Cambridge IGCSE Maths (0580) · Topic 4: Geometry · 4.2
Geometrical Constructions questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
You are constructing a triangle with sides \(7\) cm, \(5\) cm and \(4\) cm, using a ruler and compasses only. You draw the \(7\) cm side first.
What radius do you set the compasses to for the arc from each end?
Answer: \(5\) cm from one end and \(4\) cm from the other
(a) How many squares are in the net of a cube?
(b) Which shapes make the net of a square-based pyramid?
Answer: (a) \(6\) (b) \(1\) square and \(4\) triangles
A net is made from 2 triangles and 3 rectangles. Write down the name of the solid it folds to make.
Answer: triangular prism
Can a triangle be constructed with sides \(3\) cm, \(4\) cm and \(8\) cm? Give a reason.
Answer: No, because \(3 + 4 \lt 8\)
The net of a triangular prism is drawn. How many rectangles and how many triangles does it have?
Answer: \(3\) rectangles and \(2\) triangles
A cuboid measures \(5\) cm by \(3\) cm by \(2\) cm. Work out the total area of its net.
Answer: \(62\) cm²
Using a ruler and compasses only, construct triangle \(ABC\) with \(AB = 8\) cm, \(BC = 6\) cm and \(AC = 5\) cm. Leave in your construction arcs. Then measure the largest angle of the triangle.
Answer: triangle with construction arcs; angle \(ACB \approx 93^\circ\)
A triangle is constructed with sides \(6\) cm, \(8\) cm and \(10\) cm. Without measuring, find the size of its largest angle.
Answer: \(90°\)
The net of a closed cylinder is two circles of radius 3 cm and a rectangle. The height of the cylinder is 10 cm.
(a) Find the length of the rectangle. Give your answer in terms of \(\pi\).
(b) Find the total area of the net. Give your answer in terms of \(\pi\).
Answer: (a) \(6\pi\) cm (b) \(78\pi\text{ cm}^2\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Geometrical Constructions is on both tiers (syllabus 4.2), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 4 (Geometry), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision