plumiDifferential equations: OCR A‑Level Further Maths questions
Every OCR A-Level Further Maths exam question on CP.9 Differential equations, 2018–2025, with its mark scheme and examiner’s report.
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![June 2023 Pure Core 1, question 5: d y d y 5 (a) Find the general solution of the differential equation x 2 5 y 0 . [2] - + = d x 2 d 2 d y d y (b) Hence find the general solution of the differen](https://pub-e8a9dbab8e2a4d089f52b2a45e0d0b50.r2.dev/bank/y54001-jun23-05-qp.webp?v=3)
All 16 questions on Differential equations, as a list
- June 2025, Pure Core 1, Q9 (9 marks): A pendulum comprises an object P of mass m kg and a string of length 7 m. One end of the string is attached to P and the other end is attached to a fixed point
- June 2025, Pure Core 2, Q9 (13 marks): When light hits a certain photo-sensitive cell, at time t = 0, there is an electrical response in the cell which is denoted by y (t) where both y and t are meas
- June 2024, Pure Core 1, Q10 (10 marks): - . 1 10 A particle B, of mass 3 kg, moves in a straight line and has velocity ms v 1 At time t seconds, where 0 t 1 r, a variable force of ( 15 sin 4 t 6 v tan
- June 2024, Pure Core 2, Q8 (13 marks): A children’s play centre has two rooms, a room full of bouncy castles and a room full of ball pits. At any given instant, each child in the centre is playing ei
- June 2023, Pure Core 1, Q5 (6 marks): d y d y 5 (a) Find the general solution of the differential equation x 2 5 y 0 . [2] - + = d x 2 d 2 d y d y (b) Hence find the general solution of the differen
- June 2023, Pure Core 1, Q7 (11 marks): An engineer is modelling the motion of a particle P of mass 0.5 kg in a wind tunnel. P is modelled as travelling in a straight line. The point O is a fixed poin
- June 2023, Pure Core 2, Q8 (11 marks): A surge in the current, I units, through an electrical component at a time, t seconds, is to be modelled. The surge starts when t = 0 and there is initially no
- June 2022, Pure Core 1, Q8 (13 marks): A biologist is studying the effect of pesticides on crops. On a certain farm pesticide is regularly applied to a particular crop which grows in soil. Over time,
- June 2022, Pure Core 2, Q6 (10 marks): A particle, P, positioned at the origin, O, is projected with a certain velocity along the x-axis. P is then acted on by a single force which varies in such a w
- November 2021, Pure Core 1, Q11 (5 marks): The displacement of a door from its equilibrium (closed) position is measured by the angle, i radians, which the door makes with its closed position. The door c
- November 2021, Pure Core 2, Q8 (16 marks): A particle P of mass 2 kg can only move along the straight line segment OA, where OA is on a rough horizontal surface. The particle is initially at rest at O an
- November 2020, Pure Core 1, Q10 (13 marks): A particle of mass 0.5 kg is initially at point O. It moves from rest along the x-axis under the influence of two forces F N and F N which act parallel to the x
- November 2020, Pure Core 2, Q5 (7 marks): A capacitor is an electrical component which stores charge. The value of the charge stored by the capacitor, in suitable units, is denoted by Q. The capacitor i
- June 2019, Pure Core 1, Q11 (13 marks): A particle is suspended in a resistive medium from one end of a light spring. The other end of the spring is attached to a point which is made to oscillate in a
- June 2019, Pure Core 2, Q5 (11 marks): A particle of mass 2 kg moves along the x-axis. At time t seconds the velocity of the particle is - . v ms 1 The particle is subject to two forces. 1 • One acts
- June 2019, Pure Core 2, Q6 (6 marks): A is a fixed point on a smooth horizontal surface. A particle P is initially held at A and released from rest. It subsequently performs simple harmonic motion i
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