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Solution of Past Paper of CAIE Math 9709/12 Feb/Mar 2020 Question # 7

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This document presents most carefully worked out and thoroughly explained complete Solution of Past Paper of Cambridge AS/A Level Mathematics (9709), Pure Mathematics 1, Feb/March 2020 We also provide on-on-one online help for students who still need some help beyond our provided solution. We always openly, and in a forthcoming way, welcome all kinds of suggestions, criticism and even queries. So do not hesitate to contact us.

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CIE/GCE/AS/Math/P1/20/Mar/12/Q#7

Question




The diagram shows a sector AOB which is part of a circle with centre O and radius 6
cm and with angle AOB = 0.8 radians. The point C on OB is such that AC is
perpendicular to OB. The arc CD is part of a circle with centre O, where D lies on OA.

Find the area of the shaded region.


Solution


We are required to find the area of the shaded region.


It is evident from the diagram that;


𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆ℎ𝑎𝑑𝑒𝑑 𝑅𝑒𝑔𝑖𝑜𝑛 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑇𝑟𝑎𝑖𝑔𝑛𝑙𝑒 𝐴𝑂𝐶 − 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑆𝑒𝑐𝑡𝑜𝑟 𝐷𝑂𝐶


First, we find area of right-triangle AOB.


Expression for the area of a triangle for which two sides (a and b) and the included
angle (C ) is given;
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