0606/13 May/Jun 2025, Question 12: Equation of the Tangent Line
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 6 marks
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The question, in short
Curve y = 4/x² + ax + 7 has normal x + 4y = b at x = 2. Find constants a and b.
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Solution · 6 marks
- 1dy/dx = −8/x³ + a
- 2At x = 2: dy/dx = −1 + a = a − 1
- 3Normal gradient = −1/4, so tangent gradient = 4: a − 1 = 4, a = 5
- 4At x = 2: y = 4/4 + 10 + 7 = 18
- 5b = 2 + 4(18) = 74
Answera = 5, b = 74
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