0606/13 Oct/Nov 2025, Question 3: Connected Rates of Change and Small Changes
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
Given y = sin 5x on 0 ≤ x ≤ π/10, use calculus and the supplied table to estimate how much x changes when y rises from √3/2 by 0.01.
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Solution · 4 marks
- 1sin 5x = √3/2 gives 5x = π/3, so x = π/15
- 2dy/dx = 5 cos 5x
- 3At x = π/15: dy/dx = 5 cos(π/3) = 5/2
- 4δy ≈ (dy/dx) δx, so 0.01 = (5/2) δx
- 5δx = 0.004
Answerδx = 0.004 or 1/250
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