plumiDifferential equations: AQA A‑Level Further Maths questions
Every AQA A-Level Further Maths exam question on I Differential equations, 2019–2025, with its mark scheme and examiner’s report.
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All 23 questions on Differential equations, as a list
- June 2025, Paper 1, Q17 (11 marks): (a) Show that during the subsequent motion the particle satisfies the differential equation . d d d d + + = 2 2 4 0 6 8 0 5 x x x t t Fully justify your answer.
- June 2025, Paper 2, Q17 (15 marks): A sample of biological material is placed in a freezer, and the freezer is then turned on. The initial temperature of the sample is 38 °C The temperature u °C o
- June 2024, Paper 1, Q14 (7 marks): Solve the differential equation dy dx + ytanh x = sinh3 x given that y = 3 when x = ln2 Give your answer in an exact form. [7 marks]
- June 2024, Paper 1, Q18 (12 marks): In this question use g = 9.8 m s–2 Two light elastic strings each have one end attached to a small ball B of mass 0.5 kg The other ends of the strings are attac
- June 2024, Paper 2, Q2 (1 mark): The movement of a particle is described by the simple harmonic equation x.. = –25x where x metres is the displacement of the particle at time t seconds, and x..
- June 2024, Paper 2, Q19 (10 marks): Solve the differential equation d2y dx2 + 4 dy dx – 45y = 21e5x – 0.3x + 27x2 given that y = 37 225 and dy dx = 0 when x = 0 [10 marks]
- June 2023, Paper 1, Q4 (1 mark): The solution of a second order differential equation is f (t) The differential equation models heavy damping. Which one of the statements below could be true? T
- June 2023, Paper 1, Q15 (9 marks): Find the general solution of the differential equation d2y dx2 − 3dy dx − 4y = cos 2x + 5x [9 marks]
- June 2023, Paper 2, Q16 (16 marks): A bungee jumper of mass m kg is attached to an elastic rope. The other end of the rope is attached to a fixed point. The bungee jumper falls vertically from the
- June 2022, Paper 1, Q1 (1 mark): The displacement of a particle from its equilibrium position is x metres at time t seconds. The motion of the particle obeys the differential equation d2x dt2 =
- June 2022, Paper 1, Q11 (19 marks): In this question use g as 10 m s−2 A smooth plane is inclined at 30° to the horizontal. The fixed points A and B are 3.6 metres apart on the line of greatest sl
- June 2022, Paper 2, Q9 (14 marks): (a) A curve passes through the point (5, 12.3) and satisfies the differential equation dy dx = (x2 − 9) 1 2 + 2xy x2 − 9 x > 3 Use Euler’s step by step method o
- June 2022, Paper 2, Q14 (14 marks): On an isolated island some rabbits have been accidently introduced. In order to eliminate them, conservationists have introduced some birds of prey. At time t y
- November 2021, Paper 1, Q8 (6 marks): A particle of mass 4 kg moves horizontally in a straight line. At time t seconds the velocity of the particle is v m s−1 The following horizontal forces act on
- November 2021, Paper 1, Q15 (13 marks): In this question use g = 9.8 m s−2 A particle P of mass m is attached to two light elastic strings, AP and BP. The other ends of the strings, A and B, are attac
- November 2021, Paper 2, Q10 (13 marks): In a colony of seabirds, there are y birds at time t years. 10 (a) The rate of reduction in the number of birds due to birds dying or leaving the colony is prop
- November 2020, Paper 1, Q10 (10 marks): (a) Find the general solution of the differential equation dy dx + 2y x = x + 3 x(x − 1)(x2 + 3) (x > 1) [8 marks] 10 (b) Find the particular solution for which
- November 2020, Paper 1, Q13 (12 marks): Two light elastic strings each have one end attached to a particle B of mass 3c kg, which rests on a smooth horizontal table. The other ends of the strings are
- November 2020, Paper 2, Q12 (12 marks): (a) Given that I = (b a e2t sin t dt , show that I = [qe2t sin t + re2t cos t]b a where q and r are rational numbers to be found. [6 marks] 12 (b) A small objec
- November 2020, Paper 2, Q13 (10 marks): Charlotte is trying to solve this mathematical problem: Find the general solution of the differential equation d2y dx2 + dy dx × 2y = 10e×2x Charlotte’s solutio
- June 2019, Paper 1, Q11 (7 marks): Find the general solution of the differential equation x dy dx − 2y = x3 4 − 2x − x2 p where 0 < x < 5 p − 1 [7 marks]
- June 2019, Paper 1, Q14 (11 marks): In this question use g = 10 m s−2 A light spring is attached to the base of a long tube and has a mass m attached to the other end, as shown in the diagram. The
- June 2019, Paper 2, Q15 (14 marks): A B Two tanks, A and B, each have a capacity of 800 litres. At time t = 0 both tanks are full of pure water. When t > 0 , water flows in the following ways: * W
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