plumiDifferential equations: WJEC A‑Level Maths questions
WJEC A-Level Maths past-paper questions on 8.8 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 9 questions on Differential equations, as a list
- Summer 2024, Unit 3, Q14 (7 marks): d y 1 lnx ln x y 14. (a) Given that , show that . [2] x d x x 2 (b) Hence, solve the differential equation 2 d x x t , d t ln x 1 t 3 x . given th
- Summer 2024, Unit 4, Q9 (11 marks): 9. The diagram below shows a parcel, of mass m kg, sliding down a rough slope inclined at an 7 angle α to the horizontal, where sin . 25 α The coefficient o
- Summer 2023, Unit 3, Q12 (7 marks): 2 The rate of change of a variable y with respect to x is directly proportional to y. a) Write down a differential equation satisfied by y. [1] When x = 1 and y
- Summer 2023, Unit 4, Q10 (8 marks): A train is moving along a straight horizontal track. At time t seconds, its velocity is 1 0 v ms–1, its acceleration is a ms–2, and a is inversely proportional
- Summer 2022, Unit 4, Q9 (8 marks): 9 Megan wants to make some ice cubes. She fills a plastic ice cube tray with water of temperature 10°C and places it directly into the freezer. The temperature
- Summer 2019, Unit 3, Q13 (8 marks): Wildflowers grow on the grass verge by the side of a motorway. The area populated by 1 3 wildflowers at time t years is A m2. The rate of increase of A is direc
- Summer 2019, Unit 4, Q8 (7 marks): 8 A box of mass 2 kg is projected along a horizontal surface with an initial velocity of 5 ms–1. The box experiences a variable resistive force of 0.4v2 N, wher
- Summer 2018, Unit 3, Q15 (5 marks): 5 The variable y satisfies the differential equation 2 dy dx = 5 − 2y , where x x 0. Given that y = 1 when x = 0, find an expression for y in terms of x. [5]
- Summer 2018, Unit 4, Q7 (11 marks): An object of mass 0.5 kg is thrown vertically upwards with initial speed 24 ms–1. The 0 7 velocity of the object at time t seconds is v ms–1. During the upward
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