Cambridge & Pearson Edexcel Past Paper Questions

The complex number 1 + 2i is denoted by u. The polynomial 2x³ + ax² + 4x + b, where a and b are real constants, is denoted by p(x). It is given tha...

Find the value of x for which 3(2¹⁻ˣ) = 7ˣ. Give your answer in the form ln a / ln b, where a and b are integers.

Solve the inequality |3x – a| > 2|x + 2a|, where a is a positive constant.

Given the complex numbers u = a + ib and w = c + id, where a, b, c and d are real, prove that (u + w)* = u* + w*.

Express 4x² - 13x + 13 / (2x - 1)(x - 3) in partial fractions.

Using the expansions of sin(3x + 2x) and sin(3x - 2x), show that ½(sin 5x + sin x) = sin 3x cos 2x.

The variables x and y satisfy the differential equation e²ˣ dy/dx = 4xy², and it is given that y = 1 when x = 0. Solve the differential equation, o...

By first expanding (cos² θ + sin²θ)², show that cos⁴ θ + sin⁴θ = 1 − ½ sin² 2θ.

The equation of a curve is ye²ˣ – y²eˣ = 2.

With respect to the origin O, the position vectors of the points A and B are given by OA = (1, 2, -1) and OB = (0, 3, 1).

The equation of a curve is y = √tan x, for 0 ≤ x < ½π. [Figure X.X]

Find the quotient and remainder when 2x⁴ + 1 is divided by x² − x + 2.

Sketch the graph of y = |2x – 3|.

Solve the equation 4ˣ⁻² = 4ˣ – 4², giving your answer correct to 3 decimal places.

Find the exact value of ∫ from π/2 to π of x sin(½x) dx.

Solve the equation sin θ = 3 cos 2θ + 2, for 0° ≤ θ ≤ 360°.

By first expanding cos(x – 60°), show that the expression 2 cos(x - 60°) + cos x can be written in the form R cos(x – α), where R > 0 and 0° < α < ...

The equation of a curve is ln(x + y) = x – 2y.

In the diagram, OABCD is a pyramid with vertex D. The horizontal base OABC is a square of side 4 units. The edge OD is vertical and OD = 4 units. T...

Let f(x) = 1 / ((9-x)√x) Find the x-coordinate of the stationary point of the curve with equation y = f(x).

A large plantation of area 20 km² is becoming infected with a plant disease. At time t years the area infected is x km² and the rate of increase of...

The complex number –√3 + i is denoted by u.

A bus moves from rest with constant acceleration for 12 s. It then moves with constant speed for 30 s before decelerating uniformly to rest in a fu...

Two small smooth spheres A and B, of equal radii and of masses km kg and m kg respectively, where k > 1, are free to move on a smooth horizontal pl...

Coplanar forces of magnitudes 24 N, P N, 20 N and 36 N act at a point in the directions shown in the diagram. The system is in equilibrium. Given t...

A car of mass 1600 kg travels at constant speed 20 m s⁻¹ up a straight road inclined at an angle of sin⁻¹ 0.12 to the horizontal.

A particle P moves in a straight line starting from a point O and comes to rest 14 s later. At time t s after leaving O, the velocity v m s⁻¹ of P ...

Two particles A and B of masses 2 kg and 3 kg respectively are connected by a light inextensible string. Particle B is on a smooth fixed plane whic...

The diagram shows a velocity-time graph which models the motion of a car. The graph consists of six straight line segments. The car accelerates fro...

A van of mass 3600 kg is towing a trailer of mass 1200 kg along a straight horizontal road using a light horizontal rope. There are resistance forc...

The diagram shows a semi-circular track ABC of radius 1.8 m which is fixed in a vertical plane. The points A and C are at the same horizontal level...

A cyclist starts from rest at a point A and travels along a straight road AB, coming to rest at B. The displacement of the cyclist from A at time t...

A railway engine of mass 75 000 kg is moving up a straight hill inclined at an angle α to the horizontal, where sin α = 0.01. The engine is travell...

A block of mass 5 kg is held in equilibrium near a vertical wall by two light strings and a horizontal force of magnitude X N, as shown in the diag...

Particles P and Q have masses m kg and 2m kg respectively. The particles are initially held at rest 6.4 m apart on the same line of greatest slope ...

A metal post is driven vertically into the ground by dropping a heavy object onto it from above. The mass of the object is 120 kg and the mass of t...

A particle of mass 8kg is suspended in equilibrium by two light inextensible strings which make angles of 60° and 45° above the horizontal.

A ball of mass 1.6 kg is released from rest at a point 5 m above horizontal ground. When the ball hits the ground it instantaneously loses 8 J of k...

A car of mass 1400kg is moving on a straight road against a constant force of 1250 N resisting the motion.

A particle P moves in a straight line, starting from rest at a point O on the line. At time t s after leaving O the acceleration of P is k(16 – t²)...

The diagram shows a particle of mass 5 kg on a rough horizontal table, and two light inextensible strings attached to it passing over smooth pulley...

Two fair coins are thrown at the same time. The random variable X is the number of throws of the two coins required to obtain two tails at the same...

A summary of 40 values of x gives the following information: Σ(x − k) = 520, Σ(x − k)² = 9640, where k is a constant.

For her bedtime drink, Suki has either chocolate, tea or milk with probabilities 0.45, 0.35 and 0.2 respectively. When she has chocolate, the proba...

A fair spinner has edges numbered 0, 1, 2, 2. Another fair spinner has edges numbered –1, 0, 1. Each spinner is spun. The number on the edge on whi...

Raman and Sanjay are members of a quiz team which has 9 members in total. Two photographs of the quiz team are to be taken. For the first photograp...

The weights, in kg, of 15 rugby players in the Rebels club and 15 soccer players in the Sharks club are shown below. Rebels 75 78 79 80 82 82 83 84...

The times, in minutes, that Karli spends each day on social media are normally distributed with mean 125 and standard deviation 24.

Each of the 180 students at a college plays exactly one of the piano, the guitar and the drums. The numbers of male and female students who play th...

A group of 6 people is to be chosen from 4 men and 11 women.