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S3 Maths: Linear Inequalities in One Unknown (Paper 2 (intermediate))
Tutor Prep Guide · Inequality rules, adding and subtracting both sides, multiplying and dividing by positive or negative numbers, reversing the sign, removing brackets and denominators, integer solutions
S3 Maths: Linear Inequalities in One Unknown (Paper 2 (intermediate))
Paper 2 (intermediate): ten questions on linear inequalities in one unknown, with answers and notes.
Direct answers Level: S3 maths; format: solving inequalities, inequality rules, brackets and denominators, integer solution problems.
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 |
02 Questions (10 items)
- FoundationSolve the inequality x over 2 > 3.
- FoundationSolve the inequality x + 7 is at most 2.
- FoundationSolve the inequality 6x is at least minus 18.
- IntermediateSolve the inequality 5 – 2x < 1.
- IntermediateSolve the inequality 3x + 2 is at most x + 10.
- IntermediateSolve the inequality 2(x + 3) > 5x – 3.
- ChallengeSolve the inequality (x – 1) over 2 is at least (x + 2) over 3.
- ChallengeThe sum of four consecutive even numbers is at least 44. Find the smallest one.
- ChallengeA rectangle is 3 cm longer than it is wide and its perimeter is at most 30 cm. Find the greatest possible width.
- Error redoError clinic: a student solves 3 – x < 5 as x < 2. What is the correct solution?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x > 6 | Multiply both sides by 2 to obtain x > 6. |
| 2 | x ≤ -5 | Subtract 7 from both sides to obtain x at most minus 5. |
| 3 | x ≥ -3 | Divide both sides by 6 to obtain x at least minus 3. |
| 4 | x > 2 | Subtract 5 to get -2x < -4, then divide by minus 2 and reverse to obtain x > 2. |
| 5 | x ≤ 4 | Subtract x and 2 to get 2x at most 8, so x at most 4. |
| 6 | x < 3 | Expand and collect to get -3x > -9, then divide by minus 3 and reverse to obtain x < 3. |
| 7 | x ≥ 7 | Multiply both sides by 6 to clear the denominators, giving 3x – 3 at least 2x + 4, so x at least 7. |
| 8 | 8 | Let the smallest be n, the sum is 4n + 12, so n is at least 8 and the smallest number is 8. |
| 9 | 6 cm | With width w the perimeter 4w + 6 is at most 30, so w is at most 6 and the greatest width is 6 cm. |
| 10 | x > -2 | Collect to get -x < 2, then divide by minus 1 and reverse to obtain x > -2. |
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.
Adding or subtracting the same number keeps the inequality sign, while multiplying or dividing by a negative number reverses it. For at least or at most, set up the inequality first and then test the boundary value.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.
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