SPM 2022 Add Maths Paper 1, Question 7Circular Measure

Solved on video in English and Bahasa Melayu · Form 5, Circular Measure · 4:54 video

The question

(a)

7 Diagram 2 shows sectors AOB and COD inscribed in a circle with centre O. The radius of the circle and the radius of the sector COD are h cm and k cm respectively. The lengths of arc CP and arc PD are equal. It is given that the perimeter of the minor sector AOB is 15.235 cm and the area of the shaded region is 8.376 cm². [Use pi = 3.142] (a) State the angle COD, in terms of pi.

(b)

Hence, calculate the value of h and of k to the nearest integer. [Use pi = 3.142; perimeter of minor sector AOB = 15.235 cm; area of shaded region = 8.376 cm²; arc CP = arc PD; angle COD = (2/3)pi from part (a)]

SPM 2022 Add Maths Paper 1, Question 7: the question as drawn in Eduly's video

Part (a)

Step 1

The reflex angle at O (the major sector) is 240°, so the non-reflex angle COD = 360° − 240° = 120°.

Why this step

The diagram gives the reflex angle (the long way round). A full turn is 360°, so we subtract to get the angle we actually need.

1 more step, with the reason for it, in the full solution

Final answer

∠COD = 2π/3 rad (= 120°)

Where students lose marks

Watch out: give the angle in radians in terms of π (2π/3), not in degrees or as a decimal like 2.0947.

Part (b)

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

Final answer

h = 5 cm, k = 3 cm

Watch every step of this question solved on video (4:54), with the reason behind each step and a box that checks your own answer.

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