中文（繁體）
中文（简体）
English
S1 Maths: Ratio and Proportion (Paper 2 (intermediate))
S1 Maths: Ratio and Proportion (Paper 2 (intermediate))
Paper 2 (intermediate): 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)
- FoundationSimplify the ratio 12 : 16 : 20.
- FoundationIf A : B = 3 : 4 and B : C = 4 : 7, find A : C.
- FoundationDivide $250 into three parts in the ratio 2 : 3 : 5.
- IntermediateA map has a scale of 1 : 25 000. What real distance does 4.4 cm represent in km?
- IntermediateA car covers 180 km in 2.5 hours. Find its average speed in km/h.
- IntermediateMix 3 kg of coffee at $40 per kg with 2 kg at $65 per kg. Find the price per kg of the mixture.
- ChallengeDivide 24 pens between A and B in the ratio 3 : 5.
- ChallengeA dozen pencils cost $84. At the same unit price, what do 15 pencils cost?
- ChallengeGiven 5 : 8 = 35 : x, find x.
- Error redoError clinic: a student added 2 to both terms of 3 : 4 and claimed 5 : 6 is equal. What is a correct equivalent ratio?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 12 : 16 : 20 = 3 : 4 : 5. | All three terms share the factor 4. |
| 2 | A : C = 3 : 7. | B is 4 parts in both ratios, so link the first term to the last directly. |
| 3 | The three parts are $50, $75 and $125. | There are 10 parts in total, so each part is $25. |
| 4 | It represents 110000 cm, which is 1.1 km. | Multiply by 25 000 to get cm, then divide by 100 000 to get km. |
| 5 | The average speed is 72 km/h. | Speed is distance divided by time. |
| 6 | The mixture costs $50 per kg. | Total cost divided by total mass gives the average price. |
| 7 | A gets 9 and B gets 15. | One part is 24 divided by 8, which is 3 pens. |
| 8 | Fifteen pencils cost $105. | A dozen is 12, so the unit price is $7. |
| 9 | x = 56. | The first term is multiplied by 7, so multiply the second term by 7 too. |
| 10 | They are not equal; multiply both terms instead, for example 3 : 4 = 6 : 8. | Only multiplication or division by the same number keeps a ratio unchanged. |
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.
© TutorZone · www.tutorzone.com.hk · For personal study and teaching use only.