plumiFirst order: integrating factor: OCR MEI A‑Level Further Maths questions
OCR MEI A-Level Further Maths past-paper questions on 9.1 First order: integrating factor, 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 9 questions on First order: integrating factor, as a list
- June 2025, Core Pure, Q13 (11 marks): y d 2 13 The gradient of a curve y f ( ) x satisfies the differential equation x x 2 y 2 x . = - = + d - . (a) Show that the integrating factor for this differe
- 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 2025, Further Pure with Technology, Q3 (18 marks): This question concerns the family of differential equations d y ex x y a sin ( ) y (**) = - + d x where a is a constant. (a) In this part of the question a 0 .
- 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, Core Pure, Q11 (7 marks): y d - 11 Solve the differential equation cosh x x 2 y sinh x cosh x , given that y = when x 1 0 . [7] = = d
- June 2022, Core Pure, Q12 (9 marks): d y 2 12 Solve the differential equation ( x xy given that y = 1 when x = 0, giving your 4 ) 1 , - - = d x answer in the form y = f (x). [9]
- 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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