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0606/13 May/Jun 2025, Question 1: Sketching Cubics and Cubic Inequalities

Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

From a sketched cubic curve, work out the integer constants in its factorised equation and use the sketch to solve an inequality.

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

Part (a) · 2 marks

Determine the integers a, b and c in the factorised cubic whose graph is shown.

  1. 1The curve crosses the x-axis at x = −2, −0.5 and 1
  2. 22x + a = 0 at x = −0.5, so a = 1
  3. 3x + b and x + c give roots −2 and 1, so b = 2, c = −1 (or the other way round)
  4. 4Check: y(0) = (1)(2)(−1) = −2, matching the graph

Answera = 1, b = 2, c = −1 (or b = −1, c = 2)

Part (b) · 3 marks

Using the graph, state the x-values where the curve is at or above 2.

  1. 1Draw the line y = 2 across the graph
  2. 2It meets the curve at x ≈ −1.7, x = −1 and x ≈ 1.2
  3. 3The curve is on or above y = 2 between −1.7 and −1, and for x ≥ 1.2
  4. 4−1.7 ≤ x ≤ −1 or x ≥ 1.2

Answer−1.7 ≤ x ≤ −1, x ≥ 1.2

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Also searched as: 0606/13/M/J/25 · 0606_s25_qp_13 · 0606 s25 13 · question 1.
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