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4MA1/1F Jun 2022, Question 5: Real Numbers

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1F (Foundation) · Calculator · 5 marks

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The question, in short

From the list 3 6 7 8 11 25 27, pick numbers meeting four properties, then insert brackets into 2² + 5 × 2 + 3² = 99 to make it true.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

Choose an even number from the given list.

  1. 1Look for even numbers in the list: 3, 6, 7, 8, 11, 25, 27
  2. 2Even numbers are divisible by 2
  3. 36 and 8 are even
  4. 4Write down one of them

Answer6 or 8

Part (aii) · 1 mark

Choose a multiple of 9 from the given list.

  1. 1Look for a multiple of 9 in the list: 3, 6, 7, 8, 11, 25, 27
  2. 227 ÷ 9 = 3
  3. 3So 27 is a multiple of 9

Answer27

Part (aiii) · 1 mark

Choose a square number from the given list.

  1. 1Look for a square number in the list: 3, 6, 7, 8, 11, 25, 27
  2. 225 = 5 × 5
  3. 3So 25 is a square number

Answer25

Part (aiv) · 1 mark

Choose a prime number from the given list.

  1. 1Look for prime numbers in the list: 3, 6, 7, 8, 11, 25, 27
  2. 2Prime numbers have exactly two factors
  3. 33, 7, and 11 are prime
  4. 4Write down one of them

Answer3 or 7 or 11

Part (b) · 1 mark

Add brackets to 2² + 5 × 2 + 3² = 99 so the statement holds.

  1. 1Without brackets: 4 + 10 + 9 = 23, not 99
  2. 299 = 9 × 11, with 2² + 5 = 9 and 2 + 3² = 11
  3. 3(2² + 5) × (2 + 3²) = 99

Answer(2² + 5) × (2 + 3²) = 99

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