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

4 marks · Easy difficulty · Short Answer

Find the next term in three different numerical sequences and calculate the product of a positive integer and a negative integer.

Practise this question

Question

Question 1 consisting of four 1-mark parts: Part (a) asks to write down the next number in the sequence 1, 4, 7, 10. Part (b) asks to write down the next number in the sequence 2, 4, 8, 16. Part (c) asks to write down the next number in the sequence 20, 14, 8, 2. Part (d) asks to work out 3 multiplied by negative 6.

Mark scheme

Show the mark scheme Mark scheme table for Question 1: Part 1(a) gives answer 13 with mark B1. Part 1(b) gives answer 32 with mark B1. Part 1(c) gives answer -4 with mark B1. Part 1(d) gives answer -18 with mark B1.

How to answer it

Number Sequences and Directed Numbers

📋 What this question tests

This introductory Foundation question assesses your core arithmetic and pattern recognition skills:

  • Identifying the term-to-term rule in linear (arithmetic) sequences, including those with increasing and decreasing terms.
  • Recognising geometric sequences (doubling patterns / powers of 2).
  • Subtracting across zero into negative numbers.
  • Multiplying a positive integer by a negative integer.

Question 1 (a)

Write down the next number in the sequence: 1, 4, 7, 10

✅ Correct Answer

13

Mark Scheme: 1 mark (B1) for the correct value.

📐 Step-by-Step Working

  1. Find the difference between consecutive terms:
    4 − 1 = +3
    7 − 4 = +3
    10 − 7 = +3
  2. The term-to-term rule is add 3.
  3. Apply the rule to the last term: 10 + 3 = 13.

🧠 Exam Technique

Always write the differences between numbers directly onto the question paper above or between the terms. Checking at least two pairs confirms you have found a constant rule.

❌ Common Errors

Miscounting by 1 (e.g., writing 12 or 14) due to rushed mental addition.

Question 1 (b)

Write down the next number in the sequence: 2, 4, 8, 16

✅ Correct Answer

32

Mark Scheme: 1 mark (B1) for the correct value.

💡 Key Knowledge

This is a geometric sequence because the terms are multiplied by a constant number (the common ratio) rather than having a constant number added.

Each term is a power of 2: 2¹ = 2, 2² = 4, 2³ = 8, 2⁴ = 16, 2⁵ = 32.

📐 Step-by-Step Working

  1. Check the relationship between terms:
    2 × 2 = 4
    4 × 2 = 8
    8 × 2 = 16
  2. The rule is multiply by 2 (double each number).
  3. Next term: 16 × 2 = 32.

❌ Common Errors

  • Assuming it is an addition sequence: adding 8 (the last jump) to get 24, or mistakenly adding 4 to get 20.
  • Doubling errors resulting in 34 or 36.

Question 1 (c)

Write down the next number in the sequence: 20, 14, 8, 2

✅ Correct Answer

−4

Mark Scheme: 1 mark (B1) for −4.

📐 Step-by-Step Working

  1. Find the difference between terms:
    14 − 20 = −6
    8 − 14 = −6
    2 − 8 = −6
  2. The rule is subtract 6.
  3. Calculate the next term across zero:
    2 − 2 = 0
    0 − 4 = −4

🧠 Exam Technique

When subtracting across zero, use a quick mental number line: moving 6 steps left from 2 takes you 2 steps down to 0, leaving 4 more steps into the negative region, landing on −4.

❌ Common Errors

  • Missing the negative sign: Writing 4 instead of −4 (doing 6 − 2 rather than 2 − 6).
  • Off-by-one errors: Writing −3 or −5 from miscounting steps on the number line.

Question 1 (d)

Work out 3 × (−6)

✅ Correct Answer

−18

Mark Scheme: 1 mark (B1) for −18.

💡 Key Knowledge

Rules for multiplication of directed numbers:

  • positive × positive = positive
  • positive × negative = negative
  • negative × positive = negative
  • negative × negative = positive

📐 Step-by-Step Working

  1. Multiply the absolute values first: 3 × 6 = 18.
  2. Apply the sign rule: a positive number multiplied by a negative number gives a negative result.
  3. Result: −18.

❌ Common Errors

  • Writing +18 (ignoring the negative sign).
  • Confusing multiplication with addition: computing 3 + (−6) = −3.

Topics

Algebra · Number · 3.1.1 Structure and calculation · 3.2.4 Sequences

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.