SPM 2020 Add Maths Paper 1, Question 18Circular Measure

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

The question

Diagram 8 shows a semicircle with centre O. ORQ is a straight line and PQ is a tangent to the semicircle at point P. The angle POR = alpha rad. It is given the arc length PR is beta cm and the area of the shaded region is beta/(2*alpha) cm². Express the length, in cm, of PQ in terms of beta.

[4 marks]

SPM 2020 Add Maths Paper 1, Question 18: the question as drawn in Eduly's video4:54

Step 1

OP = OR = r (radii). Arc PR subtends angle alpha at O, so arc = r*alpha = beta, giving r = beta/alpha.

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

Final answer

PQ = (β + 1) cm

Where students lose marks

Watch out: the shaded region is triangle OPQ minus sector OPR. Using only the triangle stops you writing PQ in terms of β.

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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