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0606/22 May/Jun 2025, Question 4: Tangents, Normals and Stationary Points (Further)

Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 9 marks

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The question, in short

For y = 4 sin 2x cos 2x, find dy/dx at x = π/6, then find where the normal at that point crosses the x-axis.

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Part (a) · 4 marks

Differentiate y = 4 sin 2x cos 2x and evaluate the gradient at x = π/6.

  1. 1Product rule: dy/dx = 4(cos 2x × 2cos 2x + sin 2x × (−2sin 2x))
  2. 2dy/dx = 8cos²2x − 8sin²2x
  3. 3At x = π/6: 2x = π/3, cos(π/3) = 1/2, sin(π/3) = √3/2
  4. 4dy/dx = 8(1/4) − 8(3/4) = −4

Answer−4

Part (b) · 5 marks

Find the exact coordinates of P where the normal to the curve at x = π/6 meets the x-axis.

  1. 1When x = π/6, y = 4 × (√3/2) × (1/2) = √3
  2. 2Gradient of normal = −1/(−4) = 1/4
  3. 3Normal: y − √3 = (1/4)(x − π/6)
  4. 4At y = 0: −√3 = (1/4)(x − π/6)
  5. 5x = π/6 − 4√3, so P is (π/6 − 4√3, 0)

Answer(π/6 − 4√3, 0)

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Also searched as: 0606/22/M/J/25 · 0606_s25_qp_22 · 0606 s25 22 · question 4.
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