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S4 Mathematics: Quadratic Equations (Paper 3)
S4 Mathematics: Quadratic Equations (Paper 3)
Ten original application and review questions: solve (2x minus 1)(x plus 3), 4x squared minus 25, x squared minus 2x minus 15 and 5x squared plus x. The advanced items use Pythagoras with legs x and x plus 1 and hypotenuse 5, solve 2x squared minus 8x plus 3 to two decimals, and find where y equals x squared minus 6x plus 5 meets the x axis. The challenge items model a square that is 10 more than three times a number and an open box of volume 18 cubic centimetres, and the paper ends with the error of dividing by x.
Direct answer Introduce a variable, form the equation, and reject roots that do not fit the context.
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 (2x minus 1)(x plus 3) equals zero.
- FoundationSolve 4x squared minus 25 equals zero.
- FoundationSolve x squared minus 2x minus 15 equals zero.
- FoundationSolve 5x squared plus x equals zero.
- IntermediateA right-angled triangle has legs of x cm and (x plus 1) cm and a hypotenuse of 5 cm. Find x.
- IntermediateSolve 2x squared minus 8x plus 3 equals zero, correct to two decimal places.
- IntermediateWhere does the curve y equals x squared minus 6x plus 5 meet the x axis?
- ChallengeThe square of a positive number is 10 more than three times the number. Find it.
- ChallengeA rectangular sheet is 3 cm longer than it is wide. After cutting a 1 cm square from each corner it folds into an open box of volume 18 cubic centimetres. Find the original width.
- Error redoError repair: a student divides both sides of x squared equals 4x by x and gets only x equals 4. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x equals one half or x equals minus 3 | Set each factor to zero, giving one half and minus three. |
| 2 | x equals five halves or minus five halves | Rewrite as two x squared equals five squared, then take roots. |
| 3 | x equals 5 or x equals minus 3 | The factors are x minus five and x plus three. |
| 4 | x equals 0 or x equals minus one fifth | Factor out x to get x times five x plus one; never divide by x. |
| 5 | x equals 3, so the legs are 3 cm and 4 cm | Pythagoras gives x squared plus x minus twelve equals zero, so x is three and the negative root is rejected. |
| 6 | x is about 3.58 or 0.42 | The discriminant is forty, whose root is about 6.32, so the roots are about 3.58 and 0.42. |
| 7 | At x equals 1 and x equals 5 | Setting y to zero gives x squared minus 6x plus 5 equals zero, whose roots are one and five. |
| 8 | 5 | Set up n squared minus 3n minus 10 equals zero, giving five and minus two, and the positive answer is five. |
| 9 | The width is 5 cm, giving a base of 3 cm by 6 cm | The base is (w minus 2) by (w plus 1) with height one, giving w squared minus w minus 20 equals zero, so w is five. |
| 10 | x equals 0 or x equals 4 | Rearrange to x times (x minus 4) equals zero; dividing by x assumes x is not zero and loses that root. |
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.
