plumiParametric equations: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on C.3 Parametric equations, 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 8 questions on Parametric equations, as a list
- 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 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, Q1 (1 mark): A curve is defined by the parametric equations x = cos y and y = siny where 0 − y − 2p Which of the options shown below is a Cartesian equation for this curve?
- 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, 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 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 1, Q15 (10 marks): (a) At time t hours after a high tide, the height, h metres, of the tide and the velocity, v knots, of the tidal flow can be modelled using the parametric equat
- 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
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