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Tangents and normals to a curve: AQA Level 2 Further Maths questions

Every AQA Level 2 Further Maths exam question on 4.4 Tangents and normals to a curve, 2021–2025, with its mark scheme and examiner’s report.

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259 questions

  1. Q20

    June 2025 · Paper 2

    5 marks4.4 Tangents and normals to a curve4.7 Stationary points
    The whole paper ↗

  2. Q6

    June 2023 · Paper 1

    4 marks4.4 Tangents and normals to a curve
    The whole paper ↗

  3. Q13

    November 2021 · Paper 2

    4 marks4.4 Tangents and normals to a curve4.3 Differentiating powers of x
    The whole paper ↗

  4. Q15

    Specimen · Paper 1

    9 marks4.4 Tangents and normals to a curve2.15 Simultaneous equations
    The whole paper ↗
All 4 questions on Tangents and normals to a curve, as a list
  1. June 2025, Paper 2, Q20 (5 marks): Here is a sketch of the curve with equation y = 4 + 2x – x2 The tangent to the curve at the turning point P is shown. The normal to the curve at Q meets this ta
  2. June 2023, Paper 1, Q6 (4 marks): The equation of a curve is y = x6 + 4x2 – 7 Work out the equation of the tangent to the curve at the point (1, –2) Give your answer in the form y = mx + c Answe
  3. November 2021, Paper 2, Q13 (4 marks): P is the point on the curve y = ax3 + 10x2 where x = 2 The gradient of the normal to the curve at P is – 1 4 Work out the value of a. Answer
  4. Specimen, Paper 1, Q15 (9 marks): Point A lies on the curve y = x2 + 5x + 8 The x-coordinate of A is – 4 15 (a) Show that the equation of the normal to the curve at A is 3y = x + 16 15 (b) The n

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