Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
The lines l and m have vector equations l: r = 2i+j-3k+λ(-i+2k) and m: r = 2i+j-3k+µ(2i−j+5k). Lines l and m intersect at the point P.
The parametric equations of a curve are x = 3 sin 2t, y = tan t + cot t, for 0 < t < ¦π.
Let f(x) = 7a² / ((a-2x)(3a+x)), where a is a positive constant.
A water tank is in the shape of a cuboid with base area 40000 cm². At time t minutes the depth of water in the tank is h cm. Water is pumped into t...
The diagram shows the curve y = 2sinx√2+cosx, for 0 ≤ x ≤ 2π, and its minimum point M, where x = a. [Figure 11.1]
Two particles, of masses 1.8 kg and 1.2kg, are connected by a light inextensible string that passes over a fixed smooth pulley. The particles hang ...
A particle of mass 7.5kg, starting from rest at A, slides down an inclined plane AB. The point B is 12.5 metres vertically below the level of A, as...
Coplanar forces of magnitudes 52N, 39N and PN act at a point in the directions shown in [Figure 3.1]. The system is in equilibrium. Find the values...
A bus travels between two stops, A and B. The bus starts from rest at A and accelerates at a constant rate of a ms⁻² until it reaches a speed of 16...
A particle, A, is projected vertically upwards from a point O with a speed of 80 ms⁻¹. One second later a second particle, B, with the same mass as...
A particle of mass 1.2kg is placed on a rough plane which is inclined at an angle θ to the horizontal, where sin θ = 3/25. The particle is kept in ...
A car has mass 1200kg. When the car is travelling at a speed of vms⁻¹, there is a resistive force of magnitude kv N. The maximum power of the car’s...
A particle P moves in a straight line, passing through a point O with velocity 4.2 ms⁻¹. At time t s after P passes O, the acceleration, a ms⁻², of...
The velocity of a particle moving in a straight line at time t seconds after leaving a fixed point O is vms⁻¹. The diagram shows a velocity-time gr...
A block of mass 20kg is held at rest at the top of a plane inclined at 30° to the horizontal. The block is projected with speed 5ms⁻¹ down a line o...
A cyclist is riding along a straight horizontal road. The total mass of the cyclist and his bicycle is 90kg. The power exerted by the cyclist is 25...
The diagram shows two particles, A and B, of masses 0.2kg and 0.1 kg respectively. The particles are suspended below a horizontal ceiling by two st...
Two particles, P and Q, of masses 2mkg and mkg respectively, are held at rest in the same vertical line. The heights of P and Q above horizontal gr...
A particle, P, travels in a straight line, starting from a point O with velocity 6 ms⁻¹. The acceleration of P at time t s after leaving O is a ms⁻...
Two particles, A and B, of masses 0.2kg and 0.3 kg respectively, are attached to the ends of a light inextensible string. The string passes over a ...
An athlete has mass mkg. The athlete runs along a horizontal road against a constant resistance force of magnitude 24 N. The total work done by the...
Coplanar forces of magnitudes 16N, 12N, 24N and 8N act at a point in the directions shown in the diagram. [Figure 2]
A car of mass 1600kg travels up a slope inclined at an angle of sin⁻¹0.08 to the horizontal. There is a constant resistance of magnitude 240N actin...
Two particles, A and B, of masses 3 kg and 6 kg respectively, lie on a smooth horizontal plane. Initially, B is at rest and A is moving towards B w...
A particle of mass 12kg is going to be pulled across a rough horizontal plane by a light inextensible string. The string is at an angle of 30° abov...
A particle moves in a straight line. It starts from rest, at time t = 0, and accelerates at 0.6tms⁻² for 4s, reaching a speed of Ums⁻¹. The particl...
Two particles, A and B, of masses 3 kg and 5 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulley. ...
Nicola throws an ordinary fair six-sided dice. The random variable X is the number of throws that she takes to obtain a 6.
The random variable X takes the values -2, -1, 0, 2, 3. It is given that P(X = x) = k(x² + 2), where k is a positive constant.
The time taken, in minutes, to walk to school was recorded for 200 pupils at a certain school. These times are summarised in the following table. T...
Rahul has two bags, X and Y. Bag X contains 4 red marbles and 2 blue marbles. Bag Y contains 3 red marbles and 4 blue marbles. Rahul also has a coi...
The weights of the green apples sold by a shop are normally distributed with mean 90 grams and standard deviation 8 grams.
The heights of the female students at Breven college are normally distributed: • 90% of the female students have heights less than 182.7 cm. • 40% ...
The word INTELLECT has 9 letters.
At a college, the students choose exactly one of tennis, hockey or netball to play. The table shows the numbers of students in Year 1 and Year 2 at...
Find the number of different arrangements of the 9 letters in the word ALGEBRAIC.
A fair coin and an ordinary fair six-sided dice are thrown at the same time. The random variable X is defined as follows. • If the coin shows a tai...
The heights, in metres, of white pine trees are normally distributed with mean 19.8 and standard deviation 2.4. In a certain forest there are 450 w...
In a class of 21 students, there are 10 violinists, 6 guitarists and 5 pianists. A group of 7 is to be chosen from these 21 students. The group wil...
Teams of 15 runners took part in a charity run last Saturday. The times taken, in minutes, to complete the course by the runners from the Falcons a...
In a game, players attempt to score a goal by kicking a ball into a net. The probability that Leno scores a goal is 0.4 on any attempt, independent...
30% of the residents of Wimfield own an electric car. Three residents are chosen at random.
A red fair six-sided dice has faces labelled 1, 1, 1, 2, 2, 2. A blue fair six-sided dice has faces labelled 1, 1, 2, 2, 3, 3. Both dice are thrown...
In Molimba, the heights, in cm, of adult males are normally distributed with mean 176cm and standard deviation 4.8 cm.
On a certain day, the heights of 150 sunflower plants grown by children at a local school are measured, correct to the nearest cm. These heights ar...
A factory produces chocolates. 30% of the chocolates are wrapped in gold foil, 25% are wrapped in red foil and the remainder are unwrapped. Indigo ...
The 9 letters in the word HAPPINESS are divided at random into a group of 5 and a group of 4.
The heights of a certain species of deer are known to have standard deviation 0.35 m. A zoologist takes a random sample of 150 of these deer and fi...