AQA GCSE Mathematics Paper 2 (Higher), June 2025: Question 6

1 mark · Easy difficulty · Short Answer

Identify which given algebraic expression is a factor of 3x + 15.

Practise this question

Question

Question 6 asks to 'Circle the expression which is a factor of 3x + 15' for 1 mark. Four multiple choice options are presented horizontally: 3x, x + 12, x + 5, and x + 15.

Mark scheme

Show the mark scheme A mark scheme table showing Question 6 with the Answer 'x + 5', Mark 'B1', and no additional comments.

How to answer it

Factoring Linear Expressions: Finding Algebraic Factors

📋 What This Question Tests

This question evaluates your core understanding of algebraic factorisation, including:

  • Identifying the highest common factor (HCF) of terms in a linear expression.
  • Understanding that a factor divides an entire expression completely without leaving a remainder.
  • Distinguishing between terms (parts added together) and factors (parts multiplied together).
Question 6 [1 Mark]

Circle the expression which is a factor of 3x + 15

Multiple Choice Options: 3x  |  x + 12  |  x + 5  |  x + 15

✅ Correct Answer

x + 5

Mark Scheme Breakdown:
• B1: Circle or unambiguously indicate x + 5 .

💡 Key Knowledge

  • Factor: A number or expression that multiplies with another to give the original expression.
  • To find factors of ax + b , factorise by finding the highest common factor of the numerical coefficients.
  • Here, the common factor between 3x and 15 is 3 .

📐 Step-by-Step Solution

  1. Find the Highest Common Factor (HCF) of the numbers:
    The two terms are 3x and 15 .
    Factors of 3: 1, 3
    Factors of 15: 1, 3, 5, 15
    Highest common factor = 3.
  2. Factorise out the common factor 3:
    3x ÷ 3 = x
    15 ÷ 3 = 5
    Therefore: 3x + 15 = 3(x + 5)
  3. Identify the factors:
    The factors of 3x + 15 are 3 and (x + 5) .
    Looking at the options, x + 5 is the correct factor.

❌ Common Traps & Wrong Options

  • Choosing 3x : Students see 3x at the start of the expression and pick it. However, 3x does not divide evenly into 15 .
  • Choosing x + 12 : Confusing division with subtraction (e.g., thinking 15 - 3 = 12 ). Factorising requires division, not subtraction.
  • Choosing x + 15 : Dividing only the first term by 3 ( 3x ÷ 3 = x ) while forgetting to divide the second term by 3.

🧠 Examiner Tips & Quick Checks

  • Reverse Check (Expand): Multiply the option by the factor you took out: 3 × (x + 5) = 3x + 15 . If it returns the original expression, it is definitely correct!
  • Clear Intent: If you change your mind, cross out the incorrect ring clearly and draw a new circle around your final choice. Ambiguous marks lose the B1 mark.

Topics

Algebra · 3.2.1 Notation, vocabulary and manipulation

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 2 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.