plumiImplicit and parametric differentiation: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on G.8 Implicit and parametric differentiation, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 14 questions on Implicit and parametric differentiation, as a list
- June 2025, Paper 1, Q11 (7 marks): The equation of a curve is x2y + 4y3 = 8x The curve has two stationary points. 11 (a) Use implicit differentiation to show that at the stationary points y = 4 x
- June 2025, Paper 1, Q13 (9 marks): A curve C has parametric equations x = 4(4t + 1)2 y = e–4t for – 1 4 ≤ t ≤ 0 13 (a) Find dy dx in terms of t [3 marks] 13 (b) Find an equation of the tangent to
- June 2024, Paper 1, Q19 (7 marks): A curve has equation y3e2x + 2y – 16x = k where k is a constant. The curve has a stationary point on the y-axis. Determine the value of k [7 marks]
- June 2023, Paper 1, Q15 (9 marks): The curve with equation x2 + 2y3 − 4xy = 0 has a single stationary point at P as shown in the diagram below. O P y x 15 (a) Show that the y-coordinate of P sati
- June 2023, Paper 3, Q9 (12 marks): A water slide is the shape of a curve PQ as shown in Figure 1 below. Figure 1 O P Q The curve can be modelled by the parametric equations x = t − 1 t + 4:8 y =
- June 2022, Paper 1, Q13 (9 marks): Figure 2 shows the approximate shape of the vertical cross section of the entrance to a cave. The cave has a horizontal floor. The entrance to the cave joins th
- June 2022, Paper 3, Q6 (9 marks): A design for a surfboard is shown in Figure 1. Figure 1 length width The curve of the top half of the surfboard can be modelled by the parametric equations x =
- November 2021, Paper 1, Q12 (8 marks): The equation of a curve is (x + y)2 = 4y + 2x + 8 The curve intersects the positive x-axis at the point P. 12 (a) Show that the gradient of the curve at P is −
- November 2021, Paper 1, Q14 (10 marks): The curve C is defined for t × 0 by the parametric equations x = t2 + t and y = 4t2 − t3 C is shown in the diagram below. x y O 14 (a) Find the gradient of C at
- November 2020, Paper 1, Q12 (13 marks): A curve C has equation x3 siny + cos y = Ax where A is a constant. C passes through the point P 3 p , p 6 12 (a) Show that A = 2 [2 marks] 12 (b) (i) Show that
- November 2020, Paper 2, Q8 (10 marks): The curve defined by the parametric equations x = t2 and y = 2t − 2 p × t × 2 p is shown in Figure 1 below. Figure 1 x y O 8 (a) Find a Cartesian equation of th
- June 2019, Paper 3, Q9 (15 marks): A curve has equation x2y2 + xy4 = 12 9 (a) Prove that the curve does not intersect the coordinate axes. [2 marks] 9 (b) (i) Show that dy dx = − 2xy + y3 2x2 + 4
- June 2018, Paper 1, Q5 (6 marks): A curve is defined by the parametric equations x = 4 × 2−t + 3 y = 3 × 2t − 5 5 (a) Show that dy dx = −3 4 × 22t [3 marks] 5 (b) Find the Cartesian equation of
- June 2018, Paper 2, Q6 (7 marks): Find the coordinates of the stationary point of the curve with equation (x + y − 2)2 = ey − 1 [7 marks]
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