AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 10

3 marks · Easy difficulty · Short Answer

Work out the value of the algebraic expression 2(a² + 3a) when a = 4.

Practise this question

Question

Question 10 reads: 'Work out the value of 2(a^2 + 3a) when a = 4' followed by four blank working lines and an 'Answer' line, worth 3 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 10 showing three alternative methods to achieve 3 marks. Alternative 1 awards M1 for evaluating 4 squared as 16 or 3 times 4 as 12, M1dep for 2 times (16 + 12), and A1 for the final answer 56. Alternative 2 and 3 involve expanding or factorising first, each leading to the answer 56 with corresponding method marks. Additional guidance notes on partial marks if a is still included.

How to answer it

Evaluating Algebraic Expressions by Substitution

📌 What this question tests

This question assesses your ability to substitute a numerical value into an algebraic expression containing powers, terms with coefficients, and brackets, followed by applying the correct order of operations (BIDMAS/BODMAS) to find a single numerical answer.

Question 10 • 3 Marks

Work out the value of 2(a² + 3a) when a = 4

📐 Step-by-Step Calculation

Method 1: Substitute directly into brackets first (Recommended)

  1. Replace a with 4 :
    2( (4)² + 3(4) )
  2. Evaluate the terms inside the brackets (Powers & Multiplication first):
    4² = 4 × 4 = 16
    3 × 4 = 12
    [Scores 1st method mark: M1]
  3. Add the terms inside the brackets:
    16 + 12 = 28
    Expression becomes: 2 × 28
    [Scores 2nd method mark: M1dep]
  4. Multiply by the outside factor:
    2 × 28 = 56
    [Scores accuracy mark: A1]

✅ Final Answer & Mark Breakdown

56

Mark Scheme Breakdown:
  • M1: Correct evaluation of any part: 4² = 16 or 3 × 4 = 12 (or finding 28 ).
  • M1 (dep): Fully correct substitution with correct order of operations: 2 × (16 + 12) or 2 × 28 .
  • A1: Final correct numerical answer of 56.

💡 Alternative Valid Methods

  • Method 2 (Expand first):
    Expand brackets: 2a² + 6a
    Substitute a = 4 :
    2(4²) + 6(4) = 2(16) + 24 = 32 + 24 = 56
  • Method 3 (Factorise first):
    Factorise fully: 2a(a + 3)
    Substitute a = 4 :
    2(4) × (4 + 3) = 8 × 7 = 56

🧠 Top Exam Techniques

  • Always use brackets when substituting: Write (4)² and 3(4) . This avoids misreading numbers (e.g. confusing 3a as 34).
  • BIDMAS reminder: Indices (powers) must always be calculated before multiplying by the outer number. Do not do (2 × 4)² .
  • Show intermediate lines: Even if you make an arithmetic slip at the end, showing 16 + 12 or 28 guarantees you pick up the method marks.

❌ Common Errors & Examiner Warnings

  • Leaving variables in the final answer: Writing 56a or 32a caps your score at a maximum of 1 mark. Once you substitute, no algebraic letters should remain!
  • Incomplete expansion: Writing only 2 × a² + 2 × 3a without substituting values scores only 1 mark (M1 M0 A0).
  • Squaring error: Thinking 4² = 8 instead of 4 × 4 = 16 .
  • Missing the outer bracket: Calculating 2 × 16 + 12 = 44 instead of multiplying the entire sum inside the bracket by 2.

Topics

Algebra · Number · 3.2.1 Notation, vocabulary and manipulation · 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.