plumiDifferential equations: OCR A‑Level Maths questions
OCR A-Level Maths past-paper questions on 1.08.9 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 11 questions on Differential equations, as a list
- June 2025, Paper 1, Q12 (11 marks): 4 x + 12 (a) Express ( in partial fractions. [4] x 1 x )( 1 x ) + - d = y 2 4 x + The gradient of a curve is given by and the curve passes through the d x x ( 1
- June 2024, Paper 2, Q5 (8 marks): A scientist is monitoring the decline in the population of a certain endangered species of animal in an area where their natural habitat has been damaged. As a
- June 2023, Paper 3, Q7 (12 marks): 7 A car C is moving horizontally in a straight line with velocity ms v - at time t seconds, where - , of C is modelled by the equation 2 v 0 and t 0 . The accel
- June 2022, Paper 1, Q11 (9 marks): d y 2 3 x ln x 11 The gradient function of a curve is given by d . = x 3 y e The curve passes through the point (e, 1). 3 = y (a) Find the equation of this curv
- June 2022, Paper 2, Q8 (7 marks): 50cm 30° hcm The diagram shows a water tank which is shaped as an inverted cone with semi-vertical angle 30° and height 50 cm. Initially the tank is full, and t
- November 2021, Paper 1, Q12 (13 marks): A cake is cooling so that, t minutes after it is removed from an oven, its temperature is i °C. When the cake is removed from the oven, its temperature is 160 °
- November 2021, Paper 3, Q7 (8 marks): A curve C in the x-y plane has the property that the gradient of the tangent at the point P x y is ( , ) three times the gradient of the line joining the point
- November 2020, Paper 1, Q12 (9 marks): Find the general solution of the differential equation d y 3 2 ( 2 x 3 x 11 x 6 ) y ( 20 x 35 ) . - - + = - d x Give your answer in the form y = f(x). [9]
- November 2020, Paper 2, Q8 (9 marks): d P 8 The rate of change of a certain population P at time t is modelled by the equation ( 100 P ) . = - d t Initially P = 2000. (a) Determine an expression for
- June 2019, Paper 1, Q8 (8 marks): A cylindrical tank is initially full of water. There is a small hole at the base of the tank out of which the water leaks. The height of water in the tank is x
- June 2018, Paper 3, Q7 (9 marks): = ^ h is given by the differential equation 7 y x The gradient of the curve f ^ h d y 3 2 2 x 1 4 y 0 - + = d x ^ h. By solving this differential equation show
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