2025 SCGS PRELIMS P1 Q7
2025 SCGS PRELIMS P1 Q7
Secondary 4
8 marks
- State the amplitude and period of the graph of \(y = 3\sin \frac{x}{2}+1\).[2]
- Sketch the graph of \(y = 3\sin \frac{x}{2}+1\) for \(0 \le x \le 4\pi\).[3]
- By adding another suitable curve on your sketch, determine the number of solutions of the equation \(\sin \frac{x}{2} = -\frac{1}{3} - \frac{2}{3}\cos \frac{x}{2}\).[3]
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Answer:(a) \(\text{Amplitude}=3\), \(\text{period}=4\pi\text{ radians}\). (b) \(y=1\), with a smooth sine curve through \((0,1)\), \((\pi,4)\), \((2\pi,1)\), \((3\pi,-2)\), and \((4\pi,1)\). (c) \(2\) solutions.
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