中文（繁體）
中文（简体）
English
S5 Maths: Variation: Paper 4 (Error Replay)
S5 Maths: Variation: Paper 4 (Error Replay)
Ten items on the usual slips: whether k needs multiplication or division, table checks and lucky answers.
Direct answers Items 1-3: 5, 3, 6. Items 4-6: (8, 26) should be 28, 0.5, no. Items 7-9: $126, 5, 18. Item 10: k = 36, y = 4.
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: S5 Maths: Variation |
| Level | Error Replay |
02 Questions (10 items)
- Foundationy varies directly as x, and y = 8 when x = 2. Find x when y = 20.
- Foundationy varies inversely as x, and y = 9 when x = 2. Find y when x = 6.
- Foundationy varies directly as x^2, and y = 50 when x = 5. Find x when y = 72 (x > 0).
- IntermediateA table claims y varies directly as x: (2, 7), (4, 14), (6, 21), (8, 26). Which pair does not fit?
- Intermediatey varies inversely as x^2, and y = 2 when x = 3. Find y when x = 6.
- IntermediateDoes “y decreases as x increases” mean y varies inversely as x? Give an example.
- ChallengeThe cost C varies directly as the weight w, and 3 kg cost $54. Find the cost of 7 kg.
- Challengey varies inversely as x, and y = 15 when x = 4. Find x when y = 12.
- Challengez varies jointly as x and y, and z = 30 when x = 2 and y = 5. Find z when x = 4 and y = 1.5.
- Error redoA student treats inverse variation as y = kx, gets k = 4 from x = 3, y = 12, then answers y = 4 at x = 9. Is the answer right by luck? What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5 | k = 8 / 2 = 4, and 4x = 20 gives x = 5. |
| 2 | 3 | k = 9 x 2 = 18, so y = 18 / 6 = 3. |
| 3 | 6 | k = 50 / 25 = 2, so x^2 = 36 and x = 6. |
| 4 | (8, 26); it should be 28 | The other three pairs all give y / x = 3.5, while 26 / 8 = 3.25. |
| 5 | 0.5 | k = 2 x 9 = 18, so y = 18 / 36 = 0.5. |
| 6 | No; for example y = 10 – x, where xy is not constant | Inverse variation requires a constant product xy; any decreasing relation need not be inverse variation. |
| 7 | $126 | k = 54 / 3 = 18, so 7 x 18 = $126. |
| 8 | 5 | k = 15 x 4 = 60, and 12x = 60 gives x = 5. |
| 9 | 18 | k = 30 / 10 = 3, so z = 3 x 4 x 1.5 = 18. |
| 10 | Right by luck only: k = 36, and y = 4 comes from 36 / 9 | Inverse variation is y = k / x, so k must be found from the product xy. |
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.
Write one line for each slip, such as “multiplied instead of divided when finding k”.Tutor Registration →
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.