Cambridge & Pearson Edexcel Past Paper Questions

The complex number 1 + 2i is denoted by u.

The line l has equation r = 4i + 3j – k + μ(i + 2j – 2k). The plane p has equation 2x – 3y – z = 4.

Two particles A and B, of masses 0.8 kg and 0.2 kg respectively, are connected by a light inextensible string that passes over a fixed smooth pulle...

The three coplanar forces shown in the diagram are in equilibrium.

A girl, of mass 40 kg, slides down a slide in a water park. The girl starts at the point A and slides to the point B which is 7.2 metres vertically...

A particle of mass 12 kg is on a rough plane inclined at an angle of 25° to the horizontal. A force of magnitude P N acts on the particle. This for...

A small rocket is fired vertically upwards, starting from rest at ground level, and moves with constant acceleration. The rocket reaches a height o...

A car of mass 1200 kg has a greatest possible constant speed of 60 m s¯¹ along a straight level road. When the car is travelling at a speed of v m ...

A particle P moves in a straight line. The velocity v m s¯¹ at time t s is given by v = 4 + 0.2t for 0 ≤ t ≤ 10, v = -2 + 800/t² for 10 ≤ t ≤ 20.

A uniform rectangular block has a square base ABCD with AB = BC = 0.4 m. The height of the block is h m. The block is placed with its base on a rou...

An object is projected with speed 15 m s¯¹ at an angle of 35° above the horizontal from a point on horizontal ground. Find the speed and direction ...

A small ball B is connected to one end of a light elastic string of natural length 0.4 m and modulus of elasticity 12 N. The other end of the strin...

A particle P is projected from a point O on horizontal ground. At the instant t s after projection, the horizontal and vertically upwards displacem...

One end of a light inextensible string of length 0.4 m is attached to the lowest point of a hemisphere of radius 0.4 m fixed with its axis vertical...

A small object of mass 0.2 kg rests at a point O on a rough horizontal surface. The coefficient of friction between the object and the surface is 0...

ABCD is a uniform square lamina with sides of length 0.6 m. A circular hole of radius r m is made in the lamina. The centre of the hole is 0.3 m fr...

There are 900 students in a certain year-group. An identical puzzle is given to each student and the time taken, t minutes, to complete the puzzle ...

A selection of 3 letters from the 8 letters of the word COLLIDER is made.

Last Saturday, Sarah recorded the colour and type of 160 cars in a car park. All the cars that were not red or silver in colour were grouped togeth...

The discrete random variable X has the following probability distribution. X|-2|0|1|3|4 P(X = x)|0.2|0.1|p|0.1|q

A summary of n values of x gave the following information: Σ(x – 20) = 136, Σ(x – 20)² = 2888. The mean of the n values of x is 24.25.

The digits 1, 3, 5, 6, 6, 6, 8 can be arranged to form many different 7-digit numbers.

The weights of packets of a certain type of biscuit are normally distributed with mean 400 grams and standard deviation σ grams.

The results of a survey at a certain large college show that the proportion of students who own a car is 1/4.

The coefficient of x³ in the expansion of (1 – px)⁵ is –2160. Find the value of the constant p.

A curve with equation y = f(x) passes through the points (0, 2) and (3, -1). It is given that f'(x) = kx² – 2x, where k is a constant. Find the val...

In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD is...

A curve has equation y = (2x – 1)⁻¹ + 2x.

Two vectors, u and v, are such that u = (2) (q) (6) and v = (8) (q-1) (q²-7) , where q is a constant.

The first and second terms of a geometric progression are p and 2p respectively, where p is a positive constant. The sum of the first n terms is gr...

Solve the equation 3 sin²2θ + 8 cos 2θ = 0 for 0° ≤ θ ≤ 180°.

Express x² – 4x + 7 in the form (x + a)² + b.

The diagram shows part of the curve with equation y = √(x³ + x²). The shaded region is bounded by the curve, the x-axis and the line x = 3. [Figure...

The diagram shows the curve with equation y = 4x^(1/2). [Figure X.X]

Solve the equation sec² θ + tan² θ = 5 tan θ + 4 for 0° < θ < 180°. Show all necessary working.

Given that x satisfies the equation |2x + 3| = |2x – 1|, find the value of |4x – 3| – |6x|.

The variables x and y satisfy the equation y = AePx+P, where A and p are constants. The graph of ln y against x is a straight line passing through ...

Find the quotient when 4x³ + 8x² + 11x + 9 is divided by (2x + 1), and show that the remainder is 5.

The equation of a curve is y = e^(2x) / (4x + 1) and the point P on the curve has y-coordinate 10.

Show that ∫⁴₁ (2/x + 2/(2x+1)) dx = ln 48.

The parametric equations of a curve are x = 2t - sin 2t, y = 5t + cos 2t, for 0 ≤ t ≤ ½π. At the point P on the curve, the gradient of the curve is 2.

Show that the equation log10(x - 4) = 2 – log10 x can be written as a quadratic equation in x.

The sequence of values given by the iterative formula x_n+1 = (2x_n^6 + 12x_n) / (3x_n^5 + 8) with initial value x₁ = 2, converges to α.

Given that sin(θ + 45°) + 2 cos(θ + 60°) = 3 cos θ, find the exact value of tan θ in a form involving surds. You need not simplify your answer.

Show that ∫₁⁴ x^(-1/2) ln x dx = 2 – ln 4.

The variables x and y satisfy the relation sin y = tan x, where –½π < y < ½π. Show that dy/dx = 1 / (cos x √(cos 2x)).

The variables x and y satisfy the differential equation dy/dx = ky³e⁻ˣ, where k is a constant. It is given that y = 1 when x = 0, and that y = √e w...

Showing all working and without using a calculator, solve the equation (1 + i)z² – (4 + 3i)z + 5 + i = 0. Give your answers in the form x + iy, whe...

Let f(x) = (12 + 12x - 4x²) / ((2 + x)(3 – 2x)).

Two planes have equations 2x + 3y – z = 1 and x – 2y + z = 3.