2024 CGSS P2 Q6
2024 CGSS P2 Q6
9 marks
The diagram shows a figure \(PQRST\) which consists of a rectangle \(PQST\) and an isosceles triangle \(QRS\).
It is given that \(PQ = 4\) cm and \(QR = 8\) cm.
- Given angle \(SQR =\) angle \(QSR = x\) radians and the area of \(PQRST\) is given by \(A\) \(\text{cm}^2\), show that \(A = 64\cos x + 32\sin 2x\).[4]
- Find the value of \(x\) for which \(A\) has a stationary value.[3]
- Hence find the exact stationary value of \(A\) and determine whether it is a maximum or a minimum.[2]
Solution:
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Answer:(a) \(A=64\cos x+32\sin2x\) (shown) (b) \(x=\dfrac\pi6\) (c) Maximum \(48\sqrt3\text{ cm}^2\).
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