2025 AHS PRELIMS P1 Q7
2025 AHS PRELIMS P1 Q7
Secondary 4
8 marks
- The surface area of a solid cube is increasing at \(0.2\,\text{cm}^2/\text{s}\). Find the rate of increase of the volume when the length of a side is \(1\,\text{cm}\).[4]
- A curve has the equation \(y=e^{1-8x}(\cos 2x)\), where \(0\le x\le \dfrac{\pi}{4}\). Find the gradient of the curve at the point where \(y=0\), leaving your answer in exact form.[4]
Solution:
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Answer:(a) \(\dfrac{\mathrm{d}V}{\mathrm{d}t}=0.05\,\text{cm}^3/\text{s}\) (b) \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=-2e^{1-2\pi}\)
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