AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 16

1 mark · Easy difficulty · Short Answer

Rearrange the equation a + 3 = b to make a the subject.

Practise this question

Question

Question 16 asks to rearrange the equation a + 3 = b to make a the subject. It is worth 1 mark and ends with an answer line that reads 'a ='.

Mark scheme

Show the mark scheme Mark scheme for Question 16 gives B1 for the answer 'b - 3' or '-3 + b'. Additional guidance states to allow upper case B (e.g. a = B - 3), but awards B0 for 'b - +3', 'b + -3', or '3 - b'.

How to answer it

Rearranging a Simple Linear Formula

What this question tests
  • Changing the subject of a single-step formula.
  • Applying inverse operations to isolate a target variable.
  • Maintaining balance across an equals sign.

Question 16

Rearrange a + 3 = b to make a the subject. [1 mark]

✅ Correct Answer

On the answer line, write:

b − 3  or  −3 + b

1 Mark awarded:
  • B1: for b − 3 or −3 + b (upper case B is allowed, e.g., B − 3 ).

📐 Step-by-Step Method

  1. Identify the target: You want a on its own.
  2. Look at what is happening to a : Currently, 3 is being added to it ( + 3 ).
  3. Apply the inverse operation: The inverse of + 3 is − 3 .
  4. Apply to both sides:
    a + 3 − 3 = b − 3
    a = b − 3

💡 Key Knowledge

  • Subject of a formula: A variable is the "subject" when it sits completely alone on one side of the equals sign with a coefficient of 1.
  • Inverse operations:
    • Addition ( + ) reverses Subtraction ( − )
    • Multiplication ( × ) reverses Division ( ÷ )
  • Since a = is already printed on the answer line, you only need to write the expression for the right-hand side.

🧠 Exam Technique

  • Check by substitution: Pick simple numbers to verify your formula.
    Let a = 2 .
    From the original equation: 2 + 3 = 5 , so b = 5 .
    Now test your answer: a = b − 3 = 5 − 3 = 2 . It works!
  • Always use the same letter: Keep the letter b ; do not introduce new letters or switch variables.

❌ Common Errors (Mark Scheme Traps)

  • 3 − b (0 marks): Subtraction is not commutative. Reversing the order gives the negative of the correct expression.
  • b − +3 or b + −3 (0 marks): Do not leave unsimplified double signs. Expressions must be simplified cleanly.
  • a = b + 3 (0 marks): Forgetting to change the sign when moving a term across the equals sign.

Topics

Algebra · 3.2.1 Notation, vocabulary and manipulation

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.