Every geometrical terms and nets question from 14 Cambridge IGCSE Mathematics (0580) past papers (May/June 2025 to May/June 2026), syllabus section 4.1. 23 questions covering Core and Extended tiers, ordered from Core to Extended. Each question is labelled with its question paper code (for example 0580/11/M/J/26) and every final answer matches the official Cambridge mark scheme. Try each question first, then click “Show solution” to check your working. This page is part of our IGCSE Maths 0580 Geometry past paper questions.
0580 Geometrical Terms and Nets past paper questions: Core (Papers 1 and 3)
May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q3
(a) Measure angle a.
(b) Write down the mathematical name for this type of angle.
Show solution
- Put the centre of the protractor on the corner (vertex) of the angle.
- Line up 0° along one arm and read the scale where the other arm crosses it.
- Angle a = 46°
- The angle is bigger than 0° but smaller than 90°.
- It is an acute angle
May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q4
(a) Points A and B lie on a circle, centre O. Write down the mathematical name for line AB.
(b) A quadrilateral has four equal sides, no right angles and opposite angles that are equal. Write down the mathematical name for this quadrilateral.
Show solution
- A straight line that joins two points on the circumference (and does not have to pass through the centre) is called a chord.
- AB is a chord
- Four equal sides narrows it to a square or a rhombus. A square has four right angles, so it cannot be a square.
- The quadrilateral is a rhombus
May/June 2026 · Paper 1 · 0580/11/M/J/26 · Q11
A cuboid measures 5 cm by 4 cm by 2 cm. On the 1 cm² grid, complete a net of this cuboid. One face (5 cm by 2 cm) has been drawn for you.
Show solution
- A cuboid has 6 faces in 3 matching pairs: two 5 × 2, two 5 × 4 and two 4 × 2 rectangles.
- Attach a 5 × 4 face along a 5 cm edge of the given 5 × 2 face.
- Continue the strip with the second 5 × 2 face, then the second 5 × 4 face.
- Add the two 4 × 2 faces to the sides of one of the 5 × 4 faces.
- Check: every edge that folds onto another edge must have the same length, and no faces overlap.
May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q12
To make a solid, a net is drawn on the 1 cm² grid. Point X is marked on the diagram.
(a) Write down the mathematical name for the solid.
(b) When the net is folded, there are two other points that meet at X. Mark each of these two points with an X.
Show solution
- Every face of the net is a rectangle, and there are 6 faces.
- The solid is a cuboid
- Imagine folding the net. Three faces meet at each corner of a cuboid.
- Fold the faces that touch the corner X and follow which corners land on X. Mark those two points.
May/June 2026 · Paper 1 · 0580/12/M/J/26 · Q15
Write down two geometrical properties of a parallelogram.
Show solution
- A parallelogram is a quadrilateral with two pairs of parallel sides. Write any two correct properties:
- Opposite sides are parallel
- Opposite sides are equal in length
- Tip: “Opposite angles are equal” and “the diagonals bisect each other” are also correct.
May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q3
A and B are points on the circumference of a circle, centre O. Write down the mathematical name for (a) the line AB (b) the shaded region (bounded by two radii and an arc).
Show solution
- A straight line joining two points on the circumference is a chord.
- AB is a chord
- A region bounded by two radii and an arc is like a slice of pizza.
- It is a sector
May/June 2026 · Paper 1 · 0580/13/M/J/26 · Q14(a)
The diagram shows a right-angled triangular prism. The triangle has sides 3 cm, 4 cm and 5 cm and the prism has length 4 cm. On the 1 cm² grid, complete the net of this prism. One face (4 cm by 4 cm) has been drawn for you.
Show solution
- A triangular prism has 3 rectangular faces and 2 triangular ends.
- The rectangles are 4 × 3, 4 × 4 (already drawn) and 4 × 5, because the prism is 4 cm long.
- Place the 4 × 3 and 4 × 5 rectangles beside the given square to make a strip.
- Attach a 3-4-5 right-angled triangle at each end of the strip.
- Check: each triangle edge must touch a rectangle edge of the same length.
