The diagram shows part of the curve $y = \frac{5}{x}$, $y = \pi$ and $x = \frac{3\pi}{2}$. The

Question

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 $Q$. Find the coordinates of $P$ and of $Q$ in terms of $\pi$.[2] Find the area of the shaded region bounded by $y=\frac{5}{3}, y=\pi, x=\frac{3\pi}{2}$, the y-axis and the x-axis.[3] Explain why the area of the shaded region is between 5 units$^2$ and $\frac{3\pi2}{2}$ units$^2$.[1]

Accepted Answer

(i)$P:(\frac{5}{\pi},\pi), Q:(\frac{3\pi}{2},\frac{10}{3\pi})$ (ii)10.4 units $^2$

2025 SST PRELIMS P1 Q10

2025 SST PRELIMS P1 Q10