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P2 Quadrilaterals: Paper 3 Challenge
P2 Quadrilaterals: Paper 3 Challenge
This paper asks pupils to reason backwards: recover a side from a perimeter or an area, join two squares, bend one wire into different shapes, and correct the claim that every quadrilateral has four right angles.
Direct answers Answers: 1 width 6 centimetres; 2 perimeter 28 centimetres; 3 perimeter 24 centimetres; 4 perimeter 25 centimetres; 5 90 degrees; 6 6 centimetres; 7 side 6 centimetres; 8 width 4 centimetres; 9 6 corners; 10 false.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P2 Quadrilaterals |
| Level | P2 |
02 Questions (10 items)
- FoundationA rectangle has a perimeter of 30 centimetres and a length of 9 centimetres. Find the width.
- FoundationA square has an area of 49 square centimetres. Find its perimeter.
- FoundationTwo squares with sides of 4 centimetres are placed side by side to form a rectangle. Find its perimeter.
- IntermediateA trapezium has sides of 6, 9, 5 and 5 centimetres. Find its perimeter.
- IntermediateThree angles of a quadrilateral are 100, 80 and 90 degrees. Find the fourth.
- IntermediateA parallelogram has a perimeter of 28 centimetres and one side of 8 centimetres. Find the side next to it.
- ChallengeA 24-centimetre wire is bent into a square. How long is each side?
- ChallengeThe same 24-centimetre wire is bent into a rectangle 8 centimetres long. Find its width.
- ChallengeA square is cut along one diagonal into two triangles. How many corners are there in total?
- Error redoError clinic: “every quadrilateral has four right angles.” Is this true?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 6 centimetres. Half the perimeter is 15, and 15 minus 9 is 6. | Halve the perimeter to get one length plus one width, then subtract the length. |
| 2 | 28 centimetres. The side is 7 centimetres and 7 times 4 is 28. | Work back from the area to the side, then multiply by four. |
| 3 | 24 centimetres. The rectangle is 8 by 4, so the perimeter is 24. | The joined edge lies inside the shape and is not part of the perimeter. |
| 4 | 25 centimetres. 6 + 9 + 5 + 5 = 25. | A trapezium has one parallel pair; the other two sides may differ. |
| 5 | 90 degrees. 360 minus 270 is 90. | The angle sum is fixed at 360 degrees, so subtract to find the missing one. |
| 6 | 6 centimetres. Half the perimeter is 14, and 14 minus 8 is 6. | Two neighbouring sides of different lengths make up half the perimeter. |
| 7 | 6 centimetres. 24 divided by 4 is 6. | The wire length is the perimeter and a square has four equal sides. |
| 8 | 4 centimetres. Half the perimeter is 12, and 12 minus 8 is 4. | The perimeter stays the same while the shape changes, so the width changes too. |
| 9 | 6 corners, because each triangle has 3 and 2 times 3 is 6. | Each triangle keeps its own three corners, so count them twice. |
| 10 | False. Only rectangles and squares must have four right angles; parallelograms, trapeziums and rhombuses need not. | A quadrilateral guarantees four sides and four corners, not the size of the angles. |
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.