2025 JVSS PRELIMS P1 Q9
2025 JVSS PRELIMS P1 Q9
Secondary 4
9 marks
2025 Jurongville Secondary School Prelims A Math Paper 1
Mathematical correction: the stationary point \(P\) is a maximum. The earlier wording said minimum; the equation and assessed parts are unchanged.
A curve \(y=\dfrac{1+3\ln x}{x^2}\) has a maximum point at \(P\).
Find \(\dfrac{\mathrm{d}y}{\mathrm{d}x}\).
[2]Show that the \(x\)-coordinate of \(P\) is \(\mathrm{e}^{\frac{1}{6}}\).
[2]Find the equation of normal to the curve at the point \(x=\mathrm{e}\). Leave your answer in terms of \(\mathrm{e}\).
[5]
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Answer:(a) \(\dfrac{1-6\ln x}{x^3}\)
(c) \(y =\dfrac{\mathrm{e}^3}{5}x-\frac{1}{5}\mathrm{e}^4 + \frac{4}{\mathrm{e}^2}\)
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