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P6 maths ratio and proportion paper 4 (error review): simplifying, three-term ratios and scale
P6 maths ratio and proportion paper 4 (error review): simplifying, three-term ratios and scale
Ten items on the usual slips: simplifying ratios, missing terms, three-term ratios, map scale and speed ratios, with answers.
Direct answers Try each item first, then check the answer table in section 03 and note why any slip happened.
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: P6 Maths Ratio and Proportion |
| Level | P6 |
02 Questions (10 items)
- FoundationSimplify 18 : 24.
- FoundationGiven 5 : 8 = 15 : x, find x.
- FoundationShare $240 between A and B in the ratio 3 : 5. How much does each get?
- IntermediateThree numbers are in the ratio 2 : 3 : 4 and their total is 45. Find them.
- IntermediateA map has a scale of 1 : 20 000. What real distance does 4.5 cm represent, in metres?
- IntermediateA : B = 3 : 4 and B : C = 6 : 7. Find A : C.
- ChallengeA mixture has A : B = 5 : 3 and a total of 640 mL. How much more A than B is there?
- ChallengeA rectangle has length : width = 7 : 4 and a perimeter of 88 cm. Find its length and width.
- ChallengeA and B travel at speeds in the ratio 3 : 5 from the same point at the same time. When A has gone 54 km, how far has B gone?
- Error redoA student writes 1.2 : 0.8 as 12 : 8 and says it is already in simplest form. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3 : 4 | Divide both terms by the H.C.F., 6. |
| 2 | x = 24 | The first term was multiplied by 3, so the second must be too. |
| 3 | A gets $90 and B gets $150 | There are 8 parts in all, so one part is $30. |
| 4 | 10, 15 and 20 | There are 9 parts in all, so one part is 5. |
| 5 | 900 m | 4.5 x 20 000 = 90 000 cm, which is 900 m. |
| 6 | 9 : 14 | Make the B terms match at 12: then A is 9 and C is 14. |
| 7 | 160 mL | 8 parts make 640 mL, so one part is 80 mL and the gap is 2 parts. |
| 8 | Length 28 cm, width 16 cm | Length plus width is 44 cm; 11 parts means one part is 4 cm. |
| 9 | 90 km | Over the same time the distances follow the speeds, so 54 / 3 x 5. |
| 10 | It must be reduced further to 3 : 2 | Clearing the decimals is only the first step; both terms still share the factor 4. |
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.
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