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

Special Offers & Problem-Solving: Calculating Savings

📋 What this question tests

This multi-step question assesses your ability to apply real-world financial arithmetic: finding fractions/percentages of amounts ("half price"), multi-step addition, interpreting remainders in context (rounding up when saving discrete amounts), and evaluating the real-world impact when mathematical assumptions change.

Question 7 (a) · 3 Marks

Part (a): Number of Saturdays Needed to Save

"Assume the offer is permanent. How many Saturdays does Arif need to save for? You must show your working."

📐 Step-by-Step Method

1 Find the cost of the 2nd record:
Half price = 25 ÷ 2 = £12.50

2 Calculate total cost of 2 records:
Total = £25 + £12.50 = £37.50

3 Divide by savings per week (£8):
37.50 ÷ 8 = 4.6875 Saturdays

4 Round up in context:
After 4 Saturdays: 4 × £8 = £32 (not enough).
After 5 Saturdays: 5 × £8 = £40 (enough to buy them).
Therefore, he needs 5 Saturdays.

✅ Correct Answer & Marks

Answer: 5

Mark Scheme Breakdown:

M1: Finding half price ( 25 ÷ 2 or 12.50 ) or total cost implied by 37.50 .
M1 (dep): Complete method to find number of weeks: (25 + 12.5) ÷ 8 giving 4.6... OR listing multiples of 8 ( 32, 40 ).
A1: Correct answer of 5 with full valid working and no arithmetic errors.
Special Case (SC1): Giving an answer of 7 from working out 2 full-priced records ( 50 ÷ 8 = 6.25 → 7 ).

💡 Key Knowledge: Contextual Rounding

Division with remainders: Normal mathematical rounding says 4.6875 rounds to 5, but remember the context: even if the answer were 4.125 , you would still need 5 Saturdays because saving for 4 weeks would leave him short of money!
Listing multiples: An equally valid approach is listing weekly totals: Week 1 (£8), Week 2 (£16), Week 3 (£24), Week 4 (£32 - short by £5.50), Week 5 (£40 - enough!).

❌ Common Errors to Avoid

Arithmetic slips in division: Writing 37.5 ÷ 8 = 4.2 or 5.2 and then writing 5 loses the final accuracy mark (A0). The division must be correctly calculated to at least 4.6.
Rounding down: Truncating 4.6875 to 4 because 4 full weeks have passed. At 4 weeks, he only has £32 and cannot buy the records.
Ignoring the offer: Calculating £25 × 2 = £50, then 50 ÷ 8 = 6.25 → 7 Saturdays. This only gets 1 special case mark (SC1).

Question 7 (b) · 1 Mark

Part (b): Interpreting a Change in Assumptions

"In fact, the offer is only for 1 week and there are no new offers. What does this mean about the number of Saturdays he needs to save for? Tick one box."

✅ Correct Answer

Tick box 3:

[ ✓ ] It is greater than the answer to part (a)

B1: Awarded for selecting "It is greater than the answer to part (a)" only.

🧠 Exam Technique & Logical Reasoning

Evaluate the timing: He saves £8 each Saturday. To buy both records during the offer, he needed £37.50, which takes 5 weeks.
Effect of the expired offer: Since the offer ends after just 1 week, Arif cannot buy the records while the offer lasts.
Resulting cost: He will have to pay the normal price for both records ( 2 × £25 = £50 ).
Impact on savings time: Since £50 is more than £37.50, he must save for more weeks ( 50 ÷ 8 = 6.25 → 7 Saturdays). 7 is greater than 5.