ranges were also seen at times. Values did not need to be given as part of a reason but any values quoted had to be correct or follow through correctly from the table in part (a). Students should be encouraged to avoid ambiguous statements using words such as "whereas" and “but” when attempting to compare statistical values. A simple comparison that one value is higher or lower than the other is sufficient. The best responses were concise.
Coach A ages are 41,42,44,48,52,53,53,53,56,57,57,59,60,61,63,64,64,66,67,69,74,77,79. Coach B: median 70, LQ 54, UQ 73, least 42, greatest 85.
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 · 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 2H · Q3 · 3 marks
3 marks
Examiner report
In part (i) almost all students correctly interpreted the table and scored both marks. When errors occurred it was usually down to premature rounding. There were a number of questions where this caused an issue and centres must reiterate the importance of not rounding until the end of a problem. A typical error seen every year is to write 1/3 as 0.3 and then proceed with an inaccurate calculation. A small number of students worked out 195/30 as 6.5 but then rounded this to 7 before working out 7 × 10. Explain questions continue to challenge students, but part (ii) was answered quite well. Many students understood the important point about the sample being representative of the population and were able to gain the mark.
From 195 students, Hannah samples 30: Theme Park 10, Theatre 5, Sports Centre 8, Seaside 7.
Edexcel 1MA1 · June 2019 · Paper 2H · Q11 · 6 marks
6 marks
Examiner report
Cumulative frequency is generally a well answered question. Most students this summer were able to gain the mark in part (a) for correctly completing the table, Of those who gained the mark in (a) almost all gained at least one mark in (b). Those who did drop a mark usually plotted at mid-interval values rather than the end of interval values. This was catered for in the special case on the mark scheme. The success rate in (c) often depended on the success of (b), but not exclusively. Those who had the correct graph, almost always gained at least one mark for taking a correct reading from their cumulative frequency graph. Of these, a good proportion then dealt with this value correctly to find the correct percentage. There were a number of students who didn’t use the graph to answer (c) and reverted to their table in (a). This method is not on the specification, but will have been seen by students studying GCSE Statistics, and so was catered for in the mark scheme, as the table would lead to the value of 74 and subsequently 6.
For 80 workers, grouped journey times (minutes) have frequencies: 0<t≤20:5; 20<t≤40:30; 40<t≤60:20; 60<t≤80:15; 80<t≤100:8; 100<t≤120:2.
Edexcel 1MA1 · June 2019 · Paper 3F · Q7 · 2 marks
2 marks
Examiner report
A frequent incorrect answer was 10, where the students had only dealt with the circles, perhaps from not reading the question carefully. Many gained full marks, but it was not uncommon for one mark to be given for showing 33 or 27 from the first stage of subtracting two numbers logically from the table. There was much evidence of unnecessary errors, such as 33 – 27 = 7 or 26 + 7 = 34.
A bag contains 16 red circles, 26 green circles, 11 red squares and 7 green squares. There are more green counters than red counters.
Edexcel 1MA1 · June 2019 · Paper 3F · Q18 · 3 marks
3 marks
Examiner report
In part (a) only about half the students gave the correct answer, with 5 being the most common incorrect answer, or 7 from using the frequencies rather than the number of points. In part (b) students appeared well prepared with most showing their calculations. The main error was to calculate 0 × 4 as 4. Those who did not understand the concept of calculating the total number of points often added either column of numbers and gave 15 or 30 as their answer. A minority wrote out all the 30 figures but usually made an arithmetic error in adding them.
Thirty students scored points in a quiz: score 0 had frequency 4; score 1, frequency 3; score 2, frequency 7; score 3, frequency 5; score 4, frequency 6; score 5, frequency 5.
Edexcel 1MA1 · June 2019 · Paper 3F · Q26 · 3 marks
3 marks
Examiner report
Part (a) was not answered well, with very few able to state the correct class interval. Most common answers were to give the group above the one required. Part (b) was another question without any distractors which was done poorly. The most common error was to misread the scales, or not join the points. Some drew a line of best fit, but this was ignored.
The heights h cm of 80 plants are grouped: 10 < h <= 20: 7; 20 < h <= 30: 13; 30 < h <= 40: 14; 40 < h <= 50: 12; 50 < h <= 60: 16; 60 < h <= 70: 18.
Edexcel 1MA1 · June 2019 · Paper 3F · Q27 · 2 marks
2 marks
Examiner report
In general, the statements made were not specific enough to be awarded marks. Stating “the scale is wrong” is insufficient; students need to refer to the axis and what is wrong with the scale. It was clear from the responses that many students did not know what a time series graph should look like and interpreted it as an attempt at a scatter graph, or a line graph. Many incorrectly thought the vertical axis should have integer values. Marks were most commonly awarded for students who stated that the points should have been joined using straight lines, or that the horizontal axis was confusing or misleading in some way (some making references to missing labels, but rarely the absent 1).
A time-series graph shows visitor numbers, in thousands. The vertical-axis labels are 6, 6.5, 7, 7.5, 8, 8.5, 9 and 10. Under each year, the horizontal-axis labels are 2, 3 and 4. The plotted points are 2016 quarter 3 at 10.2 and quarter 4 at 8.0; 2017 quarters 2, 3 and 4 at 8.4, 9.8 and 7.0; and 2018 quarters 2, 3 and 4 at 8.0, 8.8 and 7.0. Successive points are joined by a smooth curved line.
Edexcel 1MA1 · June 2019 · Paper 3H · Q3 · 3 marks
3 marks
Examiner report
A majority of students scored full marks on this question. The most common error seen in part (a) was to give 30 ˂ h ≤ 40 as the class in which the median lies. Common errors in drawing the frequency polygon included plotting points at the upper or lower boundary of each interval instead of the midpoint and joining the points with a curve, not straight lines. Points were generally carefully plotted at the correct heights.
The table shows information about the heights of 80 plants. Height (h cm) Frequency 10 h 20 7 20 h 30 13 30 h 40 14 40 h 50 12 50 h 60 16 60 h 70 18
Edexcel 1MA1 · June 2019 · Paper 3H · Q4 · 2 marks
2 marks
Examiner report
This question was quite well answered and descriptions of the things wrong with the time series graph were generally well described. There were a variety of possible acceptable answers but students needed to state them clearly and unambiguously. For example, “the axis does not start at 0” would not be worthy of any credit but “the y axis does not start at 0” would score a mark. Similarly, “the scale on the x axis” would not be enough but “it is not clear what the 2, 3, 4 on the x axis means” would get a mark. A number of students stated there should be a line of best fit drawn. This was not an acceptable response.
