Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2025, Question 9: Solving Equations with Surds

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 10 marks

The question, in short

Using the curves y = √(2x) and y = 12 − √x meeting at P, describe transformations of y = √x and y = −√x, then solve for P's coordinates exactly.

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

Part (ai) · 2 marks

Describe the single transformation mapping y = √x onto y = √(2x).

  1. 1√(2x) is √x with x replaced by 2x
  2. 2Replacing x by 2x is a stretch parallel to the x-axis, scale factor ½
  3. 3(Also √(2x) = √2 × √x: a stretch parallel to the y-axis, scale factor √2)

AnswerA stretch parallel to the x-axis with scale factor ½ (or equivalently a stretch parallel to the y-axis with scale factor √2)

Part (aii) · 2 marks

Describe the single transformation mapping y = −√x onto y = 12 − √x.

  1. 112 − √x = −√x + 12
  2. 2Adding 12 to y is a translation 12 units up, vector (0, 12)

AnswerA translation of 12 units up, by the vector (0, 12)

Part (bi) · 3 marks

Show that P's x coordinate satisfies √x = 12(√2 − 1).

  1. 1At P: √(2x) = 12 − √x
  2. 2√2 √x + √x = 12, so √x(√2 + 1) = 12
  3. 3√x = 12/(√2 + 1)
  4. 4Multiply top and bottom by (√2 − 1): √x = 12(√2 − 1)/(2 − 1) = 12(√2 − 1)

AnswerShown: √(2x) = 12 − √x gives √x(√2 + 1) = 12, so √x = 12/(√2 + 1) = 12(√2 − 1)

Part (bii) · 3 marks

Using the previous result, find the exact coordinates of P in simplest form.

  1. 1x = [12(√2 − 1)]² = 144(2 − 2√2 + 1)
  2. 2x = 144(3 − 2√2) = 432 − 288√2
  3. 3y = 12 − √x = 12 − 12(√2 − 1) = 24 − 12√2
  4. 4P(432 − 288√2, 24 − 12√2)

AnswerP(432 − 288√2, 24 − 12√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 2025 · WMA11/01 · wma11 jun25 · IAS Maths Pure Mathematics 1 June 2025 · question 9.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.