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WMA11/01 Oct 2022, Question 4: Cubic Equations and Curve Meetings

Pearson Edexcel International AS Level Mathematics · Pure Mathematics 1 (WMA11) · Calculator · 6 marks

The question, in short

Show detailed reasoning without calculator methods: solve f(x) = 0 for f(x) = x²(2x + 1) − 15x, then use that result to solve a related equation in y > 0, giving a simplified surd.

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

Part (a) · 4 marks

Solve f(x) = 0 where f(x) = x²(2x + 1) − 15x, showing full algebraic working without calculator reliance.

  1. 1f(x) = 2x³ + x² − 15x = x(2x² + x − 15)
  2. 2x(2x − 5)(x + 3) = 0
  3. 3x = 0, x = 5/2, x = −3

Answerx = 0, x = 5/2, x = −3

Part (b) · 2 marks

Hence solve y^(4/3)(2y^(2/3) + 1) − 15y^(2/3) = 0 for y > 0, giving the answer in simplified surd form.

  1. 1The equation is f(y^(2/3)) = 0, with x = y^(2/3)
  2. 2y > 0 so y^(2/3) > 0, so y^(2/3) = 5/2
  3. 3y = (5/2)^(3/2) = 5√5/(2√2)
  4. 4y = 5√10/4

Answery = (5/4)√10

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