Feb/Mar 2026 · Paper 1 · 0580/12/F/M/26 · Q16
A cube has volume 8 cm³. On the 1 cm² grid, draw a net for this cube.
Show solution
- The volume of a cube is side × side × side. 2 × 2 × 2 = 8, so each edge is 2 cm.
- Each face is a 2 cm by 2 cm square, and a cube has 6 faces.
- Draw six 2 × 2 squares arranged as a cube net, for example a row of four squares with one square above and one below the second square.
Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q2
The diagram shows a circle, centre O. On the diagram (a) draw a diameter (b) mark a point on the circumference and label it C.
Show solution
- A diameter is a straight line that passes through the centre and joins two points on the circle.
- Use a ruler to draw a straight line through the centre O from one side of the circle to the other
- The circumference is the curved edge of the circle.
- Mark C anywhere on the circle itself
Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q3
Write down the mathematical name of this polygon.
Show solution
- Count the sides of the polygon: there are 6.
- A six-sided polygon is a hexagon
Oct/Nov 2025 · Paper 1 · 0580/11/O/N/25 · Q12
A cuboid measures 5 cm by 4 cm by 3 cm. Complete the net of this cuboid on the 1 cm² grid. One face has been drawn for you.
Show solution
- A cuboid has 6 faces in 3 matching pairs: two 5 × 4, two 5 × 3 and two 4 × 3 rectangles.
- Make a strip of four faces that wrap round the cuboid, attached to the face already drawn.
- Add the two end faces on opposite sides of the strip.
- Check: every edge must meet the edge it folds onto with the same length, and no faces overlap.
Oct/Nov 2025 · Paper 1 · 0580/12/O/N/25 · Q13
The diagram shows a right-angled triangular prism. The triangle has sides 3 cm, 4 cm and 5 cm and the prism has length 4 cm. Complete the net of this prism on the 1 cm² grid. One face has been drawn for you.
Show solution
- A triangular prism has 5 faces: 3 rectangles and 2 triangles.
- The rectangles are 3 × 4, 4 × 4 and 5 × 4 (each side of the triangle times the length of the prism).
- The two ends are 3-4-5 right-angled triangles.
- Draw the two missing rectangles in a strip with the given face, then attach one triangle on each side of the strip.
- Check: each triangle edge must touch a rectangle edge of the same length.
Oct/Nov 2025 · Paper 1 · 0580/13/O/N/25 · Q1
(a) Measure the length of line AB in centimetres. (b) Draw a line that is parallel to line AB.
Show solution
- Put the 0 of the ruler exactly on A and read the scale at B.
- AB = 5.6 cm
- Parallel lines go in the same direction and never meet.
- Line a ruler up with AB, slide a set square along it, and rule a new line the same distance from AB all the way along.
Oct/Nov 2025 · Paper 1 · 0580/13/O/N/25 · Q5
The diagram shows quadrilateral ABCD on a 1 cm² grid.
(a) Write down the coordinates of point B. (b) Write down the mathematical name of quadrilateral ABCD.
(c) Find the area of quadrilateral ABCD. (d) On the grid, plot the point E at (−3, 2).
Show solution
- Read across the x-axis first, then up the y-axis. B is 1 left and 2 up.
- B = (−1, 2)
- BC and AD are both horizontal, so they are parallel. AB and CD are not parallel.
- A quadrilateral with exactly one pair of parallel sides is a trapezium
- The parallel sides are BC = 3 cm and AD = 5 cm, and the distance between them is 4 cm.
- Area = 1⁄2(a + b)h = 1⁄2 × (3 + 5) × 4 = 1⁄2 × 8 × 4 = 16 cm²
- From the origin go 3 left and 2 up and mark E at (−3, 2)
Oct/Nov 2025 · Paper 3 · 0580/31/O/N/25 · Q1
(a) Measure the length of line AB in centimetres. (b) Draw a line that is perpendicular to the line AB.
Show solution
- Put the 0 of the ruler exactly on A and read the scale at B.
- AB = 4.7 cm
- Perpendicular means at right angles (90°).
