/en-tutor-prep-s4-maths-quadratic-equations-discriminant-practice-1/
/en-tutor-prep-s4-maths-quadratic-equations-discriminant-practice-1/
General Inquiry: info@TutorZone.com.hk
Office Hours: Monday to Saturday - 9:00 AM to 6:00 PM
WhatsApp Monday to Sunday - 24 hours
Hotline: +852 6828 1809
Instant Support: +852 9061 3106

S4 Maths: Quadratic Equations and the Discriminant (Paper 1 (basics))

S4 Maths: Quadratic Equations and the Discriminant (Paper 1 (basics))

  • 2026-11-15

Tutor Prep Guide · Solving quadratic equations by factorising and by the formula, the sign of the discriminant, the sum and product of roots, forming an equation from given roots, and finding the range of a parameter

S4 Maths: Quadratic Equations and the Discriminant (Paper 1 (basics))

Paper 1 (basics): ten questions on quadratic equations and the discriminant with answers and one-line notes.

Direct answers　Level: S4 maths; format: factorising, the quadratic formula, the discriminant, sum and product of roots.

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: S4 Maths: Quadratic Equations and the Discriminant
Level S4

02　Questions (10 items)

  1. FoundationSolve x^2 – 5x + 6 = 0.
  2. FoundationFind the discriminant of x^2 + 4x + 4 = 0 and state the repeated root.
  3. FoundationFind the discriminant of 2x^2 + 3x – 2 = 0.
  4. IntermediateSolve x^2 – 2x – 15 = 0.
  5. IntermediateWithout solving, decide whether x^2 + x + 1 = 0 has real roots.
  6. IntermediateSolve 3x^2 – 6x + 3 = 0.
  7. ChallengeFor x^2 – 7x + 10 = 0 with roots alpha and beta, find alpha + beta and alpha times beta.
  8. ChallengeGiven that x = 3 is a root of x^2 – kx + 6 = 0, find k.
  9. ChallengeSolve 4x^2 – 4x + 1 = 0.
  10. Error redoError clinic: find the discriminant of x^2 + 3x + 2 = 0.

03　Answers and one-line notes

# Answer One-line note
1 x = 2 or x = 3. Factorising gives (x – 2)(x – 3) = 0, so the roots are 2 and 3.
2 Discriminant = 0, repeated root x = -2. The discriminant is 16 – 16 = 0, and -4 divided by 2 gives -2.
3 Discriminant = 25. It is 3 squared minus 4 times 2 times minus 2, that is 9 + 16 = 25.
4 x = 5 or x = -3. Factorising gives (x – 5)(x + 3) = 0, so the roots are 5 and -3.
5 Discriminant = -3, so there are no real roots. The discriminant is 1 – 4 = -3, which is negative, so no real root exists.
6 x = 1 (repeated root). The discriminant is 36 – 36 = 0, so both roots equal 1.
7 alpha + beta = 7 and alpha times beta = 10. The sum is minus b over a, giving 7, and the product is c over a, giving 10.
8 k = 5. Substituting 3 gives 9 – 3k + 6 = 0, so 3k = 15 and k = 5.
9 x = 0.5 (repeated root). The discriminant is 16 – 16 = 0, and 4 divided by 8 gives 0.5.
10 Discriminant = 1. It is 3 squared minus 4 times 1 times 2, that is 9 – 8 = 1, so keep the minus sign.

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.

© TutorZone · www.tutorzone.com.hk · For personal study and teaching use only.

Join as a tutor or coach — academic, music, sports, arts, STEM. Free to register. See how it works →