A time-series graph shows visitor numbers, in thousands. The vertical-axis labels are 6, 6.5, 7, 7.5, 8, 8.5, 9 and 10. Under each year, the horizontal-axis labels are 2, 3 and 4. The plotted points are 2016 quarter 3 at 10.2 and quarter 4 at 8.0; 2017 quarters 2, 3 and 4 at 8.4, 9.8 and 7.0; and 2018 quarters 2, 3 and 4 at 8.0, 8.8 and 7.0. Successive points are joined by a smooth curved line.
Edexcel 1MA1 · June 2019 · Paper 3H · Q21 · 4 marks
4 marks
Examiner report
Though a significant number of students did not attempt this question, a good proportion of those students who did attempt it scored full marks for a complete and correct solution. The most common errors made by those students who followed a correct method, that of finding the total number of onions weighing less than 60g or more than 120g, usually involved obtaining an incorrect frequency for the number of onions weighing between 120g and 135g or for the number of onions weighing between 135g and 180g, or both. This usually arose because of using an incorrect class interval . Students who used the strategy of finding that there were 420 onions weighing between 60g and 120g were generally more successful. Some students opted to work with percentages, either giving their final answer as a percentage, or rounding a recurring decimal to 1decimal place and hence introducing a rounding error. In these cases the final accuracy mark was usually lost. There were a significant number of students who used the heights of the bars to represent frequencies. This approach could not be awarded any credit.
A histogram has classes and frequency densities: 0 <= w < 60: 2; 60 <= w < 90: 5; 90 <= w < 120: 9; 120 <= w < 135: 6; 135 <= w < 180: 2. Onions below 60 g are pickled, onions above 120 g are sold, and the rest go to a food-processing factory. A pie chart represents these groups.
Edexcel 1MA1 · November 2018 · Paper 1F · Q7 · 3 marks
3 marks
Examiner report
A large proportion of students successfully completed the pictogram. Those students who did not obtain full marks had often made errors in their arithmetic or did not get all three of the frequencies for apple trees, cherry trees and pear trees correct. The final representation for the number of plum trees appeared in several different acceptable forms.
An orchard contains only apple, cherry, pear and plum trees. A pictogram uses one full symbol to represent 4 trees. The Apple row contains 3 full symbols, the Cherry row contains 1 full symbol and 1/4 symbol, and the Pear row contains 1 full symbol and 1/2 symbol. There are 30 trees in total.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 1H · Q9 · 6 marks
6 marks
Examiner report
In part (a), the most common error from those students who understood anything about cumulative frequency graphs was to consider 4 , 2 and 4 of 50 instead of 48 resulting in an inaccurate box; the whiskers were usually correct gaining one mark. Many responses were seen where the whiskers were correct, but no box was drawn. In part (b), far too many students simply compared specific values. Students need to know that, at this level, comparisons must be made of spread and central tendencies within the context of the question. Students found it difficult to interpret the data often confusing it with the number of trains delayed as opposed to delay time in minutes. Referring to delay time was necessary to put their comparisons into context. Answers to part (c) clearly showed that very few students fully understand the dynamics of cumulative frequency diagrams. Rarely was any reference made to the parts of the diagram between 17 and 25 and 30 and 33. This is an area where centres could concentrate on when delivering this topic.
The delays of 48 trains were recorded on Monday and Tuesday.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 2F · Q21 · 2 marks
2 marks
Examiner report
It was encouraging that most students identified the incorrect line of best fit or the problem with the scale on the height axis and many students identified both things wrong with Sean’s answer. Some students wrote down two statements about the line of best fit and scored only one mark. A number of answers were given that received no credit. These included explanations that the scales should started at 0; that the axes are the wrong way round; that there is no x or y; and that there is no title. Some students stated that the height axis should start from 170, not from 140. Although this might give a better scatter graph it is not an error with the graph provided.
A scatter graph has height in centimetres on the horizontal axis and weight in kilograms on the vertical axis. The horizontal-axis labels shown at equal visual intervals are 140, 160, 170, 180, 190 and 200. The vertical-axis labels are 85, 90, 95, 100 and 105. The plotted data points are approximately (175, 89), (179, 88), (179, 93), (183, 96), (184, 93), (185, 99), (186, 100), (190, 102), (191, 103) and (192, 100). A straight candidate line runs from approximately (140, 85) to (200, 105).
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 2H · Q2 · 2 marks
2 marks
Examiner report
Most students recognised that the line of best fit was in the wrong place. Those who gave two references to the line of best fit limited themselves to a maximum of 1 mark. A minority of students identified a problem with the horizontal scale. Others tried to find fault with where the graph started.
A scatter graph has height in centimetres on the horizontal axis and weight in kilograms on the vertical axis. The horizontal-axis labels shown at equal visual intervals are 140, 160, 170, 180, 190 and 200. The vertical-axis labels are 85, 90, 95, 100 and 105. The plotted data points are approximately (175, 89), (179, 88), (179, 93), (183, 96), (184, 93), (185, 99), (186, 100), (190, 102), (191, 103) and (192, 100). A straight candidate line runs from approximately (140, 85) to (200, 105).
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 3F · Q12 · 3 marks
3 marks
Examiner report
It is really pleasing to see how many Foundation Tier students are able to access pie charts. A great number were able to score three marks for a complete correct chart. Those who failed to gain full marks generally lost marks by inaccurate drawing of angles, and came after students had shown their understanding of proportion and were able to correctly calculate the sizes of the three angles. Some students used a method of trying to find percentages for each category, but this was unable to gain credit until they then found percentages of 360°, which most using this method unfortunately didn’t.
Joan asked each of 60 people to name their favourite vegetable. Here are her results. Vegetable Frequency Peas 24 Carrots 16 Mushrooms 20 Draw an accurate pie chart for her results.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 3F · Q23 · 6 marks
6 marks
Examiner report
This question was generally poorly done. Few understood how to find a percentage from the chart. Typically, students tried to build up a percentage to match their reading from the chart, but with very limited success. In part (b) many were able to gain one mark for extracting the correct frequencies from the graph (although the scale caused further issues for some), but couldn’t then progress further. Of those who knew to calculate fx many struggled to extract the correct midpoints, and as a result were unable to get to the final solution.
A grouped bar chart gives these frequencies: 0-4: 11, 5-9: 8, 10-14: 13, 15-19: 6, 20-24: 2.
Pearson does not publish a direct link to this question paper.
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.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 3H · Q7 · 2 marks
2 marks
Examiner report
Students should always check the plotting of their values carefully as marks were frequently lost due to plotting errors. The usual errors seen on the question were points not plotted at mid-values, first point joined to last point to form a closed polygon, points plotted and not joined at all or points plotted and joined with a curve rather than line segments.
