AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 18

3 marks · Medium difficulty · Multi-step Problem

Calculate the number of matches lost using information given in a pie chart where 30 matches correspond to the won sector.

Practise this question

Question

A pie chart displaying the results of matches played by a team. A vertical diameter splits the circle in half, with the left semicircle labelled 'Won'. The right semicircle is divided into two sectors: 'Lost' with an angle of 132 degrees and 'Drew' with an angle of 48 degrees. The text states that 30 matches were won, and asks how many matches were lost.

Mark scheme

Show the mark scheme Mark scheme outlining three alternative methods: 1) Proportion using angles, e.g., (132/180) * 30; 2) Finding degrees per match (180 / 30 = 6 degrees per match) and calculating 132 / 6; 3) Finding matches per degree (30 / 180) and multiplying by 132. Each method awards M1 for initial relationship, M1dep for full calculation, and A1 for the correct answer of 22. A special case SC1 is awarded for 11 (if 30 matches was taken as the total).

How to answer it

Calculating Quantities from a Pie Chart

📋 What this question tests
  • Angles in a circle & on a straight line: Knowing a full circle contains 360° and a straight line/semicircle contains 180°.
  • Proportional reasoning: Linking a known sector frequency (30 matches) to its sector angle to find the scale factor (degrees per match or matches per degree).
  • Calculating sector frequencies: Using ratio or proportion to determine the frequency of another sector ("Lost").

Question 18 (3 Marks)

Results of team matches represented in a pie chart

💡 Key Knowledge

  • A complete pie chart totals 360°.
  • The line between "Won" and the other two sectors is a straight diameter line:
    132° + 48° = 180°
  • Therefore, the angle for "Won" is:
    360° - 180° = 180° (or a half of the chart).
  • The Core Relationship:
    180° represents 30 matches.

🧠 Exam Technique

  • Read carefully: 30 is the number of matches won, not the total number of matches played!
  • Find the unit rate:
    • Degrees per match: 180° ÷ 30 = 6° per match
    • Matches per degree: 30 ÷ 180 = 1/6 match per degree
  • Once you know 1 match = 6° , divide any angle by 6 to get its frequency immediately.

📐 Step-by-Step Solutions

Method 1: Unitary Method (Degrees per Match) – Recommended

  1. Calculate the angle for "Won":
    Angle = 360° - (132° + 48°) = 180°
    [1 mark (M1)]
  2. Find how many degrees represent 1 match:
    180° ÷ 30 matches = 6° per match
  3. Calculate the number of lost matches:
    132° ÷ 6° = 22 matches
    [1 method mark (M1dep) + 1 accuracy mark (A1)]

Method 2: Fractional Proportion

  1. Set up the fraction of won matches:
    Lost matches are in proportion to won matches by their angles:
    Lost / Won = 132° / 180°
    [1 mark (M1)]
  2. Multiply by the frequency of won matches:
    Number of lost matches = (132 / 180) × 30
    [1 mark (M1dep)]
  3. Simplify:
    (132 ÷ 6) = 22 matches
    [1 mark (A1)]

✅ Correct Answer & Mark Breakdown

Answer: 22

Mark Scheme Allocation:
  • M1: For finding the angle for Won ( 180° ) and calculating degrees per match ( 180 ÷ 30 or 6 ), OR for setting up a correct ratio/fraction such as 132/180 or 30/180 .
  • M1dep: For completing the calculation: 132 ÷ 6 or (132/180) × 30 .
  • A1: For the final answer of 22.

❌ Common Misconceptions & Examiner Traps

  • Assuming 30 was the total number of matches:
    A very common student error was computing (132 ÷ 360) × 30 = 11 .
    Examiner Note: The mark scheme awards a Special Case mark (SC1) for 11, but you lose 2 marks for misreading the question!
  • Premature rounding:
    Using decimal approximations like 30 ÷ 180 ≈ 0.17 and multiplying: 0.17 × 132 = 22.44 . Even if rounded to 22 at the end, examiners often penalise premature rounding if not clearly justified ( M1 M1 A0 ). Always keep exact fractions!
  • Finding "Drew" instead of "Lost":
    48 ÷ 6 = 8 matches were drawn. Double-check you are answering for lost matches.

Topics

Statistics · Ratio, proportion and rates of change · 3.6 Statistics · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.