Cambridge & Pearson Edexcel Past Paper Questions

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.

The diagram shows curves with equations y = 2x¹/² + 13x⁻¹/² and y = 3x⁻¹/² + 12. The curves intersect at points A and B. [Diagram provided]

The equation of a curve is y = f(x), where f(x) = (4x – 3)³/² - 20x.

The coordinates of points A, B and C are (6, 4), (p, 7) and (14, 18) respectively, where p is a constant. The line AB is perpendicular to the line BC.

It is given that θ is an acute angle in degrees such that sin θ = 3/5. Find the exact value of sin(θ + 60°).

A curve has equation y = 3 tan (1/2)x cos 2x. Find the gradient of the curve at the point for which x = 5/6 π.

Find ∫₄¹⁰ 4/(2x-5) dx, giving your answer in the form ln a, where a is an integer.

Sketch, on the same diagram, the graphs of y = |3x – 5| and y = 2x + 7.

The polynomial p(x) is defined by p(x) = 6x³ + ax² + bx – 20, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that th...

Show that cosec θ(3 sin 2θ + 4 sin³ θ) = 4 + 6 cos θ – 4 cos² θ.

The curve with equation e²ˣ – 18x + y³ + y = 11 has a stationary point at (p, q).

When the polynomial ax³ + 4ax² -7x - 5 is divided by (x + 2), the remainder is 33.

Solve the equation sec θcos(θ – 60°) = 4 for −180° < θ < 180°.

The diagram shows the curve with equation y = 6e⁻¹/²x. The points on the curve with x-coordinates 0 and 2 are denoted by A and B respectively. The ...

Sketch, on the same diagram, the graphs of y = |3 – x| and y = 9 – 2x.

Find the quotient when 6x³ – 5x² – 24x – 4 is divided by (2x + 1), and show that the remainder is 6.

The diagram shows the curve with parametric equations x = 3 ln(2t – 3), y = 4t ln t. The curve crosses the y-axis at the point A. At the point B, t...

Prove that sin 2x(cot x + 3 tan x) = 4 – 2 cos 2x.

Find ∫ from 4 to 10 of (4 / (2x-5)) dx, giving your answer in the form ln a, where a is an integer.

The curve with equation e^(2x) – 18x + y³ + y = 11 has a stationary point at (p, q).

Find the exact coordinates of the points on the curve y = x² / (1-3x) at which the gradient of the tangent is equal to 8.

The variables x and y are related by the equation y = ab^x, where a and b are constants. The diagram shows the result of plotting In y against x fo...

The complex number u is defined by u = (3 + 2i) / (a - 5i), where a is real.