Should a challenge item be drawn?

Yes: sketch the solid and label the counts beside it, which is the safest way to avoid a miscount.

Why treat gluing and cutting differently?

Gluing hides two faces so the count drops, while cutting adds two, so the changes go opposite ways.

P1 Maths: 3D Shapes (10 Challenge Items)

2026-11-08

Ten reasoning items: the faces, edges and vertices of a cone, face counts after gluing and cutting, working back from the number of faces to the prism, and correcting the ideas that spheres stack and that every solid rolls.

Reasoning　Write down what is known about faces, edges and vertices, then use the relation or simple arithmetic for the unknown.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Intermediate 2 · Challenge 6 · Error redo 2
Chapter	Chapter: P1 Maths: 3D Shapes
Level	P1 Maths

02　Questions (10 items)

IntermediateHow many faces, edges and vertices does a cone have?
IntermediateCheck a hexagonal prism: 12 − 18 + 8. What is the result?
ChallengeThree cubes are glued in a row. How many faces does the long cuboid have?
ChallengeSmall cubes are used to build a bigger cube with 2 per side. How many are needed?
ChallengeA cube is cut in half to make two equal cuboids. How many faces in total?
ChallengeA solid has 6 faces, 8 vertices and 12 edges but its faces are not all squares. What is it?
ChallengeA square pyramid and a triangular prism both have 5 faces. How many more edges does the prism have?
ChallengeA prism has 8 faces. How many sides does its base have, and how many edges?
Error redoA student stacks five spheres and the tower falls. What went wrong, and how could it be fixed?
Error redoA student says every solid can roll. What is wrong, and what is a counter-example?

03　Answers and one-line notes

#	Answer	One-line note
1	2 faces (one circle and one curved surface), 1 edge and 1 vertex.	The single edge of a cone is the rim of its circular base, with one point on top.
2	12 − 18 + 8 = 2.	With so many faces and edges it is easy to miscount; this check catches it at once.
3	6 × 3 − 2 × 2 = 14 faces.	Each join hides two faces, and three cubes give two joins.
4	2 × 2 × 2 = 8 small cubes.	Length, width and height must all match, so cube the number per side.
5	6 + 2 = 8 faces.	One cut creates two new faces, so the total rises by two.
6	A cuboid: the counts match a cube but the faces are rectangles.	Counts alone cannot tell a cube from a cuboid; the shape of the faces decides.
7	The prism has 9 edges and the pyramid 8, so the prism has 1 more.	Equal face counts do not mean equal edge counts, so count each separately.
8	8 − 2 = 6, so it is a hexagonal prism with 18 edges.	A prism has (number of base sides + 2) faces and three times as many edges.
9	Spheres touch at a single point, so they cannot stack; use solids with flat faces.	Stacking depends on flat faces meeting; curved contact is only a point and topples.
10	Only solids with curved surfaces roll; a cube or cuboid has flat faces and only slides.	Rolling needs a curved surface; a flat face presses on the ground and slides instead.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.