Pearson Edexcel GCSE (9–1) Mathematics
1MA1
Original practice paper written in the style of Edexcel papers — not a Pearson publication. This pack is untiered and can include both Foundation and Higher content.
Name: __________________________________
Class: __________________________________
Answer every question. Show all stages of your working. The total number of marks is 90.
This topic pack mixes calculator and non-calculator practice. Each question states whether a calculator may be used.
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.
Either calculator policy
(a)Use this information to estimate the total number of fish in the lake.
(2)
(b)Give one reason why this estimate may not be reliable.
(1)
(Total for Question 1 is 3 marks)
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.
Either calculator policy
(a)Work out the size of the angle that would represent Science on the pie chart.
(2)
(b)Write the fraction of students who chose Maths in its simplest form.
(1)
(Total for Question 2 is 3 marks)
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.
Either calculator policy
(a)Find the median number of points scored.
(1)
(b)The coach says, "The mean is the best statistic to describe our typical score." The mean of the 11 scores is just over 25. Explain why the coach is wrong.
(1)
(Total for Question 3 is 2 marks)
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).
Either calculator policy
(a)Describe the correlation shown by the scatter graph.
(1)
(b)Use the line of best fit to estimate the test mark of a student who revised for 5 hours.
(2)
(c)Explain why using the line of best fit to estimate the mark for a student who revised 15 hours may not be reliable.
(1)
(Total for Question 4 is 4 marks)
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.
Either calculator policy
(a)Compare the results of the two classes. Make two clear comparisons, referring to the figures given.
(2)
(b)Give one reason why the range may not be a reliable measure of spread.
(1)
(Total for Question 5 is 3 marks)
6
The table shows how 72 people travel to work: Car 30, Bus 18, Walk 15, Cycle 9.
Either calculator policy
(a)Work out the angle that would represent 'Bus' on a pie chart.
(2)
(b)Write the fraction of the people who cycle to work, giving your answer in its simplest form.
(1)
(Total for Question 6 is 3 marks)
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.
Either calculator policy
(a)Work out the number of emails received on Monday.
(1)
(b)On Wednesday the company received 45 emails. Work out the number of circles that should be drawn for Wednesday.
(1)
(c)Work out the total number of emails received on Monday, Tuesday and Wednesday together.
(2)
(Total for Question 7 is 4 marks)
8
Here are five numbers: 5, 8, 3, 8, 6
Either calculator policy
(a)Work out the mean.
(2)
(b)Work out the median.
(1)
(c)Work out the range.
(1)
(Total for Question 8 is 4 marks)
9
A council wants to find out how often adults in a town exercise. A researcher asks 40 people as they leave a gym.
Either calculator policy
Explain why this sample may not represent all adults in the town. Suggest a better sampling method.
(2)
(Total for Question 9 is 2 marks)
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.
Non-calculator
(a)Work out how many components are inspected.
(2)
(b)State one possible limitation of this systematic sample.
(1)
(Total for Question 10 is 3 marks)
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.
Calculator
(a)Estimate the total number of ladybirds in the greenhouse.
(2)
(b)State two assumptions needed for this estimate to be reliable.
(2)
(c)Some marked ladybirds moved out of the greenhouse before the second sample. Explain how this is likely to affect the estimate.
(1)
(Total for Question 11 is 5 marks)
12
The travel methods used by 10 students are: bus, walk, cycle, bus, bus, walk, cycle, bus, walk, bus.
Non-calculator
(a)Complete a frequency list for the three travel methods.
(2)
(b)Write down the total frequency.
(1)
(Total for Question 12 is 3 marks)
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.
Calculator
(a)Describe the trend in the number of visitors.
(2)
(b)Work out the percentage increase from January to June. Give your answer to 1 decimal place.
(2)
(Total for Question 13 is 4 marks)
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.
Either calculator policy
(a)Show that the total frequency is 25.
(1)
(b)A vertical line chart is drawn for this distribution. Write the four coordinate pairs (number of books, frequency) that are plotted.
