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Exam-Style Questions.Problems adapted from questions set for previous Mathematics exams. |
1. | IGCSE Core |
A bricklayer estimates the number of bricks he will need to build a wall by dividing the area of the wall by the area of the face of a brick.
The wall is 16 metres long and 1.2 metres tall.
The bricks he will use are each 25 centimetres long and 12 centimetres tall.
Calculate an estimate for the number of bricks the bricklayer will need to build the wall.
The diagram above of part of the wall is not drawn to scale.
2. | GCSE Higher |
The diagram shows a water tank in the shape of a cylinder. It has a diameter of 76cm anf a height of 36cm.
It is filled at the rate of 0.3 litres per second. How long does it take to completely fill the tank?
[1 litre = 1000 cm3]
3. | GCSE Higher |
Babatunde has to paint four containers.
Each container is in the shape of a cylinder with a diameter of 1.2m and a length of 3.2m.
How many tins of paint will Babatunde need to buy to completely cover each of the four containers if each tin of paint covers 6m2?
You must show all of your working.
[The surface area of a cylinder of radius \(r\) and height (or length) \(h\) is \(2\pi rh + 2\pi r^2\)]
4. | GCSE Higher |
The diagram shows a red square placed on top of a grey square.
The length of each side of the grey square is 4cm longer than the length of each side of the red square.
The area of the grey square is 56cm2 greater than the area of the red square.
Find the area of the grey square giving your answer correct to 3 significant figures.
5. | GCSE Higher |
The trapezium and rectangle shown here have the same perimeters. The diagrams are not drawn to scale and the measurements are in centimetres. Calculate the area of the trapezium.
6. | GCSE Higher |
The diagram below shows two rectangles not drawn to scale.
The perimeter of rectangle EFGH is 41cm and the area of rectangle ABCD is 55cm2.
Find the length of AD.
7. | GCSE Higher |
A container is in the shape of a cuboid as shown in the diagram below.
The container is three quarters full of water.
A glass holds 250 ml of water.
What is the greatest number of glasses that can be completely filled with water from the container?
8. | GCSE Higher |
The illustration shows a greenhouse in the shape of a pentagonal prism. The front of the greenhouse is a pentagon with a single line of symmetry. The sides of the greenhouse are vertical.
Find the volume of the greenhouse in cubic metres correct to the nearest integer.
9. | GCSE Higher |
Triangle JKL is the cross-section of a prism of length 25cm.
JK = 7cm, KL = 10cm and LJ = 14cm.
(a) Find the area of triangle JKL correct to 2 decimal places.
(b) Find the volume of the prism.
(c) Find the total surface area of the prism.
(d) A mathematically similar prism has a volume of one litre.
Calculate the total surface area of this similar prism.
Give your answer correct to 2 significant figures.
10. | GCSE Higher |
Walter Wall is planning to renovate a remote building by installing new flooring. A diagram showing the area required to be covered by the flooring can be seen below.
ABCDEFG is a regular heptagon with sides of length 5m.
O is the centre of the heptagon and M is the midpoint of AB.
(a) Find angle AOM
(b) Calculate the area of the heptagon in square metres.
Walter may be able to save money by purchasing some second-hand flooring material in the shape of a circle.
(c) Find the area of the circle that passes through the vertices of the heptagon.
11. | GCSE Higher |
A red square has sides of length \(x\) cm. A blue rectangle has sides of length \(3x-1\) cm and \(x-2\) cm. The diagrams below are not drawn to scale.
The area of the rectangle is \(132\) cm2 greater than the area of the square.
The difference between the perimeters of the two shapes is \(p\) cm.
Find the value of \(p\).
You must show all your working.
12. | GCSE Higher |
A square has sides of length \(x\) cm.
The equilateral triangle next to it has sides which are each 3cm more than the length of a side of the square.
(a) Find the perimeter of the square if it is equal to the perimeter of the triangle.
The diagram above show the same square and triangle.
The length of the diagonal of the square is \(d\) cm and the height of the triangle is \(h\) cm.
(b) Which has the greater value, \(d\) or \(h\)?
13. | GCSE Higher |
The diagram shows a water tank in the shape of a trapezoidal prism.
Winthrop begins filling the tank with a hose pipe. After 30 minutes there are 900 litres of water in the tank. How many more minutes will it take until the tank is half full? ( \( 1m^3 = 1000 \) litres )
14. | IB Applications and Interpretation |
A wedge is to be cut from a log in the shape of a cylinder as shown in the diagram below (not to scale).
The length of the log is 240cm and its radius is 40cm. The cross section of the wedge to be removed is a sector with an angle of 130o.
What is the volume of the remaining piece of the log after the wedge has been removed?
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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
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