Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2019, Question 2: Solving Equations with Surds

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

The question, in short

Rationalise a surd fraction and use the result to solve a linear equation, giving both answers in the specified rational-plus-surd forms.

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

Part (a) · 2 marks

Simplify 1/(4 − 2√2) into the form a + b√2 with a and b rational.

  1. 1Multiply top and bottom by (4 + 2√2)
  2. 2= (4 + 2√2)/(16 − 8)
  3. 3= (4 + 2√2)/8 = 1/2 + (1/4)√2

Answer1/2 + (1/4)√2

Part (b) · 3 marks

Solve 4x = 2√2 x + 20√2, giving x as p + q√2 with p and q rational.

  1. 14x − 2√2 x = 20√2, so (4 − 2√2)x = 20√2
  2. 2x = 20√2 × 1/(4 − 2√2)
  3. 3x = 20√2 (1/2 + (1/4)√2)
  4. 4x = 10√2 + 10 = 10 + 10√2

Answerx = 10 + 10√2

Stuck on a step? Read the free lesson: Solving Equations with Surds

Practise more solving equations with surds questions

Real XMA01 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on solving equations with surds

Also searched as: WMA11 June 2019 · WMA11/01 · wma11 jun19 · IAS Maths Pure Mathematics 1 June 2019 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.