2025 SST PRELIMS P2 Q10

2025 SST PRELIMS P2 Q10

Secondary 4
6 marks
2025 School of Science and Technology Prelims A Math Paper 2

The diagram shows part of the curve \(y=\frac{5}{x}\), \(y=\pi\) and \(x=\frac{3\pi}{2}\). The curve \(y=\frac{5}{x}\) cuts the line \(y=\pi\) at \(P\) and cuts the line \(x=\frac{3\pi}{2}\) at \(Q\).

  1. Find the coordinates of \(P\) and of \(Q\) in terms of \(\pi\).[2]
  2. Find the area of the shaded region bounded by \(y=\frac{5}{x}\), \(y=\pi\), \(x=\frac{3\pi}{2}\), the \(y\)-axis and the \(x\)-axis.[3]
  3. Explain why the area of the shaded region is between 5 units\(^2\) and \(\frac{3\pi^2}{2}\) units\(^2\).[1]

Solution:

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Answer:(i) \(P\left(\frac{5}{\pi},\pi\right)\), \(Q\left(\frac{3\pi}{2},\frac{10}{3\pi}\right)\) (ii) \(\text{Area}=5+5\ln\left(\frac{3\pi^2}{10}\right)=10.4\text{ units}^2\) (iii) \(5<\text{Area}<\frac{3\pi^2}{2}\text{ units}^2\)

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