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4PM1/02 Jan 2023, Question 1: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 7 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) · 2 marks

Solve the linear inequality 2(3x − 1) < 4 − 3x for x.

  1. 16x − 2 < 4 − 3x
  2. 29x < 6
  3. 3x < 2/3

Answerx < 2/3

Part (b) · 4 marks

Solve the quadratic inequality 3x² − 8x − 3 < 0 for x.

  1. 13x² − 8x − 3 = (3x + 1)(x − 3)
  2. 2Critical values x = −1/3 and x = 3
  3. 3Inside region: −1/3 < x < 3

Answer−1/3 < x < 3

Part (c) · 1 mark

Find the x values satisfying both 2(3x − 1) < 4 − 3x and 3x² − 8x − 3 < 0.

  1. 1Combine x < 2/3 with −1/3 < x < 3
  2. 2−1/3 < x < 2/3

Answer−1/3 < x < 2/3

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

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