Cambridge & Pearson Edexcel Past Paper Questions

A lorry of mass 15000kg moves on a straight horizontal road in the direction from A to B. It passes A and B with speeds 20ms⁻¹ and 25ms⁻¹ respectiv...

A particle starts from rest from a point O and moves in a straight line. The acceleration of the particle at time ts after leaving O is a m s¯², wh...

An elevator is pulled vertically upwards by a cable. The elevator accelerates at 0.4ms⁻² for 5 s, then travels at constant speed for 25 s. The elev...

The diagram shows the vertical cross-section XYZ of a rough slide. The section YZ is a straight line of length 2 m inclined at an angle of α to the...

A summary of 50 values of x gives Σ(x – q) = 700, Σ(x − q)² = 14235, where q is a constant.

A different committee of 6 people is to be chosen from 6 men and 8 women. Three of the 6 men are brothers.

Find the number of different arrangements of the 8 letters in the word COCOONED.

A mathematical puzzle is given to a large number of students. The times taken to complete the puzzle are normally distributed with mean 14.6 minute...

The populations of 150 villages in the UK, to the nearest hundred, are summarised in the table. Population | 100 – 800 | 900 – 1200 | 1300 – 2000 |...

Eli has four fair 4-sided dice with sides labelled 1, 2, 3, 4. He throws all four dice at the same time. The random variable X denotes the number o...

A children's wildlife magazine is published every Monday. For the next 12 weeks it will include a model animal as a free gift. There are five diffe...

The random variable X takes the values –2, 2 and 3. It is given that P(X = x) = k(x² – 1), where k is a constant.

A sports event is taking place for 4 days, beginning on Sunday. The probability that it will rain on Sunday is 0.4. On any subsequent day, the prob...

The following back-to-back stem-and-leaf diagram represents the monthly salaries, in dollars, of 27 employees at each of two companies, A and B. Co...

A fair 5-sided spinner has sides labelled 1, 2, 3, 4, 5. The spinner is spun repeatedly until a 2 is obtained on the side on which the spinner land...

The lengths of Western bluebirds are normally distributed with mean 16.5cm and standard deviation 0.6 cm. A random sample of 150 of these birds is ...

In a group of 25 people there are 6 swimmers, 8 cyclists and 11 runners. Each person competes in only one of these sports. A team of 7 people is se...

Two fair coins are thrown at the same time repeatedly until a pair of heads is obtained. The number of throws taken is denoted by the random variab...

Anil is a candidate in an election. He received 40% of the votes. A random sample of 120 voters is chosen. Use an approximation to find the probabi...

The random variable X takes the values 1, 2, 3, 4. It is given that P(X = x) = kx(x + a), where k and a are constants.

The times taken, in minutes, to complete a cycle race by 19 cyclists from each of two clubs, the Cheetahs and the Panthers, are represented in the ...

Jasmine throws two ordinary fair 6-sided dice at the same time and notes the numbers on the uppermost faces. The events A and B are defined as foll...

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg. On 10% of days less than 16kg of grapes a...

Find the number of different arrangements of the 10 letters in the word CASABLANCA in which the two Cs are not together.

In a certain country, 20540 adults out of a population of 6012300 have a degree in medicine.

The graph of the function f is a straight line segment from (0, 0) to (2, 1). [Figure for part (a)] The graph of the function g is a semicircle, ce...

In the past, the annual amount of wheat produced per farm by a large number of similar sized farms in a certain region had mean 24.0 tonnes and sta...

A certain train journey takes place every day throughout the year. The time taken, in minutes, for the journey is normally distributed with varianc...

Large packets of rice are packed in cartons, each containing 20 randomly chosen packets. The masses of these packets are normally distributed with ...

A sample of 5 randomly selected values of a variable X is as follows: 1 2 6 1 a where a > 0. Given that an unbiased estimate of the varianc...

The number of accidents per week at a certain factory has a Poisson distribution. In the past the mean has been 1.9 accidents per week. Last year, ...

In a survey of 200 randomly chosen students from a certain college, 23% of the students said that they owned a car. Calculate an approximate 93% co...

The random variable W has a Poisson distribution. State the relationship between E(W) and Var(W).

The masses, in kilograms, of newborn babies in country A are represented by the random variable X, with mean u and variance σ². The masses of a ran...

The number, X, of books received at a charity shop has a constant mean of 5.1 per day.

Two random variables X and Y have the independent distributions N(7, 3) and N(6, 2) respectively. A random value of each variable is taken. Find th...

When a child completes an online exercise called a Mathlit, they might be awarded a medal. The publishers claim that the probability that a randoml...

The diagram shows the graph of the probability density function, f, of a random variable X which takes values between 0 and 4 only. Between these t...

A random variable X has probability density function f, where f(x) = { (3/2)(1-x²) 0 ≤ x ≤ 1, 0 otherwise. } Find E(X).

A club has 264 members, numbered from 1 to 264. Donash wants to choose a random sample of members for a survey. In order to choose the members for ...

In a random sample of 100 students at Luciana's college, x students said that they liked exams. Luciana used this result to find an approximate 90%...

The mass, in tonnes, of steel produced per day at a factory is normally distributed with mean 65.2 and standard deviation 3.6. It can be assumed th...

Last year the mean time for pizza deliveries from Pete's Pizza Pit was 32.4 minutes. This year the time, t minutes, for pizza deliveries from Pete'...

It is known that 1 in 5000 people in Atalia have a certain condition. A random sample of 12500 people from Atalia is chosen for a medical trial. Th...

A random variable X has probability density function f, where the graph of y = f(x) is a semicircle with centre (0, 0) and radius √(2/π), entirely ...

A new light was installed on a certain footpath. A town councillor decided to use a hypothesis test to investigate whether the number of people usi...

The coefficient of x² in the expansion of (1 – 4x)⁶ is 12 times the coefficient of x² in the expansion of (2+ax)⁵. Find the value of the positive c...

The curve y = x² is transformed to the curve y = 4(x-3)²-8. Describe fully a sequence of transformations that have been combined, making clear the ...

Show that the equation 7 tan θ cos θ + 12 = 0 can be expressed as 12 sin²θ – 7 sin θ – 12 = 0.

The function f is defined as follows: f(x) = √x−1 for x > 1. The diagram shows the graph of y = g(x) where g(x) = 1/(x²+2) for x ∈ R. The function ...