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S2 Maths Pythagoras’ Theorem Paper 4: Error Review
S2 Maths Pythagoras’ Theorem Paper 4: Error Review
Ten original error-review items, each with an answer and a one-line explanation.
Direct answers Items 1-3 revisit adding the two sides instead of squaring, 4-6 cover hypotenuse versus leg and the right-angle test, 7-9 apply the theorem to rectangles, ladders and area, and item 10 unpicks the a + b = c confusion. Cover the answers first, then check each note.
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: S2 Maths Pythagoras’ Theorem |
| Level | S2 |
02 Questions (10 items)
- FoundationError review: a right-angled triangle has legs 9 cm and 12 cm. How long is the hypotenuse?
- FoundationError review: the hypotenuse is 13 cm and one leg is 5 cm. Find the other leg.
- FoundationError review: legs 6 cm and 8 cm are said to give a 14 cm hypotenuse. What is the correct value?
- IntermediateError review: an isosceles right-angled triangle has two legs of 7 cm. Find the hypotenuse (2 d.p.).
- IntermediateError review: is a triangle with sides 8 cm, 15 cm and 17 cm right-angled?
- IntermediateError review: sides 5 cm, 12 cm and 14 cm are called right-angled because 5 and 12 look familiar. Is that right?
- ChallengeError review: a rectangle is 12 cm by 9 cm. How long is a diagonal?
- ChallengeError review: a 5 m ladder leans on a vertical wall with its foot 3 m away. How high does it reach?
- ChallengeError review: a triangle has sides 10 cm, 24 cm and 26 cm. Find its area.
- Error redoError review: a pupil writes hypotenuse = 6 + 8 = 14. What is wrong and what is the answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 15 cm | Hypotenuse = square root of 81 + 144 = 225, i.e. 15 cm; adding the legs to get 21 is wrong. |
| 2 | 12 cm | 169 − 25 = 144 and the square root is 12 cm; adding gives 18 only if 13 were a leg. |
| 3 | 10 cm | 6² + 8² = 100 and its square root is 10 cm; 14 is just 6 + 8 with no squaring. |
| 4 | about 9.90 cm | It is 7 times the square root of 2, about 9.90 cm; 14 cm wrongly doubles the leg. |
| 5 | Yes, since 8² + 15² = 17² = 289 | The squares of the two shorter sides add to 64 + 225 = 289, matching the longest side, so it is right-angled. |
| 6 | No: 5² + 12² = 169, but 14² = 196 | Check the actual sides: 169 is not 196, so it is not right-angled; 5, 12 and 13 would be. |
| 7 | 15 cm | The diagonal splits the rectangle into right-angled triangles: 144 + 81 = 225, so 15 cm. |
| 8 | 4 m | The ladder is the hypotenuse: 25 − 9 = 16, so 4 m; adding 5 and 3 to get 8 m is the usual slip. |
| 9 | 120 cm² | Since 100 + 576 = 676, the legs are 10 and 24, so area = 10 x 24 / 2 = 120 cm². |
| 10 | Square, add, then take the root: 10 | The theorem is a² + b² = c², not a + b = c: 36 + 64 = 100, so c = 10. |
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.