AQA GCSE Mathematics Paper 2 (Foundation), June 2025: Question 14

4 marks · Easy difficulty · Short Answer

Match four verbal descriptions involving a variable to their correct algebraic expressions.

Practise this question

Question

Matching activity with two columns of boxes. The left column lists word descriptions: '2 more than n' (already connected with a line to 'n + 2'), 'n doubled', 'n multiplied by itself', 'half of n', and '2 less than n'. The right column lists algebraic expressions: 2n, n + 2, square root of n, n/2, n - 2, n^2, and 2 - n.

Mark scheme

Show the mark scheme Mark scheme diagram showing 4 correct matches: 'n doubled' connects to 2n, 'n multiplied by itself' connects to n^2, 'half of n' connects to n/2, and '2 less than n' connects to n - 2. Award B4 for all four correct, or B1 for each correct match.

How to answer it

Matching Worded Descriptions to Algebraic Expressions

What this question tests

This question assesses your ability to translate everyday mathematical phrases into formal algebraic notation. It checks understanding of algebraic conventions, including writing multiplication without a multiplication sign (e.g. 2n), index notation for repeated multiplication (n²), division as fractions (n/2), and avoiding order errors in subtraction.

Question 14 • Total: 4 Marks

Matching Words to Expressions

Foundations of Algebra

✅ Correct Answers & Matching Pairs

Description (Left box) Match Correct Expression (Right box) Marks Awarded
2 more than n → n + 2 (Given in the question)
n doubled → 2n B1
n multiplied by itself → n² B1
half of n → n / 2 B1
2 less than n → n − 2 B1

Unused distractors on the right-hand side: √n and 2 − n .

📐 Step-by-Step Breakdown for Each Term

  1. "n doubled": "Doubling" means multiplying by 2. In algebra, 2 × n is written as 2n (the number always comes before the letter without a multiplication sign).
  2. "n multiplied by itself": This means n × n. When a number or variable multiplies itself, we write it using a power (exponent): n².
  3. "half of n": Finding half means dividing by 2. In algebra, division is written as a fraction: n / 2.
  4. "2 less than n": Starting with n and taking 2 away gives n − 2. Notice that "2 less than n" is completely different from "n less than 2" (which would be 2 − n).

💡 Key Knowledge & Conventions

  • Coefficient first: Write 2n , never n2 or 2 × n .
  • Powers vs Multiples:
    • n + n = 2n (two lots of n)
    • n × n = n² (n squared)
  • Fractions for division: Division is standardly shown as n / 2 rather than using the division symbol ÷.
  • Square root: The symbol √n means "the square root of n", which undoes squaring.

🧠 Exam Technique & Guidance

  • Substitute a number: If you are unsure, pick a simple number like n = 10.
    • "2 less than 10" = 8 → 10 − 2 = 8, but 2 − 10 = −8. So it must be n − 2 !
  • Count your lines: There are 4 descriptions to match, so you should draw exactly 4 straight lines.
  • Never leave double lines: The mark scheme states: "More than one line from a box on the left is incorrect for that box." If you change your mind, cross out the incorrect line clearly!
  • Use a ruler: Neat lines avoid ambiguous answers where examiners cannot tell which box you aimed for.

❌ Common Traps & Student Misconceptions

  • Confusing n² and 2n: A very common error is mixing up squaring and doubling. Remember that multiplying by itself gives a power ( n² ), whereas multiplying by 2 gives a coefficient ( 2n ).
  • Order of subtraction trap (2 − n vs n − 2): Because "2" appears first in the words "2 less than n", many students instinctively write 2 − n . Remember: subtraction is not commutative! You start with n and subtract 2, giving n − 2 .
  • Confusing square root and half: √n is a distractor. Halving is dividing by 2 ( n / 2 ), not square rooting.
Examiner Mark Scheme Notes: Each correct link scores 1 mark (B1 each, up to B4 total). Any unambiguous indication (such as letters or clean lines) is accepted. However, multiple links originating from a single left-hand box automatically forfeit the mark for that item.

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.