S4 Maths: Quadratic Equations and the Discriminant (Paper 3 (challenge))

S4 Maths: Quadratic Equations and the Discriminant (Paper 3 (challenge))

Paper 3 (challenge): ten questions on quadratic equations and the discriminant with answers and one-line notes.

01　Paper details (check answers afterwards)

02　Questions (10 items)

1. FoundationIf 2x^2 – 5x + k = 0 has real roots, find the range of k.
2. FoundationIf x^2 – (m + 1)x + 4 = 0 has a repeated root, find m.
3. FoundationSolve 3x^2 + 2x – 1 = 0.
4. IntermediateSolve x^2 – 2x – 2 = 0, correct to three decimal places.
5. IntermediateThe roots are 3 + sqrt(2) and 3 – sqrt(2). Write down the equation.
6. IntermediateThe roots of x^2 + px + 8 = 0 differ by 2. Find the possible values of p.
7. ChallengeIf 4x^2 + (k – 2)x + 1 = 0 has a repeated root, find k.
8. ChallengeIf alpha and beta are the roots of x^2 – 3x + 1 = 0, find alpha squared plus beta squared.
9. ChallengeIf 2x^2 + kx + 8 = 0 has no real roots, find the range of k.
10. Error redoError clinic: what does a negative discriminant mean?

03　Answers and one-line notes

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.

Write down a, b and c first, then work out the discriminant. A positive discriminant gives two distinct real roots, a zero discriminant one repeated root, and a negative one no real root. For a parameter question, form the discriminant in terms of the parameter and then set it positive, zero or negative.Tutor Registration →

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.