1992 年

Suppose $x$ varies directly as $y^2$ and inversely as $z$. Find the percentage increase of $x$ when $y$ is increased by $20\%$ and $z$ is decreased by $20\%$.

A sum of $\$10\,000$ is deposited at $4\%$ p.a., compounded yearly. Find the interest earned in the second year.

The figure shows a solid platform with steps on one side and a slope on the other. Find its volume.

In the figure, $TP$ and $TQ$ are tangents to the circle of radius $3\text{ cm}$. Find the length of the minor arc $PQ$.

Find the ratio of the volume of the tetrahedron $ACHD$ to the volume of the cube $ABCDEFGH$ in the figure.

In the figure, the equilateral triangle $ACE$ of side $4\text{ cm}$ is inscribed in the circle. Find the area of the inscribed regular hexagon $ABCDEF$.

In the figure, a cone of height $3h$ is cut by a plane parallel to its base into a smaller cone of height $h$ and a frustum. Find the ratio of the volume of the smaller cone to the volume of the frustum.

The greatest value of $1-2\sin\theta$ is

In the figure, find $\cos\theta$.

In which two quadrants will the solution(s) of $\sin\theta\cos\theta<0$ lie?