Cambridge Past Paper Questions

The diagram shows a solid cylinder. The cylinder has diameter 9 cm and height 16 cm. Work out the total surface area of the cylinder. Give your ans...

Make t the subject of the formula r = 5t – 3.

Solve the inequality 4x – 7 < 11.

Describe fully the single transformation that maps triangle A onto triangle B.

Simplify (8a³)¹/³.

Given that y = 2x³ – 3x² + 5x – 1. Find dy/dx.

Here are two similar triangles. The area of triangle ABC is 20 cm². The area of triangle PQR is 45 cm². The length of BC is 8 cm. Work out the leng...

Solve 2x² – 5x – 3 = 0. Show your working clearly. Give your answers correct to 3 significant figures.

The equation of a curve is y = x³ – 6x² + 9x – 2. Find the coordinates of the turning points of the curve.

Which of the following electromagnetic waves has the longest wavelength?

A student investigates the motor effect. A wire carrying a current is placed in a uniform magnetic field.

A sample of a radioactive isotope has a half-life of 6 hours.

A converging lens has a focal length of 10 cm. An object is placed 15 cm from the lens.

Which of the following describes the nature of alpha (α) radiation?

Describe the process of nuclear fission and explain how a chain reaction can occur.

This question is about radioactivity.

This question is about the Solar System.

This question is about waves.

This question is about specific latent heat.

11 A student investigates how the resistance of a wire depends on its length. [Figure 9] shows the circuit the student uses.

A small electric motor is connected to a 6.0 V battery. The current in the motor is 0.40 A.

This question is about mains electricity.

A student uses the apparatus shown in Figure 14 to investigate moments.

Figure 15 shows a circuit with a 12 V power supply and three resistors.

This question is about electromagnetic induction.

A student investigates the current in different types of circuit.

A student investigates radioactive decay.

A student investigates the speed of sound.

A student investigates how to make a magnet.

A student uses a loudspeaker to produce sound waves.

Which of the following is a unit of power?

A student investigates water waves in a ripple tank. [Figure 1] shows a snapshot of the waves at a particular instant.

A student sets up a circuit as shown in [Figure 2]. The circuit contains a power supply, a resistor, and a light-dependent resistor (LDR).

The points A, B and C have position vectors $\mathbf{a} = \begin{pmatrix} 2 \\ 1 \\ 3 \end{pmatrix}$, $\mathbf{b} = \begin{pmatrix} 4 \\ -1 \\ 5 \e...

A curve $C$ has equation $y = 3x^2 - 12x + 10$.

Which of the following is the correct expansion of $(2x - y)^3$?

Given that $y = (3x-1)^4$, find $\frac{\text{d}y}{\text{d}x}$.

The equation $\mathrm{e}^x - 3x = 0$ has a root $\alpha$ in the interval $[0, 1]$.

Solve the inequality $|2x - 3| \leqslant 5$.

The $n$th term of an arithmetic series is $u_n = 5n - 2$. (a) Write down the first three terms of the series. (b) Find the sum of the first 20 term...

Solve the equation $2\tan^2 \theta - 3\sec \theta = 0$ for $0^{\circ} \leqslant \theta < 360^{\circ}$. Give your answers to one decimal place where...

A particle $P$ moves in a straight line such that its velocity $v$ m/s at time $t$ seconds is given by $v = 6t^2 - 10t + 3$. The particle is initia...

The curve $C$ has equation $y = 3x^2 - 4x + 1$. The line $L$ has equation $y = x - 1$. (a) Find the coordinates of the points of intersection of $C...

A circle $C$ has equation $x^2 + y^2 - 6x + 8y - 24 = 0$. (a) Find the coordinates of the centre of $C$ and the radius of $C$. (b) The point $P(7, ...

The curve $C$ has equation $y=\frac{x}{x+2}$. The line $L$ has equation $y=x-2$.

Simplify fully $$\frac{4x^2 - 9}{2x^2 - 13x + 15}$$

The curve $C$ has equation $y = 2x^3 - 9x^2 + 12x$. The point $P$ lies on $C$ and has $x$-coordinate 2. (a) Find $\frac{\mathrm{d}y}{\mathrm{d}x}$....

The circle $C$ has equation $x^2 + y^2 - 6x + 8y - 24 = 0$. (a) Find the coordinates of the centre of $C$ and the exact radius of $C$. (b) The poin...

Given that the coefficient of $x^3$ in the expansion of $(2 - \frac{1}{4}x)^n$ is 280, find the value of the positive integer $n$.

The functions f and g are defined by $$f(x) = \frac{2x+3}{x-1}, \quad x \in \mathbb{R}, x \neq 1$$ $$g(x) = 2x^2 - 3, \quad x \in \mathbb{R}$$ (a)...