Speeds are grouped as 0 < s <= 10: 14; 10 < s <= 20: 18; 20 < s <= 30: 26; 30 < s <= 40: 12.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2018 · Paper 3H · Q17 · 5 marks
5 marks
Examiner report
Many students were able to score on this question. Many tried to draw the correct histogram but plotting errors were often seen. Common errors include drawing the last bar at the correct height but to 250 or drawing verticals for bars at 25 instead of 20 or at 75 and 85 instead of 80. A significant number of students did not understand the need for a histogram and drew a bar chart. Part (b) was not well answered. Some students did manage to identify the interval containing the median but few attempted to estimate within the interval.
Distances are grouped: 0 < d <= 20: 120; 20 < d <= 50: 90; 50 < d <= 80: 120; 80 < d <= 150: 140; 150 < d <= 200: 100.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 1F · Q12 · 7 marks
7 marks
Examiner report
In part (a), most students gained the credit for an answer of 100 although a range of 95 to 100 was acceptable. In part (b), many students simply used the upper values of 260, 340 and 440 thinking these gave the number of laptops sold in each year, and often incorrectly read the scale. Misinterpretation of the split bars on the bar chart was common. Many failed to gain both method marks by not showing their working. In order to credit work done using incorrect readings it was necessary know which part of the diagram they referred to; this wasn’t always clear. In part (c), the great majority of students correctly identified ‘tablets’ as having the greatest increase in sales over the 3 years, but many failed to give a satisfactory reason. The aim of this part was for students to simply say something along the lines of, ‘tablets had the least sales in 2015 and the greatest sales in 2017’ evidenced by the size of the blocks. However, many got caught up in trying to quantify the increase and failed due to incorrect values quoted. Many discussed social reasons rather than using the graph. In part (d), very many students seemed to agree with Alex’s assertion, although many did realise that there was insufficient information in the question to be able to make such a judgement.
A composite bar chart gives sales of desktop computers, laptops and tablets. In 2015 the numbers were 100 desktops, 160 laptops and 60 tablets. In 2016 they were 120 desktops, 220 laptops and 160 tablets. In 2017 they were 160 desktops, 280 laptops and 340 tablets.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 1H · Q10 · 5 marks
5 marks
Examiner report
Part (a) was a straightforward question for the vast majority of students who knew how to draw a box plot. Some students lost one mark for an error in plotting one of the five values. In part (b), fewer students than might have been expected realised that 3/4 of the girls have a height between 133 cm and 157 cm. Those who did were almost always able to work out 3/4 of 80 and score 2 marks. A few students just wrote 75% or 3/4 which did not gain any credit. A surprising number of students did not connect the stated values with their positions within the data set so were unable to recognise that they needed to work with 3/4 of the 80 girls. Common incorrect methods included 157 – 133 = 24, 4/5 × 80 = 64 and 24/37 × 80.
For 80 girls: min 133, lower quartile 145, median 151, upper quartile 157, max 170 cm.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 2F · Q12 · 3 marks
3 marks
Examiner report
Most students attempted the question in some way. A significant number realised that the total was 36 and so multiplied each value in the ‘number of fans’ column by 10. Many were then able to transfer the information to the pie chart with the angles drawn to the required accuracy; there were almost no examples of a student with correct calculations not attempting the pie chart. Most students who were able to calculate the angles correctly were then able to accurately construct at least one angle. Although some evidence was seen that students did then not know how to use a protractor to complete the pie chart, sometimes measuring 70o instead of 110 o or 100 o instead of 80. It was also evident that not all students used their ruler to draw the sectors. Most of the students who drew a correct pie chart also labelled it correctly.
Snack frequencies are burgers 11, pies 17 and hot dogs 8.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 2F · Q16 · 3 marks
3 marks
Examiner report
On the whole, a very well answered question with many students achieving full marks. The number 5 was usually seen in the table with limited working. Occasionally 5 was a rounded answer from incorrect working and so could not gain the marks. A common misconception was to add all the buttons and divide by the sum of the frequency or to look for a sequence of numbers in the frequency column. Unfortunately, some students reached an answer of 95 but then did not divide by 19; these students scored only 1 mark.
Bags contain 19, 20, 21 or 22 buttons. Frequencies for 20, 21 and 22 are 7, 3 and 1. Total buttons: 320.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 2H · Q17 · 4 marks
4 marks
Examiner report
It was pleasing to see a significant number of students gaining both marks in part (a) for correctly completing the frequency table. Completing histograms from tables, or tables from histograms is an area where improvements are being seen. Part (b) was a challenge to many of students. Although most students attempted the question and it was rarely left blank, many students found the mean of the midpoints or found the median of the frequencies. Some students were able to gain a single mark for using ାଵ ସ . Of those who did this, only some went to obtain the correct value, usually by using areas of the bars. It was common to see students using time rather than people to find the LQ (ie 50/4).
A histogram summarises puzzle times. The class intervals and frequency densities are 0-5: 0.8; 5-15: 0.4; 15-25: 0.6; 25-30: 1.0; 30-50: 0.2.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 3F · Q14 · 5 marks
5 marks
Examiner report
The majority of students knew what a stem and leaf diagram was in part (a) and most of those who had done an earlier unordered version completed their ordered diagram successfully to gain 2 marks. There were cases of an omitted number in the leaves; a simple check that there were 20 pieces of data would have been beneficial for these students. A key was not always present, but when offered was usually correct. In part (b) many students were able to identify 6/20 (or equivalent) from their data, though some students miscounted the number of students failing, with 7 seen quite often. Others that lost marks were comparing those that had passed instead of those that have failed. One mark was achieved by either identifying the correct number of fails (6) or by knowing a quarter of 20 was 5. Some students worked on the misconception that 71 was the percentage who passed rather than the value of the pass mark. Also, a lot of students commented on the denominator being 4, when there were 20 pieces of data, therefore not understanding the probability. It was common for students to make observations which did not make for a comparison. Many responses were not specific enough making vague statements about more or less than a quarter passed without evidence.
