0606/12 May/Jun 2025, Question 1: Sketching Cubics and Cubic Inequalities
Cambridge IGCSE Additional Mathematics 0606 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
From the graph of y = |f(x)| for a cubic f, with x-intercepts at −2, −0.5 and 3 and y-intercept 2, find both possible fully factorised expressions for f(x).
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Solution · 3 marks
- 1Roots at x = −2, −0.5, 3, so f(x) = k(x + 2)(2x + 1)(x − 3)
- 2|f(0)| = 2: |k × 2 × 1 × (−3)| = 2, so |6k| = 2
- 3k = ±1/3
- 4f(x) = ±(1/3)(x + 2)(2x + 1)(x − 3)
Answerf(x) = (1/3)(x + 2)(2x + 1)(x − 3) or f(x) = −(1/3)(x + 2)(2x + 1)(x − 3)
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