plumiImplicit and parametric differentiation: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 7.8 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 9 questions on Implicit and parametric differentiation, as a list
- Summer 2025, Unit 3, Q1 (11 marks): 1. (a) Differentiate each of the following functions with respect to x. 3 e x 2 x (i) [2] 2 x e sin3 x (ii) [3] cos2 x (iii) [3] 2 x 1 (b) A function
- Summer 2025, Unit 3, Q13 (11 marks): 13. A curve is defined parametrically by 2 3 1 y 3 t 2 x t , . Show that the gradient of the curve at the point with parameter p is 1 (a) p . [4] t . 1
- Summer 2024, Unit 3, Q11 (10 marks): 11. A curve is defined parametrically by x 2 sin2 y 1 cos2 , . Show that the gradient of the curve at the point with parameter is tan . (a) [6]
- Summer 2023, Unit 3, Q2 (13 marks): 2 a) Differentiate each of the following with respect to x. i) 5 sin x x 2 [2] 3 cos x x ii) [2] 3 x e iii) [3] sin2 x b) Find the equation of the tangent
- Summer 2022, Unit 3, Q16 (8 marks): 6 The parametric equations of the curve C are x = 3 – 4t + t2, y = (4 – t)2. a) Find the coordinates of the points where C meets the y-axis. [3] b) Show that th
- Summer 2019, Unit 3, Q6 (11 marks): A curve C has parametric equations x = sinθ, y = cos2θ. 0 6 π The equation of the tangent to the curve C at the point P where θ= is a) 4 y = mx + c. Find the ex
- Summer 2019, Unit 3, Q10 (11 marks): a) Differentiate each of the following functions with respect to x. 1 0 i) x5 lnx e3x ii) x3 −1 1 ( tan x + 7x ) iii) 2 [8] b) A function is defined implicitly
- Summer 2018, Unit 3, Q10 (14 marks): 0 The equation of a curve C is given by the parametric equations x = cos2θ , y = cosθ. a) Find the Cartesian equation of C. [2] π Show that the line x – y + 1 =
- Summer 2018, Unit 3, Q16 (11 marks): 6 a) Differentiate the following functions with respect to x, simplifying your answer wherever possible. e3tanx, i) sin2x ii) . [5] x2 b) A function is defined
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