The marks are 76, 82, 84, 69, 80, 64, 70, 81, 75, 91, 87, 67, 80, 70, 94, 76, 81, 69, 71 and 77. The pass mark is 71. Omar claims that the probability a randomly chosen student failed is 1/4.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 3F · Q15 · 2 marks
2 marks
Examiner report
About half of all students gave a correct response in part (a), this rose to around three quarters of all students in part (b). In part (a) many indicated that multiplication should be done first; but stating BODMAS or BIDMAS alone was insufficient. A common error for some students was to indicate multiplication first then −12 which then made the calculation incorrect. Those who merely gave the correct solution did not gain the mark unless they showed the correct order of operations used. In part (b) the mark was gained by either stating that the largest and smallest numbers were needed or commenting on putting the numbers in order. Saying it should be 8 – 1 = 7, or commenting that 5 and 3 were not the highest and lowest numbers were all frequently seen The explanation of why 5 – 3 was wrong seemed to be more accessible that asking for the range of a list of numbers. A few students tried to find the median or mean but the main mistake involved contradictions such as 7 – 1 = 6
Jenny evaluates 12 - 2 x 4 as (12 - 2) x 4. Rehan finds the range of 3, 1, 8, 7, 5 as 5 - 3.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 3F · Q19 · 3 marks
3 marks
Examiner report
In part (a) most students gave the correct answer “negative”. Students who used other descriptions for example descending, decreasing, falling and going down gained no mark. Only a very few students tried to describe the relationship. Some students also tried to describe the negative correlation with adjectives such as weak/strong, which was quite acceptable as long as they were not contradictory. In part (b) many students attempted to provide an explanation by making an observation without sufficient detail. Many considered the point only in terms of other students (for example her age) or observed that Kristina had the fastest time. Few considered the point in terms of its distance from the line of best fit, the way the other points correlated or how it matched the rest of the points. Use of the word “anomaly” was not enough. There were a lot of statements similar to "she was the fastest" but to be identified as an outlier it needed further expansion such as "she was much faster than all the other girls.” In part (c) few students recognised that this question was asking them about the known data range. Many agreed with Debbie using the correlation of the known data points to extrapolate for a 15 year old but failed to demonstrate the understanding of the limitations of using that correlation outside of the data range. Some students approached the question from a health or fitness point of view rather than a statistical one and commented on a girl’s running ability or general health, or provided statement such as “the older the girl, the quicker she should run”, none of which addressed the issue of lack of data at the extremity of the diagram.
A scatter diagram plots (age in years, best 100 m time in seconds) at approximately (9.8,16.5), (10.4,15.8), (11.1,16.1), (11.1,14.6), (11.8,15.2), (11.8,13.9), (12.2,14.4), (12.5,13.5), (13.0,13.3), (13.4,12.6), (13.6,14.0) and (13.8,12.8). Kristina is 11 years old and runs 100 m in 12 seconds. Debbie is 15 years old and says the diagram shows she should take less than 12 seconds.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · June 2018 · Paper 3H · Q1 · 3 marks
3 marks
Examiner report
Part (a) of this question requiring students to write down the type of correlation was very well done with few students attempting to describe the relationship between the two variables. Many students also commented on the strength of the correlation. Students who were unfamiliar with the term “negative correlation” and used words such as “decreasing” or “descending” or used expressions involving proportionality were unable to access this mark. The second and third parts of the question were answered well by a good proportion of students. In part (b) examiners could give credit where students explained that the point would be an outlier because it would lie a significant distance away from other points representing data for 11 year olds. It was not good enough to say that Kristina was faster than other 11 year olds but examiners did accept an answer stating she was much faster than other 11year olds. Statements suggesting that the point would not fit in with the correlation shown or with the pattern of the data or with the line of best fit were also awarded the mark. A common error made was for students to miss the point of the question and state a time that Kristina should take to complete the 100m, for example, “she should run 100m in 15.6 s”. In part (c) students were expected to comment that extrapolation of data, which is unreliable, would be involved if the scatter diagram was used to predict the time taken for a 15 year old to run 100 metres. Many students did not appreciate this and assumed that they could use a line of best fit to predict the time.
A scatter diagram plots (age in years, best 100 m time in seconds) at approximately (9.8,16.5), (10.4,15.8), (11.1,16.1), (11.1,14.6), (11.8,15.2), (11.8,13.9), (12.2,14.4), (12.5,13.5), (13.0,13.3), (13.4,12.6), (13.6,14.0) and (13.8,12.8). Kristina is 11 years old and runs 100 m in 12 seconds. Debbie is 15 years old and says the diagram shows she should take less than 12 seconds.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · November 2017 · Paper 1F · Q10 · 2 marks
2 marks
Examiner report
For part (a) many candidates did realise that Jakes scores were closer together but some struggled to explain why. A few stated the ranges, although sometimes they got them incorrect and therefore failed to gain the mark. Some students summed the scores for both Sarah and Jake and told us ‘Jake because he has the highest overall total’; this clearly gained no marks as it did not answer the question. A number of students stated that ‘Jake is more consistent because he has scores of 8 and above’; this statement was not sufficient to tell us that Jake’s scores had a smaller range and so gained no marks. A number of students also had the idea that the range is the mean of the differences between each number, so they found the differences between each number, added them together and divided the result. It was pleasing to see that the majority of students were able to engage with the stem and leaf diagram in part (b) and identify that the value had been read incorrectly due the key not being used. Many gave the correct answer, communicating clearly that 26 was the correct mode and some even explained what error had been made, giving examples of how the key should have been used. Others discussed the fact that 9 was the only single digit number in the diagram. Incorrect answers were usually confused or agreed that the mode was 6.
Jake and Sarah each played a computer game six times. Their scores for each game are shown below. Jake 10 9 8 11 12 8 Sarah 2 10 7 14 4 10 (a) Who had the most consistent scores, Jake or Sarah? You must give a reason for your answer. Jake played a different game 20 times. The stem and leaf diagram shows information about his scores. 0 9 1 2 3 3 4 5 Key 1 | 2 represents 12 points 2 5 6 6 6 6 7 3 1 3 4 6 8 4 0 2 9 Jake said his modal score was 6 points because 6 occurs most often in the diagram. (b) Is Jake correct? You must explain your answer.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q12 · 4 marks
4 marks
Examiner report
This was a well answered question. The majority of students were able to answer part (a) scoring full marks and then able to go on to answer part (b) and answer that correctly also. If a slip was seen in part (a), 2 marks were often awarded and the follow through applied to part (b). Most candidates were comfortable with two way tables but a small minority did reverse the entries so careful reading of the headings is required. If part (b) was incorrect often 8 was seen as the incorrect answer, some students wrote unlikely when a numerical answer was required.
Emma has 45 rabbits. 30 of the rabbits are male. 8 of the female rabbits have short hair. 12 of the rabbits with long hair are male. (a) Use the information to complete the two-way table. Male Female Total Long hair Short hair Total One of Emma's rabbits is chosen at random. (b) Write down the probability that this rabbit is a female with short hair.
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Edexcel 1MA1 · November 2017 · Paper 1F · Q27 · 4 marks
4 marks
Examiner report
For part (a) a pleasing number of students used the printed table as a basis for their calculations, clearly indicating the mid-points and showed the multiplication by the frequencies. There were quite a few students who were able to find the mid points but weren’t sure what to do next. Some went on to add the mid points together then divide by 5. A common error seen in calculations was 500 x 0 = 500 thus at least the accuracy mark was lost but if this was the only error all method marks could be attained. Students should be encouraged to go through their exam papers with questions like this and check to see if their answer is sensible, a mean outside the data range is not. Part (b) was poorly answered. Most students commented on the accuracy of the answer and not about the appropriateness of the mean average. Many just stated should have used the mode or should have used the median without explanation and this did not score the mark.
