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

2 marks · Easy difficulty · Short Answer

Calculate the total cost of 7 apples given that 4 apples cost £2.20.

Practise this question

Question

Question 12 asks: '4 apples cost £2.20. Work out the cost of 7 of these apples.' There are five blank answer lines followed by an answer line formatted as 'Answer £ [blank]', worth 2 marks.

Mark scheme

Show the mark scheme Mark scheme for question 12: M1 is awarded for finding the unit cost with 2.20 divided by 4 or 0.55 (or 220 divided by 4 or 55), or multiplying by the scale factor 7/4. A1 is awarded for the correct answer of 3.85. Additional guidance notes allow working in pence and specify how units are treated.

How to answer it

Direct Proportion: The Unitary Method

📋 What this question tests

This question assesses your ability to solve direct proportion problems in a financial context:

  • Using the unitary method (finding the cost of 1 item first).
  • Converting accurately between pounds (£) and pence (p).
  • Writing money values in correct decimal notation.

Question 12 Walkthrough

4 apples cost £2.20. Work out the cost of 7 of these apples. [2 marks]

📐 Step-by-Step Calculation

Method 1: Unitary Method (Recommended)

  1. Find the cost of 1 apple:
    £2.20 ÷ 4 = £0.55 (or 220p ÷ 4 = 55p )
    Earns M1
  2. Multiply by the target number (7 apples):
    7 × £0.55 = £3.85 (or 7 × 55p = 385p)
    Earns A1

Method 2: Multiplier (Scale Factor)

Scale factor = 7 ÷ 4 = 1.75
Total cost = 1.75 × £2.20 = £3.85

✅ Correct Answer

On the answer line:

Answer: £ 3.85

Mark Breakdown:
• M1: For 2.20 ÷ 4 , 0.55 , 220 ÷ 4 , or 55 .
• A1: For fully correct final value 3.85 .

💡 Key Knowledge

  • Direct Proportion: If the quantity of apples increases, the cost increases by the exact same multiple.
  • The Unitary Method: Always find the value of one single unit by dividing total cost by initial quantity:
    Cost of 1 item = Total Cost ÷ Number of Items
  • Working in Pence: If dividing decimals like £2.20 is difficult without a calculator, convert to pence first ( £2.20 = 220p ), divide, and then convert back by dividing by 100.

🧠 Exam Technique & Examiner Insight

  • Look at the pre-printed unit: The answer line already has a £ sign. Make sure your number matches that unit!
  • Show your working clearly: Even if you make an arithmetic mistake on the second step (e.g. 7 × 0.55), writing £2.20 ÷ 4 = £0.55 guarantees you score the method mark (M1).
  • Sanity check: 7 is nearly double 4, so the answer should be a little less than double £2.20 (£4.40). £3.85 makes complete sense.

❌ Common Errors & Traps to Avoid

  • Unit mismatch trap: Writing 385 on the answer line next to the printed £ symbol gives £385! This loses the accuracy mark (M1 A0) unless you explicitly cross out the £ sign and write "p".
  • Additive error: Thinking "7 apples is 3 more than 4, so add £3" or similar addition tricks. Direct proportion requires multiplication and division, not addition.
  • Decimal division slip: Writing £2.20 ÷ 4 = 0.52 or 0.50. Use short division (bus stop method) on 220 ÷ 4: 4 into 22 is 5 remainder 2, 4 into 20 is 5, giving 55p.

Topics

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

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