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4MA1/1FR Jun 2023, Question 8: Further Powers and Roots

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

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The question, in short

Three short arithmetic tasks: identify a prime in a given range, find a cube root, and evaluate a product of powers.

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

Part (a) · 1 mark

State the prime number that lies between 90 and 100.

  1. 1The prime numbers between 90 and 100 are checked: 91 = 7×13, 93 = 3×31, 95 = 5×19, 96, 98, 99, 100 are not prime. 97 has no factors other than 1 and itself.
  2. 297 is prime.

Answer97

Part (b) · 1 mark

Find the cube root of 79 507.

  1. 1Try cubing integers near 40: 40³ = 64,000, 45³ = 91,125.
  2. 243³ = 43 × 43 × 43 = 1849 × 43.
  3. 31849 × 40 = 73,960 and 1849 × 3 = 5,547.
  4. 473,960 + 5,547 = 79,507.
  5. 5So cube root of 79,507 is 43.

Answer43

Part (c) · 2 marks

Work out the value of 4² × 5³.

  1. 14² = 16.
  2. 25³ = 125.
  3. 316 × 125 = 2000.

Answer2000

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