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4MA1/1FR Jun 2018, Question 20: Prime Numbers

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1FR (Foundation) · Calculator · 3 marks

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The question, in short

Given E = n² + n + 5, evaluate E at n = 3, then decide whether Ali is right that E is always prime for whole-number n, giving a reason.

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

Part (a) · 1 mark

Substitute n = 3 into E = n² + n + 5 and calculate the resulting value of E.

  1. 1E = n² + n + 5 with n = 3
  2. 2E = 3² + 3 + 5
  3. 33² = 9
  4. 4E = 9 + 3 + 5
  5. 5E = 17

Answer17

Part (b) · 2 marks

State whether Ali's claim that E is prime for every whole number n holds, justifying with a suitable value of n.

  1. 1Try n = 4: E = 4² + 4 + 5 = 25
  2. 225 = 5 × 5, so 25 is not prime
  3. 3No: when n = 4, E = 25, which is not prime

AnswerNo, because when n = 4, E = 16 + 4 + 5 = 25, and 25 = 5 × 5 is not prime

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