Lemmara logoLemmaraWorked solution

WMA11/01 Jun 2024, Question 6: Simultaneous Equations with a Curve

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

The question, in short

Solve algebraically for where the line y − 5x = 75 meets the curve y = 2x² + x − 21, then describe the shaded region R using inequalities.

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

Part (a) · 4 marks

Find the coordinates of the two intersection points P and Q by algebraic methods, with no calculator reliance.

  1. 12x² + x − 21 = 5x + 75
  2. 22x² − 4x − 96 = 0, so x² − 2x − 48 = 0
  3. 3(x − 8)(x + 6) = 0, so x = −6 or x = 8
  4. 4x = −6: y = 5(−6) + 75 = 45; x = 8: y = 5(8) + 75 = 115
  5. 5P(−6, 45), Q(8, 115)

AnswerP(−6, 45) and Q(8, 115)

Part (b) · 3 marks

Express the shaded region R, bounded by the curve, the line and the x-axis, as a set of inequalities.

  1. 1R is above the x-axis: y ≥ 0
  2. 2R is below the line l: y ≤ 5x + 75
  3. 3R lies outside the curve C (below its left-hand branch): y ≤ 2x² + x − 21
  4. 4Keep R to the left of the curve's right-hand part: x ≤ 0 (any bound from −3.5 to 3 works)

Answery ≥ 0, y ≤ 5x + 75, y ≤ 2x² + x − 21, x ≤ 0 (strict inequalities also accepted)

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 2024 · WMA11/01 · wma11 jun24 · IAS Maths Pure Mathematics 1 June 2024 · question 6.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.