0606/21 May/Jun 2026, Question 10: Tangents, Normals and Stationary Points (Further)
Cambridge IGCSE Additional Mathematics 0606 · Paper 21 (Calculator) · Calculator · 10 marks
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The question, in short
For y = x² ln(3x² + 5), find where the normal at x = −1 cuts both axes, then give the area of triangle OPQ to 3 significant figures.
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Solution · 10 marks
- 1dy/dx = 2x ln(3x² + 5) + x² × 6x/(3x² + 5)
- 2At x = −1: y = ln 8, dy/dx = −2 ln 8 − 6/8 = −4.9089…
- 3Gradient of normal = 1/(2 ln 8 + 0.75) = 0.2037…
- 4Normal: y − ln 8 = 0.2037…(x + 1)
- 5y = 0: x = −11.21 (P); x = 0: y = 2.283 (Q)
- 6Area = (1/2)(11.21)(2.283) = 12.8
Answer12.8
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Also searched as: 0606/21/M/J/26 · 0606_s26_qp_21 · 0606 s26 21 · question 10.
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