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4MA1/2H Jun 2018, Question 21: Surds

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

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The question, in short

Simplify and rewrite surd expressions: show a sum of two square roots equals 5√5, rationalise a fraction, and complete the square on a quadratic.

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

Part (a) · 2 marks

Show, with working, that √45 + √20 simplifies to 5√5.

  1. 145 = 9 × 5, so √45 = √9 × √5 = 3√5
  2. 220 = 4 × 5, so √20 = √4 × √5 = 2√5
  3. 33√5 + 2√5 = 5√5

Answer√45 + √20 = 3√5 + 2√5 = 5√5

Part (b) · 2 marks

Write 2/(√3 − 1) as p + √q with integers p and q, showing working.

  1. 1(2 / (√3 − 1)) × ((√3 + 1) / (√3 + 1)) = (2(√3 + 1)) / ((√3 − 1)(√3 + 1))
  2. 2(2(√3 + 1)) / (3 − 1) = (2(√3 + 1)) / 2 = √3 + 1
  3. 3So expression is 1 + √3

Answer1 + √3

Part (c) · 2 marks

Rewrite x² + 6√2x − 1 as (x + a)² + b, showing working.

  1. 1x² + 6√2 x + (3√2)² = (x + 3√2)²
  2. 2(x + 3√2)² − (3√2)² − 1 = (x + 3√2)² − 18 − 1
  3. 3(x + 3√2)² − 19

Answer(x + 3√2)² − 19

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