Cambridge & Pearson Edexcel Past Paper Questions

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]

Two particles P and Q of masses 0.2 kg and 0.3 kg respectively are free to move in a horizontal straight line on a smooth horizontal plane. P is pr...

A car of mass 1400 kg is travelling at constant speed up a straight hill inclined at α to the horizontal, where sin α = 0.1. There is a constant re...

A particle Q of mass 0.2 kg is held in equilibrium by two light inextensible strings PQ and QR. P is a fixed point on a vertical wall and R is a fi...

An elevator moves vertically, supported by a cable. The diagram shows a velocity-time graph which models the motion of the elevator. The graph cons...

A block of mass 5 kg is being pulled along a rough horizontal floor by a force of magnitude X N acting at 30° above the horizontal (see diagram). T...

A particle moves in a straight line. It starts from rest from a fixed point O on the line. Its velocity at time t s after leaving O is v m s⁻¹, whe...

Two particles P and Q of masses 0.5 kg and mkg respectively are attached to the ends of a light inextensible string. The string passes over a fixed...

A fair spinner with 5 sides numbered 1, 2, 3, 4, 5 is spun repeatedly. The score on each spin is the number on the side on which the spinner lands.

Georgie has a red scarf, a blue scarf and a yellow scarf. Each day she wears exactly one of these scarves. The probabilities for the three colours ...

The time spent by shoppers in a large shopping centre has a normal distribution with mean 96 minutes and standard deviation 18 minutes.

The random variable X takes the values 1, 2, 3, 4 only. The probability that X takes the value x is kx(5-x), where k is a constant.

A driver records the distance travelled in each of 150 journeys. These distances, correct to the nearest km, are summarised in the following table....

Find the total number of different arrangements of the 11 letters in the word CATERPILLAR.

There are 400 students at a school in a certain country. Each student was asked whether they preferred swimming, cycling or running and the results...

A construction company notes the time, t days, that it takes to build each house of a certain design. The results for a random sample of 60 such ho...

The diagram shows the graph of the probability density function, f, of a random variable X. [Figure 2.1]

An architect wishes to investigate whether the buildings in a certain city are higher, on average, than buildings in other cities. He takes a large...

On average, 1 in 400 microchips made at a certain factory are faulty. The number of faulty microchips in a random sample of 1000 is denoted by X.

The volumes, in litres, of juice in large and small bottles have the distributions N(5.10, 0.0102) and N(2.51, 0.0036) respectively.

It is known that 8% of adults in a certain town own a Chantor car. After an advertising campaign, a car dealer wishes to investigate whether this p...

A curve with equation y = f(x) is such that f'(x) = 2x^3 - x3. 1 - x3. It is given that f(8) = 5.

A curve has equation y = x² + 2cx + 4 and a straight line has equation y = 4x + c, where c is a constant. Find the set of values of c for which the...