The table shows information about the weekly earnings of 20 people who work in a shop. Weekly earnings (GBPx) Frequency 150 x - 250 1 250 x - 350 11 350 x - 450 5 450 x - 550 0 550 x - 650 3 (a) Work out an estimate for the mean of the weekly earnings. GBP Nadiya says, "The mean may not be the best average to use to represent this information." (b) Do you agree with Nadiya? You must justify your answer.
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Edexcel 1MA1 · November 2017 · Paper 1H · Q5 · 4 marks
4 marks
Examiner report
It was surprising to see part (a) of this question, a common one on the legacy specification, answered so poorly. Many students appeared to not understand estimating the mean at all and made no attempt to find fx. When students did it was most common to see 2 marks awarded. Some dropped the second by failing to divide by 20, many making the common error and dividing by 5. Many who scored 2 marks didn’t gain the third mark due to arithmetic errors, typically when finding their products rather than the division. Part (b) of this question proved to be too much for almost all students. It seems that more time needs to be taken within centres on choosing the most suitable average. Very few students gained the mark on this question in which they had to consider the effect of outliers on the mean, typically just stating that the mode or median would be better with no suitable reason why.
The table shows information about the weekly earnings of 20 people who work in a shop. Weekly earnings (GBPx) Frequency 150 x - 250 1 250 x - 350 11 350 x - 450 5 450 x - 550 0 550 x - 650 3 (a) Work out an estimate for the mean of the weekly earnings. GBP Nadiya says, "The mean may not be the best average to use to represent this information." (b) Do you agree with Nadiya? You must justify your answer.
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Edexcel 1MA1 · November 2017 · Paper 1H · Q12 · 5 marks
5 marks
Examiner report
Most students gained at least one mark for 3 correct values on the box plot in part (a). Those who had a good understanding gained 3 marks, and this was common place. There were a number of students who plotted an incorrect value for their minimum, this normally meant zero marks were scored as all the values were then in the wrong place on the plot. In part (b) students struggled to gain marks for comparisons of plots. Some students just stated values but made no comparisons. Some stated figures (which they didn’t need to do) and stated them incorrectly within a comparison and thus lost their marks. Typically those who made comparisons gained only one mark as they were unable to contextualise their statements.
The table shows information about the heights, in cm, of a group of Year 11 girls. height (cm) least height 154 median 165 lower quartile 161 interquartile range 7 range 20 (a) Draw a box plot for this information. Year 11 130 140 150 160 170 180 height (cm) The box plot below shows information about the heights, in cm, of a group of Year 7 girls. Year 7 130 140 150 160 170 180 height (cm) (b) Compare the distribution of heights of the Year 7 girls with the distribution of heights of the Year 11 girls.
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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 · Q8 · 2 marks
2 marks
Examiner report
In part (a) a minority of students recognised the missing “30” on the vertical axis; too many made reference to the diagram as if it were a scatter graph. But in the second part it was the majority who correctly identified the trend as increasing, though some answers were spoilt by incorrectly referring to the trend as “positive correlation”.
A line graph gives monthly on-time bus percentages Jan-Jun, with an upward trend, but its vertical scale reads 0,10,20,40,50,...,100. (a) State one error. (b) Describe the trend.
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Edexcel 1MA1 · November 2017 · Paper 2F · Q18 · 3 marks
3 marks
Examiner report
Few students scored any marks in part (a), with the commonest answer being 10, from 80 . Some scored 1 mark for working with the circumference; no marks were gained from using the area formula. Part (b) was better answered with about half gaining credit from recognising that some aspects remained constant. Unfortunately, many answered “yes” because they thought the circumference had changed.
A circle has diameter 80 m and 8 marked points. (a) Initially the points are equally spaced; find the arc distance between neighbours. (b) After four points move around the same circle, does the mean neighbour-to-neighbour distance change? Explain.
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Edexcel 1MA1 · November 2017 · Paper 2H · Q3 · 3 marks
3 marks
Examiner report
For those students who realised that they needed to use the formula for the circumference of a circle, and could recall it, this question proved to be straightforward. It was surprising to see that a significant number of students instead opted to divide the diameter by 8 to give 10 as their answer. In part (b) students who stated that the total distance or that the number of points remained constant were awarded the mark available. It was encouraging to see that this part of the question was answered quite well, sometimes even after an incorrect response to part (a). Students generally gave a clear decision coupled with a clearly expressed reason. Where this was not the case, students often referred to larger and smaller gaps between the points. Students who thought that the mean distance would change used the reason that the points would not now be equally spaced.
A circle has diameter 80 m and 8 marked points. (a) Find the equal arc distance. (b) If four points move around the same circle, does the mean neighbour gap change? Explain.
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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 · Q17 · 5 marks
5 marks
Examiner report
The majority of students drew frequency diagrams for part (a) this question, usually with bars of the correct width. Of those students who correctly calculated and used frequency density, some did not label the vertical axes correctly. Class intervals were sometimes used on the horizontal axis (rather than a linear scale). In part (b) some students were able to calculate 123 by using the table even when they had drawn a frequency diagram in the first part of the question. A significant number of students, having calculated 123 correctly, did not then go on to express this as a fraction of 150. Some students who had drawn a correct histogram attempted to calculate the probability in part (b) from frequency densities.
Heights of 150 students: 140<h<=150:15; 150<h<=155:30; 155<h<=160:51; 160<h<=165:36; 165<h<=180:18. (a) Draw a histogram. (b) Estimate the fraction between 150 and 170 cm.
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Edexcel 1MA1 · November 2017 · Paper 3F · Q6 · 3 marks
3 marks
Examiner report
The vast majority of students gained at least two marks and usually three in this question. It was common to see the three quarters (on Saturday) split into one half and one quarter circles. This was then often shown in the key. This was perfectly acceptable. Some students defined their own, incorrect key and changed the whole diagram accordingly. This received no credit. Centres should note that a key in words without showing an appropriate diagram, was not acceptable.
A pictogram shows Tuesday 1 symbol, Wednesday 2.5 symbols and Thursday 1.5 symbols, totalling 20 cycles. Complete the key and add Friday (8 cycles) and Saturday (15 cycles).
