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SPM Additional Mathematics 2018, Paper 1 (Question 11 – 13)


Question 12 (4 marks):
Diagram 5 shows a circle with centre O.

Diagram 5

PR
and QR are tangents to the circle at points P and Q respectively. It is given that the length of minor arc PQ is 4 cm and OR=5α cm.  
Express in terms of α,
(a) the radius, r, of the circle,
(b) the area, A, of the shaded region.


Solution:
(a)
Given sPQ=4   rα=4  r=4α cm

(b)

PR=(5α)2(4α)2PR=9α2PR=3αA= Area of shaded regionA= Area of quadrilateral OPRQArea of sector OPQ=2(Area of  OPR)12r2θ=2[12×3α×4α][12×(4α)2×α]=12α28α=128αα2 cm2


Question 13 (3 marks):
Diagram 6 shows the graph of a straight line x2y against 1x.  

Diagram 6

Based on Diagram 6, express y in terms of x.


Solution:

m=4(5)60=32c=5Y=x2yX=1xY=mX+cx2y=32(1x)+(5)x2y=32x5x2y=310x2xyx2=2x310xy=2x3310x

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