AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 22

4 marks · Medium difficulty · Multi-step Problem

Complete the frequency tree representing students in Year 10 and Year 11 who win or do not win a medal in a competition.

Practise this question

Question

Question 22: 330 students from Year 10 and Year 11 take part in a competition. Given that the ratio of Year 10 to Year 11 students is 1 : 2, 125 students win a medal, and 73 of the students who win a medal are in Year 11. Complete the frequency tree showing 330 branching into Year 10 and Year 11, each further branching into Medal and No medal.

Mark scheme

Show the mark scheme Mark scheme for question 22 showing 4 marks: M1 for 330 / (1 + 2) or 110 or 220; A1 for 110 in Year 10 and 220 in Year 11; B1 for 52 in Year 10 Medal and 73 in Year 11 Medal; B1ft for Year 10 No medal = 58 and Year 11 No medal = 147. A completed frequency tree diagram is shown with branches: Year 10 (110) branching into Medal (52) and No medal (58); Year 11 (220) branching into Medal (73) and No medal (147).

How to answer it

Frequency Trees with Given Ratios

📌 What this question tests

This question assesses your ability to share an amount into a given ratio, read and extract information systematically from bulleted statements, and populate a frequency tree accurately using addition and subtraction to find remaining branch values.

Question 22 (4 Marks)

Full Walkthrough & Value Breakdown

📐 Step-by-Step Calculations

  1. Split total students by ratio:
    Ratio = Year 10 : Year 11 = 1 : 2
    Total parts = 1 + 2 = 3 parts
    Value per part = 330 ÷ 3 = 110
    • Year 10 = 1 × 110 = 110
    • Year 11 = 2 × 110 = 220
  2. Distribute medal winners:
    Total medals = 125
    Year 11 medals = 73 (given directly)
    Year 10 medals = 125 − 73 = 52
  3. Calculate "No medal" branches:
    • Year 10 "No medal" = 110 − 52 = 58
    • Year 11 "No medal" = 220 − 73 = 147

✅ Final Completed Values

Every bubble in the tree represents an absolute frequency (count):

Total 330
Year 10 110
Year 11 220
Y10 Medal 52
Y10 No Medal 58
Y11 Medal 73
Y11 No Medal 147

💡 Key Knowledge

  • Branch Totals: In any frequency tree, the sum of outgoing branches must equal the incoming node (e.g., Medal + No medal = Year total).
  • Cross-Group Totals: Information can span across separate branches. Here, total medals (125) was split between Year 10 and Year 11.
  • Sharing into a ratio: Add the ratio parts together first, divide the total quantity by this sum, then multiply by each individual part.

🧠 Exam Technique & Mark Scheme Insight

  • Fill in what you know first: Write 73 directly in the Year 11 Medal bubble before doing calculations.
  • Check with reverse addition:
    • 52 + 58 = 110 ✓
    • 73 + 147 = 220 ✓
    • 110 + 220 = 330 ✓
    • 52 + 73 = 125 medals ✓
  • Diagram takes precedence: The examiner marks the numbers written in the circles of the tree. Working out on the side only secures method marks if your final diagram is incomplete.

❌ Common Errors to Avoid

  • Writing probabilities instead of frequencies: Do NOT write fractions such as 110/330 or decimals/percentages. If values are written as probabilities, the mark scheme withholds accuracy marks!
  • Swapping the ratio values: Assigning 220 to Year 10 and 110 to Year 11. Remember: Year 10 is the first part (1), and Year 11 is the second part (2).
  • Subtracting from 330 instead of group totals: Forgetting that "No medal" comes from within that specific year group (e.g. 110 − 52, not 330 − 52).
Mark Scheme Breakdown:
• M1 : Method to divide 330 by (1 + 2) or showing 110 or 220.
• A1 : Correct values of 110 in Year 10 and 220 in Year 11.
• B1 : Correct values of 52 in Year 10 Medal and 73 in Year 11 Medal.
• B1ft : Follow-through marks for both "No medal" values satisfying (Year Medal + Year No medal = Year total).

Topics

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

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.