plumiModelling with differential equations: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 9.5 Modelling with 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 6 questions on Modelling with differential equations, as a list
- June 2025, Core Pure, Q17 (18 marks): A researcher is modelling the height of a particular type of tree over its lifetime. Data suggests that the maximum possible height of this type of tree over it
- June 2024, Core Pure, Q17 (20 marks): In an industrial process, a container initially contains 1000 litres of liquid. Liquid is drawn from the bottom of the container at a rate of 5 litres per minut
- June 2023, Further Pure with Technology, Q4 (18 marks): In this question you are required to consider the family of differential equations a k d P P rP 1 , t 0 , P t ( ) 0 (*) = - H H K d t where r and K are positive
- November 2021, Core Pure, Q17 (20 marks): In a chemical process, a vessel contains 1 litre of pure water. A liquid chemical is then passed into the top of the vessel at a constant rate of a litres per m
- November 2020, Core Pure, Q16 (25 marks): The population density P, in suitable units, of a certain bacterium at time t hours is to be modelled by a differential equation. Initially, the population dens
- June 2019, Core Pure, Q17 (22 marks): A cyclist accelerates from rest for 5 seconds then brakes for 5 seconds, coming to rest at the end of the 10 seconds. The total mass of the cycle and rider is m
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