AQA GCSE Mathematics Paper 3 (Foundation), June 2025: Question 7

5 marks · Easy difficulty · Multi-step Problem

Calculate and compare the total costs of two 24-month mobile phone plans, including applying a 10% discount to one plan.

Practise this question

Question

Question 7 introduces two mobile phone plans: Plan A has a phone costing £500 plus £11 per month for 24 months; Plan B has a free phone plus £35 per month for 24 months. Part (a) asks to show that the total cost of Plan A for 24 months is £764, worth 2 marks. Part (b) states that during a sale, the total cost of Plan B is reduced by 10%, and asks which plan is cheaper for 24 months during the sale, providing tick boxes for Plan A and Plan B with space to show working, worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme for question 7. For 7(a), M1 is awarded for 11 × 24, 764 − 500, or 264; A1 for completing the full calculation 11 × 24 + 500 = 764 or equivalent. For 7(b), Alternative method 1 awards M2 for calculating the reduced total price (35 × 0.9 × 24 or 756) with M1 for partial calculations (e.g. 35 × 24 = 840 or finding 10%), and A1 for 756 and selecting Plan B. Alternative method 2 compares monthly rates (£31.8... vs £31.50) to reach Plan B.

How to answer it

Comparing Mobile Phone Plans & Percentage Discounts

📋 What this question tests

This question assesses your ability to solve multi-step financial arithmetic problems:

  • Calculating total hire/contract costs over multiple months ( monthly cost × number of months + initial fee ).
  • Structuring a rigorous mathematical proof for a "Show that" question.
  • Calculating a percentage reduction (10% discount) using mental strategies or decimal multipliers.
  • Making a clear final decision supported by correct numerical evidence.

Part (a) — Total Cost of Plan A [2 Marks]

Show that the total cost of Plan A for 24 months is £764

📐 Step-by-Step Calculation

  1. Calculate total monthly charges:
    24 months at £11 per month:
    11 × 24 = £264
  2. Add the upfront handset cost:
    £264 + £500 = £764

✅ Model Answer

11 × 24 = 264
264 + 500 = 764

Mark Breakdown:
• M1: For showing 11 × 24 or 764 − 500 or finding 264 .
• A1: For full, clear working leading correctly to 764 .

🧠 Exam Technique: "Show That" Questions

Because the final answer ( £764 ) is already given in the question, the examiner is testing your working, not the final number.

  • You must clearly show where every intermediate number comes from.
  • Never skip the multiplication step: state 11 × 24 = 264 clearly.

❌ Common Trap

Writing down simply:

500 + 264 = 764

Without showing how you obtained 264 from 11 × 24 earns only M1 A0. The second mark requires complete mathematical justification.

Part (b) — Comparing Plans with a 10% Discount [3 Marks]

During a sale, the total cost of Plan B is reduced by 10%. Which plan is cheaper for 24 months?

📐 Step-by-Step Working (Method 1: Total Cost)

  1. Calculate original total cost of Plan B:
    Phone is free, so:
    24 × £35 = £840
  2. Apply the 10% reduction:
    Using a multiplier:
    840 × 0.90 = £756
    Or step-by-step:
    10% of £840 = £84
    £840 − £84 = £756
  3. Compare with Plan A:
    Plan A = £764
    Plan B = £756
    Since £756 < £764 , Plan B is cheaper.

✅ Model Answer

Working:
35 × 24 = 840
10% of 840 = 84
840 − 84 = 756
(or 35 × 0.90 × 24 = 756)

Box ticked: ☑ Plan B

Mark Breakdown:
• M1: For 35 × 24 (= 840) or finding 10% of 35 ( 3.50 ).
• M2: Complete method to find sale price: 840 × 0.9 or 840 − 84 .
• A1: Correct value £756 and ticking Plan B.

💡 Alternative Approach (Monthly Comparison)

You can also compare the monthly costs instead of total 24-month costs:

  • Plan A monthly equivalent: 764 ÷ 24 = £31.83...
  • Plan B discounted monthly: 35 × 0.90 = £31.50
  • Since £31.50 < £31.83 , Plan B is cheaper.

❌ Common Errors to Avoid

  • Forgetting to tick the box: You must state or tick which plan is cheaper to receive the final accuracy mark.
  • Applying 10% to the wrong number: Reducing £35 by 10% to £3.50 and forgetting to subtract it from £35.
  • Stopping at £84: Finding the discount amount (£84) but forgetting to subtract it from £840 before comparing to £764.

Topics

Number · Ratio, proportion and rates of change · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages · 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.