Cambridge & Pearson Edexcel Past Paper Questions

The complex numbers v and w satisfy the equations v + iw = 5 and (1 + 2i)v - w = 3i. Solve the equations for v and w, giving your answers in the fo...

A lorry of mass 16000 kg is travelling along a straight horizontal road. The engine of the lorry is working at constant power. The work done by the...

A particle P of mass 0.4 kg is on a rough horizontal floor. The coefficient of friction between P and the floor is μ. A force of magnitude 3 N is a...

The diagram shows the vertical cross-section of a surface. A, B and C are three points on the cross-section. The level of B is h m above the level ...

A cyclist travels along a straight road with constant acceleration. He passes through points A, B and C. The cyclist takes 2 seconds to travel alon...

Coplanar forces, of magnitudes FN, 3 N, 6 N and 4 N, act at a point P, as shown in the diagram. [Figure 5.1]

On a straight horizontal test track, driverless vehicles (with no passengers) are being tested. A car of mass 1600 kg is towing a trailer of mass 7...

A particle moves in a straight line through the point O. The displacement of the particle from O at time t s is s m, where s = t² - 3t + 2 for 0 ≤ ...

The 40 members of a club include Ranuf and Saed. All 40 members will travel to a concert. 35 members will travel in a coach and the other 5 will tr...

An ordinary fair die is thrown repeatedly until a 1 or a 6 is obtained.

The weights of apples of a certain variety are normally distributed with mean 82 grams. 22% of these apples have a weight greater than 87 grams.

Richard has 3 blue candles, 2 red candles and 6 green candles. The candles are identical apart from their colours. He arranges the 11 candles in a ...

In Greenton, 70% of the adults own a car. A random sample of 8 adults from Greenton is chosen.

Box A contains 7 red balls and 1 blue ball. Box B contains 9 red balls and 5 blue balls. A ball is chosen at random from box A and placed in box B....

Helen measures the lengths of 150 fish of a certain species in a large pond. These lengths, correct to the nearest centimetre, are summarised in th...

The booklets produced by a certain publisher contain, on average, 1 incorrect letter per 30 000 letters, and these errors occur randomly. A randoml...

Lengths of a certain species of lizard are known to be normally distributed with standard deviation 3.2 cm. A naturalist measures the lengths of a ...

In the past, the mean time taken by Freda for a particular daily journey was 39.2 minutes. Following the introduction of a one-way system, Freda wi...

The number of accidents on a certain road has a Poisson distribution with mean 0.4 per 50-day period.

Bottles of Lanta contain approximately 300 ml of juice. The volume of juice, in millilitres, in a bottle is 300 + X, where X is a random variable w...

The volumes, in millilitres, of large and small cups of tea are modelled by the distributions N(200, 30) and N(110, 20) respectively.

A national survey shows that 95% of year 12 students use social media. Arvin suspects that the percentage of year 12 students at his college who us...

Find the first three terms in the expansion, in ascending powers of x, of (1 + x)5.

By using a suitable substitution, solve the equation 4 (2x-3)2 - - 3 = 0.

Solve the equation tan θ + 2 sin θ = 3 for 0° < θ < 180°. tan θ-2 sin θ

A line has equation y = 3x + k and a curve has equation y = x² + kx + 6, where k is a constant. Find the set of values of k for which the line and ...

In the diagram, the graph of y = f(x) is shown with solid lines. The graph shown with broken lines is a transformation of y = f(x). [Figure 5.1]

A curve is such that dy 6 = and A (1, -3) lies on the curve. A point is moving along the curve dx (3x-2)3 and at A the y-coordinate of the point is...

Functions f and g are defined as follows: f : x → x² + 2x + 3 for x ≤ −1, g: x → 2x + 1 for x ≥ −1.

The points A (7, 1), B (7, 9) and C (1, 9) are on the circumference of a circle.

The first term of a progression is cos θ, where 0 < θ < ½π.

The diagram shows a sector ABC which is part of a circle of radius a. The points D and E lie on AB and AC respectively and are such that AD = AE = ...

The diagram shows the curve with equation y = 9(x^(½) - 4x^(-½)). The curve crosses the x-axis at the point A. [Figure 11.1]

Sketch, on the same diagram, the graphs of y = |3x – 5| and y = x + 2.

Solve the equation sec² θ cot θ = 8 for 0 < θ < π.

The parametric equations of a curve are x = e2t cos 4t, y = 3 sin 2t. Find the gradient of the curve at the point for which t = 0.

The diagram shows part of the curve with equation y = 5x / (4x³ + 1). The shaded region is bounded by the curve and the lines x = 1, x = 3 and y = ...

Given that 2ln(x + 1) + lnx = ln(x + 9), show that x = √(9/(x + 2)).

The polynomial p(x) is defined by p(x) = x² + ax + b, where a and b are constants. It is given that (x + 2) is a factor of p(x) and that the remain...

Express 5√3 cos x + 5 sin x in the form R cos(x – α), where R > 0 and 0 < α < ½π.

Solve the equation ln(x³ – 3) = 3 ln x – ln 3. Give your answer correct to 3 significant figures.

The polynomial ax³ + 5x² – 4x + b, where a and b are constants, is denoted by p(x). It is given that (x + 2) is a factor of p(x) and that when p(x)...

By first expressing the equation tan(x + 45°) = 2 cotx + 1 as a quadratic equation in tanx, solve the equation for 0° < x < 180°.

The variables x and y satisfy the differential equation (1-cosx) dy/dx = y sinx. It is given that y = 4 when x = π.

Express √7 sin x + 2 cos x in the form R sin(x + α), where R > 0 and 0° < α < 90°. State the exact value of R and give α correct to 2 decimal place...

Let f(x) = 5a / ((2x – a)(3a – x)), where a is a positive constant.

Two lines have equations r = (1, 3, 2) + s(2, -1, 3) and r = (2, 1, 4) + t(-1, 1, 4)

The complex numbers u and v are defined by u = −4 + 2i and v = 3 + i.

Let f(x) = (e^(2x) + 1) / (e^(2x) - 1), for x > 0.

The diagram shows the curve y = sin 2x cos²x for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 10.1]