(2)
(Total for Question 14 is 3 marks)
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.
Calculator
(a)Work out the frequency density for each class.
(3)
(b)Which class has the tallest bar in the histogram?
(1)
(Total for Question 15 is 4 marks)
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.
Calculator
(a)Work out the frequency in each of the first two classes.
(2)
(b)Work out the frequency density for the class 15 < m ≤ 20.
(2)
(Total for Question 16 is 4 marks)
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.
Non-calculator
(a)Write down an estimate for the median.
(1)
(b)Work out an estimate for the interquartile range.
(2)
(c)Estimate the number of values greater than 39.
(1)
(Total for Question 17 is 4 marks)
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.
Non-calculator
(a)Work out the mean score.
(2)
(b)Write down the mode.
(1)
(c)Work out the range.
(1)
(Total for Question 18 is 4 marks)
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.
Either calculator policy
Compare the times for the two groups. Make one comparison of typical time and one comparison of spread.
(2)
(Total for Question 19 is 2 marks)
20
Six numbers have a mean of 14. Five of the numbers are 9, 11, 13, 17 and 18.
Calculator
(a)Work out the sixth number.
(3)
(b)A seventh number, 40, is added. Work out the new mean. Give your answer to 1 decimal place.
(2)
(Total for Question 20 is 5 marks)
21
In a random sample of 50 households, 12 households do not own a car. The town has 2000 households.
Calculator
Estimate the number of households in the town that do not own a car.
(2)
(Total for Question 21 is 2 marks)
22
The amounts, in pounds, spent by 10 customers are 22, 24, 25, 26, 27, 28, 29, 30, 31 and 180.
Calculator
(a)Work out the median.
(1)
(b)Work out the mean.
(2)
(c)Which average better describes a typical amount spent? Give a reason.
(1)
(Total for Question 22 is 4 marks)
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.
Calculator
(a)Use the sample to estimate how many adults in the town prefer travelling by bus.
(2)
(b)Explain why 2700 should be described as an estimate rather than the exact number.
(2)
(Total for Question 23 is 4 marks)
24
For a group of homes, the data show that as the outdoor temperature increases, the amount spent on heating generally decreases.
Either calculator policy
(a)State the type of correlation.
(1)
(b)Does this statement mean that every warmer day has a lower heating cost than every colder day? Explain your answer.
(1)
(Total for Question 24 is 2 marks)
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.
Either calculator policy
(a)Use the line of best fit to estimate the score when x = 7.
(2)
(b)Explain why the line of best fit does not prove that extra practice causes a higher score.
(2)
(Total for Question 25 is 4 marks)
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).
Calculator
(a)Identify the outlier.
(1)
(b)Use the line of best fit to estimate y when x = 4.5.
(2)
(c)State how including the outlier is likely to affect a line of best fit.
(1)
(d)Explain why using the line to predict y when x = 10 may be unreliable.
(1)
(Total for Question 26 is 5 marks)
Pearson Edexcel GCSE (9–1) Mathematics
1
(a)
Answer: 250
M1 for a correct proportion method, e.g. 8/50 = 40/N or 40 × 50 ÷ 8. A1 for 250.
(b)
Answer: e.g. the tagged fish may not have mixed evenly through the lake; fish may have entered or left the lake; some tags may have come off; the sample may be too small.
B1 for one valid limitation of the capture-recapture method (even mixing assumed / population changed / tags lost / sample size).
3 marks
2
(a)
Answer: 120°
M1 for 30/90 × 360 (or 360 ÷ 90 = 4 then × 30). A1 for 120 (degrees).
(b)
Answer: 2/9
B1 for 2/9 (or an equivalent fully simplified fraction).
3 marks
3
(a)
Answer: 21
B1 for 21 (the 6th value of the ordered list).
(b)
Answer: The 78 is an outlier which inflates the mean, so the mean (about 25) is higher than all but three of the actual scores; the median (21) describes the typical score better.
