0606/13 Oct/Nov 2025, Question 5: Equation of the Tangent Line
Cambridge IGCSE Additional Mathematics 0606 · Paper 13 (Non-calculator) · Non-calculator · 8 marks
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The question, in short
Find the x-coordinates where the normal to y = x³ + (3/2)x² − 2x + 1 at x = 0 meets the curve again at two other points.
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Solution · 8 marks
- 1dy/dx = 3x² + 3x − 2; at x = 0 the gradient of the tangent is −2
- 2Gradient of the normal = 1/2; the point is (0, 1)
- 3Normal: y = 1 + (1/2)x
- 41 + (1/2)x = x³ + (3/2)x² − 2x + 1
- 5x(2x² + 3x − 5) = 0
- 6x(x − 1)(2x + 5) = 0
- 7x = 1 and x = −5/2 (x = 0 is the original point)
Answerx = 1 and x = −5/2
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Also searched as: 0606/13/O/N/25 · 0606_w25_qp_13 · 0606 w25 13 · question 5.
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