The diagram shows the graphs of $y=x^{\frac{3}{2}}$ and $y=-x^{\frac{3}{2}}$. The line \(y=2x-1\

Question

The diagram shows the graphs of $y=x^{\frac{3}{2}}$ and $y=-x^{\frac{3}{2}}$. The line $y=2x-1$ intersects the graph of $y=x^{\frac{3}{2}}$ at $A(1, 1)$, the $x$-axis at $B$, and the graph of $y=-x^{\frac{3}{2}}$ at $C$. Show that the coordinates of $C$ are $(0.38197, -0.23607)$, correct to 5 significant figures.[5] Find the area of the shaded region.[6]

Accepted Answer

(a) $C=(0.38197,-0.23607)$ (5 s.f.). (b) $0.200\text{ units}^2$ (3 s.f.).

2025 BVSS PRELIMS P2 Q10

2025 BVSS PRELIMS P2 Q10

Solution:

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