Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 4Trigonometric Functions

Solved on video in English · Form 5, Trigonometric Functions · 3:12 video

The question

(a)

Diagram 3 shows the curve of a trigonometric function for 0 ≤ x ≤ 2π.

(a) State the equation of the graph of the trigonometric function in Diagram 3.

(b)

(b) On the same axes, sketch the graph y = |cos x| for 0 ≤ x ≤ 2π. Hence, state the number of solutions.

Step 1

The curve starts at (0, 0) and rises to a maximum before x = ½π, so it is a sine curve (passes through the origin, positive first).

Why this step

Sine starts at the origin and rises; cosine starts at a maximum. So check the starting point first, or you may wrongly write cos 2x.

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

Final answer

y = sin 2x

Where students lose marks

Watch out: count the cycles and check the start. Two cycles from the origin gives sin 2x, not sin x or cos 2x.

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

Final answer

4 solutions (sketch: see video)

Where students lose marks

Watch out: draw |cos x| with no negative parts, all above the axis, then count crossings carefully. Miscounting intersections loses the final mark.

Watch every step of this question solved on video (3:12), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.