plumiFurther differential equations: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on FP.3 Further differential equations, 2018–2025, with its mark scheme and examiner’s report.
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All 17 questions on Further differential equations, as a list
- June 2025, Further Pure 1, Q2 (8 marks): The Taylor series expansion of f(x) about x = a is given by f(x) = f(a) + (x – a)f′(a) + ( ) ! x a − 2 2 f′′(a) + ... + ( ) ! x a r r − f (r)(a) + ... Given tha
- June 2025, Further Pure 1, Q7 (11 marks): The concentration, P mg m –3, of a pollutant in a reservoir, t days after the pollutant entered the reservoir, is modelled by the differential equation 1 4 1 2
- June 2025, AS Further Pure 1, Q2 (7 marks): Water is leaking from a hole in the base of a large spherical tank. The depth of water, H metres, in the tank is modelled by the differential equation 3 (5H – H
- June 2024, Further Pure 1, Q4 (8 marks): The Taylor series ansion of x about x a is given by f exp f f f f f x a x a a x a a x a r a r r 2 2! ... ! ... The curve with equ
- June 2024, Further Pure 1, Q10 (12 marks): The motion of a particle P along the x-axis is modelled by the differential equation t x t t t x t t x t t 2 2 2 3 2 1 2 1 8 d d d d e (I) where P has displac
- June 2024, AS Further Pure 1, Q2 (6 marks): An area of woodland contains a mixture of blue and yellow flowers. A study found that the proportion, x, of blue flowers in the woodland area satisfies the diff
- June 2023, Further Pure 1, Q2 (16 marks): The vertical height, h m, above horizontal ground, of a passenger on a fairground ride, t seconds after the ride starts, where t 5, is modelled by the differe
- June 2023, AS Further Pure 1, Q4 (6 marks): A teacher made a cup of coffee. The temperature θ °C of the coffee, t minutes after it was made, is modelled by the differential equation d 0.05( 20) 0 d θ θ t
- June 2022, Further Pure 1, Q4 (6 marks): The velocity v ms–1, of a raindrop, t seconds after it falls from a cloud, is modelled by the differential equation d d v t = –0.1 v 2 + 10 t 0 Initially the
- June 2022, Further Pure 1, Q9 (13 marks): A particle P moves along a straight line. At time t minutes, the displacement, x metres, of P from a fixed point O on the line is modelled by the differential e
- June 2022, AS Further Pure 1, Q2 (7 marks): A population of deer was introduced onto an island. The number of deer, P, on the island at time t years following their introduction is modelled by the differe
- November 2021, Further Pure 1, Q8 (17 marks): A community is concerned about the rising level of pollutant in its local pond and applies a chemical treatment to stop the increase of pollutant. The concentra
- November 2020, AS Further Pure 1, Q1 (7 marks): The variables x and y satisfy the differential equation d d 2 2 y x = 2y 2 – x – 1 where d d y x = 3 and y = 0 at x = 0 Use the approximations d d 2 2 2 1 1 2 y
- June 2019, Further Pure 1, Q3 (9 marks): d d I y x x y = − 2 ( ) (a) Show that d d d d d d d d d d 5 4 3 y x ay y x b y x y x c y x 5 4 3 2 2 2 = + + ⎛ ⎝⎜ ⎞ ⎠⎟ where a, b and c are integers to be deter
- June 2019, Further Pure 1, Q6 (17 marks): The concentration of a drug in the bloodstream of a patient, t hours after the drug has been administered, where t - 6, is modelled by the differential equation
- June 2019, AS Further Pure 1, Q3 (7 marks): Julie decides to start a business breeding rabbits to sell as pets. Initially she buys 20 rabbits. After Wyears the number of rabbits, R, is modelled by the di
- June 2018, AS Further Pure 1, Q2 (7 marks): The temperature, θ °C, of coffee in a cup, t minutes after the cup of coffee is put in a room, is modelled by the differential equation d d θ t = −k(θ − 20) whe
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