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4PM1/02 Jun 2021, Question 1: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks

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The question, in short

Solve two inequalities in x and then find the values satisfying both at once.

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

Part (a) · 2 marks

Solve the linear inequality 8x − 7 < 5x + 5 for x.

  1. 18x − 5x < 5 + 7
  2. 23x < 12
  3. 3x < 4

Answerx < 4

Part (b) · 3 marks

Solve the quadratic inequality 2x² − 5x − 3 > 0 for x.

  1. 1(2x + 1)(x − 3) > 0
  2. 2Critical values x = −1/2 and x = 3
  3. 3Outside the roots: x < −1/2 or x > 3

Answerx < −1/2 or x > 3

Part (c) · 1 mark

Find the x values satisfying both 8x − 7 < 5x + 5 and 2x² − 5x − 3 > 0.

  1. 1Combine x < 4 with x < −1/2 or x > 3
  2. 2x < −1/2 or 3 < x < 4

Answerx < −1/2 or 3 < x < 4

Stuck on a step? Read the free lesson: Quadratic Inequalities

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