AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 1

3 marks · Easy difficulty · Short Answer

Solve three simple one-step linear equations: w + 8 = 19, 3x = 24, and 20 - y = 7.

Practise this question

Question

Question 1 contains three parts, each worth 1 mark. Part (a) asks to solve w + 8 = 19 with an answer line w =. Part (b) asks to solve 3x = 24 with an answer line x =. Part (c) asks to solve 20 - y = 7 with an answer line y =.

Mark scheme

Show the mark scheme Mark scheme table for Question 1. For 1(a), the answer is 11, awarded mark B1. For 1(b), the answer is 8, awarded mark B1. For 1(c), the answer is 13, awarded mark B1. Additional guidance notes state that showing the completed equation on the answer line or in working if the answer line is blank is condoned, but writing the equation in working and the RHS value on the answer line is awarded B0.

How to answer it

Solving Simple One-Step Linear Equations

📌 What this question tests

This question tests foundational algebraic skills on the Foundation Tier, specifically:

  • Understanding how to isolate an unknown variable using inverse operations (addition, subtraction, multiplication, division).
  • Basic mental arithmetic and number bonds.
  • Correct exam presentation: stating only the final numerical solution on the answer line rather than rewriting the question.
Question 1 (a)

Solve w + 8 = 19 [1 mark]

📐 Step-by-Step Calculation

  1. Identify the operation applied to w : adding 8.
  2. Apply the inverse operation (subtract 8) from both sides:
    w = 19 − 8
  3. Calculate the final value:
    w = 11

✅ Correct Answer

w = 11

Mark Scheme:
• 11 earns B1.

❌ Common Errors & Traps

  • Adding instead of subtracting: Calculating 19 + 8 = 27 . Always reverse the sign to balance the equation.
  • Rewriting the total: Writing 11 + 8 = 19 in working but accidentally putting 19 on the answer line awards 0 marks.

🧠 Examiner Insights

The mark scheme condones writing 11 + 8 = 19 directly on the answer line, but examiners strongly prefer seeing just the single numerical value 11 .

Question 1 (b)

Solve 3x = 24 [1 mark]

📐 Step-by-Step Calculation

  1. Recognise that 3x means 3 multiplied by x.
  2. Apply the inverse operation by dividing both sides by 3:
    x = 24 ÷ 3
  3. Calculate the final value:
    x = 8

✅ Correct Answer

x = 8

Mark Scheme:
• 8 earns B1.

💡 Key Knowledge

In algebra, adjacent numbers and letters indicate multiplication:

  • 3x = 3 × x
  • The inverse of multiplying by 3 is dividing by 3.

❌ Common Errors

  • Subtracting instead of dividing: Writing 24 − 3 = 21 .
  • Answer confusion: Writing 3 × 8 = 24 in the working space and writing the given total 24 on the answer line (scores 0 marks).
Question 1 (c)

Solve 20 − y = 7 [1 mark]

📐 Step-by-Step Calculation

Method 1: Direct Subtraction

  1. Ask: "What must be subtracted from 20 to leave 7?"
  2. Subtract 7 from 20: 20 − 7 = 13
  3. Therefore, y = 13

Method 2: Formal Balancing

  1. Add y to both sides: 20 = 7 + y
  2. Subtract 7 from both sides: 20 − 7 = y → y = 13

✅ Correct Answer

y = 13

Mark Scheme:
• 13 earns B1.

❌ Common Errors

  • Sign Errors: Incorrectly doing 20 + 7 = 27 or 7 − 20 = −13 . Check: 20 − (−13) = 33 ≠ 7 .
  • Copying the answer line: Writing 20 − 13 = 7 in the working and writing 7 on the answer line earns 0 marks.

🧠 Exam Tip: Always Substitute to Check

Never leave a one-mark solving question unchecked! Replace the letter with your answer in the original equation:

  • For (a): 11 + 8 = 19 (Correct)
  • For (b): 3 × 8 = 24 (Correct)
  • For (c): 20 − 13 = 7 (Correct)

Topics

Algebra · 3.2.3 Solving equations and inequalities

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.