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SPM Additional Mathematics 2017, Paper 1 (Question 14 – 16)


Question 15 (4 marks):
It is given that cos α = t where t is a constant and 0o ≤ α ≤ 90o.
Express in terms of t
(a) sin (180o + α),
(b) sec 2α.

Solution:
(a)




sin(180o+α)=sin180cosα+cos180sinα=0sinα=sinα=1t2

(b)
sec2α=1cos2α =12cos2α1 =12t21



Question 16 (3 marks):
Diagram 7 shows two sectors AOD and BOC of two concentric circles with centre O.

Diagram 7

The angle subtended at the centre O by the major arc AD is 7α radians and the perimeter of the whole diagram is 50 cm.
Given OB = r cm, OA = 2OB and ∠BOC = 2α, express r in terms of α.


Solution:

Length of major arc AOD=2r×7α=14rαLength of minor arc BOC=r×2α=2rαPerimeter of the whole diagram=50 cm14rα+2rα+r+r=5016rα+2r=508rα+r=25r(8α+1)=25r=258α+1

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