Cambridge & Pearson Edexcel Past Paper Questions

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,

Find the first 3 terms in the expansion, in ascending powers of x, of (1 – 2x²)⁸.

Prove the identity tan²x - sin²x = tan²x sin²x.

The length, x metres, of a Green Anaconda snake which is t years old is given approximately by the formula x = 0.7 √(2t – 1), where 1 ≤ t ≤ 10. Usi...

The diagram shows points A, C, B, P on the circumference of a circle with centre O and radius 3 cm. Angle AOC = angle BOC = 2.3 radians. [Figure 4.1]

The first and second terms of an arithmetic progression are 161 and 154 respectively. The sum of the first m terms is zero. Find the value of m.

A curve has equation y = kx² + 1 and a line has equation y = kx, where k is a non-zero constant.

The function f is defined by f(x) = x² – 4x +7 for x > 2.

The diagram shows part of the curve y = 2/(1-x) and the line y = 3x + 4. The curve and the line meet at points A and B. [Figure 8.1]

The diagram shows a pyramid OABCP in which the horizontal base OABC is a square of side 10 cm and the vertex P is 10cm vertically above O. The poin...

The diagram shows an open rectangular tank of height h metres covered with a lid. The base of the tank has sides of length x metres and 5/4x metres...

The diagram shows part of the curve y = 1/(3x + 1)⁴. The curve cuts the y-axis at A and the line x = 5 at B. [Figure 11.1]

Find the first 3 terms in the expansion of (2 – y)⁵ in ascending powers of y.

The functions f and g are defined for x ∈ R by f: x → 3x + a, g: x → b - 2x, where a and b are constants. Given that ff(2) = 10 and g⁻¹(2) = 3, find

Relative to an origin O, the position vectors of points A and B are given by OĀ = 5i + j + 2k and OB = 2i + 7j + pk, where p is a constant.

The equation of a curve is y² + 2x = 13 and the equation of a line is 2y + x = k, where k is a constant.

Sketch, on the same diagram, the graphs of y = sinx and y = cos 2x for 0° ≤ x ≤ 180°.

The diagram shows a circle C₁ touching a circle C₂ at a point X. Circle C₁ has centre A and radius 6 cm, and circle C₂ has centre B and radius 10 c...

A curve is such that dy/dx = 5 - 8/x². The line 3y + x = 17 is the normal to the curve at the point P on the curve. Given that the x-coordinate of ...

The equation of a curve is y = √(8x – x²). Find

The diagram shows a quadrilateral ABCD in which the point A is (-1, -1), the point B is (3, 6) and the point C is (9, 4). The diagonals AC and BD i...

(a) An arithmetic progression contains 25 terms and the first term is –15. The sum of all the terms in the progression is 525. Calculate (b) A coll...

In the expansion of (x² - a/x)⁷, the coefficient of x⁵ is –280. Find the value of the constant a.