Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
A bag contains 5 yellow and 4 green marbles. Three marbles are selected at random from the bag, without replacement. The random variable X is the n...
In how many different ways can the 9 letters of the word TELESCOPE be arranged?
In a certain region, the probability that any given day in October is wet is 0.16, independently of other days.
The times taken, in minutes, to complete a particular task by employees at a large company are normally distributed with mean 32.2 and standard dev...
The distances, x m, travelled to school by 140 children were recorded. The results are summarised in the table below. Distance, x m | x ≤ 200 | x ≤...
The 26 members of the local sports club include Mr and Mrs Khan and their son Abad. The club is holding a party to celebrate Abad's birthday, but t...
Lakeview and Riverside are two schools. The pupils at both schools took part in a competition to see how far they could throw a ball. The distances...
The times taken, in minutes, by 360 employees at a large company to travel from home to work are summarised in the following table. Time, t minutes...
Raj wants to improve his fitness, so every day he goes for a run. The times, in minutes, of his runs have a normal distribution with mean 41.2 and ...
A security code consists of 2 letters followed by a 4-digit number. The letters are chosen from {A, B, C, D, E} and the digits are chosen from {1, ...
In a game, Jim throws three darts at a board. This is called a 'turn'. The centre of the board is called the bull's-eye. The random variable X is t...
Box A contains 6 red balls and 4 blue balls. Box B contains x red balls and 9 blue balls. A ball is chosen at random from box A and placed in box B...
It is known that the height H, in metres, of trees of a certain kind has the distribution N(12.5, 10.24). A scientist takes a random sample of 25 t...
The number of enquiries received per day at a customer service desk has a Poisson distribution with mean 45.2. If more than 60 enquiries are receiv...
A random sample of 75 students at a large college was selected for a survey. 15 of these students said that they owned a car. From this result an a...
A random variable X has probability density function given by f(x) = { (9-x²) 0 0 ≤ x ≤ 3, otherwise.
The proportion of people having a particular medical condition is 1 in 100000. A random sample of 2500 people is obtained. The number of people in ...
The random variable T denotes the time, in seconds, for 100 m races run by Tania. T is normally distributed with mean µ and variance σ². A random s...
The masses, in grams, of apples from a certain farm have mean µ and standard deviation 5.2. The farmer says that the value of µ is 64.6. A quality ...
The mass, in kilograms, of a block of cheese sold in a supermarket is denoted by the random variable M. The masses of a random sample of 40 blocks ...
Andy and Jessica are doing a survey about musical preferences. They plan to choose a representative sample of six students from the 256 students at...
The probability that a certain spinner lands on red on any spin is p. The spinner is spun 140 times and it lands on red 35 times.
A certain kind of firework is supposed to last for 30 seconds, on average, after it is lit. An inspector suspects that the fireworks actually last ...
In a certain large document, typing errors occur at random and at a constant mean rate of 0.2 per page.
A machine is supposed to produce random digits. Bob thinks that the machine is not fair and that the probability of it producing the digit 0 is les...
(a) The probability density function of the random variable X is given by f(x) = { kx(4-x) 0 ≤ x ≤ 2, { 0 otherwise, where k is a consta...
A random variable X has probability density function given by f(x) = { (1/18)(9-x²) for 0 ≤ x ≤ 3, 0 otherwise. The median of X is m.
(a) The proportion of people having a particular medical condition is 1 in 100000. A random sample of 2500 people is obtained. The number of people...
Points A and B have coordinates (5, 2) and (10, −1) respectively.
The first, second and third terms of an arithmetic progression are a, 2a and a² respectively, where a is a positive constant. Find the sum of the f...
Find the set of values of k for which the equation 8x² + kx + 2 = 0 has no real roots.
A geometric progression is such that the third term is 1764 and the sum of the second and third terms is 3444. Find the 50th term.
The graph with equation y = f(x) is transformed to the graph with equation y = g(x) by a stretch in the x-direction with factor 0.5, followed by a ...
The equation of a curve is y = 4x² + 20x + 6.
Prove the identity sin θ/(sin θ + cos θ) + cos θ/(sin θ - cos θ) = (tan²θ + 1)/(tan²θ - 1).
The equation of a curve is such that dy/dx = 3x^(1/2) – 3x^(-1/2). The curve passes through the point (3, 5).
Functions f and g are defined by f(x) = x + 1/x for x > 0, g(x) = ax + 1 for x ∈ R, where a is a constant.
The diagram shows a cross-section RASB of the body of an aircraft. The cross-section consists of a sector OARB of a circle of radius 2.5m, with cen...
Find the coordinates of the minimum point of the curve y = 9/4 x² – 12x + 18.
Solve the inequality |2x – 5| > x.
Use logarithms to solve the equation 14e⁻²ˣ = 5ˣ⁺¹, giving your answer correct to 3 significant figures.
It is given that sec θ = √17 where 0 < θ < ½π. Find the exact value of tan(θ + ¼π).
By sketching a suitable pair of graphs on the same diagram, show that the equation e^(x/2) = x⁵ has exactly one real root.
A curve has equation 4e²ˣy + y² = 21. Find the gradient of the curve at the point (0, -7).
The polynomial p(x) is defined by p(x) = 12x³ – 9x² + 8x – 4.
The diagram shows the curve with equation y = (2lnx)/(3x+1). The curve crosses the x-axis at the point A and has a maximum point B. The shaded regi...
The expression f(θ) is defined by f(θ) = 12 sin θ cos θ + 16 cos² θ.
Solve the equation sec θ = 5 cosec θ for 0° < θ < 360°.
The solutions of the equation |4x − 1| = |x + 3| are x = p and x = q, where p < q. Find the exact values of p and q, and hence determine the exact ...
The variables x and y satisfy the equation y = Axk, where A and k are constants. The graph of In y against In x is a straight line passing through ...