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.
Hazeem repeatedly throws two ordinary fair 6-sided dice at the same time. On each occasion, the score is the sum of the two numbers that she obtains.
A farmer sells eggs. The weights, in grams, of the eggs can be modelled by a normal distribution with mean 80.5 and standard deviation 6.6. Eggs ar...
The times, to the nearest minute, of 150 athletes taking part in a charity run are recorded. The results are summarised in the table. Time in minut...
A red spinner has four sides labelled 1, 2, 3, 4. When the spinner is spun, the score is the number on the side on which it lands. The random varia...
In a restaurant, the tables are rectangular. Each table seats four people: two along each of the longer sides of the table (see diagram). Eight fri...
A competitor in a throwing event has three attempts to throw a ball as far as possible. The random variable X denotes the number of throws that exc...
George has a fair 5-sided spinner with sides labelled 1, 2, 3, 4, 5. He spins the spinner and notes the number on the side on which the spinner lands.
A factory produces a certain type of electrical component. It is known that 15% of the components produced are faulty. A random sample of 200 compo...
The heights, in cm, of the 11 players in each of two teams, the Aces and the Jets, are shown in the following table. Aces | 180 | 174 | 169 | 182 |...
The heights of the members of a club are normally distributed with mean 166cm and standard deviation 10cm. Find the probability that a randomly cho...
Freddie has two bags of marbles. Bag X contains 7 red marbles and 3 blue marbles. Bag Y contains 4 red marbles and 1 blue marble. Freddie chooses o...
Find the number of different arrangements of the 9 letters in the word ANDROMEDA in which no consonant is next to another consonant. (The letters D...
Becky sometimes works in an office and sometimes works at home. The random variable X denotes the number of days that she works at home in any give...
The weights of large bags of pasta produced by a company are normally distributed with mean 1.5kg and standard deviation 0.05 kg.
Tim has two bags of marbles, A and B. Bag A contains 8 white, 4 red and 3 yellow marbles. Bag B contains 6 white, 7 red and 2 yellow marbles. Tim a...
The weights, xkg, of 120 students in a sports college are recorded. The results are summarised in the following table. Weight (xkg) | x ≤ 40 | x ≤ ...
The probability that a driver passes an advanced driving test is 0.3 on any given attempt. Dipak keeps taking the test until he passes. The random ...
Jai and his wife Kaz are having a party. Jai has invited five friends and each friend will bring his wife.
A random variable X has the distribution N(410, 400). Find the probability that the mean of a random sample of 36 values of X is less than 405.
In a survey of 300 randomly chosen adults in Rickton, 134 said that they exercised regularly. This information was used to calculate an a% confiden...
A website owner finds that, on average, his website receives 0.3 hits per minute. He believes that the number of hits per minute follows a Poisson ...
The masses, in kilograms, of chemicals A and B produced per day by a factory are modelled by the independent random variables X and Y respectively,...
In the past the number of enquiries per minute at a customer service desk has been modelled by a random variable with distribution Po(0.31). Follow...
A continuous random variable X takes values from 0 to 6 only and has a probability distribution that is symmetrical. Two values, a and b, of X are...
A biologist wishes to test whether the mean concentration u, in suitable units, of a certain pollutant in a river is below the permitted level of 0...
A random variable X has the distribution Po(25).
The length, in minutes, of mathematics lectures at a certain college has mean μ and standard deviation 8.3.
A researcher read a magazine article which stated that boys aged 1 to 3 prefer green to orange. It claimed that, when offered a green cube and an o...
The height H, in metres, of mature trees of a certain variety is normally distributed with standard deviation 0.67. In order to test whether the po...
The random variable X has probability density function, f, given by f(x) = { 1/x² a < x < b, 0 otherwise, where a and b are positive constants.
A factory makes loaves of bread in batches. One batch of loaves contains X kilograms of dried yeast and Y kilograms of flour, where X and Y have th...
A random variable X has the distribution Po(2.4).
A random variable X has the distribution N(410, 400).
A biologist wishes to test whether the mean concentration μ, in suitable units, of a certain pollutant in a river is below the permitted level of 0...
The diagram shows the curve with equation y = a sin(bx)+c for 0 ≤ x ≤ 2π, where a, b and c are positive constants. [Figure X.X]
The first term of an arithmetic progression is -20 and the common difference is 5.
The equation of a curve is y = 2x² - 3. Two points A and B with x-coordinates 2 and (2 + h) respectively lie on the curve.
Find the term independent of x in the expansion of each of the following:
The function f is defined by f(x) = (2x+1)/(2x-1) for x < 1/2.
The diagram shows a metal plate OABCDEF consisting of sectors of two circles, each with centre O. The radii of sectors AOB and EOF are r cm and the...
By expressing -2x² +8x+11 in the form -a(x−b)² +c, where a, b and c are positive integers, find the coordinates of the vertex of the graph with equ...
The equation of a circle is x² + y² +px+2y+q = 0, where p and q are constants.
The equation of a curve is y = 1/2 k²x² - 2kx+2 and the equation of a line is y = kx+p, where k and p are constants with 0 < k < 1.
A function f with domain x > 0 is such that f'(x) = 8(2x-3)^(-1/2) - 10x^3. It is given that the curve with equation y = f(x) passes through the po...
The variables x and y satisfy the equation a^(2y) = e^(3x+k), where a and k are constants. The graph of y against x is a straight line.
Solve the inequality |x-7|>4x+3.
The function f is defined by f(x) = tan²(x/2) for 0 < x < π.
The polynomial p(x) is defined by p(x) = ax³ – ax² – 15x + 18, where a is a constant. It is given that (x+2) is a factor of p(x).
It is given that ∫(from a to a³) (10 / (2x+1)) dx = 7, where a is a constant greater than 1.
A curve has parametric equations x = (e^(2t)-2)/(e^(2t)+1), y = e^(3t)+1.