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WMA11/01 Oct 2023, Question 3: Surds

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Rationalise a surd fraction into the form a√3 + b√5, then use that result to solve an equation involving x with surds, giving the answer in simplest form.

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

Part (a) · 3 marks

Express (8 − √15)/(2√3 + √5) as a√3 + b√5 and find the integer values of a and b.

  1. 1Multiply top and bottom by (2√3 − √5)
  2. 2Denominator: (2√3)² − (√5)² = 12 − 5 = 7
  3. 3Numerator: 16√3 − 8√5 − 2√45 + √75 = 16√3 − 8√5 − 6√5 + 5√3
  4. 4= 21√3 − 14√5
  5. 5So (21√3 − 14√5)/7 = 3√3 − 2√5

Answer3√3 − 2√5

Part (b) · 3 marks

Solve (x + 5√3)√5 = 40 − 2x√3, using part a or otherwise, and give x in simplest form.

  1. 1Expand: x√5 + 5√15 = 40 − 2x√3
  2. 2x√5 + 2x√3 = 40 − 5√15
  3. 3x = (40 − 5√15)/(2√3 + √5) = 5(8 − √15)/(2√3 + √5)
  4. 4Using (a): x = 5(3√3 − 2√5) = 15√3 − 10√5

Answerx = 15√3 − 10√5

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Also searched as: WMA11 October 2023 · WMA11/01 · wma11 oct23 · IAS Maths Pure Mathematics 1 October 2023 · question 3.
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