2025 PHS P2 Q6
2025 PHS P2 Q6
Secondary 4
11 marks
2025 Presbyterian High School Prelims A Math Paper 2
By using a suitable substitution, or otherwise, solve the equation \(3\log_6 x = \log_x 3 + \log_x 2 + \log_5 25.\)
[4]- Sketch the graph of \(y = \log_6 x\) on the given axes. Label any axial intercepts.[1]
It is given that the equation of a curve is \(y = \mathrm{e}^{2x+1} + 2\mathrm{e}^{x+1} - 3\mathrm{e}\).
Explain why the curve has no stationary point.
[3]Find the \(x\)-intercept of the curve \(y = \mathrm{e}^{2x+1} + 2\mathrm{e}^{x+1} - 3\mathrm{e}\).
[3]
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Answer:(a) \(x=6\) or \(x=6^{-1/3}\) (b) Increasing logarithmic curve through \((1,0)\), asymptote \(x=0\). (c)(i) \(\frac{\mathrm{d}y}{\mathrm{d}x}>0\) for all real \(x\); no stationary point. (ii) \((0,0)\)
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