Cambridge & Pearson Edexcel Past Paper Questions

Three particles P, Q and R, of masses 0.6kg, 0.4 kg and 0.8 kg respectively, are at rest in a straight line on a smooth horizontal plane. The dista...

A block of mass 12kg is placed on a rough plane inclined at an angle of α to the horizontal, where α = tan⁻¹0.5. A force of X N is applied to the b...

A particle moves in a straight line. The velocity v ms⁻¹ of the particle t s after leaving a fixed point O is given by v = k(20+pt-6t²), where k an...

Jacob throws three coins at the same time. The first coin is biased so that the probability of obtaining a head when it is thrown is 1/3. The secon...

Last year, an online store sold a large number of computers. 55% of the computers were made by company F, 30% were made by company G and 15% were m...

The lengths of 250 leaves of a certain type of plant are measured, correct to the nearest centimetre. The results are summarised in the table below...

Eddie has 16 toy cars, of which 8 are white, 5 are black and 3 are silver. He places all the cars in a bag and selects three of them at random, wit...

The mass of peaches sold per day in a supermarket is normally distributed with mean 65.8kg and standard deviation 9.6kg.

Alissa has 10 different books from the series Squares and Circles. The books look similar except for their colour. There are 3 blue books, 2 red bo...

The random variables X and Y have the independent distributions N(44, 16) and N(30, 9) respectively. Find P(X-Y < 15).

A researcher records the time, T seconds, taken by adults to complete a questionnaire. The results for a random sample of 60 adults who completed t...

The random variable X has the distribution Po(1.5).

The diagram shows the graph of the probability density function, f, of a random variable X. The graph is a straight line from (0, a) to (2, b), whe...

Amir believes that 20% of the students at his college are left-handed. His friend believes that the true proportion, p, is less than 20%. Amir plan...

Nikki is investigating the views of students at her school about the school sports facilities. She plans to give a survey to a sample of students. ...

(i) Show that the equation 3(2 sin x − cos x) = 2(sin x – 3 cos x) can be written in the form tan x = -¾. (ii) Solve the equation 3(2 sin x − cos x...

The diagram shows part of the curve y = a/x, where a is a positive constant. Given that the volume obtained when the shaded region is rotated throu...

The functions f and g are defined for x ∈ R by f : x → 4x - 2x², g : x → 5x + 3. (i) Find the range of f. (ii) Find the value of the constant k for...

In the diagram, A is the point (−1, 3) and B is the point (3, 1). The line L₁ passes through A and is parallel to OB. The line L₂ passes through B ...

Relative to an origin O, the position vectors of the points A and B are given by OA = (-2/3) and OB = (4/p) (i) Find the value of p for which OA is...

(i) Find the first 3 terms in the expansion of (1 + ax)⁵ in ascending powers of x. (ii) Given that there is no term in x in the expansion of (1 – 2...

(a) Find the sum of all the multiples of 5 between 100 and 300 inclusive. (b) A geometric progression has a common ratio of -½ and the sum of the f...

A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm². (i) Ex...

The diagram shows the curve y = (x – 2)² and the line y + 2x = 7, which intersect at points A and B. Find the area of the shaded region.

The equation of a curve is y = ½(2x – 3)³ – 4x. (i) Find dy/dx. (ii) Find the equation of the tangent to the curve at the point where the curve int...

The function f: x → 4-3 sin x is defined for the domain 0 ≤ x ≤ 2π. (i) Solve the equation f(x) = 2. (ii) Sketch the graph of y = f(x). (iii) Find ...

Find ∫(x³ + 1/x²) dx.

Find the terms in x² and x³ in the expansion of (1 – ½x)⁶.

The equation x² + px + q = 0, where p and q are constants, has roots –3 and 5.

A curve has equation y = 4/(3x-4) and P (2, 2) is a point on the curve.

Prove the identity cos θ / (tan θ(1 – sin θ)) = 1 + 1/sin θ

The function f is defined by f : x → (x+3)/(2x-1), x ∈ R, x ≠ 1/2.

The line L₁ passes through the points A (2, 5) and B (10, 9). The line L₂ is parallel to L₁ and passes through the origin. The point C lies on L₂ s...

Relative to the origin O, the position vectors of the points A, B and C are given by `OA = (2 5)`, `OB = (4 3)`, `OC = (10 6)`. The point D is such...

The function f is such that f(x) = 3 – 4 cosᵏx, for 0 ≤ x ≤ π, where k is a constant.

A circle is divided into 6 sectors in such a way that the angles of the sectors are in arithmetic progression. The angle of the largest sector is 4...

The diagram shows part of the curve y = 4√x – x. The curve has a maximum point at M and meets the x-axis at O and A. [Figure X.X]

The diagram shows the region enclosed by the curve y = 6/(2x-3), the x-axis and the lines x = 2 and x = 3. Find, in terms of π, the volume obtained...

The equation of a curve is y = 4√x + 2/√x

The coefficient of x³ in the expansion of (a + x)⁵ + (2 – x)⁶ is 90. Find the value of the positive constant a.

The point A has coordinates (−1, −5) and the point B has coordinates (7, 1). The perpendicular bisector of AB meets the x-axis at C and the y-axis ...

Prove the identity tan x + 1/tan x = 1/(sin x cos x)

The diagram shows a metal plate made by removing a segment from a circle with centre O and radius 8 cm. The line AB is a chord of the circle and an...

In an arithmetic progression, the sum of the first n terms, denoted by Sn, is given by Sn = n² + 8n. Find the first term and the common difference.

The vector OA has a magnitude of 15 units and is in the same direction as the vector 3i – 4k. The vector OB has a magnitude of 14 units and is in t...

The diagram shows part of the curve y = −x² + 8x – 10 which passes through the points A and B. The curve has a maximum point at A and the gradient ...

Functions f and g are defined by f: x → 2x + 5 for x ∈ R, g: x → 8/(x-3) for x ∈ R, x ≠ 3.

A curve is such that dy/dx = 6/x² and (2, 9) is a point on the curve. Find the equation of the curve.

Find the coefficient of x² in the expansion of

The straight line y = mx + 14 is a tangent to the curve y = 12/x + 2 at the point P. Find the value of the constant m and the coordinates of P.