Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
Two particles P and Q of masses 2.5kg and 0.5kg respectively are connected by a light inextensible string that passes over a small smooth pulley fi...
Two particles P and Q of masses 0.2 kg and 0.5 kg respectively are at rest on a smooth horizontal plane. Particle P is projected with a speed 6ms⁻¹...
A particle of mass 0.2kg is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point on a verti...
A car travels along a straight road with constant acceleration a ms⁻², where a > 0. The car passes through points A, B and C in that order. The spe...
A particle travels in a straight line. The velocity of the particle at time t s after leaving a point O is v ms⁻¹, where v = kt²-4t+3. The distance...
A van of mass 4500 kg is towing a trailer of mass 750kg down a straight hill inclined at an angle of θ to the horizontal where sinθ = 0.05 . The va...
A cyclist is travelling along a straight horizontal road. The total mass of the cyclist and her bicycle is 80 kg. There is a constant resistance fo...
The diagram shows a track ABCD which lies in a vertical plane. The section AB is a straight line inclined at an angle of 30° to the horizontal and ...
A summary of 20 values of x gives Σ(x−30) = 439, Σ(x−30)² = 12405. A summary of another 25 values of x gives Σ(x−30) = 470, Σ(x−30)² = 11346.
The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm.
The heights, in cm, of 200 adults in Barimba are summarised in the following table. Height (h cm) 130 ≤ h < 150 150 ≤ h < 160 160 ≤ h < 170 170 ≤ h...
A game for two players is played using a fair 4-sided dice with sides numbered 1, 2, 3 and 4. One turn consists of throwing the dice repeatedly up ...
In a certain area in the Arctic the probability that it snows on any given day is 0.7, independent of all other days.
Harry has three coins: • One coin is biased so that the probability of obtaining a head when it is thrown is 1/5. • The second coin is biased so th...
The eight digits 1, 2, 2, 3, 4, 4, 4, 5 are arranged in a line.
Rajesh applies once every year for a ticket to a music festival. The probability that he is successful in any particular year is 0.3, independently...
Seva has a coin which is biased so that when it is thrown the probability of obtaining a head is ¹⁄₃. He also has a bag containing 4 red marbles an...
The weights of oranges can be modelled by a normal distribution with mean 131 grams and standard deviation 54 grams. Oranges are classified as smal...
The back-to-back stem-and-leaf diagram shows the annual salaries of 19 employees at each of two companies, Petral and Ravon. Petral 30 | 0 0 3 31 |...
Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in doll...
The residents of Mahjing were asked to classify their local bus service: * 25% of residents classified their service as good. * 60% of resident...
How many different arrangements are there of the 10 letters in the word REGENERATE?
The numbers on the faces of a fair six-sided dice are 1, 2, 2, 3, 3, 3. The random variable X is the total score when the dice is rolled twice.
In a certain country, the heights of the adult population are normally distributed with mean 1.64 m and standard deviation 0.25 m.
Box A contains 6 green balls and 3 yellow balls. Box B contains 4 green balls and x yellow balls. A ball is chosen at random from box A and placed ...
The times taken, in seconds, by 15 members of each of two swimming clubs, the Penguins and the Dolphins, to swim 50 metres are shown in the followi...
Salah decides to attempt the crossword puzzle in his newspaper each day. The probability that he will complete the puzzle on any given day is 0.65,...
The 9 letters of the word RECORDERS are divided at random into two groups: a group of 5 letters and a group of 4 letters.
A bus station has exactly four entrances. In the morning the numbers of passengers arriving at these entrances during a 10-second period have the i...
The random variable X has the distribution N(31.2, 10.4²). Two independent random values of X, denoted by X₁ and X₂, are chosen. Find P(X₁ > 3X₂).
The time taken in minutes for a certain daily train journey has a normal distribution with standard deviation 5.8. For a random sample of 20 days t...
Sales of cell phones at a certain shop occur singly, randomly and independently.
The diagram shows the graph of the probability density function, f, of a random variable X . The graph is a quarter circle entirely in the first qu...
Every July, as part of a research project, Rita collects data about sightings of a particular kind of bird. Each day in July she notes whether she ...
A random variable X has the distribution Po(145).
Henri wants to choose a random sample from the 804 students at his college. He numbers the students from 1 to 804 and then uses random numbers gene...
A student wishes to estimate the proportion, p, of students at her college who have exactly one brother. She surveys a random sample of 50 students...
A random variable X has the distribution N(10, 12). Two independent values of X, denoted by X₁ and X₂, are chosen at random.
The number of goals scored by a sports team in the first half of any match has the distribution X~ Po(3.1). The number of goals scored by the same ...
The masses of cereal boxes filled by a certain machine have mean 510 grams. An adjustment is made to the machine and an inspector wishes to test wh...
The probability density function, f, of a random variable X is given by [k(1+cosx) f(x) = 0 0 ≤ x ≤ π, otherwise, where k is a constant.
The random variable X has the distribution B (4000, 0.001).
The widths, wcm, of a random sample of 150 leaves of a certain kind were measured. The sample mean of w was found to be 3.12 cm. Using this sample,...
The masses in kilograms of large and small bags of cement have the independent distributions N(50, 2.4) and N(26, 1.8) respectively. Find the proba...
In this question you should not use an approximating distribution. At an election in Menham last year, 24% of voters supported the Today Party. A s...
A random variable X has probability density function f given by f(x) = {ax-x^3 for 0 ≤ x ≤ √2, 0 otherwise, where a is a constant.
The numbers of green sweets in 200 randomly chosen packets of Frutos are summarised in the table. Number of green sweets 0 1 2 3 > 3 Number of pack...
The independent random variables X and Y have the distributions Po(1.9) and Po(2.2) respectively.
The diagram shows the graphs with equations y = f(x) and y = g(x). Describe fully a sequence of two transformations which transforms the graph of y...