plumiDifferential equations: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on H.9 Differential 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 9 questions on Differential equations, as a list
- June 2025, Paper 1, Q17 (10 marks): (a) Use the substitution u = ex + 1 to show that ∫ e2x ex + 1 dx = ex – ln(ex + 1) + k [5 marks] 17 (b) Solve the differential equation ( ex + 1 e2x ) dy dx = c
- June 2024, Paper 1, Q20 (10 marks): A gardener stores rainwater in a cylindrical container. The container has a height of 130 centimetres. The gardener empties the water from the container through
- June 2023, Paper 1, Q16 (14 marks): (a) Given that 1 16 − 9x2 × A 4 − 3x + B 4 + 3x find the values of A and B [3 marks] 16 (b) An empty container, in the shape of a cuboid, has length 1.6 metres,
- June 2022, Paper 2, Q10 (15 marks): A gardener has a greenhouse containing 900 tomato plants. The gardener notices that some of the tomato plants are damaged by insects. Initially there are 25 dam
- November 2021, Paper 1, Q11 (8 marks): A curve, C, passes through the point with coordinates (1, 6) The gradient of C is given by dy dx = 1 6 (xy)2 Show that C intersects the coordinate axes at exact
- November 2021, Paper 2, Q17 (11 marks): A ball is released from a great height so that it falls vertically downwards towards the surface of the Earth. 17 (a) Using a simple model, Andy predicts that t
- November 2020, Paper 2, Q19 (8 marks): A particle moves so that its acceleration, a m s−2, at time t seconds may be modelled in terms of its velocity, v m s−1, as a = −0:1v2 The initial velocity of t
- June 2019, Paper 2, Q5 (7 marks): Solve the differential equation dt dx = ln x x2t for x > 0 given x = 1 when t = 2 Write your answer in the form t2 = f (x) [7 marks]
- June 2018, Paper 2, Q9 (14 marks): A market trader notices that daily sales are dependent on two variables: number of hours, t, after the stall opens total sales, x, in pounds since the stall ope
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