Pearson Edexcel International GCSE Mathematics A 4MA1: Statistics and probability – Practice Questions

These are original questions written for Marlbridge, for revision and practice on this content. They are not reproduced past-paper questions, and they do not replicate the exam’s exact structure, question count or mark tariffs – examination boards hold copyright in their own papers. Use these alongside the official past papers from your board or school.

These questions cover topic 6, Statistics and probability, of the Pearson Edexcel International GCSE Mathematics A (4MA1) specification, Issue 2 (November 2017), first assessed in June 2018 with papers in January and June. They test sections 6.1 (Graphical representation of data), 6.2 (Statistical measures) and 6.3 (Probability). Questions 1 to 8 use Foundation content, which both tiers need. Questions marked (Higher tier only) use content that appears only on papers 1H and 2H. A calculator may be used on every 4MA1 paper; give probabilities as fractions or decimals, and give other non-exact answers to 3 significant figures unless told otherwise.

Related: study guide, revision notes, course hub, printable checklist.

Questions

1. 120 people were asked about their favourite fruit. The results are to be shown in a pie chart.

(a) 30 people chose mango. Calculate the sector angle for mango. [1] (b) The sector for banana has an angle of 84°. Calculate how many people chose banana. [1]

2. The table shows the number of siblings of 25 students.

Siblings	0	1	2	3	4
Frequency	5	9	7	3	1

(a) Write down the mode. [1] (b) Find the median. [1] (c) Calculate the mean. [2]

3. The mean of eight numbers is 6.5. A ninth number is added and the mean of all nine numbers is 7. Calculate the ninth number. [3]

4. The table gives the masses, m kg, of 50 parcels.

Mass m (kg)	0 < m ≤ 2	2 < m ≤ 4	4 < m ≤ 6	6 < m ≤ 10
Frequency	8	15	17	10

(a) Write down the modal class. [1] (b) Calculate an estimate for the mean mass. [3] (c) Explain why your answer to (b) is only an estimate. [1]

5. In a group of 80 students, 34 study French, 29 study Spanish and 11 study both.

(a) Draw a Venn diagram to show this information, giving the number in each region. [2] (b) A student is chosen at random. Find the probability that the student studies neither language. [1] (c) Find the probability that the student studies exactly one of the two languages. [1]

6. A spinner can land on A, B, C or D. P(A) = 0.3, P(B) = 0.25, P(C) = x and P(D) = 2x.

(a) Find the value of x. [2] (b) Find the probability that the spinner lands on A or D. [1] (c) The spinner is spun 200 times. Work out the expected number of times it lands on C. [1]

7. Spinner X is numbered 1, 2, 3. Spinner Y is numbered 2, 4, 6. Both are fair. Each is spun once and the two numbers are multiplied. List the sample space of products and find the probability that the product is greater than 8. [3]

8. A dice is rolled 250 times. It lands on 6 a total of 65 times.

(a) Calculate the relative frequency of a 6. [1] (b) Use your answer to estimate the number of 6s in 600 rolls. [1] (c) Is the dice fair? Give a reason. [1]

9. (Higher tier only) The table shows the times, t seconds, taken by 90 people to complete a puzzle.

Time t (s)	0 < t ≤ 10	10 < t ≤ 15	15 < t ≤ 20	20 < t ≤ 30	30 < t ≤ 50
Frequency	12	18	22	26	12

(a) Calculate the frequency density for each class, ready to draw a histogram. [2] (b) Estimate the number of people who took more than 25 seconds. [2]

10. (Higher tier only) The table shows the time, t minutes, that 80 students spent on homework one evening.

Time t (min)	0 < t ≤ 10	10 < t ≤ 20	20 < t ≤ 30	30 < t ≤ 40	40 < t ≤ 50	50 < t ≤ 60
Frequency	6	12	22	22	12	6

(a) Complete a cumulative frequency table. [1] (b) Write down the coordinates of the points you would plot for the cumulative frequency diagram. [1] (c) Use the diagram to estimate the median. [1] (d) Estimate the interquartile range. [3] (e) Estimate the number of students who spent more than 45 minutes on homework. [2]

11. (Higher tier only) An archer hits the target with probability 0.7 on each shot. The shots are independent.

(a) Draw a tree diagram for two shots. [2] (b) Find the probability that the archer hits the target with exactly one of the two shots. [2] (c) The archer takes three shots. Find the probability that at least one shot hits the target. [2]

12. (Higher tier only) A bag contains 6 red counters and 4 white counters. Two counters are taken at random, one after the other, without replacement.

(a) Draw a tree diagram to show the probabilities. [2] (b) Find the probability that both counters are white. [2] (c) Find the probability that the counters are different colours. [2] (d) Instead, three counters are taken without replacement. Find the probability that at least one is white. [2] (e) The two-counter experiment is carried out 300 times, with both counters returned to the bag after each go. Work out the expected number of times both counters are white. [1]

Answers

1. (a) 30/120 × 360° = 90° [1] (b) 84/360 × 120 = 28 people [1] Examiner insight: Each part is a single accuracy mark, so an answer with no working that is slightly off (for example 27) gets nothing; one line of working costs seconds.

2. (a) 1 [1] (b) The median is the 13th value; running totals 5, 14 show the 13th value is 1, so median = 1 [1] (c) Σfx = 0 + 9 + 14 + 9 + 4 = 36 [1]; mean = 36 ÷ 25 = 1.44 [1] Examiner insight: Answering 9 for the mode (the highest frequency) or 7 for the median (the middle frequency) scores zero; the answer must be a number of siblings.

3. Total of eight numbers = 8 × 6.5 = 52 [1]; total of nine numbers = 9 × 7 = 63 [1]; ninth number = 63 − 52 = 11 [1] [3] Examiner insight: Averaging the two means, or adding 0.5 to 6.5, earns no method mark; the marks come from working with totals.

