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S3 Maths: Quadratic Equations – Formula and Discriminant (Paper 1 (basics))
S3 Maths: Quadratic Equations – Formula and Discriminant (Paper 1 (basics))
Paper 1 (basics): ten quadratic-equation questions with answers and one-line notes.
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: Quadratic Equations – Formula and Discriminant |
| Level | S3 |
02 Questions (10 items)
- FoundationSolve x^2 – 5x + 6 = 0.
- FoundationSolve x^2 + 2x – 15 = 0.
- FoundationSolve x^2 – 9 = 0.
- IntermediateSolve 2x^2 – 7x + 3 = 0 using the formula.
- IntermediateSolve x^2 – 4x + 1 = 0, leaving the answer in surd form.
- IntermediateSolve 3x^2 + 5x – 2 = 0 using the formula.
- ChallengeSolve x^2 + 6x + 9 = 0 and state how many real roots it has.
- ChallengeDoes 2x^2 + 3x + 5 = 0 have real roots?
- ChallengeIf alpha and beta are the roots of x^2 – 7x + 10 = 0, find alpha + beta and alpha beta.
- Error redoA student solves x^2 – 2x – 8 = 0 and writes the discriminant as 4 minus 32, then answers no real roots. What went wrong and what is the correct answer?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | x = 2 or x = 3 | The discriminant is 25 minus 24, which is 1, so the formula gives (5 plus or minus 1) over 2. |
| 2 | x = 3 or x = -5 | The discriminant is 4 plus 60, which is 64, so its root is 8 and the formula gives (-2 plus or minus 8) over 2. |
| 3 | x = 3 or x = -3 | Here b is zero: move 9 across to get x^2 = 9 and take both the positive and negative square roots. |
| 4 | x = 3 or x = 1/2 | The discriminant is 49 minus 24, which is 25, so the formula gives (7 plus or minus 5) over 4. |
| 5 | x = 2 + sqrt(3) or x = 2 – sqrt(3) | The discriminant is 16 minus 4, which is 12; root 12 simplifies to 2 root 3, which cancels with the 2 in the denominator. |
| 6 | x = 1/3 or x = -2 | The discriminant is 25 plus 24, which is 49, so the formula gives (-5 plus or minus 7) over 6. |
| 7 | x = -3, one repeated real root | The discriminant is 36 minus 36, which is zero, so the two roots coincide and there is only one real root. |
| 8 | No real roots | The discriminant is 9 minus 40, which is -31; being negative, the equation has no real roots. |
| 9 | alpha + beta = 7 and alpha beta = 10 | The sum of roots is minus b over a and the product is c over a; here a equals 1. |
| 10 | Minus a negative is plus: the discriminant is 4 plus 32, which is 36, so x = 4 or x = -2 | In minus 4ac the value c is negative, so the term becomes positive; one sign slip reverses the whole conclusion. |
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.
Before using the formula, rearrange the equation into ax^2 + bx + c = 0 and write down a, b and c clearly, because signs slip most often here. Work out the discriminant D = b^2 – 4ac first: positive means two distinct real roots, zero means a repeated root and negative means no real roots. Remember the plus-or-minus sign gives two branches, simplify the surd before cancelling with the denominator, and finish by substituting the answers back into the original equation.Tutor Registration →
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