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S5 Maths: Variation: Paper 2 (Intermediate)
S5 Maths: Variation: Paper 2 (Intermediate)
Ten items on inverse variation: multiply to get k, then handle roots and real contexts.
Direct answers Items 1-3: 3, 2, 9 days. Items 4-6: 1, 3 hours, 6. Items 7-9: 5, 12 hours, 4. Item 10: k = 40, y = 5.
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 | Intermediate |
02 Questions (10 items)
- Foundationy varies inversely as x, and y = 6 when x = 4. Find y when x = 8.
- Foundationy varies inversely as x, and y = 10 when x = 3. Find x when y = 15.
- Foundation12 workers finish a job in 6 days. How many days do 8 workers need at the same rate?
- Intermediatey varies inversely as x^2, and y = 4 when x = 3. Find y when x = 6.
- IntermediateAt 60 km/h a journey takes 4 hours. How long does it take at 80 km/h?
- Intermediatey varies inversely as x, and y = 3 when x = 8. If x is halved, what is y?
- Challengey varies inversely as x, and y = 2.5 when x = 8. Find x when y = 4.
- Challenge6 taps fill a tank in 8 hours. How long would 4 taps take?
- Challengey varies inversely as the square root of x, and y = 6 when x = 4. Find y when x = 9.
- Error redoA student handling inverse variation uses k = 10 / 4 = 2.5 when y = 10 at x = 4, then answers y = 20 at x = 8. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3 | k = 6 x 4 = 24, so y = 24 / 8 = 3. |
| 2 | 2 | k = 10 x 3 = 30, and 15x = 30 gives x = 2. |
| 3 | 9 days | Total work is 12 x 6 = 72 worker-days, and 72 / 8 = 9 days. |
| 4 | 1 | k = 4 x 9 = 36, so y = 36 / 36 = 1. |
| 5 | 3 hours | The distance is 60 x 4 = 240 km, and 240 / 80 = 3 hours. |
| 6 | 6 | k = 24, and x becomes 4, so y = 24 / 4 = 6, which is double. |
| 7 | 5 | k = 2.5 x 8 = 20, and 4x = 20 gives x = 5. |
| 8 | 12 hours | 6 x 8 = 48 tap-hours, and 48 / 4 = 12 hours. |
| 9 | 4 | k = 6 x 2 = 12, so y = 12 / 3 = 4. |
| 10 | Inverse variation needs multiplication: k = 40, so y = 5 | For y = k / x, k comes from multiplying x and y; dividing belongs to direct variation. |
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.
For each wrong item, write whether you multiplied or divided to get k.Tutor Registration →
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