SPM 2024 Add Maths Paper 2, Question 1Circular Measure

Solved on video in English and Bahasa Melayu · Form 5, Circular Measure · 4:14 video

The question

Diagram 1 shows sector BAC with centre A and sector COD with centre O. P lies on the straight line OD.

It is given that the area of sector BAC is 113.4 cm², OA = (1/2)AC and CP = 7.74 cm. [Use π = 3.142]

(a) (i) Find the length of AC, in cm. (ii) Show that θ = 0.611 when rounded to three significant figures.

(b) Hence, find the perimeter, in cm, of the whole diagram.

Step 1

Apply area of sector formula A = (1/2)r²θ with A = 113.4 cm² and θ = 2.8 rad, where r = AC:

Why this step

The formula A = (1/2)r²θ needs θ in radians, so keep 2.8 as it is. Converting to degrees first gives AC ≈ 1.19 cm, not 9 cm.

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

Final answer

AC = 9 cm; θ = 0.611 rad (shown); perimeter ≈ 60.45 cm

Where students lose marks

Watch out: keep angles in radians. Using degrees in (1/2)r²θ gives AC ≈ 1.19, and 34.983° must be converted to radians for θ.

Watch every step of this question solved on video (4:14), 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.