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S4 Mathematics: Quadratic Equations (Paper 4)
S4 Mathematics: Quadratic Equations (Paper 4)
Ten original review questions covering the whole chapter: solve by square roots, common factor and cross multiplication for x squared equals 49, x squared plus 5x, x squared minus 7x plus 12 and (x plus 3) squared equals 16; then use the formula for 2x squared plus 3x minus 2, use the discriminant to show x squared minus 6x plus 10 has no real roots, and find k from a repeated-root condition. The challenge items recover a rectangle area from its perimeter and find where a parabola meets the x axis, and the paper closes with the common error of applying the zero product rule before making the right-hand side zero.
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 49.
- FoundationSolve x squared plus 5x equals zero.
- FoundationSolve x squared minus 7x plus 12 equals zero.
- FoundationSolve (x plus 3) squared equals 16.
- IntermediateSolve 2x squared plus 3x minus 2 equals zero using the formula.
- IntermediateWithout solving, decide whether x squared minus 6x plus 10 equals zero has real roots.
- IntermediateIf x squared plus kx plus 16 equals zero has a repeated root and k is positive, find k.
- ChallengeA rectangle is 3 cm longer than it is wide and has a perimeter of 26 cm. Find its area.
- ChallengeWhere does y equals x squared minus 4x minus 12 meet the x axis?
- Error redoError repair: a student solves (x minus 2)(x plus 3) equals 6 by setting each bracket to 6 and gets 8 and 3. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x equals 7 or x equals minus 7 | Taking the square root gives both signs, so the answers are seven and minus seven. |
| 2 | x equals 0 or x equals minus 5 | Factor out x to get x times x plus five equals zero, so x is zero or minus five. |
| 3 | x equals 3 or x equals 4 | Two numbers with product twelve and sum seven are three and four. |
| 4 | x equals 1 or x equals minus 7 | Square rooting gives x plus three equals four or minus four, so x is one or minus seven. |
| 5 | x equals one half or x equals minus 2 | The discriminant is twenty-five, so x is minus three plus or minus five over four. |
| 6 | No real roots, because the discriminant is minus 4 | The discriminant is minus four, which is negative, so there are no real roots. |
| 7 | k equals 8 | A repeated root needs a zero discriminant, so k squared equals sixty-four and k is eight. |
| 8 | 40 square centimetres | Let the width be w, then twice w plus w plus three is twenty-six, so the area is forty. |
| 9 | At (minus 2, 0) and (6, 0) | Setting y to zero gives x minus six times x plus two equals zero. |
| 10 | x equals 3 or minus 4; the right-hand side must be zero before using the zero product rule | Expand and move six across to get x plus four times x minus three equals zero; the zero product rule needs zero on the right. |
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.
