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0606/21 May/Jun 2026, Question 1: Sketching Cubics and Cubic Inequalities

Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 5 marks

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The question, in short

Sketch the cubic y = (1/3)(2x − 1)(x + 3)(2x + 5) on axes, giving its axis intercepts, then solve the related inequality.

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

Part (a) · 3 marks

Sketch the curve y = (1/3)(2x − 1)(x + 3)(2x + 5) on the given axes and state where it crosses the x- and y-axes.

  1. 1Leading coefficient (1/3)(2)(1)(2) = 4/3 > 0, so the curve rises from bottom left to top right
  2. 2y = 0 when x = 1/2, x = −3, x = −5/2
  3. 3At x = 0: y = (1/3)(−1)(3)(5) = −5
  4. 4Maximum between −3 and −5/2 (2nd quadrant), minimum below the x-axis to the left of the y-axis (3rd quadrant)

AnswerPositive cubic with a maximum between x = −3 and x = −2.5 and a minimum in the third quadrant; x-intercepts −3, −2.5, 0.5; y-intercept −5

Part (b) · 2 marks

Solve (1/3)(2x − 1)(x + 3)(2x + 5) > 0, giving the range(s) of x.

  1. 1Roots: x = −3, −5/2, 1/2
  2. 2Positive cubic is above the x-axis between −3 and −5/2 and to the right of 1/2
  3. 3−3 < x < −5/2 or x > 1/2

Answer−3 < x < −5/2, x > 1/2

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Also searched as: 0606/21/M/J/26 · 0606_s26_qp_21 · 0606 s26 21 · question 1.
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