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S1 Maths: Ratio and Proportion (Paper 3 (challenge))
S1 Maths: Ratio and Proportion (Paper 3 (challenge))
Paper 3 (challenge): ten questions on ratio and proportion with answers and one-line notes.
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 and Proportion |
| Level | S1 |
02 Questions (10 items)
- FoundationShare $900 among three people in the ratio 4 : 5 : 6.
- FoundationOn a 1 : 20 000 map a rectangular plot measures 3 cm by 2 cm. Find its real area in m squared.
- FoundationIf A : B = 2 : 3 and B : C = 6 : 5, find A : B : C.
- IntermediateCoffee and milk are mixed in the ratio 2 : 3 to make 750 mL of drink. How much of each is used?
- IntermediateFour workers finish a job in 6 days. How long would 3 workers take, at the same rate?
- IntermediateTwo cars cover the same distance with speeds in the ratio 3 : 4. Find the ratio of their times.
- ChallengeBoys and girls are in the ratio 3 : 8 with 66 students in total. Find each number.
- ChallengeTwo numbers are in the ratio 5 : 7. Adding 4 to each gives the ratio 3 : 4. Find the numbers.
- ChallengeOn a 1 : 5 000 map, how long is a real distance of 350 m in cm?
- Error redoError clinic: on a 1 : 200 map a student measured 5 cm and answered “1000 m”. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | They receive $240, $300 and $360. | Fifteen parts in total, so each part is $60. |
| 2 | The plot is 600 m by 400 m, so its area is 240000 m squared. | Convert each side to metres first, then multiply; do not scale the area directly. |
| 3 | A : B : C = 4 : 6 : 5. | Make the middle term the same: A : B becomes 4 : 6. |
| 4 | Coffee 300 mL and milk 450 mL. | Each of the five parts is 150 mL. |
| 5 | It would take 8 days. | The total work is 24 worker-days, shared among 3 workers. |
| 6 | The times are in the ratio 4 : 3. | For a fixed distance, time is inversely proportional to speed. |
| 7 | There are 18 boys and 48 girls. | Eleven parts make 66 students, so each part is 6. |
| 8 | The numbers are 20 and 28. | Write them as 5k and 7k, then solve the cross-multiplied equation. |
| 9 | It should be drawn 7 cm long. | Convert to cm first, then divide by the scale factor. |
| 10 | The real length is 1 000 cm, which is 10 m, not 1 000 m. | The scale gives centimetres; 1000 cm is only 10 m. |
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.
In ratio questions the first step is always to make the parts match: divide by the highest common factor, or make the middle term of a linked ratio the same. To divide a quantity in a ratio, find the total number of parts, then the value of one part, then multiply back. A map scale is given in centimetres, so convert units before scaling. Rates such as speed and unit price are ratios of two quantities, and an average speed uses total distance over total time. Worker-days and speed-time pairs are inverse relations, so invert the ratio.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.
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