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P2 Quadrilaterals: Paper 4 Error Clinic
P2 Quadrilaterals: Paper 4 Error Clinic
This paper targets the most common quadrilateral slips: shutting squares out of rectangles, giving a trapezium two parallel pairs, quoting area as perimeter, and assuming right angles in parallelograms or rhombuses, with reverse-side and joining items to consolidate.
Direct answers Answers: 1 yes; 2 false, one pair only; 3 22 centimetres; 4 side 10, area 100; 5 30 centimetres; 6 70 degrees; 7 width 6, area 72; 8 6 centimetres shorter; 9 square side 8, rectangle width 6; 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)
- FoundationError clinic: is a square also a rectangle? Why?
- FoundationTrue or false: a trapezium has two pairs of parallel sides.
- FoundationA rectangle is 7 centimetres by 4 centimetres. Find its perimeter, and say what is wrong with the answer 28.
- IntermediateA square has a perimeter of 40 centimetres. Find its side and its area.
- IntermediateA parallelogram has neighbouring sides of 9 and 6 centimetres. Find its perimeter.
- IntermediateThree angles of a quadrilateral are 85, 95 and 110 degrees. Find the fourth angle.
- ChallengeA rectangle has a perimeter of 36 centimetres and a length of 12 centimetres. Find the width and the area.
- ChallengeTwo squares with sides of 3 centimetres are joined into one rectangle. How much shorter is the new perimeter than the two perimeters added together?
- ChallengeA 32-centimetre wire is bent into a square; then the same wire is bent into a rectangle 10 centimetres long. Find the side of the square and the width of the rectangle.
- Error redoError clinic: “a rhombus has four right angles.” Is this true?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Yes. A square has four right angles and equal opposite sides, so it meets the definition of a rectangle; all four sides just happen to be equal. | A rectangle needs four right angles; a square adds four equal sides, which makes it a special rectangle. |
| 2 | False. A trapezium has only one pair of parallel sides; two pairs make a parallelogram. | Count the pairs of parallel sides to tell a trapezium from a parallelogram. |
| 3 | The perimeter is 22 centimetres. 28 is the area (7 times 4), not the perimeter; the perimeter is (7 + 4) times 2. | Area is in square centimetres and perimeter in centimetres, so the unit is a useful check. |
| 4 | The side is 10 centimetres and the area is 100 square centimetres: 40 divided by 4 is 10, and 10 times 10 is 100. | Divide the perimeter by four for the side, then square the side for the area. |
| 5 | 30 centimetres. Opposite sides are equal, so (9 + 6) times 2 is 30. | Only two sides need measuring because the other two match them. |
| 6 | 70 degrees. 360 minus (85 + 95 + 110) is 360 minus 290, which is 70. | The four angles add to 360 degrees, so subtract instead of assuming a right angle. |
| 7 | The width is 6 centimetres and the area is 72 square centimetres: half of 36 is 18, and 18 minus 12 is 6. | Halve the perimeter first, then subtract the length once. |
| 8 | It is 6 centimetres shorter: 24 centimetres at first and 18 after joining, so 24 minus 18 is 6. | The joined edge is counted twice before joining and not at all afterwards. |
| 9 | The square side is 8 centimetres and the rectangle width is 6 centimetres: 32 divided by 4 is 8, and half of 32 minus 10 is 6. | The wire length is the perimeter, which stays the same whatever the shape. |
| 10 | False. A rhombus has four equal sides, but its angles may be 60 and 120 degrees; only a square has four equal sides and four right angles. | Equal sides and right angles are two separate conditions, so keep them apart. |
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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