- Place a set square or protractor on AB and draw a line that meets AB at 90°
Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q1
A, B and C are points on a circle, centre O. (a) Write down the mathematical name for line OC. (b) Write down the mathematical name for line AB.
Show solution
- OC goes from the centre O to a point on the circle.
- A line from the centre to the circumference is a radius
- AB joins two points on the circle and does not have to pass through the centre.
- A line joining two points on the circumference is a chord
Oct/Nov 2025 · Paper 3 · 0580/32/O/N/25 · Q9
(a) Shape A is a quadrilateral with only one pair of parallel lines. Write down its mathematical name.
(b) Shape B is a quadrilateral with two pairs of parallel lines, all four sides equal and no right angles. Write down its mathematical name.
Show solution
- A quadrilateral with exactly one pair of parallel sides is a trapezium
- Two pairs of parallel sides make it a parallelogram. All four sides equal makes it a rhombus or a square.
- There are no right angles, so it is not a square: rhombus
Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q2
A and B lie on a circle, centre O. (a) Write down the mathematical name of the line AB. (b) On the diagram, draw a radius.
Show solution
- AB joins two points on the circle and does not pass through the centre.
- A line joining two points on the circumference is a chord
- A radius goes from the centre to the circumference.
- Draw a straight line from O to any point on the circle
Oct/Nov 2025 · Paper 3 · 0580/33/O/N/25 · Q4
(a) Write down the mathematical name of the solid shown. (b) A triangle has three angles of 60°. Write down the mathematical name of this type of triangle.
Show solution
- The solid has two equal circular ends joined by a curved surface.
- It is a cylinder
- A triangle with three equal angles also has three equal sides.
- It is an equilateral triangle
May/June 2025 · Paper 1 · 0580/11/M/J/25 · Q15
The diagram shows a cuboid measuring 6 cm by 4 cm by 3 cm. Complete a net of this cuboid on the 1 cm² grid. One face has been drawn for you.
Show solution
- A cuboid has 6 faces in three matching pairs.
- 6 cm × 4 cm (two of these), 6 cm × 3 cm (two) and 4 cm × 3 cm (two).
- Put the faces round the given face so that edges which touch are the same length.
- Check that the net would fold into a closed box with no faces overlapping.
- A correct net with all six faces: two 6 × 4, two 6 × 3 and two 4 × 3 rectangles in the correct places.
May/June 2025 · Paper 1 · 0580/12/M/J/25 · Q4
The diagram shows a line AB and a point P on the line.
(a) Measure the length of line AB in millimetres.
(b) Draw a line through point P that is perpendicular to line AB.
Show solution
- Put the 0 of the ruler exactly on A and read the scale at B in millimetres.
- AB = 83 mm
- Perpendicular means at 90° (a right angle).
- Place a set square or protractor on AB with its corner at P, and draw a ruled line through P at right angles to AB
May/June 2025 · Paper 1 · 0580/13/M/J/25 · Q2
(a) Write down the mathematical name for an angle between 90° and 180°.
(b) Write down the mathematical term that describes two polygons that are the same shape and size.
Show solution
- Angle types: acute is less than 90°, right is exactly 90°, obtuse is between 90° and 180°, reflex is more than 180°.
- An angle between 90° and 180° is obtuse
- Shapes that are exactly the same shape and size are congruent
- Tip: “Similar” means the same shape but not necessarily the same size.
0580 Geometrical Terms and Nets past paper questions: Extended (Papers 2 and 4)
Oct/Nov 2025 · Paper 2 · 0580/23/O/N/25 · Q3
The diagram shows a net for a dice with faces numbered 1 to 6. The sum of each pair of opposite faces is 7. The numbers 1, 4 and 5 are shown. Write the missing numbers on the net.
Show solution
- Opposite faces add up to 7: 1 is opposite 6, 4 is opposite 3, and 5 is opposite 2.
- On a net, two faces that are opposite each other never share an edge. Fold the net in your head to see which squares end up opposite.
- Place each missing number opposite its partner: 2 in the top square, 6 to the right of the 5 and 3 in the bottom square
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