9709 · topic questions
Differential equations
12 past-paper questions on Differential equations
Using partial fractions, solve the differential equation and obtain an expression for t in terms of a single logarithm involving…
Practise the full question →The variables x and y satisfy the differential equation sin 4y dy/dx = x sin 2y sin 3x. It is given that y = π/12 when x = π/6.…
Practise the full question →The variables x and θ satisfy the differential equation (x²+9)sinθ dθ/dx = (x+3)cos⁴θ. It is given that x = 3 when θ = π/3. Solve…
Practise the full question →The variables x and θ satisfy the differential equation sin 2θ dx/dθ = (4x+3) cos 2θ, and x = 0 when θ = 1/12π. Solve the…
Practise the full question →Solve the differential equation in part (a), obtaining an expression for t in terms of r.
Practise the full question →Solve the differential equation, obtaining an expression for t in terms of x.
Practise the full question →At time t = 0 the tap is opened. It is given that h = 4 when t = 0 and that h = 2.25 when t = 20. Solve the differential equation…
Practise the full question →A container in the shape of a cuboid has a square base of side x and a height of (10-x). It is given that x varies with time, t,…
Practise the full question →It is given that when t = 0, h = 50. Find the time taken for the depth of water in the tank to reach 80 cm. Give your answer…
Practise the full question →A large cylindrical tank is used to store water. The base of the tank is a circle of radius 4 metres. At time t minutes, the…
Practise the full question →A balloon in the shape of a sphere has volume V and radius r. Air is pumped into the balloon at a constant rate of 40π starting…
Practise the full question →In a field there are 300 plants of a certain species, all of which can be infected by a particular disease. At time t after the…
Practise the full question →
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Differential equations (9709) past-paper questions — marked instantly
These are real Cambridge Mathematics past-paper questions on Differential equations. Open one, attempt it, then upload your working — MarkScheme grades it against the official 9709 mark scheme so you see exactly where the marks are won and lost on this topic.
Frequently asked questions
- How many Differential equations questions are there for 9709?
- This page collects 12 recent Cambridge Mathematics (9709) past-paper questions tagged to Differential equations. Each links straight to instant marking against the official 9709 scheme.
- How are Differential equations answers marked?
- Type or photograph your working and MarkScheme scores it against the real 9709 mark scheme for this topic — method, accuracy and any band descriptors — so you see exactly where the marks are.
- Where can I learn Differential equations first?
- Start with the free Mathematics lesson on Differential equations, then come back and drill past-paper questions under timed conditions.