Cambridge & Pearson Edexcel Past Paper Questions

Last Sunday, teams of runners took part in a charity event. The time taken, in seconds, to run 50m was recorded, correct to 1 decimal place, for ea...

Every Saturday, a particular community holds a ‘Puzzle' event to raise money for a new Leisure Centre. Competitors attempt to solve a puzzle as qui...

In a group of 20 musicians, there are 9 guitarists, 6 pianists and 5 drummers. 6 musicians are selected from these 20 to perform at a concert.

A bag contains 10 marbles, of which 4 are red and 6 are blue. Four marbles are selected from the bag at random, without replacement. The random var...

Rachel has three coins. The first coin is biased so that the probability of obtaining a head when it is thrown is. The second coin is biased so tha...

In Millford, 70% of the residents own a bicycle. A random sample of 160 residents is selected.

A bag contains 4 blue marbles and 12 red marbles. One marble is selected at random from the bag. If this marble is blue, it is replaced in the bag,...

Vehicles approaching a certain road junction from Bromley must go either left, right or straight on. Over time, it is known that 30% turn left, 25%...

The times taken, t minutes, by 300 students to travel to Hollowton College are recorded. The results are summarised in the table below. Time (t min...

Find the number of different ways in which the 10 letters in the word AMALGAMATE can be arranged so that...

Kestrels are birds whose adult wingspans are normally distributed with mean 74.8cm and standard deviation 3.2 cm. A random sample of 120 adult kest...

For a set of 40 values of x, it is found that Σ(x-k) = 836.0, Σ(x−k)² = 25410.8, where k is a constant.

At a large college, all students who study Science also study exactly one of Art or Drama or Music. 20% of these students study Art, 45% study Dram...

A fair six-sided dice with faces labelled 1, 2, 3, 4, 5, 6 is thrown repeatedly until a 3 is obtained. The number of throws taken is denoted by the...

84 people attempt a particular puzzle. The times taken, in minutes, to complete the puzzle are recorded. These times are represented in the cumulat...

Bag A contains 6 red marbles, 5 blue marbles and 1 green marble. Bag B contains 5 red marbles and 3 blue marbles. A marble is chosen at random from...

A company sells bags of pasta. The masses of large bags of pasta are normally distributed with mean 2.50kg and standard deviation 0.12kg. (a) Find ...

A set of friends consists of 7 men and 4 women. Three of the men are brothers: Ali, Ben and Charlie.

It is known that 1% of houses in a certain area have a wind turbine. A random sample of 400 houses in this area is chosen for a survey on domestic ...

The random variable X has the distribution B(8, 3/4). A random sample of 100 values of X is chosen, and the sample mean, X̅, is found.

The time, T minutes, for a certain daily bus journey is normally distributed. The bus company claims that the mean of T is 45. A passenger believes...

At an entertainment centre, the cost for using a particular video game is $0.40 per minute. The number of minutes for which people use the video ga...

The random variables W and X have the independent distributions Po(1.2) and Po(2.3) respectively.

A manufacturer of cell phones claims that 25% of students own a Pumpkin phone. Jeyeraj thinks that the proportion of students at his large college ...

X is a random variable with probability density function given by f(x) = { 1/π (1+cos πx) 0 ≤ x ≤ 1, { 0 otherwise.

One of a group of three students is to be chosen at random. The times, in minutes, taken by students to complete a test are normally distributed wi...

The height of a certain species of plant is denoted by Hcm. The heights of a random sample of 100 plants were measured, and the following results w...

The random variable X has the distribution Po(15). It is given that P(X = n) = P(X = n+1).

A biased spinner has four sides. Each side is of a different colour: yellow, red, green or black. The probability, p, that the spinner will land on...

The amount of time, in minutes, spent by a customer on one visit to a certain shop is modelled by the random variable X ~ N(μ, σ²). In the past, th...

Use suitable approximating distributions to answer the following.

The random variable X has probability density function given by f(x) = { kx² / a² for 0 ≤ x ≤ a, { 0 otherwise, where k and a are positive c...

Birgitte has a six-sided dice. She suspects that the dice is biased so that the probability, p, that it will show a six on one throw is less than 1...

At a certain shop, customers arrive independently and randomly at a constant average rate of 23.4 per hour.

The lengths of pencils made at a factory are normally distributed. The standard deviation of the lengths is σcm, and the mean is supposed to be 10c...

A machine dispenses coffee into cups. The volume, Vcm³, of coffee in a cup was measured for a random sample of 150 cups. The results were summarise...

Emma needs to choose one person at random from three people, P, Q and R. She plans to throw two fair coins and note the number, n, of heads. If n i...

In Urberia, the masses, in kilograms, of men have the distribution N(70.3, 5.9²). A certain footbridge in Urberia can take a maximum safe load of 1...

A random variable X has probability density function given by f(x) = { ax for 0 ≤ x ≤ b, { 0 otherwise, where a and b are constants.

In the past, one quarter of job applicants at a certain firm had first-class degrees. A change is made in the job description and a director of the...

The equation of a curve is such that dy/dx = 3/√x - x. Given that the curve passes through the point (4, 6), find the equation of the curve.

Find, in terms of the non-zero constant k, the first 4 terms in the expansion of (k + x)⁸ in ascending powers of x.

A progression has a second term of 96 and a fourth term of 54. Find the first term of the progression in each of the following cases:

The function f is defined by f : x → 5 – 3 sin 2x for 0 ≤ x ≤ π.

Prove the identity (sin x + cos x)(1 − sin x cos x) = sin³ x + cos³ x.

In the diagram, OABCDEFG is a cube in which each side has length 6. Unit vectors i, j and k are parallel to OA, OC and OD respectively. The point P...

A piece of wire of length 50 cm is bent to form the perimeter of a sector POQ of a circle. The radius of the circle is r cm and the angle POQ is θ ...

The function f is such that f(x) = 3/(2x + 5) for x ∈ R, x ≠ −2.5.

The diagram shows a rectangle ABCD. The point A is (0, -2) and C is (12, 14). The diagonal BD is parallel to the x-axis. [Figure X.X]

the x-coordinates of A and B,