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Edexcel 1MA1 · November 2017 · Paper 3F · Q19 · 3 marks
3 marks
Examiner report
In part (a), many students simply selected the middle interval of the five intervals in the table; showing a lack of understanding of the concept of median in such a context. In part (b), most students scored at least one mark for making at most one error in their diagram. It was common for plots to be at the end of the intervals and many students insisted upon joining their first and last plots. Quite a few students having accurately plotted the points failed to make any attempt to join them. Many weaker students just drew a histogram. This gained no credit even when all heights were ‘correct’.
Heights of 80 children: 130<h<=140:4; 140<h<=150:11; 150<h<=160:24; 160<h<=170:22; 170<h<=180:19. (a) Find the median class. (b) Draw a frequency polygon.
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Edexcel 1MA1 · November 2017 · Paper 3H · Q1 · 3 marks
3 marks
Examiner report
Part (a) was not answered particularly well. A common error was to choose the class interval 150 < h ≤ 160 which is in the middle of the five class intervals in the table. Some students chose the class interval 170 < h ≤ 180, often because 19 is the median of the five frequencies. Part (b) was not answered as well as might have been expected considering that frequency polygons have featured regularly on examination papers for a number of years. Points were frequently plotted at the ends of the intervals or at the beginnings of the intervals rather than at the midpoints. Many students did join their points with line segments; some joined them with a curve and some did not join them at all. Some otherwise correct frequency polygons were spoilt by students joining the first point to the last point. A number of students drew histograms.
Heights of 80 children: 130<h<=140:4; 140<h<=150:11; 150<h<=160:24; 160<h<=170:22; 170<h<=180:19. Find the median class and draw a frequency polygon.
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Edexcel 1MA1 · November 2017 · Paper 3H · Q11 · 4 marks
4 marks
Examiner report
In part (a) many students correctly read the value of the median from the cumulative frequency graph. Common incorrect answers were 60, 38 and 55. Correct answers were rarely seen in part (b). Most students either stated that Jamil is correct because the range is the largest value minus the smallest value or stated that he is incorrect because his calculation should have been 80 – 30 = 50. Very few students appreciated that the greatest value could be less than 80 or that the smallest value could be less than 40. Many students gained one mark in part (c) for reading from the graph. This was usually done from a weight of 65g and resulted in a cumulative frequency value of 48 or 49. The successful students subtracted this value from 60 to find the number of potatoes with a weight greater than 65g and then either worked out this number of potatoes as a percentage of 60 or worked out 25% of 60 (15). A common error was failing to subtract the reading from 60. Some students got no further than reading from the graph.
A cumulative-frequency graph for 60 potatoes gives median about 57 g and CF at 65 g about 48-49. Jamil uses 80-40=40 g as the range. Assess this and show fewer than 25% exceed 65 g.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q14 · 4 marks
4 marks
Examiner report
A good number of students were able to score a mark for either one correct calculation of an angle or for one correct sector of the pie chart; this often then allowed them so gain the mark for labelling the sectors. However, full marks in part (a) was relatively rare and more time needs to be spent on dealing with pie charts without a calculator to ensure students are familiar with dividing by total frequencies like 120 here, or other factors of 360 Very few students were able to understand the difference between a larger proportion and a greater frequency in pie charts and as a result most scored zero in part (b).
Year 9 students from Halle School were asked to choose one language to study. The table shows information about their choices. Language Number of students French 56 Spanish 40 German 24 (a) Draw an accurate pie chart to show this information. Year 9 students from Lowry School were also asked to choose one language to study. This accurate pie chart shows information about their choices. German Spanish French Shameena says, " The pie chart shows that French was chosen by more Year 9 students at Lowry School than at Halle School." (b) Is Shameena right? You must explain your answer.
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Edexcel 1MA1 · June 2017 · Paper 1F · Q21 · 5 marks
5 marks
Examiner report
This was a question that was answered well by almost all students. In part (a) almost every student scored the mark. Of those that didn’t it was normally down to a misread scale, giving answers such as (10, 17) and (9.5, 18.5) or occasionally reversing the coordinates giving (19, 10) Nearly all students stated “positive” in part (b) which was required for the mark. It is worth centres knowing that at this level no extra detail such as “strong” or “weak” is required although, if present, it was not penalised provided “positive” was also present. Part (c) was answered generally well with most students giving an answer in the range shown in the mark scheme. Whilst drawing in the line of best fit it is not a required to gain any marks (provided the answer given is within the range on the mark scheme), it is good practice and greater use of a line of best fit would have certainly led to more correct responses. In part (d) many students were able to write a suitable sentence referring to the positive correlation of the scatter graph.
The scatter graph shows the maximum temperature and the number of hours of sunshine in fourteen British towns on one day. 20 18 16 Maximum temperature ( degreesC) 14 12 10 7 9 11 13 15 17 Number of hours of sunshine One of the points is an outlier. (a) Write down the coordinates of this point. ( (b) For all the other points write down the type of correlation. On the same day, in another British town, the maximum temperature was 16.4 degreesC. (c) Estimate the number of hours of sunshine in this town on this day. A weatherman says, "Temperatures are higher on days when there is more sunshine." (d) Does the scatter graph support what the weatherman says? Give a reason for your answer.
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Edexcel 1MA1 · June 2017 · Paper 1H · Q1 · 5 marks
5 marks
Examiner report
This was a well answered question. In part (a) nearly all candidates correctly identified the outlier; there were only a few who reversed the coordinates. In part (b) it was again very common for the mark to be awarded; candidates who exemplified their statement of “positive” with additional statements (eg strong, hard) were not penalised as long as there was no contradiction. In part (c) the majority of candidates successfully found a correct prediction within the required range. Mistakes were usually due to incorrect reading of the scales. The candidates that drew an appropriate line of best fit usually went on to score full marks. A few candidates drew a horizontal line from the vertical axis but often misread the scale and plotted at 16.2 In part (d) many stated positive correlation or gave two relevant sets of points to show it was true. Occasionally an explanation of the relationship was lacking, with a few candidates stating that it did not prove the statement due to the outlier.
The scatter graph shows the maximum temperature and the number of hours of sunshine in fourteen British towns on one day. 20 18 16 Maximum temperature ( degreesC) 14 12 10 7 9 11 13 15 17 Number of hours of sunshine One of the points is an outlier. (a) Write down the coordinates of this point. ( (b) For all the other points write down the type of correlation. On the same day, in another British town, the maximum temperature was 16.4 degreesC. (c) Estimate the number of hours of sunshine in this town on this day. A weatherman says, "Temperatures are higher on days when there is more sunshine." (d) Does the scatter graph support what the weatherman says? Give a reason for your answer.
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Edexcel 1MA1 · June 2017 · Paper 1H · Q7 · 3 marks
3 marks
Examiner report
Generally a well answered question, with many fully correct responses. If candidates knew how to get started with this question they usually progressed to gain full marks. Many candidates could calculate 30 × 60 but fell down on the multiplication of 54 × 20. Very few used an alternate method. The number 66 was seen as the answer in a number of cases where candidates did not appreciate the difference in the number of boys to girls. A very small handful of responses showed an excellent level of ratio knowledge.
