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P4 Maths Perimeter and Area Applications Paper 3: Challenge
P4 Maths Perimeter and Area Applications Paper 3: Challenge
Ten original items, each with an answer and a one-line explanation.
Direct answers Items 1-3 are basic, 4-6 intermediate and 7-9 challenge, with item 10 as the error review. Time yourself first, then check each answer and redo what is wrong.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P4 Maths Perimeter and Area Applications |
| Level | P4 |
02 Questions (10 items)
- FoundationA 36 m fence encloses a rectangle with whole-metre sides. Find the largest possible area.
- FoundationA 12 m by 9 m plot contains a 5 m by 4 m flower bed. Find the area outside the flower bed.
- FoundationA wall is 8 m by 3 m with a 2 m by 1 m door. Painting costs $60 per m², door not painted. Find the total cost.
- IntermediateA park is 40 m by 25 m. Trees are planted every 5 m all round the edge, corners included. How many trees?
- IntermediateThe side of a square grows from 5 cm to 7 cm. By how much does the area increase?
- IntermediateRectangle A is 8 cm by 3 cm and B is 6 cm by 4 cm. Find both areas and perimeters, and say which perimeter is longer.
- ChallengeA carpet of area 12 m² exactly covers a rectangular room 3 m wide. Find the perimeter of the room.
- ChallengeA 30 m by 20 m plot has a 12 m by 9 m house. Find the garden area.
- ChallengeA square of side 10 cm is folded in half to make a rectangle. Find the perimeter of that rectangle.
- Error redoError review: a pupil says doubling both length and width doubles both area and perimeter. Is that right?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 81 m² | With a fixed perimeter the area is largest when length and width are closest: 9 m by 9 m gives 81 m². |
| 2 | 88 m² | The plot is 108 m² and the bed is 20 m², leaving 88 m². |
| 3 | $1320 | The wall is 24 m², less the 2 m² door, so 22 m² are painted at $60 each, costing $1320. |
| 4 | 26 trees | The perimeter is 130 m, and on a closed loop 130 divided by 5 = 26 trees. |
| 5 | 24 cm² | The new area is 49 cm² and the old is 25 cm², an increase of 24 cm². |
| 6 | A: area 24 cm², perimeter 22 cm; B: area 24 cm², perimeter 20 cm; A is longer | Both areas are 24 cm², but A has perimeter 22 cm and B has 20 cm, so equal area does not mean equal perimeter. |
| 7 | 14 m | The length is 12 divided by 3 = 4 m, so the perimeter is 14 m. |
| 8 | 492 m² | The plot is 600 m² and the house 108 m², so the garden is 492 m². |
| 9 | 30 cm | The folded rectangle is 10 cm by 5 cm, so its perimeter is 30 cm. |
| 10 | No: the area becomes 4 times as large, only the perimeter doubles | For 2 cm by 3 cm the area is 6 cm² and perimeter 10 cm; at 4 cm by 6 cm the area is 24 cm² (4 times) and the perimeter 20 cm (2 times). |
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.