Selangor Trial 2025 Add Maths Paper 1, Question 6Circular Measure

Solved on video in English · Form 5, Circular Measure · 4:45 video

The question

(a)(i)

Diagram 3 shows rectangle ABCD with AB = 5 cm, BC = 16 cm and O is the midpoint of BC. OAED is a sector of a circle with centre O. [Use π = 3.142]

(a)(i) State the length of AO, in cm.

(a)(ii)

142]

(a)(ii) Find the ∠AOD, in radians.

(b)

142]

(b) Hence, find the perimeter, in cm, of the shaded region.

Step 1

O is the midpoint of BC, so BO = OC = 16/2 = 8 cm.

Why this step

O is the midpoint, so BO is only half of BC. Using the full 16 is the classic slip, and it ruins the Pythagoras step.

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

Final answer

AO = √89 = 9.434 cm

Where students lose marks

Watch out: O is the midpoint, so BO = 8, not 16. Then use Pythagoras; AO is not just 5 or 8.

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

Final answer

∠AOD = 2.024 rad

Where students lose marks

Watch out: ∠AOD is π − 2∠AOB, not ∠AOB itself. Stay in radians, and use tan = opposite/adjacent = 5/8.

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

Final answer

Perimeter = 37.96 cm

Where students lose marks

Watch out: the boundary is two radii plus the arc AED, not the chord AD. Use r = √89 for everything.

Watch every step of this question solved on video (4:45), with the reason behind each step and a box that checks your own answer.

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