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4PM1/02R Jan 2022, Question 1: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · 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 the same time.

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

Part (a) · 1 mark

Solve the linear inequality 5x − 10 > 4x − 7 for x.

  1. 15x − 4x > −7 + 10
  2. 2x > 3

Answerx > 3

Part (b) · 3 marks

Solve the quadratic inequality 2x² − 11x + 5 < 0 for x.

  1. 12x² − 11x + 5 = (2x − 1)(x − 5)
  2. 2Critical values x = 1/2 and x = 5
  3. 3The quadratic is negative between the roots: 1/2 < x < 5

Answer1/2 < x < 5

Part (c) · 1 mark

Find the x values satisfying both 5x − 10 > 4x − 7 and 2x² − 11x + 5 < 0.

  1. 1Combine x > 3 with 1/2 < x < 5
  2. 23 < x < 5

Answer3 < x < 5

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

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