Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
Two particles A and B, of masses 0.4kg and 0.2kg respectively, are moving down the same line of greatest slope of a smooth plane. The plane is incl...
Small smooth spheres A and B, of equal radii and of masses 5 kg and 3 kg respectively, lie on a smooth horizontal plane. Initially B is at rest and...
Coplanar forces of magnitudes 60N, 20N, 16N and 14N act at a point in the directions shown in the diagram. [Figure 2.1]
Two particles A and B, of masses 2.4kg and 1.2kg respectively, are connected by a light inextensible string which passes over a fixed smooth pulley...
A particle A, moving along a straight horizontal track with constant speed 8ms⁻¹, passes a fixed point O. Four seconds later, another particle B pa...
A block of mass 12kg is placed on a plane which is inclined at an angle of 24° to the horizontal. A light string, making an angle of 36° above a li...
A car of mass 900kg is moving up a hill inclined at sin⁻¹ 0.12 to the horizontal. The initial speed of the car is 11 ms⁻¹. After 12s, the car has t...
A particle P moves in a straight line. The velocity vms⁻¹ at time t seconds is given by v = 0.5t for 0≤t≤ 10, v = 0.25t² – 8t + 60 for 10 ≤ t ≤ 20.
Two particles P and Q, of masses 0.3kg and 0.2kg respectively, are at rest on a smooth horizontal plane. P is projected at a speed of 4ms⁻¹ directl...
A particle P is projected vertically upwards from horizontal ground. P reaches a maximum height of 45 m. After reaching the ground, P comes to rest...
The displacement of a particle moving in a straight line is s metres at time t seconds after leaving a fixed point O. The particle starts from rest...
The diagram shows a block of mass 10kg suspended below a horizontal ceiling by two strings AC and BC, of lengths 0.8 m and 0.6 m respectively, atta...
A cyclist is riding along a straight horizontal road. The total mass of the cyclist and her bicycle is 70kg. At an instant when the cyclist's speed...
Two particles P and Q, of masses 0.3kg and 0.2kg respectively, are attached to the ends of a light inextensible string. The string passes over a fi...
A particle P moves in a straight line through a point O. The velocity vms⁻¹ of P, at time t s after passing O, is given by `v = 9/4 + b / (t+1)² - ...
There are 6 men and 8 women in a Book Club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
The times taken to travel to college by 2500 students are summarised in the table. Time taken (t minutes) | 0 ≤ t < 20 | 20 < t < 30 | 30 ≤ t < 40 ...
Jacob has four coins. One of the coins is biased such that when it is thrown the probability of obtaining a head is 7/10. The other three coins are...
The lengths, in cm, of the leaves of a particular type are modelled by the distribution N(5.2, 1.5²).
Janice is playing a computer game. She has to complete level 1 and level 2 to finish the game. She is allowed at most two attempts at any level. • ...
For n values of the variable x, it is given that Σ(x – 200) = 446 and Ex = 6846.
A fair 6-sided die has the numbers 1, 2, 2, 3, 3, 3 on its faces. The die is rolled twice. The random variable X denotes the sum of the two numbers...
The back-to-back stem-and-leaf diagram shows the diameters, in cm, of 19 cylindrical pipes produced by each of two companies, A and B. Company A | ...
The weights, in kg, of bags of rice produced by Anders have the distribution N(2.02, 0.03²).
In a large college, 28% of the students do not play any musical instrument, 52% play exactly one musical instrument and the remainder play two or m...
The 9 letters in the word CROCODILE are: C (2), R (1), O (2), D (1), I (1), L (1), E (1).
Hanna buys 12 hollow chocolate eggs that each contain a sweet. The eggs look identical but Hanna knows that 3 contain a red sweet, 4 contain an ora...
The time taken, t minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table. Time taken (t minut...
Twenty children were asked to estimate the height of a particular tree. Their estimates, in metres, were as follows. 4.1, 4.2, 4.4, 4.5, 4.6, 4.8, ...
The random variable X takes the values −2, 1, 2, 3. It is given that P(X = x) = kx², where k is a constant.
Ramesh throws an ordinary fair 6-sided die.
Farmer Jones grows apples. The weights, in grams, of the apples grown this year are normally distributed with mean 170 and standard deviation 25. A...
Sajid is practising for a long jump competition. He counts any jump that is longer than 6 m as a success. On any day, the probability that he has a...
A group of 15 friends visit an adventure park. The group consists of four families. • Mr and Mrs Kenny and their four children • Mr and Mrs Lizo an...
The diameters, x millimetres, of a random sample of 200 discs made by a certain machine were recorded. The results are summarised below. n = 200 Σx...
Arvind uses an ordinary fair 6-sided die to play a game. He believes he has a system to predict the score when the die is thrown. Before each throw...
The lengths, in centimetres, of two types of insect, A and B, are modelled by the random variables X ~ N(6.2, 0.36) and Y ~ N(2.4, 0.25) respectively.
The independent random variables X and Y have distributions Po(2) and B(20, ¹/₄) respectively.
Cars arrive at a fuel station at random and at a constant average rate of 13.5 per hour.
A random variable X has probability density function f. The graph of f(x) is a straight line segment parallel to the x-axis from x = 0 to x = a, wh...
In the past, the mean time for Jenny's morning run was 28.2 minutes. She does some extra training and she wishes to test whether her mean time has ...
A javelin thrower noted the lengths of a random sample of 50 of her throws. The sample mean was 72.3 m and an unbiased estimate of the population v...
In the past, the mean height of plants of a particular species has been 2.3m. A random sample of 60 plants of this species was treated with fertili...
It is known that 1.8% of children in a certain country have not been vaccinated against measles. A random sample of 200 children in this country is...
The number of cars arriving at a certain road junction on a weekday morning has a Poisson distribution with mean 4.6 per minute. Traffic lights are...
A random variable X has probability density function given by f(x) = {1/16 (4x-x²) for 2 ≤ x ≤ 4, 0 otherwise.
The masses, in kilograms, of large and small sacks of grain have the distributions N(53, 11) and N(14, 3) respectively.
X is a random variable with distribution Po(2.90). A random sample of 100 values of X is taken.
The number of characters in emails sent by a particular company is modelled by the distribution N(1250, 480²).