Example 1 · level 1 — a gentle start
How many vertices does a octagon have?
- 8
- 9
- 7
- 10
Answer: 8 — A octagon has 8 sides and 8 lines of symmetry.
11+ shape properties and symmetry questions
Shape properties and symmetry comes up in the maths paper of every major 11+ format. Here is what the questions look like, the method that works under time pressure, and five worked examples with the full reasoning, from a gentle start to a hard paper.
Maths · examined by GL and CEM · 5 worked examples
What your child needs to know
- A shape's sides and vertices (corners) always match: a pentagon has 5 of each.
- A line of symmetry is a fold where both halves match exactly. A square has 4; a kite has 1.
Where marks get lost: For solids, count faces (flat surfaces), edges (where two faces meet) and vertices (points).
Worked examples
Every question below is generated by the same engine your child practises on, and every answer is derived by our checker rather than written by hand — which is why we can put them on a public page at all.
Example 2 · level 2 — typical of early practice
How many sides does a rectangle have?
- 2
- 3
- 5
- 4
Answer: 4 — A rectangle has 4 sides and 2 lines of symmetry.
Example 3 · level 3 — standard paper difficulty
How many vertices does a square-based pyramid have?
- 8
- 4
- 6
- 5
Answer: 5 — A square-based pyramid has 5 faces, 8 edges and 5 vertices.
Example 4 · level 4 — a harder paper
How many edges does a triangular prism have?
- 5
- 9
- 10
- 6
Answer: 9 — A triangular prism has 5 faces, 9 edges and 6 vertices.
Example 5 · level 5 — the level that separates candidates
How many vertices does a octagon have?
- 7
- 10
- 9
- 8
Answer: 8 — A octagon has 8 sides and 8 lines of symmetry.
How to practise this at home
- Work in short, frequent sessions. Ten minutes daily beats an hour at the weekend, because the recall gap is what builds memory.
- Insist on written working, even for questions your child can do in their head — under exam pressure the method is what survives.
- When an answer is wrong, ask them to explain their reasoning before you correct it. The error is almost always in one step, not the whole approach.
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