Cambridge & Pearson Edexcel Past Paper Questions

A particle P travels in a straight line, starting at rest from a point O. The acceleration of P at time t s after leaving O is denoted by a ms⁻², w...

A particle P is projected vertically upwards with speed ums¯¹ from a point on the ground. P reaches its greatest height after 3 s.

A box of mass 5kg is pulled at a constant speed of 1.8 ms¯¹ for 15s up a rough plane inclined at an angle of 20° to the horizontal. The box moves a...

A ring of mass 4kg is threaded on a smooth circular rigid wire with centre C. The wire is fixed in a vertical plane and the ring is kept at rest by...

A particle P travels in the positive direction along a straight line with constant acceleration. P travels a distance of 52 m during the 2nd second...

Particles X and Y move in a straight line through points A and B. Particle X starts from rest at A and moves towards B. At the same instant, Y star...

A car of mass 1750kg is pulling a caravan of mass 500kg. The car and the caravan are connected by a light rigid tow-bar. The resistances to the mot...

Particles of masses 1.5kg and 3kg lie on a plane which is inclined at an angle of α to the horizontal, where tan α = 3/4. The section of the plane ...

The probability distribution table for a random variable X is shown below. x -2 -1 0.5 1 2 P(X = x) 0.12 p q 0.16 0.3 Give...

The residents of Persham were surveyed about the reliability of their internet service. 12% rated the service as 'poor', 36% rated it as 'satisfact...

The Lions and the Tigers are two basketball clubs. The heights, in cm, of the 11 players in each of their first team squads are given in the table....

In a large population, the systolic blood pressure (SBP) of adults is normally distributed with mean 125.4 and standard deviation 18.6. Three adult...

A game is played with an ordinary fair 6-sided die. A player throws the die once. If the result is 2, 3, 4 or 5, that result is the player's score ...

A Social Club has 15 members, of whom 8 are men and 7 are women. The committee of the club consists of 5 of its members. The 15 members are having ...

On any day, Kino travels to school by bus, by car or on foot with probabilities 0.2, 0.1 and 0.7 respectively. The probability that he is late when...

The lengths of the rods produced by a company are normally distributed with mean 55.6mm and standard deviation 1.2 mm.

Three fair 6-sided dice, each with faces marked 1, 2, 3, 4, 5, 6, are thrown at the same time repeatedly. The score on each throw is the sum of the...

The times taken, in minutes, to complete a word processing task by 250 employees at a particular company are summarised in the table. Time taken (t...

Eric has three coins. One of the coins is fair. The other two coins are each biased so that the probability of obtaining a head on any throw is 1/4...

At a company’s call centre, 90% of callers are connected immediately to a representative. A random sample of 12 callers is chosen.

Find the number of different arrangements of the 9 letters in the word ALLIGATOR in which the two As are together and the two Ls are together.

50 values of the variable x are summarised by Σ(x – 20) = 35 and Σχ² = 25 036. Find the variance of these 50 values.

In a large college, 32% of the students have blue eyes. A random sample of 80 students is chosen. Use an approximation to find the probability that...

The times, t minutes, taken to complete a walking challenge by 250 members of a club are summarised in the table. Time taken (t minutes) t≤20 t≤30 ...

Three fair 4-sided spinners each have sides labelled 1, 2, 3, 4. The spinners are spun at the same time and the number on the side on which each sp...

Company A produces bags of sugar. An inspector finds that on average 10% of the bags are underweight. 10 of the bags are chosen at random. The weig...

Find the number of different arrangements of the 9 letters in the word ACTIVATED.

Sam and Tom are playing a game which involves a bag containing 5 white discs and 3 red discs. They take turns to remove one disc from the bag at ra...

The heights, in metres, of a random sample of 10 mature trees of a certain variety are given below. 5.9 6.5 6.7 5.9 6.9 6.0 6.4 6.2 ...

A spinner has five sectors, each printed with a different colour. Susma and Sanjay both wish to test whether the spinner is biased so that it lands...

Drops of water fall randomly from a leaking tap at a constant average rate of 5.2 per minute.

Each month a company sells X kg of brown sugar and Y kg of white sugar, where X and Y have the independent distributions N(2500, 120²) and N(3700, ...

A builders' merchant sells stones of different sizes.

The diagram shows the graph of the probability density function of a random variable X that takes values between –1 and 3 only. It is given that th...

In the past Laxmi's time, in minutes, for her journey to college had mean 32.5 and standard deviation 3.1. After a change in her route, Laxmi wishe...

Each of a random sample of 80 adults gave an estimate, h metres, of the height of a particular building. The results were summarised as follows. n ...

In the past, the mean length of a particular variety of worm has been 10.3 cm, with standard deviation 2.6cm. Following a change in the climate, it...

1.6% of adults in a certain town ride a bicycle. A random sample of 200 adults from this town is selected.

The number of faults in cloth made on a certain machine has a Poisson distribution with mean 2.4 per 10m². An adjustment is made to the machine. It...

X is a random variable with distribution B(10, 0.2). A random sample of 160 values of X is taken.

The masses, in grams, of small and large bags of flour have the distributions N(510, 100) and N(1015, 324) respectively. André selects 4 small bags...

[Figure 7.1] The diagram shows the graph of the probability density function, f, of a random variable X which takes values between –3 and 2 only.

The coefficient of x³ in the expansion of (3 + 2ax)⁵ is six times the coefficient of x² in the expansion of (2 + ax)⁶. Find the value of the consta...

Find the exact solution of the equation π + tan⁻¹(4x) = − cos⁻¹(½√3).

The equation of a curve is such that dy/dx = ½x + 72/x⁴. The curve passes through the point P (2, 8).

The diagram shows the shape of a coin. The three arcs AB, BC and CA are parts of circles with centres C, A and B respectively. ABC is an equilatera...

The first, second and third terms of a geometric progression are sin θ, cos θ and 2 – sin θ respectively, where θ radians is an acute angle.

The equation of a curve is y = x² – 8x + 5.

Verify the identity (2x – 1)(4x² + 2x – 1) = 8x³ – 4x + 1.

Functions f and g are defined by f(x) = (x + a)² – a for x ≤ −a, g(x) = 2x - 1 for x ∈ R, where a is a positive constant.