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S3 Maths: Linear Inequalities in One Unknown (Paper 2: intermediate)
S3 Maths: Linear Inequalities in One Unknown (Paper 2: intermediate)
This second paper concentrates on negative signs and brackets, where most errors happen. Whenever you divide by a negative number, write a small reminder to reverse the sign.
Direct answers After each question substitute one value that should satisfy the answer, which is faster than rereading the steps.
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 -2x > 8.
- FoundationSolve the inequality -3x <= 12.
- FoundationSolve the inequality 2(x + 3) <= 14.
- IntermediateSolve the inequality 3(x – 2) > 9.
- IntermediateSolve the inequality x / 2 + 1 < 4.
- IntermediateSolve the inequality 5 – x >= 2.
- ChallengeSolve the inequality 4x + 1 < 2x + 9.
- ChallengeSolve the inequality 7 – 2x > 1.
- ChallengeWhat is the greatest integer solution of 2x < 9?
- Error redoA student solves -5x >= 20 and answers x >= -4. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x < -4 | Divide both sides by -2; dividing by a negative number reverses the sign and 8 / (-2) = -4. |
| 2 | x >= -4 | Divide by -3, which turns <= into >=, and 12 / (-3) = -4. |
| 3 | x <= 4 | Expand to 2x + 6 <= 14, subtract 6, then divide by 2 to get 4. |
| 4 | x > 5 | Expand to 3x – 6 > 9, add 6, then divide by 3 to get 5. |
| 5 | x < 6 | Subtract 1 to get x / 2 < 3, then multiply by 2 to get 6. |
| 6 | x <= 3 | Rearrange to -x >= -3, and multiplying by -1 reverses the sign to x <= 3. |
| 7 | x < 4 | Subtract 2x to get 2x + 1 < 9, subtract 1, then divide by 2 to get 4. |
| 8 | x < 3 | Rearrange to -2x > -6, then divide by -2 and reverse the sign to get x < 3. |
| 9 | 4 | The solution is x < 4.5, and the greatest integer below 4.5 is 4. |
| 10 | The correct answer is x <= -4 | Dividing by -5 reverses the sign, so >= must become <=. |
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.
The intermediate trap is a negative number: multiplying or dividing by a negative number reverses the inequality sign. Remove brackets first, clear fractions by multiplying by the denominator, then substitute a value to check.Tutor Registration →
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