B1 for identifying that 78 is an outlier/extreme value which distorts (inflates) the mean, so the median describes the typical score better.
2 marks
4
(a)
Answer: Positive correlation.
B1 for positive (correlation).
(b)
Answer: 48 marks
M1 for a correct method using the two given points, e.g. gradient (66 − 30)/(8 − 2) = 6 then 30 + 6 × 3, or a clear proportional step along the line. A1 for 48 (the line is defined by the two given points, so the value is exact; ft an arithmetic slip only with a correct method shown).
(c)
Answer: 15 hours is outside the range of the data, so this is extrapolation and the trend may not continue.
B1 for identifying that 15 hours is outside the data range (extrapolation) so the prediction is unreliable.
4 marks
5
(a)
Answer: Class A had a higher median (62 compared with 55), so on average Class A scored higher. Class B had a smaller range (10 compared with 24), so Class B's marks were more consistent / less spread out.
B1 for a correct comparison of averages using the medians with figures (A higher, 62 vs 55). B1 for a correct comparison of spread using the ranges with figures (B smaller/more consistent, 10 vs 24).
(b)
Answer: The range depends only on the highest and lowest values, so a single extreme value (outlier) can make it misleading.
B1 for a valid reason (range uses only two values / is distorted by an outlier).
3 marks
6
(a)
Answer: 90°
M1 for 18/72 × 360 (or 360 ÷ 72 = 5 then × 18). A1 for 90.
(b)
Answer: 1/8
B1 for 1/8 (from 9/72).
3 marks
7
(a)
Answer: 35
B1 for 35 (3.5 × 10).
(b)
Answer: 4.5 circles
B1 for 4.5 (45 ÷ 10).
(c)
Answer: 100
M1 for 35 + 20 + 45 (Tuesday = 2 × 10 = 20). A1 for 100.
4 marks
8
(a)
Answer: 6
M1 for (5 + 8 + 3 + 8 + 6) ÷ 5 (= 30 ÷ 5). A1 for 6.
(b)
Answer: 6
B1 for 6 (middle value of ordered list 3, 5, 6, 8, 8).
(c)
Answer: 5
B1 for 5 (8 − 3).
4 marks
9
Answer: People leaving a gym are likely to exercise more often than adults in the town as a whole, so the sample is biased. A better method is to take a random sample of adults from across the town.
B1 for explaining that gym users are likely to exercise more and so the sample is biased / not representative. B1 for a suitable improvement, such as a random sample of adults from across the town.
2 marks
10
(a)
Answer: 50
M1 for 1250 ÷ 25. A1 for 50.
(b)
Answer: If a repeating pattern in production also has a cycle of 25, the sample may be biased and not representative.
B1 for a valid limitation, such as a production pattern matching the sampling interval or the day's production not representing other days.
3 marks
11
(a)
Answer: 240
M1 for 12/60 = 48/N or 48 × 60 ÷ 12. A1 for 240.
(b)
Answer: Any two of: marked ladybirds mixed evenly with the population; marks were not lost and did not affect recapture; the population did not change between samples; each ladybird had the same chance of being caught.
B2 for two valid assumptions. B1 for one valid assumption.
(c)
Answer: Fewer marked ladybirds would be recaptured, making the marked fraction too small, so the calculated population estimate would be too large.
B1 for explaining that fewer marked recaptures make the estimate too large / an overestimate.
5 marks
12
(a)
Answer: bus 5, walk 3, cycle 2
B2 for all three frequencies correct. B1 for two correct frequencies.
(b)
Answer: 10
B1 for 10.
3 marks
13
(a)
Answer: The number of visitors generally increases, with a small decrease from March to April.
B1 for a generally increasing trend. B1 for identifying the decrease from March to April.
(b)
Answer: 54.2%
M1 for (185 - 120)/120 × 100. A1 for 54.2% to 1 decimal place.
4 marks
14
(a)
Answer: 4 + 7 + 9 + 5 = 25
B1 for 4 + 7 + 9 + 5 = 25.
