plumiFirst order: integrating factor: AQA A‑Level Further Maths questions
AQA A-Level Further Maths past-paper questions on I.1 First order: integrating factor, 2019–2025, 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 7 questions on First order: integrating factor, as a list
- 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 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
- 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 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
- 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]
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