Home / iGCSE Mathematics (0580) :C4.2 Geometrical constructions Exam Style Questions Paper 1

iGCSE Mathematics (0580) : C4.2 Geometrical constructions Exam Style Questions Paper 1- New Syllabus

Question

Complete a net of this cuboid on the grid. One face has been drawn for you.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

C4.2 Geometrical constructions
▶️ Answer/Explanation
The given drawn face on the grid has a size of $6\text{ cm} \times 4\text{ cm}$. A complete cuboid net requires six rectangular faces in total: two $6 \times 4$ faces, two $6 \times 3$ faces, and two $4 \times 3$ side faces. To complete it symmetrically, you can add a $6 \times 3$ rectangle attached directly below the given face, followed by another $6 \times 4$ rectangle, and then a final $6 \times 3$ rectangle to complete the main vertical band. Lastly, attach the two remaining $4 \times 3$ side wings on the left and right sides of one of the central panels.

Answer: Net completed with the remaining 5 rectangular faces correctly attached to match the $6 \times 4 \times 3$ cuboid proportions.

Question

(a) Measure the length of line \(AB\) in centimetres.

(b) Draw a line that is parallel to line \(AB\).

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

Topic C4.1 Geometrical terms and relationships: Use and interpret the geometrical terms: point, line, parallel (Core)
Topic C4.2 Geometrical constructions
▶️ Answer/Explanation

(a)
Using a ruler, measure the straight distance between point \(A\) and point \(B\) on the original exam paper.
Answer: \(5.6 \text{ cm}\)

(b)
Using a ruler, draw any straight line that goes in the exact same direction as \(AB\) so that they would never intersect.

Answer: A ruled line parallel to \(AB\).

Question

Complete the net of this cuboid on the \(1\) cm² grid.
One face has been drawn for you.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

TOPIC C4.2 Geometrical constructions: Draw, use and interpret nets — draw nets of cubes, cuboids, prisms and pyramids (Core)
TOPIC C4.1 Geometrical terms: Use and interpret the vocabulary of simple solids including cuboid (Core)
▶️ Answer/Explanation
A cuboid with dimensions \(5\) cm \(\times\) \(4\) cm \(\times\) \(3\) cm has 6 faces: two \(5 \times 4\) faces, two \(5 \times 3\) faces, and two \(4 \times 3\) faces.
Starting from the given face, attach the remaining 5 faces in a cross-like layout, ensuring each face is connected along a shared edge with the correct matching dimension.
A valid net must fold up into the cuboid without any faces overlapping.

Full marks (3): Fully correct net drawn on the grid with all 6 faces in correct positions and correct sizes.
Partial credit (B2): 3 correct extra faces in correct places; (B1): 1 correct extra face in correct place.
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