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0580/22 May/Jun 2026, Question 23: Tangents and normals

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Non-calculator · 7 marks

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The question, in short

For the curve y = 2x² − 11x + 12, find the tangent gradient at x = 2, then the equation of the line through that point perpendicular to the tangent.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 3 marks

Gradient of the tangent at x = 2.

  1. 1The gradient of the tangent is the value of dy/dx at that point
  2. 22x² → 4x, −11x → −11, 12 → 0
  3. 3dy/dx = 4x − 11
  4. 4At x = 2: 4 × 2 − 11 = 8 − 11 = −3

Answer−3

Part (b) · 4 marks

Equation of the perpendicular line L at x = 2.

  1. 1At x = 2: y = 2 × 4 − 22 + 12 = −2
  2. 2dy/dx = 4x − 11, so tangent gradient at x = 2 is 8 − 11 = −3
  3. 3Gradient of L = −1 ÷ (−3) = 1/3
  4. 4y − (−2) = 1/3(x − 2), so y = 1/3 x − 8/3

Answery = 1/3 x − 8/3 or 3y − x + 8 = 0

Stuck on a step? Read the free lesson: Equation of the Tangent Line

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Also searched as: 0580/22/M/J/26 · 0580_s26_qp_22 · 0580 s26 22 · question 23.
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