SPM 2021 Add Maths Paper 1, Question 6Circular Measure

Solved on video in English and Bahasa Melayu · Form 5, Circular Measure · 6:27 video

The question

(a)

Diagram 3 shows a trapezium FECA. Sector ABHG is a quadrant of a circle with centre A, and AHD is an arc of a circle with centre B. It is given that G is the midpoint of AF, BC = CE = 8 cm and CD = 3DE. [Use π = 3.142] Find ∠CBD, in radians correct to four decimal places.

(b)

Hence, calculate the perimeter, in cm, of the shaded region. [Use π = 3.142]

SPM 2021 Add Maths Paper 1, Question 6: the question as drawn in Eduly's video6:27

Part (a)

Step 1

On the right side, CE = CD + DE and CD = 3DE, so CE = 3DE + DE = 4DE = 8, giving DE = 2 cm and CD = 6 cm.

Why this step

CD is 3 parts and DE is 1 part, so CE is 4 parts in total. Treat the ratio as equal pieces of CE.

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

Final answer

∠CBD = 0.6436 rad

Where students lose marks

Watch out: 36.87° is not the final answer. The question asks for radians, so multiply by π/180 to convert.

Part (b)

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

Final answer

53.3817 cm

Where students lose marks

Watch out: 'hence' means reuse ∠CBD in radians from (a). Recomputing in degrees gave a wrong perimeter of about 50.537 cm.

Watch every step of this question solved on video (6:27), with the reason behind each step and a box that checks your own answer.

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