Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 3Quadratic Functions

Solved on video in English · Form 4, Quadratic Functions · 5:04 video

The question

(a)

Given that q and 3q are the roots of a quadratic equation, form a quadratic equation by using the given roots, in terms of q.

(b)

The straight line y = 2kx − m intersects the curve 5 = 5x² − 2xy at one point. Express k in terms of m.

Step 1

Sum of roots = q + 3q = 4q; product of roots = q × 3q = 3q².

Why this step

Multiply the numbers and the letters separately: 3 × q × q = 3q². Not 3q, because q times q is q².

2 more steps, each with the reason for it, in the full solution

Final answer

x² − 4qx + 3q² = 0

Where students lose marks

Watch out: the x term is minus the sum of roots, so write −4qx, not +4qx, and the product q × 3q = 3q².

5 more steps, each with the reason for it, in the full solution

Final answer

k = (m² + 25)/20

Where students lose marks

Watch out: use discriminant = 0 for one point of intersection, and take care with signs in −4(5 − 4k)(−5).

Watch every step of this question solved on video (5:04), with the reason behind each step and a box that checks your own answer.

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