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S1 Linear Equations and Word Problems Paper 2 (intermediate)
S1 Linear Equations and Word Problems Paper 2 (intermediate)
Ten intermediate items on brackets, fractions, unknowns on both sides and two-step problems.
Direct answers Q1 x = 6, Q2 x = 7, Q3 x = 10, Q4 x = 6, Q5 x = 5, Q6 8 km, Q7 17 and 28, Q8 40 pupils, Q9 1 hour, Q10 3 was not multiplied, x = 6.
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 Linear Equations and Word Problems |
| Level | S1 |
02 Questions (10 items)
- FoundationSolve 2(x + 3) = 18.
- FoundationSolve 3(x – 2) = x + 8.
- FoundationSolve x/3 + x/6 = 5.
- IntermediateSolve 5x – 3 = 2x + 15.
- IntermediateSolve 4(x + 1) = 2(x + 7).
- IntermediateA taxi charges $24 to start and $6 per kilometre. A fare of $72 covers how many kilometres?
- ChallengeTwo numbers add up to 45 and differ by 11. Find the larger and the smaller.
- ChallengeA class of x pupils is 3/5 girls, and there are 8 more girls than boys. Find x.
- ChallengeChi-ming walks at 4 km/h for t hours, then rides at 40 km/h for half an hour, covering 24 km in all. Find t.
- Error redoA pupil solves 2(x + 3) = 18 by writing 2x + 3 = 18. What is wrong, and what is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 6 | Divide both sides by 2 to get x + 3 = 9, then x = 6. |
| 2 | x = 7 | Expand to 3x – 6 = x + 8, so 2x = 14 and x = 7. |
| 3 | x = 10 | Multiply by 6: 2x + x = 30, so 3x = 30 and x = 10. |
| 4 | x = 6 | Subtract 2x to get 3x – 3 = 15, then 3x = 18 and x = 6. |
| 5 | x = 5 | Expand to 4x + 4 = 2x + 14, so 2x = 10 and x = 5. |
| 6 | 8 kilometres | Let k be the distance: 24 + 6k = 72, so 6k = 48 and k = 8. |
| 7 | 17 and 28 | With smaller s: s + s + 11 = 45, so 2s = 34 and the numbers are 17 and 28. |
| 8 | 40 pupils | Girls are 3x/5 and boys 2x/5, so x/5 = 8 and x = 40. |
| 9 | t = 1 hour | Set up 4t + 40 x 0.5 = 24, so 4t + 20 = 24 and t = 1 hour. |
| 10 | Only x was multiplied; it must be 2x + 6 = 18, so x = 6 | Every term inside the bracket must be multiplied by 2; missing the 3 makes the answer too large. |
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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