AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 12

4 marks · Medium difficulty · Multi-step Problem

Evaluate the representativeness of a lunchtime survey sample, then calculate the number of students who gave a particular response using given percentages and frequencies.

Practise this question

Question

Question 12 has two parts: (a) Greg asks 15 people at lunchtime chess club whether lunchtime clubs are important; state one reason why his results may not represent the whole school (1 mark). (b) Hanna's survey results show 62% answered Important, 24% answered Not Important, and the rest answered Don't Know. Given that 93 students answered Important, calculate how many students answered Don't Know (3 marks).

Mark scheme

Show the mark scheme Mark scheme for 12(a) awards B1 for stating the sample is biased (e.g. only asks chess club members or people who already attend a club) or the sample is too small (e.g. only 15 people). Mark scheme for 12(b) awards M1 for finding the remaining percentage 100 - 62 - 24 = 14% or finding total students 93 / 0.62 = 150; M1dep for a complete method such as 14 * 1.5 or 0.14 * 150; and A1 for the final answer of 21.

How to answer it

Survey Sampling & Reverse Percentages

What this question tests

  • Statistical sampling: Identifying bias, unrepresentative samples, and sample size limitations.
  • Complementary percentages: Using the rule that total percentages sum to 100%.
  • Proportional reasoning / Reverse percentages: Working backwards from a known percentage amount to find the total or find other sub-quantities using the unitary method.
Part 12 (a) · 1 Mark

Critiquing Greg's Sampling Method

Evaluating why 15 students at a chess club may not represent the whole school

✅ Acceptable Answers (Any One)

You can focus on bias or sample size:

  • "The sample is biased"
  • "He only asks people at the chess club" (or "people who already attend a club")
  • "The sample is too small"
  • "He has only asked 15 people"

💡 Key Knowledge: Representative Samples

  • A sample must be unbiased: people who attend chess club already enjoy lunchtime clubs, so their opinions will lean positively.
  • A sample must be large enough: 15 students is far too small to represent a school population of hundreds.

❌ Common Errors & Mark Losses

  • Restating the question without comment: Writing "He asked 15 people" gets 0 marks. You must state that 15 is too small or only 15.
  • Describing chess rather than the issue: "These 15 play chess, he doesn't ask other clubs" gets 0 marks.
  • Saying he must ask everyone: Writing "He should have asked all pupils in the school" contradicts the point of taking a sample and scores 0 marks.

🧠 Exam Technique

When critiquing sampling, always think of two core pillars:

  1. Location/Group: Are they predisposed to a certain view? (Bias)
  2. Quantity: Is the sample size large enough to give reliable conclusions?
Mark Scheme [B1]: 1 mark for any valid reason regarding bias or insufficient sample size.
Part 12 (b) · 3 Marks

Finding the Missing Group Frequency

Calculating how many students answered "Don't Know"

📐 Step-by-Step Solutions

Method 1: Unitary Method (Finding 1% first) — Recommended

  1. Find the percentage for "Don't Know":
    Total percentage = 100%
    100% − 62% − 24% = 14%
  2. Find the value of 1%:
    62% represents 93 students.
    1% = 93 ÷ 62 = 1.5 students
  3. Calculate the number for "Don't Know":
    14% = 14 × 1.5 = 21 students

Method 2: Finding the Total Survey Population

  1. Find the total number of students surveyed:
    93 ÷ 0.62 = 150 students
  2. Find 14% of the total:
    100% − 62% − 24% = 14%
    0.14 × 150 = 21 students

🧠 Mark Breakdown

  • M1 : Correct method to find the missing percentage ( 100 − 62 − 24 = 14% ) OR finding the value of 1% ( 93 ÷ 62 = 1.5 ) OR finding the total population ( 93 ÷ 0.62 = 150 ).
  • M1dep : A complete multi-step method using the correct proportions (e.g. 14 × 1.5 or 0.14 × 150 ).
  • A1 : Accurate final answer of 21 .

❌ Common Error Trap

Calculating 14% of 93:

A classic exam mistake is working out 0.14 × 93 = 13.02 .

Remember: 93 is not the total! 93 only represents the 62% who answered "Important". Always link the given frequency directly to its own percentage.

Final Answer: 21

Topics

Statistics · Number · 3.6 Statistics · 3.1.2 Fractions, decimals and percentages

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.