(b)
Answer: (0, 4), (1, 7), (2, 9), (3, 5)
B2 for all four coordinate pairs correct. B1 for two or three correct coordinate pairs.
3 marks
15
(a)
Answer: 0.8, 2.4, 1.2 respectively
M1 for using frequency density = frequency ÷ class width. A2 for all three densities 0.8, 2.4 and 1.2. A1 for two correct densities.
(b)
Answer: 10 < t ≤ 15
B1 for 10 < t ≤ 15, ft their largest positive density.
4 marks
16
(a)
Answer: 12 and 11 respectively
M1 for using frequency = class width × frequency density. A1 for 12 and 11.
(b)
Answer: 3.4
M1 for remaining frequency 40 - 12 - 11 = 17. A1 for 17 ÷ 5 = 3.4.
4 marks
17
(a)
Answer: 27
B1 for 27.
(b)
Answer: 21
M1 for upper quartile 39 and lower quartile 18. A1 for 39 - 18 = 21.
(c)
Answer: 20
B1 for 80 - 60 = 20.
4 marks
18
(a)
Answer: 2.4
M1 for (1×2 + 2×3 + 3×4 + 4×1)/(2 + 3 + 4 + 1). A1 for 2.4.
(b)
Answer: 3
B1 for 3.
(c)
Answer: 3
B1 for 4 - 1 = 3.
4 marks
19
Answer: Group A is typically faster because its median time is lower, 18 minutes compared with 21 minutes. Group A's times are also more consistent because its interquartile range is smaller, 6 minutes compared with 11 minutes.
B1 for Group A faster / lower typical time, supported by medians 18 and 21. B1 for Group A more consistent / less spread, supported by IQRs 6 and 11.
2 marks
20
(a)
Answer: 16
M1 for total 6 × 14 = 84. M1 for 84 - (9 + 11 + 13 + 17 + 18). A1 for 16.
(b)
Answer: 17.7
M1 for (84 + 40) ÷ 7. A1 for 17.7 to 1 decimal place.
5 marks
21
Answer: 480
M1 for 12/50 × 2000. A1 for 480.
2 marks
22
(a)
Answer: 27.5
B1 for (27 + 28) ÷ 2 = 27.5.
(b)
Answer: 42.2
M1 for a correct total of 422 divided by 10. A1 for 42.2.
(c)
Answer: The median, because £180 is an outlier that pulls the mean upwards.
B1 for the median with a reason referring to the £180 outlier / the outlier distorting the mean.
4 marks
23
(a)
Answer: 2700
M1 for 180/300 × 4500. A1 for 2700.
(b)
Answer: Only a sample of the adults was asked. A different random sample could contain a different proportion who prefer bus travel.
B1 for explaining that only a sample, not the whole population, was surveyed. B1 for recognising that another random sample may give a different proportion / sampling variation.
4 marks
24
(a)
Answer: Negative correlation
B1 for negative correlation.
(b)
Answer: No. Correlation describes an overall trend, so individual homes or days can differ from the trend.
B1 for no, with an explanation that correlation is an overall trend and individual points can vary.
2 marks
25
(a)
Answer: 30
M1 for gradient (42 - 18)/(10 - 4) = 4 or an equivalent proportional step. A1 for 30.
(b)
Answer: Correlation does not prove causation; another factor, such as prior experience, could affect both practice time and score.
B1 for stating that correlation does not imply causation. B1 for a plausible other factor or explanation.
4 marks
26
(a)
Answer: (7, 70)
B1 for (7, 70).
(b)
Answer: 26
M1 for gradient (32 - 12)/(6 - 1) = 4 and use of the line through (1, 12). A1 for 26.
(c)
Answer: It is likely to pull the line upwards, giving larger predicted y-values.
B1 for the line being pulled upwards / predictions being increased.
(d)
Answer: x = 10 is outside the observed range, so this is extrapolation and the trend may not continue.
B1 for identifying extrapolation outside the data range and that the trend may not continue.
5 marks