Mathematics 0580 · syllabus C4.2, E4.2
Cambridge IGCSE Mathematics 0580 — Constructions and nets topical past papers
Measuring and drawing lines and angles, constructing triangles from three sides with a ruler and compasses, and drawing and using nets of solids.
- Questions
- 208
- Years
- 2009–2026
- With mark scheme
- 89%
- Questions 2022–2026
- 59
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Constructions and nets covers
Geometrical constructions are accurate drawings made with a ruler, a protractor and a pair of compasses. You measure lengths to the nearest millimetre and angles to the nearest degree, draw them to a given size, and construct a triangle when all three sides are given: draw one side, set the compasses to each of the other two lengths in turn, draw arcs from the two ends, and join the point where the arcs cross to both ends. The construction arcs must be left visible, and every straight edge must be ruled. The same method builds quadrilaterals made of two triangles.
A net is a flat shape that folds to make a solid. You draw the nets of solids such as cuboids, prisms and pyramids on a grid, recognise which arrangements fold into a given solid, and work out a solid's surface area or volume from the lengths on its net. The total area of a net is the surface area of its solid, so a cuboid's net, made of three pairs of matching rectangles, shows its surface area at a glance.
Constructions and nets are Core content, so they can be set on all four papers, and every paper allows a ruler, protractor and compasses. The current syllabus does not require constructions of perpendicular bisectors or angle bisectors, and loci are not part of it, so skip older questions that ask for them. Nets lead straight into surface area in mensuration, and accurate drawing supports scale drawings and bearings.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C4.2 Geometrical constructions
- E4.2 Geometrical constructions
What you should be able to do
- Measure lines in centimetres or millimetres and angles to the nearest degree
- Draw lines and angles of given sizes accurately
- Construct a triangle from three given sides with a ruler and compasses, leaving the arcs
- Draw the net of a cube, cuboid, prism or pyramid on a grid
- Decide whether a net folds into a given solid, and which edges meet
- Use a net to find the surface area or volume of a solid
Key ideas
- A triangle with sides a, b and c can be constructed only if the longest side is shorter than the other two added together
- Arcs with radii b and c, drawn from the two ends of side a, meet at the third vertex
- The area of a net equals the surface area of the solid it folds into
- Every net of a cube has six squares, and none has more than four squares in a row
How Constructions and nets has been examined
From 2022 to 2026, Constructions and nets was on Paper 3 · Calculator (Core) in 9 of 14 exam series, worth about 5% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 31 | 5% | 14 of 14 |
| Paper 2 · Non-calculator (Extended) | 4 | 1% | 4 of 14 |
| Paper 3 · Calculator (Core) | 19 | 5% | 9 of 14 |
| Paper 4 · Calculator (Extended) | 5 | 1% | 4 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 3.
Filed in Momentum under: Constructions and Loci, Net.
A worked example
A net of a triangular prism is made of two right-angled triangles with sides 6 cm, 8 cm and 10 cm, and three rectangles of length 15 cm. Find the surface area and the volume of the prism.
- The triangles are right-angled with shorter sides 6 cm and 8 cm, so each has area ½ × 6 × 8 = 24 cm².
- The three rectangles have areas 6 × 15 = 90 cm², 8 × 15 = 120 cm² and 10 × 15 = 150 cm².
- Surface area = 2 × 24 + 90 + 120 + 150 = 408 cm².
- The triangle is the prism's cross-section, so the volume = 24 × 15 = 360 cm³.
Answer: Surface area 408 cm²; volume 360 cm³
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Rubbing out the construction arcs: they are the evidence of the method, and a triangle drawn without them can lose the marks.
- Measuring from the end of the ruler instead of from zero, which puts every length out by the same amount.
- Reading the wrong scale on a protractor, giving 130° for an angle of 50°: decide first whether the angle is acute or obtuse.
- Drawing a net with a face in the wrong place, so two faces overlap when folded: imagine folding it, and check that the edges that meet are the same length.
- Drawing a straight edge freehand: every straight line has to be drawn with a ruler.
Exam technique
- Use a sharp pencil, and draw the longest side first when constructing a triangle.
- Estimate an angle before reading the protractor, so you choose the right scale.
- When drawing a net on a grid, label each face with its lengths and check that edges which meet when folded match.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.