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4MA1/1H Jan 2020, Question 17: Surds

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks

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The question, in short

Show the given squaring identity with full working, then simplify an algebraic expression raised to a negative fractional power.

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

Part (a) · 3 marks

Expand (6 + 2√12)² step by step and show it equals 12(7 + 4√3).

  1. 1(6 + 2√12)² = 36 + 2 × 6 × 2√12 + 4 × 12
  2. 2= 84 + 24√12
  3. 3√12 = 2√3, so 24√12 = 48√3
  4. 484 + 48√3 = 12(7 + 4√3)

Answer(6 + 2√12)² = 36 + 24√12 + 48 = 84 + 48√3 = 12(7 + 4√3)

Part (b) · 3 marks

Simplify fully (27a¹²/t¹⁵)^(−2/3), giving the result in its simplest form.

  1. 1A negative power flips the fraction: (t¹⁵ / 27a¹²)^(2/3)
  2. 2Power 2/3 means cube root, then square
  3. 3Cube root: t⁵ / (3a⁴)
  4. 4Square: t¹⁰ / (9a⁸)

Answert¹⁰ / (9a⁸)

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