Chapter 5 Practice Paper: Direct and Inverse Proportion — mark scheme
QuizQuipPractice Series
QQ/S2MATH/CH5
Secondary 2 · Lower Secondary Mathematics (G2 / G3)
Mark scheme
Direct and Inverse Proportion
Chapter 5 Practice Paper · Maximum mark: 30
Notes for markers
- Award one mark for each point marked [1], up to the marks shown for the part.
- Accept answers worded differently that show the same understanding.
- Units are required where the answer line shows one. ecf: allow an error carried forward.
Section A: Multiple-choice questions[10 marks]
| Question | Answer | |
|---|---|---|
| 1 | Ak = 9 ÷ 3 = 3, so y = 3x. | 1 |
| 2 | CDirect proportion is linear and passes through (0, 0). | 1 |
| 3 | DOne book costs $7, so eight cost $56. | 1 |
| 4 | By = 60 ÷ 12 = 5. | 1 |
| 5 | CDirect proportion multiplies both quantities by the same factor. | 1 |
| 6 | ATheir product, the distance, is fixed — the inverse-proportion signature. | 1 |
| 7 | DThe constant ratio is 10 ÷ 2 = 5, so (3, 15) fits; the others break the ratio. | 1 |
| 8 | Bk = 6 × 40 = 240 tap-minutes, so eight taps need 240 ÷ 8 = 30 minutes. | 1 |
| 9 | CEvery product is 5 in the third table; the others fail the product test. | 1 |
| 10 | Ak = 32 ÷ 16 = 2, so m = 2 × 36 = 72. | 1 |
Section B: Structured questions[20 marks]
| Question | Answer and marking points | Marks |
|---|---|---|
| 1(a) | 8 litres [1] | 1 |
| 1(b) | Fuel rate = 24/300 = 0.08 L per km, so 500 × 0.08 = 40 litres.
| 2 |
| 1(c) | 30 ÷ 0.08 = 375 km.
| 2 |
| Total for Question 1 | 5 | |
| 2(a) | k = 3 × 8 = 24
| 1 |
| 2(b) | y = 24/x [1] | 1 |
| 2(c) | y = 6 [1] | 1 |
| 2(d) | 12 = 24/x, so x = 24 ÷ 12 = 2.
| 2 |
| Total for Question 2 | 5 | |
| 3(a) | Depth ÷ time equals 3 for every row, so the ratio is constant.
| 2 |
| 3(b) | 21 cm [1] | 1 |
| 3(c) | Time = 30 ÷ 3 = 10 minutes.
| 2 |
| Total for Question 3 | 5 | |
| 4(a) | 45 = k × 9, so k = 5.
| 2 |
| 4(b) | 125 m [1] | 1 |
| 4(c) | 5t² = 20 gives t² = 4, so t = 2 seconds.
| 2 |
| Total for Question 4 | 5 |
— End of mark scheme —