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S1 Linear Equations and Word Problems Paper 3 (challenge)
S1 Linear Equations and Word Problems Paper 3 (challenge)
Ten challenge items on multi-step equations, decimals, coins, tickets and mixtures with one note each.
Direct answers Q1 x = 6, Q2 x = 11, Q3 x = 8, Q4 6 coins, Q5 108 cm², Q6 24, Q7 7 tickets, Q8 x = 12, Q9 x = 15 g, Q10 the 1 was not multiplied by 3, 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 3(2x – 1) = 4x + 9.
- FoundationSolve (x + 1)/2 = (x – 3)/4 + 4.
- FoundationSolve 0.4x + 1.2 = 0.6x – 0.4.
- IntermediateA box holds a $2 coins and 4 more $5 coins than $2 coins, worth $62 in all. Find a.
- IntermediateA rectangle is three times as long as it is wide and has a perimeter of 48 cm. Find its area.
- IntermediateThree consecutive integers add up to 72. Find the middle one.
- ChallengeAdult tickets cost $80 and child tickets $50. Twelve people pay $810 in all. Find the number of adult tickets.
- ChallengeWorker A makes x parts per hour and B makes 5 more. Together they make 87 parts in 3 hours. Find x.
- ChallengeMixing 30 g of 20% salt solution with x g of 50% solution gives a 30% solution. Find x.
- Error redoA pupil expands 3(2x – 1) = 4x + 9 as 6x – 1 = 4x + 9. What is wrong, and what is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 6 | Expand to 6x – 3 = 4x + 9, so 2x = 12 and x = 6. |
| 2 | x = 11 | Multiply by 4: 2(x + 1) = (x – 3) + 16, so 2x + 2 = x + 13 and x = 11. |
| 3 | x = 8 | Subtract 0.4x to get 1.2 = 0.2x – 0.4, so 1.6 = 0.2x and x = 8. |
| 4 | 6 coins | Set up 2a + 5(a + 4) = 62, so 7a + 20 = 62, 7a = 42 and a = 6. |
| 5 | 108 cm² | With width w: 8w = 48, so w = 6 and the length is 18; the area is 108 cm². |
| 6 | 24 | With middle m: (m – 1) + m + (m + 1) = 72, so 3m = 72 and m = 24. |
| 7 | 7 tickets | Set 80a + 50(12 – a) = 810, so 30a + 600 = 810 and a = 7. |
| 8 | x = 12 | Set 3x + 3(x + 5) = 87, so 6x + 15 = 87 and x = 12. |
| 9 | x = 15 g | Salt is conserved: 6 + 0.5x = 0.3(30 + x), so 0.2x = 3 and x = 15 g. |
| 10 | The 1 inside the bracket was not multiplied by 3; it must be 6x – 3 = 4x + 9, so x = 6 | Only 2x was multiplied; every term needs the 3, and the corrected equation gives 2x = 12. |
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 each answer by substitution; if it fails, recheck the expansion and the moves.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.