Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2022, Question 6: Simultaneous Equations with a Curve

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

The question, in short

Show all working without calculator methods to derive a quartic equation from two given equations, then solve the simultaneous equations exactly in surd form.

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

Part (a) · 2 marks

Eliminate y between the two given equations to show that 2x⁴ − 15x² − 50 = 0.

  1. 1From the second equation y = x³ − 6x
  2. 22x(x³ − 6x) − 3x² = 50
  3. 32x⁴ − 12x² − 3x² − 50 = 0, so 2x⁴ − 15x² − 50 = 0

AnswerShown: 2x(x³ − 6x) − 3x² = 50 ⇒ 2x⁴ − 12x² − 3x² − 50 = 0 ⇒ 2x⁴ − 15x² − 50 = 0

Part (b) · 5 marks

Using the result from part a, solve the simultaneous equations, giving answers in fully simplified surd form.

  1. 1(2x² + 5)(x² − 10) = 0
  2. 22x² = −5 has no real solution, so x² = 10 and x = ±√10
  3. 3x = √10: y = (√10)³ − 6√10 = 10√10 − 6√10 = 4√10
  4. 4x = −√10: y = −10√10 + 6√10 = −4√10
  5. 5Solutions: (√10, 4√10) and (−√10, −4√10)

Answerx = √10, y = 4√10 and x = −√10, y = −4√10

Stuck on a step? Read the free lesson: Simultaneous Equations with a Curve

Practise more simultaneous equations with a curve 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 simultaneous equations with a curve

Also searched as: WMA11 June 2022 · WMA11/01 · wma11 jun22 · IAS Maths Pure Mathematics 1 June 2022 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.