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S5 Maths: Variation: Paper 1 (Basics)
S5 Maths: Variation: Paper 1 (Basics)
Ten starters on direct variation: find k first, then substitute.
Direct answers Items 1-3: 28, 50, 9. Items 4-6: 3, $192, 270 km. Items 7-9: 25, 9 times, 60. Item 10: k = 3, y = 24.
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 | Basics |
02 Questions (10 items)
- Foundationy varies directly as x, and y = 12 when x = 3. Find y when x = 7.
- Foundationy varies directly as x^2, and y = 18 when x = 3. Find y when x = 5.
- Foundationy varies directly as x, and y = 20 when x = 5. Find x when y = 36.
- Intermediatey varies directly as x^3, and y = 24 when x = 2. Find x when y = 81.
- IntermediateThe total cost C of books varies directly as the number n, and 5 books cost $120. Find the cost of 8 books.
- IntermediateThe distance d travelled varies directly as the time t, and the car covers 180 km in 3 hours. How far in 4.5 hours?
- Challengey varies directly as x^2, and y = 4 when x = 2. Find y when x = 5.
- Challengey varies directly as x^2. If x is tripled, by what factor does y change?
- Challengey varies directly as x, and y = 45 when x = 9. Find y when x = 12.
- Error redoA student sees “y varies directly as x” and uses k = 15 x 5 = 75 (y = 15 when x = 5), then answers y = 75 when x = 8. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 28 | k = 12 / 3 = 4, so y = 4 x 7 = 28. |
| 2 | 50 | k = 18 / 9 = 2, so y = 2 x 25 = 50. |
| 3 | 9 | k = 20 / 5 = 4, and 4x = 36 gives x = 9. |
| 4 | 3 | k = 24 / 8 = 3, so x^3 = 27 and x = 3. |
| 5 | $192 | k = 120 / 5 = 24, so 8 books cost 24 x 8 = $192. |
| 6 | 270 km | k = 180 / 3 = 60, so 4.5 x 60 = 270 km. |
| 7 | 25 | k = 4 / 4 = 1, so y = 25. |
| 8 | 9 times | Squaring: (3x)^2 = 9x^2, so y becomes 9 times as large. |
| 9 | 60 | k = 45 / 9 = 5, so y = 5 x 12 = 60. |
| 10 | Direct variation needs division: k = 15 / 5 = 3, so y = 24 | For y = kx, k comes from dividing y by x; multiplying belongs to inverse 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.
Rewrite any wrong item and state whether it is direct or inverse variation.Tutor Registration →
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