AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 2

✅ Correct Answer

15

💡 Key Knowledge

A multiple of a number is found in its times table. Multiples of 5 always end in either 0 or 5.

• 5 × 1 = 5
• 5 × 2 = 10
• 5 × 3 = 15

📐 Check the Set

Testing each number for divisibility by 5:

• 8 ÷ 5 = 1.6 ❌
• 13 ÷ 5 = 2.6 ❌
• 15 ÷ 5 = 3 (whole number) ✅
• 27, 32, 36 do not end in 0 or 5 ❌

❌ Common Errors

• Confusing factors with multiples: Writing a number that divides 5 (such as 1 or 5) rather than a number in the 5 times table.
• Writing a number not on the card: Writing 5, 10, or 20. The question specifies from the card.

✅ Correct Answer

8

💡 Key Knowledge

A factor is a whole number that divides into another number completely with no remainder.

All factor pairs of 40 are:

• 1 × 40
• 2 × 20
• 4 × 10
• 5 × 8

📐 Verification

1. Check 40 ÷ 8 = 5 (no remainder, so 8 is a factor).
2. Check other card numbers:
   • 40 ÷ 13 = 3.07... ❌
   • 40 ÷ 15 = 2.66... ❌
   • 40 ÷ 27 = 1.48... ❌
   • 40 ÷ 32 = 1.25 ❌
   • 40 ÷ 36 = 1.11... ❌

❌ Common Errors

• Factor vs Multiple mix-up: Looking for a multiple of 40 (e.g. 80, 120) instead of a factor. Remember: "Factors fit into, Multiples multiply out."
• Picking 15 because 40 ends in 0 and 15 ends in 5, incorrectly assuming 15 divides 40.

✅ Correct Answer

13

💡 Key Knowledge

A prime number has exactly two distinct factors: 1 and itself.

First ten prime numbers to memorise:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

📐 Process of Elimination

• 8: Factors are 1, 2, 4, 8 (not prime)
• 13: Only divisible by 1 and 13 ✅ PRIME
• 15: 3 × 5 = 15 (composite)
• 27: 3 × 9 = 27 (composite)
• 32: Even number greater than 2, divisible by 2 (composite)
• 36: Even number, divisible by 2, 3, 6, etc. (composite)

❌ Common Errors

• Assuming all odd numbers are prime: Students frequently select 27 or 15 simply because they are odd numbers. Always check if 3 divides into odd numbers!
• Forgetting that 2 is the only even prime number.

✅ Correct Answer

36

💡 Key Knowledge

A square number is the product of an integer multiplied by itself (n × n = n²).

• 1² = 1
• 2² = 4
• 3² = 9
• 4² = 16
• 5² = 25
• 6² = 36

📐 Step-by-Step Test

1. Take the square root of candidate numbers:
   • √8 ≈ 2.83 ❌ (8 is a cube number: 2³ = 8, not square)
   • √27 ≈ 5.20 ❌ (27 is a cube number: 3³ = 27, not square)
   • √32 ≈ 5.66 ❌
   • √36 = 6 ✅ (exact integer)

❌ Common Errors

• Confusing square numbers with cube numbers: Writing 8 (2³) or 27 (3³). Always verify by multiplying an integer by itself twice (e.g. 6 × 6 = 36).
• Halving instead of square rooting: thinking 32 is square because 32 ÷ 2 = 16.