plumiDifferential equations: Edexcel A‑Level Further Maths questions
Every Edexcel A-Level Further Maths exam question on CP.9 Differential equations, 2018–2025, with its mark scheme and examiner’s report.
Find questions824
All 17 questions on Differential equations, as a list
- June 2025, Core Pure 1, Q4 (8 marks): (a) Determine the general solution of the differential equation d d d d e 2 2 3 4 4 2 y x y x y x giving your answer in the form y = f (x) (5) Given that y = 5
- June 2025, Core Pure 1, Q8 (12 marks): A rambler starts a walk at the bottom of a hill at 10 am. The rambler walks all the way to the top of the hill and then turns around and walks back down to the
- June 2024, Core Pure 1, Q5 (9 marks): A raindrop falls from rest from a cloud. The velocity, v m s –1 vertically downwards, of the raindrop, t seconds after the raindrop starts to fall, is modelled
- June 2024, Core Pure 1, Q8 (15 marks): A scientist is studying the effect of introducing a population of type A bacteria into a population of type B bacteria. At time t days, the number of type A bac
- June 2024, Core Pure 2, Q6 (14 marks): The motion of a particle P along the x-axis is modelled by the differential equation 2 5 2 4 12 2 2 d d d d x t x t x t where P is x metres from the origin O at
- June 2023, Core Pure 1, Q6 (12 marks): Water is flowing into and out of a large tank. Initially the tank contains 10 litres of water. The rate of flow of the water is modelled so that • there are V l
- June 2023, Core Pure 2, Q9 (14 marks): A patient is treated by administering an antibiotic intravenously at a constant rate for some time. Initially there is none of the antibiotic in the patient. At
- June 2022, Core Pure 1, Q3 (6 marks): (a) Determine the general solution of the differential equation cos sin cos x y x y x x x d d e + = 2 2 giving your answer in the form y = f(x) (3) Given that y
- June 2022, Core Pure 1, Q10 (14 marks): θ Figure 3 The motion of a pendulum, shown in Figure 3, is modelled by the differential equation 2 2 d 1 9 cos3 d 2 θ θ t t + = where θ is the angle, in radians
- November 2021, Core Pure 1, Q6 (12 marks): A tourist decides to do a bungee jump from a bridge over a river. One end of an elastic rope is attached to the bridge and the other end of the elastic rope is
- November 2021, Core Pure 1, Q8 (9 marks): Two different colours of paint are being mixed together in a container. The paint is stirred continuously so that each colour is instantly dispersed evenly thro
- November 2020, Core Pure 1, Q5 (17 marks): Two compounds, X and Y, are involved in a chemical reaction. The amounts in grams of these compounds, t minutes after the reaction starts, are x and y respectiv
- November 2020, Core Pure 1, Q7 (11 marks): A sample of bacteria in a sealed container is being studied. The number of bacteria, P, in thousands, is modelled by the differential equation ( ) ( ) 1 1 1 2 +
- November 2020, Core Pure 2, Q3 (14 marks): A scientist is investigating the concentration of antibodies in the bloodstream of a patient following a vaccination. The concentration of antibodies, x, measur
- June 2019, Core Pure 1, Q5 (13 marks): $WDQNDWDFKHPLFDOSODQWKDVDFDSDFLW\RIOLWUHV7KHWDQNLQLWLDOO\FRQWDLQV OLWUHVRISXUHZDWHU 6DOWZDWHUHQWHUVWKHWDQNDWDUDWHRI
- June 2019, Core Pure 1, Q8 (18 marks): $VFLHQWLVWLVVWXG\LQJWKHHIIHFWRILQWURGXFLQJDSRSXODWLRQRIZKLWHFODZHGFUD\ILVKLQWR DSRSXODWLRQRIVLJQDOFUD\ILVK $WWLPHt\HDUVWKHQXPEHUR
- June 2019, Core Pure 2, Q5 (12 marks): An engineer is investigating the motion of a sprung diving board at a swimming pool. Let E be the position of the end of the diving board when it is at rest in
Questions, mark schemes and examiner’s reports are © Pearson Edexcel, from their published past papers. Plumi isn’t affiliated with any exam board. Want whole papers? Every Edexcel A-Level Further Maths paper.
Rather write your answers by hand on iPad? Plumi marks them against the same mark schemes.