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P1 Maths: 3D Shapes (10 Advanced Items)
P1 Maths: 3D Shapes (10 Advanced Items)
Ten items counting faces, edges and vertices for a cuboid, triangular prism, square pyramid and hexagonal prism, checking with vertices minus edges plus faces, plus gluing and rolling direction.
Counting Count faces, edges and vertices separately, then check with vertices minus edges plus faces equals two.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 1 · Intermediate 5 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P1 Maths: 3D Shapes |
| Level | P1 Maths |
02 Questions (10 items)
- FoundationHow many faces, edges and vertices does a cuboid have?
- IntermediateHow many faces, edges and vertices does a triangular prism have?
- IntermediateHow many faces, edges and vertices does a square pyramid have?
- IntermediateHow many faces, edges and vertices does a hexagonal prism have?
- IntermediateWork out vertices minus edges plus faces for a cube. What do you get?
- IntermediateHow many faces does a cylinder have in total, and which one is curved?
- ChallengeTwo cubes are glued side by side into a cuboid. How many faces does it have?
- ChallengeWhich solid rolls in only one direction, and why?
- ChallengeA solid has 5 faces and 8 edges. Use vertices − edges + faces = 2 to find its vertices.
- Error redoA student says a cube has 12 faces and 6 edges. What is wrong, and what is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 6 faces, 12 edges and 8 vertices. | A cuboid has the same counts as a cube, but its faces need not be squares. |
| 2 | 5 faces, 9 edges and 6 vertices. | A triangular prism has two triangular ends plus three rectangular sides. |
| 3 | 5 faces (one square base and four triangles), 8 edges and 5 vertices. | All side faces of a pyramid are triangles sharing the single top vertex. |
| 4 | 8 faces, 18 edges and 12 vertices. | A hexagonal prism has two hexagonal ends and six rectangular sides. |
| 5 | 8 − 12 + 6 = 2. | Most solids give 2 from this expression, so it is a check against miscounting. |
| 6 | Three faces: two circular flat ends and one curved side. | Its side is curved, which is why a cylinder rolls in only one direction. |
| 7 | 6 + 6 − 2 = 10 faces. | The two touching faces are hidden, so subtract two instead of adding blindly. |
| 8 | A cylinder, because its curved side bends in one direction only. | The direction of the curvature decides the roll; a sphere curves both ways. |
| 9 | Vertices = 8 − 5 + 2 = 5, so it has 5 vertices and is a square pyramid. | Rearranging the relation gives the vertex count from faces and edges. |
| 10 | Faces and edges were swapped; a cube has 6 faces, 12 edges and 8 vertices. | Faces are flat surfaces and edges are where two faces meet, so edges always outnumber faces here. |
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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