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WMA11/01 Oct 2024, Question 2: Surds

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 7 marks

The question, in short

Show full working without calculator methods: simplify an algebraic fraction with powers, and find the exact value of a in a surd equation, giving it as p√3 + q.

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

Part (i) · 3 marks

Simplify fully the expression 3y³(2x⁴)³ ÷ (4x²y⁴), showing all stages of working.

  1. 1(2x⁴)³ = 8x¹²
  2. 2Numerator = 3y³ × 8x¹² = 24x¹²y³
  3. 324x¹²y³ ÷ 4x²y⁴ = 6x¹⁰y⁻¹ = 6x¹⁰/y

Answer6x¹⁰/y

Part (ii) · 4 marks

Find the exact value of a in 16 ÷ (√3 + 1) = a√27 + 4, giving the answer as p√3 + q with simplified rational constants.

  1. 1√27 = 3√3
  2. 216/(√3 + 1) × (√3 − 1)/(√3 − 1) = 16(√3 − 1)/2 = 8√3 − 8
  3. 38√3 − 8 = 3√3 a + 4, so 3√3 a = 8√3 − 12
  4. 4a = 8√3/(3√3) − 12/(3√3) = 8/3 − 4/√3
  5. 5a = −(4/3)√3 + 8/3

Answera = −(4/3)√3 + 8/3

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Also searched as: WMA11 October 2024 · WMA11/01 · wma11 oct24 · IAS Maths Pure Mathematics 1 October 2024 · question 2.
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