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4PM1/02 Jan 2020, Question 2: 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, a linear one and a quadratic one, 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

Find the values of x satisfying the linear inequality 3 + 2x ≤ x + 2.

  1. 13 + 2x ≤ x + 2
  2. 2x ≤ −1

Answerx ≤ −1

Part (b) · 4 marks

Find the set of x values satisfying the quadratic inequality 8x² + 10x < 3.

  1. 18x² + 10x − 3 < 0
  2. 2(4x − 1)(2x + 3) = 0 gives critical values x = 1/4, x = −3/2
  3. 3The quadratic is negative between its roots
  4. 4−3/2 < x < 1/4

Answer−3/2 < x < 1/4

Part (c) · 1 mark

Find the x values that satisfy both 3 + 2x ≤ x + 2 and 8x² + 10x < 3 together.

  1. 1Combine x ≤ −1 with −3/2 < x < 1/4
  2. 2−3/2 < x ≤ −1

Answer−3/2 < x ≤ −1

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

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