4. (a) 4 < m ≤ 6 [1] (b) Midpoints 1, 3, 5, 8, giving f × midpoint = 8, 45, 85, 80 [1]; Σfx ÷ Σf = 218 ÷ 50 [1]; = 4.36 kg [1] (c) The midpoint of each class is used, because the exact masses are not known [1] Examiner insight: The last class is 6 < m ≤ 10, so its midpoint is 8, not 7; using the wrong midpoint can still earn the mark for dividing Σfx by 50, but not the final mark.

5. (a) Overlap 11, French only 34 − 11 = 23, Spanish only 29 − 11 = 18 [1]; outside both 80 − 52 = 28 [1] (b) 28/80 = 7/20 [1] (c) (23 + 18)/80 = 41/80 [1] Examiner insight: Writing 34 and 29 in the “only” regions double-counts the 11 and makes every later answer wrong; allow follow-through in (b) and (c) from your own diagram if the method is right.

6. (a) 0.3 + 0.25 + x + 2x = 1, so 3x = 0.45 [1]; x = 0.15 [1] (b) 0.3 + 2 × 0.15 = 0.6 [1] (c) 0.15 × 200 = 30 [1] Examiner insight: The first mark in (a) is for using the fact that the probabilities add to 1; a bare x = 0.15 with no equation can still score both marks, but a wrong bare answer scores none.

7. Sample space of products: 2, 4, 6, 4, 8, 12, 6, 12, 18 (9 equally likely outcomes) [1]; three products are greater than 8 (12, 12, 18) [1]; probability = 3/9 = 1/3 [1] [3] Examiner insight: A product of 8 is not “greater than 8”, so including it gives 4/9 and loses the final two marks; listing all nine outcomes is what earns the first mark.

8. (a) 65/250 = 0.26 [1] (b) 0.26 × 600 = 156 [1] (c) Probably not fair: a fair dice gives a 6 with probability 1/6 ≈ 0.17, and 0.26 is much higher after a large number of rolls [1] Examiner insight: In (c) the mark needs a comparison with 1/6 (or the expected count of about 42); “No, it landed on 6 a lot” is not enough.

9. (a) Class widths 10, 5, 5, 10, 20 [1]; frequency densities 1.2, 3.6, 4.4, 2.6, 0.6 [1] (b) Half of the 20 < t ≤ 30 class: 26 ÷ 2 = 13 [1]; 13 + 12 = 25 people [1] Examiner insight: Dividing every frequency by 10 (treating all classes as width 10) gives three wrong densities and loses both marks in (a).

10. (a) Cumulative frequencies 6, 18, 40, 62, 74, 80 [1] (b) (0, 0), (10, 6), (20, 18), (30, 40), (40, 62), (50, 74), (60, 80) [1] (c) Read across at 80 ÷ 2 = 40: median ≈ 30 minutes [1] (d) Lower quartile: read at 20, about 21 minutes [1]; upper quartile: read at 60, about 39 minutes [1]; IQR ≈ 39 − 21 = 18 minutes [1] (e) Cumulative frequency at 45 minutes ≈ 68 [1]; 80 − 68 = 12 students [1] Examiner insight: Readings from a curve are accepted within a small range around the true value, but only if the reading heights are right; reading at 25 and 75 for an 80-person total loses the quartile marks.

11. (a) First shot: hit 0.7, miss 0.3 [1]; second shot: hit 0.7, miss 0.3 on both branches [1] (b) P(hit, miss) = 0.7 × 0.3 = 0.21 [1]; two routes: 2 × 0.21 = 0.42 [1] (c) P(no hits) = 0.3³ = 0.027 [1]; P(at least one) = 1 − 0.027 = 0.973 [1] Examiner insight: Giving 0.21 in (b) shows only one of the two routes and keeps just the first mark.

12. (a) First pick: red 6/10, white 4/10 [1]; second pick: after red, red 5/9 and white 4/9; after white, red 6/9 and white 3/9 [1] (b) 4/10 × 3/9 [1] = 12/90 = 2/15 [1] (c) 6/10 × 4/9 + 4/10 × 6/9 [1] = 48/90 = 8/15 [1] (d) P(all red) = 6/10 × 5/9 × 4/8 = 1/6 [1]; P(at least one white) = 1 − 1/6 = 5/6 [1] (e) 300 × 2/15 = 40 [1] Examiner insight: Using 4/10 × 4/10 in (b) treats the picks as independent and scores zero; the second fraction must show both the numerator and the denominator reduced by one.

Where marks are usually lost

• Giving a frequency instead of a value for the mode or median from a table.
• Using the wrong midpoint for a wider class in a grouped-mean question.
• Dividing by the number of classes instead of the total frequency.
• Plotting cumulative frequency at midpoints instead of upper class boundaries.
• Using frequency, not frequency density, for unequal class widths.
• Reading quartiles at 25% and 75% of 100 instead of the actual total.
• Putting the set totals, rather than the “only” numbers, in a Venn diagram.
• Missing one of the routes in “exactly one” tree-diagram questions.
• Keeping the same denominator on the second pick without replacement.
• Writing probabilities as ratios or in words.

Next steps

• Revision notes for this topic
• Study guide for this topic
• Edexcel IGCSE Mathematics hub
• Printable 4MA1 checklist
• All free 10-minute diagnostics
• Book a free trial class

Official syllabus

Pearson Edexcel International GCSE in Mathematics (Specification A) (4MA1), Specification Issue 2, November 2017, Pearson Education Limited. Topic 6, Statistics and probability: 6.1 Graphical representation of data, 6.2 Statistical measures and 6.3 Probability, with Foundation and Higher tier content.