中文（繁體）
中文（简体）
English
S4 Mathematics: Quadratic Equations (Paper 1)
S4 Mathematics: Quadratic Equations (Paper 1)
Ten original questions on factorisation and taking square roots: x squared equals 36, x squared minus 9x equals zero, x squared minus 8x plus 15 equals zero and (x minus 4) squared equals 25 come first, then x squared plus 7x plus 10, 2x squared minus 5x minus 3 and 3x squared equals 12x. The challenge items solve x squared minus 6x plus 4 by completing the square and use a rectangle of area 96 square centimetres, and the paper ends with the error of writing only the positive root.
Direct answer Move everything to one side, factorise, and take both signs when square rooting.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S4 Mathematics: Quadratic Equations |
| Level | Four basic, three advanced, two challenge and one error-repair item |
02 Questions (10 items)
- FoundationSolve x squared equals 36.
- FoundationSolve x squared minus 9x equals zero.
- FoundationSolve x squared minus 8x plus 15 equals zero.
- FoundationSolve (x minus 4) squared equals 25.
- IntermediateSolve x squared plus 7x plus 10 equals zero.
- IntermediateSolve 2x squared minus 5x minus 3 equals zero.
- IntermediateSolve 3x squared equals 12x.
- ChallengeSolve x squared minus 6x plus 4 equals zero, leaving the answer in surd form.
- ChallengeA rectangle is 4 cm longer than it is wide and has area 96 square centimetres. Find its width.
- Error redoError repair: a student solves x squared equals 25 and writes only x equals 5. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x equals 6 or x equals minus 6 | Taking square roots gives both signs, since six squared and minus six squared both give thirty-six. |
| 2 | x equals 0 or x equals 9 | Factor out x to get x times (x minus 9) equals zero, so either factor is zero. |
| 3 | x equals 3 or x equals 5 | The expression factorises as (x minus 3)(x minus 5), since three plus five is eight and their product is fifteen. |
| 4 | x equals 9 or x equals minus 1 | Take square roots first, then add four to both possible values. |
| 5 | x equals minus 2 or x equals minus 5 | Two numbers that add to minus seven and multiply to ten are minus two and minus five. |
| 6 | x equals 3 or x equals minus one half | Cross multiplication gives (2x plus 1)(x minus 3) equals zero. |
| 7 | x equals 0 or x equals 4 | Rearrange and factor out three x; do not divide by x or the root zero is lost. |
| 8 | x equals 3 plus root 5 or 3 minus root 5 | Complete the square to get (x minus 3) squared equals five, then take roots. |
| 9 | The width is 8 cm, with length 12 cm | Let the width be w, giving w squared plus 4w minus 96 equals zero, so w is eight and the negative root is rejected. |
| 10 | x equals 5 or x equals minus 5 | Square rooting gives plus or minus five; writing only the positive root loses one solution. |
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.
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.
