Cambridge & Pearson Edexcel Past Paper Questions

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.

The diagram shows the curve y = sin³x √(cos x) for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 10.1]

A small ring P of mass 0.03 kg is threaded on a rough vertical rod. A light inextensible string is attached to the ring and is pulled upwards at an...

A particle is projected vertically upwards with speed 30 m s¯¹ from a point on horizontal ground.

Four coplanar forces of magnitudes FN, 5 N, 25 N and 15 N are acting at a point P in the directions shown in the diagram. Given that the forces are...

A car of mass 1500 kg is pulling a trailer of mass 300 kg along a straight horizontal road at a constant speed of 20 m s⁻¹. The system of the car a...

The velocity of a particle moving in a straight line is v m s⁻¹ at time t seconds after leaving a fixed point O. The diagram shows a velocity-time ...

A particle moves in a straight line. It starts from rest at a fixed point O on the line. Its acceleration at time t s after leaving O is a m s⁻², w...

The diagram shows the vertical cross-section PQR of a slide. The part PQ is a straight line of length 8 m inclined at angle α to the horizontal, wh...

A particle is projected with speed 24 m s¯¹ at an angle of 30° above the horizontal. Find the speed and direction of motion of the particle at the ...

A uniform object is made by joining together three solid cubes with edges 3m, 2m and 1m. The object has an axis of symmetry, with the cubes stacked...

A small ball is projected from a point O on horizontal ground. At time ts after projection the horizontal and vertically upwards displacements of t...

A particle P of mass 0.3 kg is attached to a fixed point A by a light elastic string of natural length 0.8 m and modulus of elasticity 16 N. The pa...

A particle P of mass 0.3 kg is attached to one end of a light elastic string of natural length 0.6 m and modulus of elasticity 24 N. The other end ...

Fig. 1 shows the cross-section of a solid cylinder through which a cylindrical hole has been drilled to make a uniform prism. The radius of the cyl...

A particle P is projected horizontally from a point O on a rough horizontal surface. The coefficient of friction between the particle and the surfa...

On each day that Tamar goes to work, he wears either a blue suit with probability 0.6 or a grey suit with probability 0.4. If he wears a blue suit ...

For 40 values of the variable x, it is given that ∑(x − c)² = 3099.2, where c is a constant. The standard deviation of these values of x is 3.2.

The times taken, in minutes, for trains to travel between Alphaton and Beeton are normally distributed with mean 140 and standard deviation 12.

The random variable X takes the values −1, 1, 2, 3 only. The probability that X takes the value x is kx², where k is a constant.

The weights, in kg, of the 11 members of the Dolphins swimming team and the 11 members of the Sharks swimming team are shown below. Dolphins 62 75...

The results of a survey by a large supermarket show that 35% of its customers shop online.

Find the number of different arrangements that can be made of all 9 letters in the word CAMERAMAN in each of the following cases.