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4MA1/2FR Jan 2020, Question 12: Prime Factorization

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2FR (Foundation) · Calculator · 6 marks

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The question, in short

Practice index laws and prime factorisation: combine repeated terms, express products as single powers, and factorise 800 into primes.

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

Part (a) · 1 mark

Add four identical terms, each k, and give the result in its simplest form.

  1. 1k + k + k + k = 4k

Answer4k

Part (bi) · 1 mark

Express the product of four 9s as one power with base 9.

  1. 19 is multiplied by itself 4 times
  2. 29 × 9 × 9 × 9 = 9⁴

Answer9⁴

Part (bii) · 1 mark

Express that same product of four 9s as one power with base 3.

  1. 19 = 3²
  2. 29⁴ = (3²)⁴ = 3⁸

Answer3⁸

Part (c) · 1 mark

Combine 5 to the power 17 multiplied by 5 squared into one power of 5.

  1. 1Same base, so add the powers: 17 + 2 = 19
  2. 25¹⁷ × 5² = 5¹⁹

Answer5¹⁹

Part (d) · 2 marks

Break 800 down into prime factors, showing each step of the working.

  1. 1Divide by 2 again and again: 800, 400, 200, 100, 50, 25
  2. 2That uses five 2s and leaves 25
  3. 325 = 5 × 5
  4. 4800 = 2×2×2×2×2×5×5

Answer2×2×2×2×2×5×5

Stuck on a step? Read the free lesson: Prime Factorization

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