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S3 Maths: Linear Inequalities in One Unknown (Paper 4: mistake clinic)
S3 Maths: Linear Inequalities in One Unknown (Paper 4: mistake clinic)
This last paper revisits the high frequency errors from the first three: a missed reversal after dividing by a negative, a missed sign change when moving a term, and rounding an integer answer the wrong way. Check those three points after every question.
Direct answers If one cause appears twice, write it on the first page of your notes and read only that page before the exam.
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: S3 Maths: Linear Inequalities in One Unknown |
| Level | S3 Maths |
02 Questions (10 items)
- FoundationSolve the inequality x – 9 >= -4.
- FoundationSolve the inequality -4x < 20.
- FoundationSolve the inequality 3(x + 2) >= 18.
- IntermediateSolve the inequality 6 – 2x <= 2.
- IntermediateSolve the inequality x / 3 – 2 > 1.
- IntermediateIf x < 7, what is the greatest integer value of x?
- ChallengeSolve the inequality 2x – 3 > 5x + 6.
- ChallengeA lift is limited to 500 kg and each passenger weighs 65 kg. What is the greatest number of passengers?
- ChallengeThe sum of three consecutive even numbers is less than 60. What is the greatest possible value of the smallest?
- Error redoA student solves 4 – x < 1 and answers x < 3. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x >= 5 | Add 9 to both sides: -4 + 9 = 5, and the sign stays the same. |
| 2 | x > -5 | Divide by -4 and reverse the sign, with 20 / (-4) = -5. |
| 3 | x >= 4 | Expand to 3x + 6 >= 18, subtract 6, then divide by 3 to get 4. |
| 4 | x >= 2 | Rearrange to -2x <= -4, then divide by -2 and reverse the sign to get x >= 2. |
| 5 | x > 9 | Add 2 to get x / 3 > 3, then multiply by 3 to get x > 9. |
| 6 | 6 | The greatest integer below 7 is 6 because 7 itself does not satisfy a strict inequality. |
| 7 | x < -3 | Subtract 5x to get -3x – 3 > 6, add 3 to get -3x > 9, then divide by -3 and reverse the sign to get x < -3. |
| 8 | 7 passengers | 65n <= 500 gives n <= 7.69, so round down to 7 passengers at 455 kg. |
| 9 | 8 | With the smallest as n, 3n + 6 < 60 gives n < 9, and since n is even the greatest value is 8. |
| 10 | The correct answer is x > 3 | Rearrange to -x < -3, and multiplying by -1 reverses the sign to x > 3. |
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.
Use three columns in the error log: question, cause, corrected steps. The three commonest causes are a missed sign reversal for negatives, a missed sign change when moving a term, and rounding an integer answer the wrong way.Tutor Registration →
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