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WMA11/01 Jun 2022, Question 3: Surds

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 5 marks

The question, in short

Without a calculator, work through both parts: prove a surd fraction involving √180, √80 and √5 equals a whole number, and rewrite a fraction with 4√5, 5, 7 and 3√5 as a + b√5.

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

Part (i) · 2 marks

Demonstrate that (√180 − √80) ÷ √5 comes to a whole number, and state that number.

  1. 1√180 = 6√5 and √80 = 4√5
  2. 2(6√5 − 4√5)/√5 = 2√5/√5 = 2

Answer2

Part (ii) · 3 marks

Express (4√5 − 5) ÷ (7 − 3√5) as a + b√5 with a and b rational.

  1. 1Multiply top and bottom by 7 + 3√5
  2. 2Top: (4√5 − 5)(7 + 3√5) = 28√5 + 60 − 35 − 15√5 = 25 + 13√5
  3. 3Bottom: 49 − 45 = 4
  4. 4= 25/4 + (13/4)√5

Answer25/4 + (13/4)√5

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