AQA GCSE Mathematics Paper 1 (Higher), June 2025: Question 7

Mark scheme

Show the mark scheme

Q Answer Mark Comments

330 ÷ (1 + 2) or 110 or 220 M1 oe

110 in Year 10 and 220 in Year 11 A1

52 in Year 10 Medal

and B1

73 in Year 11 Medal

Year 10 Medal + Year 10 No medal ft their values

= Year 10

and B1ft

Year 11 Medal + Year 11 No medal

= Year 11

Additional Guidance

Diagram takes precedence

If the values are given as probabilities, with the required value as the

numerator, withhold the first A mark or B mark

M1A1B1B1

How to answer it

Completing a Frequency Tree Using Ratios

AQA GCSE Mathematics • Number & Statistics • 4 Marks

What this question tests

This problem assesses your ability to combine ratio problem-solving with data organisation tools:

Ratio division: Splitting a total amount into a given ratio ( 1 : 2 ).
Interpreting multi-step word problems: Extracting given values and deducing missing values using basic subtraction.
Frequency tree structure: Ensuring that branches at every junction sum correctly to the value of the preceding node.

Question 7 Walkthrough (4 Marks)

Total: 330 students • Year 10 : Year 11 = 1 : 2 • 125 win medals • 73 Year 11 win medals

📐 Step-by-Step Calculations

Split the 330 students into Year groups (Ratio 1 : 2):
Total parts = 1 + 2 = 3 parts
Value of 1 part = 330 ÷ 3 = 110
• Year 10 = 1 × 110 = 110
• Year 11 = 2 × 110 = 220
Find the number of Year 10 medal winners:
Total medals = 125; Year 11 medals = 73
• Year 10 Medal = 125 − 73 = 52
• Year 11 Medal = 73 (given in question)
Calculate the "No medal" branches:
• Year 10 No medal = 110 − 52 = 58
• Year 11 No medal = 220 − 73 = 147

✅ Final Completed Tree Values

Fill each blank circle on the exam diagram with whole numbers:

Year 10 total: 110
Year 11 total: 220
Year 10 → Medal: 52
Year 10 → No medal: 58
Year 11 → Medal: 73
Year 11 → No medal: 147

Mark Scheme Breakdown:
• M1: 330 ÷ (1 + 2) or finding 110 or 220.
• A1: Correctly entering 110 for Year 10 and 220 for Year 11.
• B1: Correctly entering 52 (Year 10 Medal) and 73 (Year 11 Medal).
• B1ft: Both "No medal" branches correctly follow from their branch totals (Year 10 total − Medal, Year 11 total − Medal).

Visual Diagram of the Completed Branches

Start: 330
└─ Year 10: 110 &longrightarrow; Medal: 52 | No medal: 58 (52 + 58 = 110)
┌─ Year 11: 220 &longrightarrow; Medal: 73 | No medal: 147 (73 + 147 = 220)

🧠 Exam Technique & Examiner Insight

Check each branch sum: Each set of sub-branches must add up to the node they split from. Always do a quick check:
• 110 + 220 = 330 ✓
• 52 + 58 = 110 ✓
• 73 + 147 = 220 ✓
Follow-through (ft) marks exist: Even if you make an arithmetic error when dividing the ratio, you can still gain the final B1ft mark if your "No medal" values correctly complete your branch totals.
Diagram takes precedence: The examiner marks what is inside the circles on the diagram. Ensure working in the margins is clearly transferred into the tree.

❌ Common Errors to Avoid

Writing probabilities or fractions: This is a frequency tree, not a probability tree. The mark scheme explicitly notes: "If the values are given as probabilities, withhold the first A or B mark." Write integer counts only (e.g. write 52 , NOT 52/110 ).
Dividing by 2 instead of 3: A ratio of 1 : 2 has 1 + 2 = 3 parts. Dividing 330 by 2 is a frequent trap.
Misreading Year 11 vs Year 10: 73 is the number of Year 11 medal winners. Placing 73 in the Year 10 branch immediately loses marks.

Topics

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