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4PM1/02 Jun 2025, Question 2: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 5 marks

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The question, in short

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

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

Part (a) · 1 mark

Solve the linear inequality 9 − 3x > 11x + 2 for x.

  1. 17 > 14x
  2. 2x < 1/2

Answerx < 1/2

Part (b) · 3 marks

Solve the quadratic inequality 10x² + 7x < 12 for x.

  1. 110x² + 7x − 12 < 0
  2. 2(5x − 4)(2x + 3) < 0
  3. 3Critical values x = 4/5 and x = −3/2
  4. 4−3/2 < x < 4/5

Answer−3/2 < x < 4/5

Part (c) · 1 mark

Find the x values satisfying both 9 − 3x > 11x + 2 and 10x² + 7x < 12.

  1. 1Overlap of x < 1/2 and −3/2 < x < 4/5
  2. 2−3/2 < x < 1/2

Answer−3/2 < x < 1/2

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

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