Cambridge Past Paper Questions

A car of mass 900 kg is moving on a straight horizontal road ABCD. There is a constant resistance of magnitude 800 N in the sections AB and BC, and...

A particle P moves in a straight line starting from a point O and comes to rest 35 s later. At time t s after leaving O, the velocity v m s⁻¹ of P ...

Two particles of masses 1.2 kg and 0.8 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang v...

A small ball is projected with speed 15 m s¯¹ at an angle of 60° above the horizontal. Find the distance from the point of projection of the ball a...

A cylindrical container is open at the top. The curved surface and the circular base of the container are both made from the same thin uniform mate...

A particle P is projected with speed 20 m s¯¹ at an angle of 60° below the horizontal, from a point O which is 30 m above horizontal ground.

The diagram shows a uniform lamina ABCD with AB = 0.75 m, AD = 0.6m and BC = 0.9 m. Angle BAD = angle ABC = 90°. [Figure X.X]

Two particles P and Q have masses 0.4 kg and m kg respectively. P is attached to a fixed point A by a light inextensible string of length 0.5 m whi...

O and A are fixed points on a rough horizontal surface, with OA = 1 m. A particle P of mass 0.4 kg is projected horizontally with speed U m s⁻¹ fro...

One end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N is attached to a fixed point O. The other end of the strin...

Twelve values of x are shown below. 1761.6 1758.5 1762.3 1761.4 1759.4 1759.1 1762.5 1761.9 1762.4 1761.9 1762.8 1761.0 Find the mean and standard ...

A bag contains 10 pink balloons, 9 yellow balloons, 12 green balloons and 9 white balloons. 7 balloons are selected at random without replacement. ...

It is found that 10% of the population enjoy watching Historical Drama on television. Use an appropriate approximation to find the probability that...

The weights in kilograms of packets of cereal were noted correct to 4 significant figures. The following stem-and-leaf diagram shows the data. 747 ...

A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number ...

Pack A consists of ten cards numbered 0, 0, 1, 1, 1, 1, 1, 3, 3, 3. Pack B consists of six cards numbered 0, 0, 2, 2, 2, 2. One card is chosen at r...

The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standard deviation σ. It is found th...

Solve the inequality |5x + 2| > |4x + 3|.

A curve has equation y = 4x sin ½ x. Find the equation of the tangent to the curve at the point for which x = π.

The polynomial p(x) is defined by p(x) = 4x³ + 4x² – 29x – 15.

It is given that ∫₋ₐ²ᵃ 4e⁻²ˣ dx = 25, where a is a positive constant.

The diagram shows part of the curve defined by the parametric equations x = t² + 4t, y = t³ – 3t². The curve has a minimum point at M and crosses t...

Use the trapezium rule with three intervals to estimate the value of ∫₀^(π/4) √(1 – tan x) dx, giving your answer correct to 3 decimal places.

Expand ∛(1 – 4x) in ascending powers of x, up to and including the term in x³, simplifying the coefficients.

The variables x and y satisfy the equation yⁿ = Ax³, where n and A are constants. It is given that y = 2.58 when x = 1.20, and y = 9.49 when x = 2.51.

The parametric equations of a curve are x = 2t + sin 2t, y = 1 – 2 cos 2t, for −½π < t < ½π.

The variables x and θ satisfy the differential equation x cos² θ (dx/dθ) = 2 tan θ + 1, for 0 ≤ θ < ½π and x > 0. It is given that x = 1 when θ = ¼π.

Let f(x) = (5x² + x + 27) / ((2x + 1)(x² + 9)).

The complex number 1 + 2i is denoted by u.

The line l has equation r = 4i + 3j – k + μ(i + 2j – 2k). The plane p has equation 2x – 3y – z = 4.

Two particles A and B, of masses 0.8 kg and 0.2 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulle...

The three coplanar forces shown in the diagram are in equilibrium.

A girl, of mass 40 kg, slides down a slide in a water park. The girl starts at the point A and slides to the point B which is 7.2 metres vertically...

A particle of mass 12 kg is on a rough plane inclined at an angle of 25° to the horizontal. A force of magnitude P N acts on the particle. This for...

A small rocket is fired vertically upwards, starting from rest at ground level, and moves with constant acceleration. The rocket reaches a height o...

A car of mass 1200 kg has a greatest possible constant speed of 60 m s¯¹ along a straight level road. When the car is travelling at a speed of v m ...

A particle P moves in a straight line. The velocity v m s¯¹ at time t s is given by v = 4 + 0.2t for 0 ≤ t ≤ 10, v = -2 + 800/t² for 10 ≤ t ≤ 20.

A uniform rectangular block has a square base ABCD with AB = BC = 0.4 m. The height of the block is h m. The block is placed with its base on a rou...

An object is projected with speed 15 m s¯¹ at an angle of 35° above the horizontal from a point on horizontal ground. Find the speed and direction ...

A small ball B is connected to one end of a light elastic string of natural length 0.4 m and modulus of elasticity 12 N. The other end of the strin...

A particle P is projected from a point O on horizontal ground. At the instant t s after projection, the horizontal and vertically upwards displacem...

One end of a light inextensible string of length 0.4 m is attached to the lowest point of a hemisphere of radius 0.4 m fixed with its axis vertical...

A small object of mass 0.2 kg rests at a point O on a rough horizontal surface. The coefficient of friction between the object and the surface is 0...

ABCD is a uniform square lamina with sides of length 0.6 m. A circular hole of radius r m is made in the lamina. The centre of the hole is 0.3 m fr...

There are 900 students in a certain year-group. An identical puzzle is given to each student and the time taken, t minutes, to complete the puzzle ...

A selection of 3 letters from the 8 letters of the word COLLIDER is made.