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4PM1/01 Jan 2022, Question 2: Quadratic Inequalities

Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 1 · Calculator · 7 marks

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The question, in short

For f(x) = 2x² − 12x + 5, express it as a(x + b)² + c with integers a, b, c, then use that form to solve an inequality.

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

Part (a) · 3 marks

Find the integer values of a, b and c when f(x) is written in completed-square form a(x + b)² + c.

  1. 1f(x) = 2(x² − 6x) + 5
  2. 2= 2[(x − 3)² − 9] + 5
  3. 3= 2(x − 3)² − 13
  4. 4a = 2, b = −3, c = −13

Answera = 2, b = −3, c = −13

Part (b) · 4 marks

Using your completed-square form, find the set of x values satisfying f(x) − 37 > 0.

  1. 12(x − 3)² − 13 > 37
  2. 2(x − 3)² > 25
  3. 3Critical values x − 3 = ±5: x = −2, 8
  4. 4Outside region: x < −2 or x > 8

Answerx < −2 or x > 8

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