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S1 Maths: Ratio, Rate and Proportion (Paper 3 (challenge))
Tutor Prep Guide · simplifying ratios; sharing in a ratio; direct and inverse proportion; speed conversion; average speed
S1 Maths: Ratio, Rate and Proportion (Paper 3 (challenge))
Paper 3 (challenge): ten questions on simplifying ratios, missing terms, sharing in a ratio, direct and inverse proportion, speed conversion and average speed, with answers and one-line notes.
Direct answers Level: S1 maths; format: simplifying ratios, sharing in a ratio, proportion equations, speed and average speed.
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: S1 Maths: Ratio, Rate and Proportion |
| Level | S1 |
02 Questions (10 items)
- FoundationThree numbers are in the ratio 3 : 4 : 6 and the largest minus the smallest is 45. Find them.
- FoundationA map has scale 1 : 25 000. What real distance does 4 cm represent?
- FoundationA trip of 120 km takes 2 hours and the return trip takes 3 hours. Find the average speed for the whole journey.
- IntermediateBoys to girls is 5 : 4. After 10 more boys join, the ratio becomes 3 : 2. How many boys were there at first?
- IntermediateFour machines take 6 hours. How long do six machines take?
- IntermediateA 10 m long train at 90 km/h passes through a 200 m tunnel. How many seconds does it take?
- Challenge200 items are shared in the ratio 2 : 3 : 5. What is the difference between the largest and smallest shares?
- ChallengeIf a : b = 2 : 3 and b : c = 4 : 5, find a : b : c.
- ChallengeSolve the proportion 3 : x = 6 : 10.
- Error redoError clinic: why is the average speed not 50 km/h for 120 km out in 2 hours and back in 3 hours?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 45, 60 and 90. | The gap of 3 parts is 45, so each part is 15, giving 45, 60 and 90. |
| 2 | 1 km. | 4 times 25 000 is 100 000 cm, which is 1 km. |
| 3 | 48 km/h. | The total is 240 km in 5 hours, so the average speed is 48 km/h; do not average the two speeds. |
| 4 | 50 boys. | With boys 5k and girls 4k, the equation gives k = 10, so there were 50 boys. |
| 5 | 4 hours. | The machine-hours are fixed at 24, so 24 divided by 6 is 4 hours. |
| 6 | 8.4 seconds. | 90 km/h is 25 m/s and the train must cover 210 m, which takes 8.4 seconds. |
| 7 | 60 items. | The shares are 40, 60 and 100, so the difference is 60 items. |
| 8 | 8 : 12 : 15. | Taking 12 as the common value of b gives a : b : c = 8 : 12 : 15. |
| 9 | x = 5. | Cross multiplying gives 6x = 30, so x is 5. |
| 10 | It is 48 km/h. | 50 km/h simply averages the two speeds; the average speed must use total distance over total time, 240 divided by 5. |
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.
Check the answers; find the highest common factor when reducing, and fix the total for inverse proportion.Tutor Registration →
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