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S1 Maths | Linear Equations and Word Problems Lesson Prep Guide (for tutors) | Balancing, brackets and forming equations: Paper 4 (Error Clinic)
S1 Maths | Linear Equations and Word Problems Lesson Prep Guide (for tutors) | Balancing, brackets and forming equations: Paper 4 (Error Clinic)
Ten items on transposition, brackets and setting up unknowns in word problems.
Direct answers Items 1-3: x = 5, 10, 16. Items 4-6: x = 8, 5, 200 dollars. Items 7-8: 12 years, 2.5 hours. Item 9: 48 dollars. Item 10: x = 5.
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 | Linear Equations and Word Problems Lesson Prep Guide (for tutors) | Balancing, brackets and forming equations |
| Level | Error clinic |
02 Questions (10 items)
- FoundationSolve 3x + 5 = 20.
- FoundationSolve 2(x – 3) = 14.
- FoundationSolve x/4 + 3 = 7.
- IntermediateSolve 5x – 7 = 3x + 9.
- IntermediateSolve 7(x + 2) = 4x + 29.
- IntermediateAn item costs c dollars and sells for 250 after a 25% mark-up. Find c.
- ChallengeA father is now three times his son age. In 12 years he will be twice as old. Find the son age.
- ChallengeTwo towns are 250 km apart. Cars leave towards each other at 60 km/h and 40 km/h. When do they meet?
- ChallengeMix 30 kg at 40 dollars per kg with 20 kg at 60 dollars per kg. Find the average price per kg.
- Error redoError clinic: solve 3(x – 2) = x + 4. A pupil expanded it as 3x – 2 = x + 4 and got x = 3. Give the correct answer.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 5 | Subtract 5 from both sides, then divide by 3: 15 / 3 = 5. |
| 2 | x = 10 | Divide by 2 first, then add 3: 7 + 3 = 10. |
| 3 | x = 16 | Subtract 3 to get 4, then multiply by 4: x = 16. |
| 4 | x = 8 | Collect terms to get 2x = 16, so x = 8. |
| 5 | x = 5 | Expand to 7x + 14 = 4x + 29, so 3x = 15 and x = 5. |
| 6 | 200 dollars | The price is 1.25c, so c = 250 / 1.25 = 200. |
| 7 | The son is 12 (father 36) | With son age a, 3a + 12 = 2(a + 12) gives a = 12 and the father is 36. |
| 8 | 2.5 hours | Their combined speed is 100 km/h, so 250 / 100 = 2.5 hours. |
| 9 | 48 dollars per kg | Total value 1200 + 1200 = 2400 over 50 kg, so 48 per kg. |
| 10 | x = 5 | The bracket expands to 3x – 6, so 2x = 10 and x = 5; the constant was not multiplied. |
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.
Write the reason for each slip beside it, then redo the paper.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.