Cambridge Past Paper Questions
Browse 23,045questions from 25 years of O-Level & A-Level exams. Click any question to practice.
On each day that Alexa goes to work, the probabilities that she travels by bus, by train or by car are 0.4, 0.35 and 0.25 respectively. When she tr...
A fair spinner has sides numbered 1, 2, 2. Another fair spinner has sides numbered –2, 0, 1. Each spinner is spun. The number on the side on which ...
Every day Richard takes a flight between Astan and Bejin. On any day, the probability that the flight arrives early is 0.15, the probability that i...
The heights, in cm, of the 11 basketball players in each of two clubs, the Amazons and the Giants, are shown below. Amazons 205 198 181 182 190 215...
The heights in cm of 160 sunflower plants were measured. The results are summarised on the following cumulative frequency curve. [Figure 1.1: Cumul...
The random variable X can take only the values -2, -1, 0, 1, 2. The probability distribution of X is given in the following table. [Table: X: -2, -...
A sports club has a volleyball team and a hockey team. The heights of the 6 members of the volleyball team are summarised by Σx = 1050 and Σx² = 19...
Three fair six-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time, repeatedly. For a single throw of the three dice, ...
The lengths of the leaves of a particular type of tree are modelled by a normal distribution. A scientist measures the lengths of a random sample o...
The word REQUIREMENT has 11 letters.
In the region of Arka, the total number of households in the three villages Reeta, Shan and Teber is 800. Each of the households was asked about th...
Accidents at two factories occur randomly and independently. On average, the numbers of accidents per month are 3.1 at factory A and 1.7 at factory B.
The time, in minutes, taken by students to complete a test has the distribution N(125, 36).
The graph of the probability density function of a random variable X is symmetrical about the line x = 4.
100 randomly chosen adults each throw a ball once. The length, l metres, of each throw is recorded. The results are summarised below. n = 100 Σl = ...
On average, 1 in 75000 adults has a certain genetic disorder.
The probability density function, f, of a random variable X is given by f(x) = { k(6x - x²) for 0 ≤ x ≤ 6, 0 otherwise, where k is a constant.
The masses, in kilograms, of large and small sacks of flour have the distributions N(55, 3²) and N(27, 2.5²) respectively.
At a certain large school it was found that the proportion of students not wearing correct uniform was 0.15. The school sent a letter to parents as...
In a game, a ball is thrown and lands in one of 4 slots, labelled A, B, C and D. Raju wishes to test whether the probability that the ball will lan...
The random variable X has the distribution B(400, 0.01).
The random variable X takes values in the range 1 ≤ x ≤ p, where p is a constant. The graph of the probability density function of X is shown in th...
Wendy's journey to work consists of three parts: walking to the train station, riding on the train and then walking to the office. The times, in mi...
The time, in minutes, spent by customers at a particular gym has the distribution N(μ, 38.2). In the past the value of μ has been 42.4. Following t...
The heights, h centimetres, of a random sample of 100 fully grown animals of a certain species were measured. The results are summarised below. n =...
Customers arrive at a particular shop at random times. It has been found that the mean number of customers who arrive during a 5-minute interval is...
The number of goals scored by a team in a match is independent of other matches, and is denoted by the random variable X, which has a Poisson distr...
In the past, the time, in hours, for a particular train journey has had mean 1.40 and standard deviation 0.12. Following the introduction of some n...
The local council claims that the average number of accidents per year on a particular road is 0.8. Jane claims that the true average is greater th...
The masses, m kilograms, of flour in a random sample of 90 sacks of flour are summarised as follows. n = 90 Σm = 4509 Σm² = 225 950
Most plants of a certain type have three leaves. However, it is known that, on average, 1 in 10000 of these plants have four leaves, and plants wit...
Alethia models the length of time, in minutes, by which her train is late on any day by the random variable X with probability density function giv...
The coefficient of x⁴ in the expansion of (3 + x)⁵ is equal to the coefficient of x² in the expansion of (2x + a/x)⁶. Find the value of the positiv...
The second and third terms of a geometric progression are 10 and 8 respectively. Find the sum to infinity.
The equation of a curve is such that dy/dx = 3(4x - 7)½ − 4x⁻½. It is given that the curve passes through the point (4, 3/2). Find the equation of ...
The first, second and third terms of an arithmetic progression are k, 6k and k + 6 respectively.
The equation of a curve is y = 4x² - kx + (1/2)k² and the equation of a line is y = x - a, where k and a are constants.
The diagram shows the curve with equation y = 5x^(1/2) and the line with equation y = 2x + 2. Find the exact area of the shaded region which is bou...
The diagram shows a sector OBAC of a circle with centre O and radius 10cm. The point P lies on OC and BP is perpendicular to OC. Angle AOC = π/6 an...
The equation of a circle is x² + y² + ax + by − 12 = 0. The points A (1, 1) and B (2, −6) lie on the circle.
The equation of a curve is y = 3x + 1 − 4(3x + 1)½ for x > -1/3.
Functions f and g are defined as follows: f(x) = (2x + 1)/(2x - 1) for x ≠ 1/2, g(x) = x² + 4 for x ∈ ℝ. [Figure 10.1]
The function f is given by f(x) = 4cos⁴x + cos²x − k for 0 ≤ x ≤ 2π, where k is a constant.
The variables x and y satisfy the equation y = 4^(2x-a), where a is an integer. As shown in the diagram, the graph of ln y against x is a straight ...
The diagram shows the curve with equation y = 3 sin x − 3 sin 2x for 0 ≤ x ≤ π. The curve meets the x-axis at the origin and at the points with x-c...
A curve has equation x²y + 2y³ = 48. Find the equation of the normal to the curve at the point (4, 2), giving your answer in the form ax + by + c =...
A curve has equation y = (9e^(2x) + 16) / (e^x - 1).