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S3 Maths: Linear Inequalities in One Unknown (Paper 3 (challenge))
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 3 (challenge))
Paper 3 (challenge): 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 -3x is at most 12.
- FoundationSolve the inequality x divided by minus 2 < 5.
- FoundationSolve the inequality 2x – 9 < x + 1.
- IntermediateSolve the inequality 7 – 4x is at least 3 – 2x.
- IntermediateSolve the inequality 3(2x – 1) < 4(x + 2).
- IntermediateSolve the inequality (2x + 1) over 3 is at most (x – 2) over 2.
- ChallengeSolve minus 3 < 2x + 1 at most 7 and count the integer solutions.
- ChallengeA taxi charges 24 dollars to start plus 6 dollars per kilometre. With a budget of at most 90 dollars, what is the greatest whole number of kilometres?
- ChallengeA test has 25 questions: 4 marks for a correct answer and 1 mark deducted for a wrong one. If a student attempts 20 questions, what is the least number of correct answers needed to score above 60?
- Error redoError clinic: a student solves -2(x – 3) > 6 as x > 0. What is the correct solution?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x ≥ -4 | Divide both sides by minus 3 and reverse the sign to get x at least minus 4. |
| 2 | x > -10 | Multiply both sides by minus 2 and reverse the sign to get x > -10. |
| 3 | x < 10 | Subtract x and add 9 to obtain x < 10. |
| 4 | x ≤ 2 | Collect to get -2x at least -4, then divide by minus 2 and reverse to obtain x at most 2. |
| 5 | x < 11/2 (that is x < 5.5) | Expand to 6x – 3 < 4x + 8, then 2x < 11, so x < 11 over 2. |
| 6 | x ≤ -8 | Multiply both sides by 6 to get 4x + 2 at most 3x – 6, so x at most minus 8. |
| 7 | 5 integers | Subtract 1 and divide by 2 to get -2 < x at most 3, giving the integers minus 1 to 3, that is five values. |
| 8 | 11 km | With k kilometres the cost 24 + 6k is at most 90, so k is at most 11 and the trip can cover 11 km. |
| 9 | 17 questions | With c correct answers the score is 4c – (20 – c), so 5c – 20 > 60 gives c > 16 and at least 17 correct answers are needed. |
| 10 | x < 0 | Expand to -2x + 6 > 6, so -2x > 0, and dividing by minus 2 reverses the sign to give x < 0. |
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 →
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