There are 10 boys and 20 girls in a class. The class has a test. The mean mark for all the class is 60 The mean mark for the girls is 54 Work out the mean mark for the boys.
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Edexcel 1MA1 · June 2017 · Paper 2F · Q3 · 5 marks
5 marks
Examiner report
A large majority of students scored at least four of the five marks available in this question. Parts (a), (b) and (c) were all answered very well. The final part of the question was often correctly answered but many students found only the number of students in year 6 and did not double their answer to find the total number of students in years 5 and 6. Students who made errors in their addition but showed their method were able to gain partial credit.
A teacher asks the students in Year 6 what type of transport they use to get to school. The dual bar chart shows some of the results. 10 9 8 7 6 Key: Frequency 5 4 3 2 1 0 Car Bus Walk Cycle Other (a) What is the most popular type of transport used by the boys? 7 girls walk to school. (b) Show this information on the dual bar chart. More of the students get to school by car than by bus. (c) How many more? The number of students in Year 5 is the same as the number of students in Year 6 (d) What is the total number of students in Years 5 and 6?
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Edexcel 1MA1 · June 2017 · Paper 2F · Q5 · 2 marks
2 marks
Examiner report
Most students were able to express one thing wrong with the tally chart and one thing wrong with the pictogram with sufficient clarity to score the marks available in this question. In part (a) examiners were looking for responses which suggested that the tally and frequencies for Monday were not consistent. Nearly all students identified this. A small number of students made statements which were too vague, for example, stating that the frequencies are wrong. Other responses which could not be given any credit included comments such as “there is no title”, “they have missed off some days” or “there is no total column”. In part (b) most students either identified the inconsistency between the diagram and frequency for at least one of the two days or stated that it is inappropriate to represent a half of a CD on the pictogram. Some students simply stated that “half of 3 is 1.5” without a supporting conclusion. A few students suggested that the pictogram did not show how many CDs a semicircle represented. This is clearly not the case as the key was quite clear. Similarly some students stated that there was no frequency or total column. Examiners could not give these responses any credit.
David sells CDs in a shop. The tally chart shows information about the number of CDs David sold on Monday, on Tuesday and on Wednesday. Tally Frequency Monday | | | | | | | | | | | 12 Tuesday | | | | | | | | | | | | | | | 18 Wednesday | | | | | | | 8 (a) Write down one thing that is wrong with the tally chart. David drew this pictogram to show the information for Tuesday and Wednesday. Tuesday Key: represents 3 CDs Wednesday (b) Write down one thing that is wrong with this pictogram.
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Edexcel 1MA1 · June 2017 · Paper 2H · Q8 · 2 marks
2 marks
Examiner report
This question was in general answered well. Many students correctly read off a cumulative frequency value of 48 but then failed to subtract from 60 to find those students with a height greater than 160 cm. A number of students thought that "greater than 160 cm" meant they had to take a reading at 161cm. A significant number of students thought that the required number could be found by finding the area under the graph, usually reading off the 48 value correctly and gaining some credit. Having found the answer some rounded it because they were asked to find an estimate.
The cumulative frequency graph shows some information about the heights, in cm, of 60 students. 60 50 40 Cumulative frequency 30 20 10 0 120 130 140 150 160 170 Height (cm) Work out an estimate for the number of these students with a height greater than 160 cm.
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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 3F · Q6 · 5 marks
5 marks
Examiner report
In part (a), the majority of students knew that the median is the middle number and were able to explain that Bridgit had not ordered the numbers. A few students stated that the median is 15, sometimes showing an ordered list of numbers, but did not answer the question by explaining what is wrong with Bridgit’s method and gained no mark. Part (b) was answered very well with most students able to find the range correctly. Errors were often the result of students using an incorrect highest or lowest value. Some students, though, did identify these as 22 and 12 but did not know how to combine them. In part (c), the majority of students knew how to work out the mean. Errors included keying into a calculator so that only the final value was divided by 7 and adding up the numbers but arriving at an incorrect total. In such cases, those who showed their working were able to get one of the two marks available. Errors in this question were often the result of students confusing the measures, eg giving the mean for the range and vice versa.
Here is a list of numbers. 12 15 14 17 22 19 13 Bridgit says, "To work out the median you find the middle number, so the median of these numbers is 17" Bridgit's answer is not correct. (a) What is wrong with Bridgit's method? (b) Work out the range of the numbers in the list. (c) Work out the mean of the numbers in the list.
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Edexcel 1MA1 · June 2017 · Paper 3F · Q17 · 2 marks
2 marks
Examiner report
Part (a) was not well answered. Many students chose to write out a list of the 25 dress sizes and these students were usually able to find the median dress size. Common incorrect answers were 11 (the median of 8, 10, 12 and 14) and 7 (the median of the four frequencies). Part (b) was answered very poorly indeed with relatively few students able to explain that Zoe is not correct because some of the women could have both a shoe size of 7 and a dress size of 14. The majority of those who said that Zoe is not correct gave explanations that focused on the fraction calculation rather than on the context, eg stating that she should have multiplied the fractions. Many students thought that Zoe is correct.
The table shows some information about the dress sizes of 25 women. Dress size Number of women 8 2 10 9 12 8 14 6. (a) Find the median dress size. Three of the 25 women have a shoe size of 7. Zoe says that, if one of the 25 women is chosen at random, the probability that she has either a shoe size of 7 or a dress size of 14 is 9/25 because 3/25 + 6/25 = 9/25. (b) Is Zoe correct? You must give a reason for your answer.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q3 · 2 marks
2 marks
Examiner report
Part (a) was well answered by the majority of students. Some wrote out all the data and then found the median from their list. Incorrect answers seen were often when the student tried to work out the mean instead of stating the median. Part (b) was intended to assess one of the new assessment objectives and was not well answered by students. Many felt that any combination of probabilities required either adding or multiplying dependent upon the ‘or’ or the ‘and’ in the question. Few looked at the concept being described and considered that the qualities being discussed were not mutually exclusive. This phrase was not essential for the mark but a description of a person being able to have both attributes was required.
The table shows some information about the dress sizes of 25 women. Dress size Number of women 8 2 10 9 12 8 14 6. (a) Find the median dress size. Three of the 25 women have a shoe size of 7. Zoe says that, if one of the 25 women is chosen at random, the probability that she has either a shoe size of 7 or a dress size of 14 is 9/25 because 3/25 + 6/25 = 9/25. (b) Is Zoe correct? You must give a reason for your answer.
