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4PM1/02R Jan 2023, Question 2: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2R · Calculator · 6 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 3x − 8 < 5x + 3 for x.

  1. 13x − 8 < 5x + 3
  2. 2−11 < 2x
  3. 3x > −11/2

Answerx > −11/2

Part (b) · 4 marks

Solve the quadratic inequality 4x² − 7x + 1 > 6 − 2x² for x.

  1. 16x² − 7x − 5 > 0
  2. 2(3x − 5)(2x + 1) > 0
  3. 3Critical values x = 5/3, x = −1/2
  4. 4Outside region: x < −1/2 or x > 5/3

Answerx < −1/2, x > 5/3

Part (c) · 1 mark

Find the values of x satisfying both inequalities simultaneously.

  1. 1Combine x > −11/2 with x < −1/2 or x > 5/3
  2. 2−11/2 < x < −1/2 or x > 5/3

Answer−11/2 < x < −1/2, x > 5/3

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