MRSM Trial 2025 Add Maths Paper 2, Question 7Circular Measure

Solved on video in English · Form 5, Circular Measure · 8:34 video

The question

(a)(i)

Diagram 5 shows a stage in a hall. The sector OPRT centred at O with radius 13 m is the main stage. The shaded region will be filled with decoration. QS is a tangent to the arc PRT at point R with a length of 24 m. PQ and TS are perpendicular to QS and PQ = TS. [Use π = 3.142]

(a)(i) LED strip lights will be installed around the shaded region. Calculate the length, in m, of the LED strip lights.

(a)(ii)

Diagram 5 shows a stage in a hall (sector OPRT centred at O, radius 13 m; QS a tangent to arc PRT at R, length 24 m; PQ = TS perpendicular to QS). [Use π = 3.142]

(a)(ii) A spotlight will be installed at T and will illuminate the circular area with radius 6 m. Find the area, in m², of the main stage that will be illuminated by the spotlight.

(b)

(b) Derive the formula for the area of a sector, L = ½ j²θ.

MRSM Trial 2025 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video8:34

Part (a)(i)

Step 1

QS (length 24) is tangent to the arc at R, so R is the midpoint and QR = RS = 12; OR = 13 is the radius perpendicular to the tangent.

Why this step

A tangent meets the radius at 90°. Because PQ = TS, the stage is symmetric, so OR cuts QS exactly in half.

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

Final answer

70.58 m

Where students lose marks

Watch out: the arc is jθ (not 2πj), and the perimeter must also include PQ, TS and QS, not just the arc.

Part (a)(ii)

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

Final answer

25.48 m²

Where students lose marks

Watch out: the lit area is only the overlap with the stage, not the whole spotlight circle (36π). Use radians in ½j²θ.

Part (b)

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

Final answer

Derived: L = ½ j²θ

Where students lose marks

Watch out: start from the ratio of sector to circle; just quoting L = ½j²θ is not a derivation.

Watch every step of this question solved on video (8:34), with the reason behind each step and a box that checks your own answer.

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