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Edexcel 1MA1 · June 2017 · Paper 3H · Q9 · 5 marks
5 marks
Examiner report
The vast majority of students scored well on this question. The odd silly mistake led to the loss of a mark or an irrelevant explanation was given for part (c). Generally students found the interquartile range for part (a). Occasionally the scale was misread or the numbers added. In part (b) many correct diagrams were seen. The most common errors seen were to mis-plot one point or to not use the given grid. Centres are asked to remind students that they should use grids given as this aids them to make comparisons and the use of a different or an inaccurate scale is not appropriate. For part (c) most comments related to the median or the highest value spent. These were usually appropriate answers with correct interpretation seen. Occasionally the word average or medium were used, these are not acceptable when comparing the medians. Any figures quoted must be correct and some students did not gain the mark because they gave incorrect figures in their explanations. Some explanations were lengthy and over complicated, often resulting in contradiction which meant the mark could not be awarded.
The box plot shows information about the distribution of the amounts of money spent by some male students on their holidays. Male students - - - - - - - - - - - 0 100 200 300 400 500 600 700 800 900 1000 Money spent (GBP) (a) Work out the interquartile range for the amounts of money spent by these male students. GBP The table below shows information about the distribution of the amounts of money spent by some female students on their holidays. Smallest Lower quartile Median Upper quartile Largest Money spent (GBP) 60 180 300 350 650 (b) On the grid above, draw a box plot for the information in the table. Chris says, "The box plots show that the female students spent more money than the male students." (c) Is Chris correct? Give a reason for your answer.
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Edexcel 1MA1 · sample · Paper 1F · Q14 · 4 marks
4 marks
An orchard has 45 apple trees, 20 pear trees and 25 plum trees. In the pictogram, the apple row contains 9 identical symbols, the pear row contains 4 symbols and the plum row contains 5 symbols.
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Edexcel 1MA1 · sample · Paper 1F · Q27 · 3 marks
3 marks
There are 1200 students at a school.
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Edexcel 1MA1 · sample · Paper 1H · Q7 · 3 marks
3 marks
There are 1200 students at a school.
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Edexcel 1MA1 · sample · Paper 1H · Q14 · 5 marks
5 marks
Ben played 15 games of basketball. Here are the points he scored in each game. 17 18 18 18 19 20 20 22 23 23 23 26 27 28 28
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Edexcel 1MA1 · sample · Paper 1H · Q22 · 2 marks
2 marks
Bhavna recorded the lengths of time, in hours, that some adults watched TV last week.
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Edexcel 1MA1 · sample · Paper 2F · Q8 · 3 marks
3 marks
Sam and Max work in a shop from Monday to Friday.
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Edexcel 1MA1 · sample · Paper 2F · Q9 · 2 marks
2 marks
Here is a list of numbers
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Edexcel 1MA1 · sample · Paper 2F · Q27 · 4 marks
4 marks
The table shows some information about the foot lengths of 40 adults. Foot length ( f cm) Number of adults 16 ≤ f < 18 3 18 ≤ f < 20 6 20 ≤ f < 22 10 22 ≤ f < 24 12 24 ≤ f < 26 9
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Edexcel 1MA1 · sample · Paper 2H · Q5 · 4 marks
4 marks
The table shows some information about the foot lengths of 40 adults. Foot length ( f cm) Number of adults 16 ≤ f < 18 3 18 ≤ f < 20 6 20 ≤ f < 22 10 22 ≤ f < 24 12 24 ≤ f < 26 9
Pearson does not publish a direct link to this question paper.
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 · 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 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).
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · sample · Paper 3H · Q7 · 6 marks
6 marks
The cumulative frequency table shows the marks some students got in a test. Mark (m) Cumulative frequency 0 < m ≤ 10 8 0 < m ≤ 20 23 0 < m ≤ 30 48 0 < m ≤ 40 65 0 < m ≤ 50 74 0 < m ≤ 60 80
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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 · Q15 · 2 marks
2 marks
Ages at a party are grouped as follows: 11–20: 6; 21–30: 16; 31–40: 10; 41–50: 8.
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Edexcel 1MA1 · specimen2 · Paper 1H · Q13 · 2 marks
2 marks
Ten girls have mean 70%; fifteen boys have mean 80%. Nick claims the whole-class mean is 75%.
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Edexcel 1MA1 · specimen2 · Paper 1H · Q19 · 4 marks
4 marks
A histogram covers 70–80, 80–85, 85–90, 90–100 and 100–120 minutes. Seven cyclists are in 70–80; the 100–120 bar has frequency density 1.2.
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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 · Q23 · 4 marks
4 marks
A time-series graph shows the percentage of people using a village shop, decreasing from about 35% in 1980 to about 20% in 2010.
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Edexcel 1MA1 · specimen2 · Paper 2H · Q2 · 4 marks
4 marks
A time-series graph shows the percentage of people using a village shop, decreasing from about 35% in 1980 to about 20% in 2010.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 2H · Q11 · 6 marks
6 marks
Cumulative-frequency curves show finishing times for 100 male and 100 female marathon runners. At 240 minutes the male cumulative frequency is about 43. The approximate medians are 250 minutes for males and 275 minutes for females; the interquartile ranges are about 71 and 69 minutes respectively.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q10 · 4 marks
4 marks
A stem-and-leaf diagram gives these speeds: 38; 41, 43, 44, 46, 47, 48, 48, 49, 49; 52, 52, 54, 56, 57, 57, 58, 58, 59; 61, 61, 62, 62, 62, 62, 63; 70.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 3F · Q16 · 2 marks
2 marks
A fair six-sided die is rolled 30 times. The frequencies for scores 1 to 6 are 7, 5, 4, 4, 6 and 4 respectively.
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Edexcel 1MA1 · specimen2 · Paper 3F · Q26 · 2 marks
2 marks
Katie measured the length and width of each of 10 pine cones from the same tree and plotted the results on a scatter graph. Both axes start at zero, and one plotted point is an outlier with an unusually small width for its length.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 3H · Q5 · 2 marks
2 marks
Katie measured the length and width of each of 10 pine cones from the same tree and plotted the results on a scatter graph. Both axes start at zero, and one plotted point is an outlier with an unusually small width for its length.
Pearson does not publish a direct link to this question paper.
Edexcel 1MA1 · specimen2 · Paper 3H · Q14 · 5 marks
5 marks
The table gives the speeds, in km/h, of 81 cars: 90 < s ≤ 100: 13; 100 < s ≤ 105: 16; 105 < s ≤ 110: 18; 110 < s ≤ 120: 22; 120 < s ≤ 140: 12.
Pearson does not publish a direct link to this question paper.
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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 statistics is where the marks keep going, I teach it one to one from the mark schemes. Free intro call, then a free first lesson.