AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 5

3 marks · Easy difficulty · Multi-step Problem

Find an unknown number given that dividing it by 8 gives a quotient of 43 and a remainder of 5.

Practise this question

Question

Question 5 states: 'A number is divided by 8. The answer is 43 remainder 5. Work out the number.' Blank working space is provided above an 'Answer' line, with the question worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme for question 5 gives method mark M1 for '8 × 43' (oe), accuracy mark A1 for '344', and accuracy mark A1ft for '349' (ft their 344 + 5 correctly evaluated with M1 awarded). Additional guidance specifies that trial and improvement earns 0 or 3 marks, and 8 × 43.5 = 348 scores M0A0A0.

How to answer it

AQA GCSE Mathematics • Number • Foundation Tier

Reversing Division with a Remainder

What this question tests

  • Understanding the relationship between division, multiplication, and remainders.
  • Applying inverse operations to reconstruct an original dividend.
  • Basic mental or written long multiplication ( 8 × 43 ) and single-digit addition.
  • Avoiding the decimal-conversion trap for whole-number remainders.

Question 5 (3 Marks)

A number is divided by 8. The answer is 43 remainder 5. Work out the number.

📐 Step-by-Step Calculation

  1. Set up the inverse operation:
    To reverse dividing by 8, multiply the quotient (43) by 8.
    8 × 43
    [M1] Awarded for setting up the multiplication 8 × 43 (or equivalent method).
  2. Calculate the product:
    Break it down: 8 × 40 = 320 and 8 × 3 = 24
    320 + 24 = 344
    [A1] Awarded for the correct intermediate evaluation: 344 .
  3. Add the remainder:
    The remainder represents what was left over after dividing into equal groups of 8.
    344 + 5 = 349
    [A1ft] Awarded for correctly adding 5 to their intermediate product (follow-through applies if M1 was awarded).

✅ Final Answer

349

Full marks: 3 / 3

💡 Key Knowledge

  • Division Rule:
    Number = (Divisor × Quotient) + Remainder
  • Here, Divisor = 8 , Quotient = 43 , Remainder = 5 .
  • Always check backwards:
    349 ÷ 8 = 43 with 5 left over.

🧠 Exam Technique & Examiner Insight

  • Show all working: Writing down 8 × 43 guarantees method marks even if an arithmetic slip occurs.
  • Follow-through (ft): If you miscalculate 8 × 43 as 354, but clearly add 5 to get 359, you still secure 2 out of the 3 marks ( M1 A0 A1ft ).
  • Avoid Trial and Improvement: The mark scheme notes trial and improvement gives 0 or 3 marks—no partial method marks if it doesn't work!

❌ Common Errors & Pitfalls

  • The Decimal Error: Writing remainder 5 as .5 and calculating 8 × 43.5 = 348 scores 0 marks. A remainder of 5 means 5/8 , not 0.5 !
  • Subtracting the Remainder: Working out 344 - 5 = 339 instead of adding the leftover amount.
  • Adding Before Multiplying: Calculating (43 + 5) × 8 = 48 × 8 = 384 violates standard order of operations.

Topics

Number · 3.1.1 Structure and calculation

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.