2006 年

A sum of $\$14\,000$ is deposited at $4\%$ per annum for $5$ years, compounded yearly. Find the interest correct to the nearest dollar.

In the figure, the 1st pattern consists of $3$ dots. For any positive integer $n$, the $(n+1)$th pattern is formed by adding $(2n+3)$ dots to the $n$th pattern. Find the number of dots in the 6th pattern.

Let $x$, $y$ and $z$ be non-zero numbers. If $x:y=1:2$ and $y:z=3:1$, then $(x+y):(y+z)=$

It is given that $x$ varies directly as $y$ and inversely as $z^2$. If $y$ is decreased by $10\%$ and $z$ is increased by $20\%$, then $x$ is decreased by

The scale of a map is $1:8\,000$. If the area of a park on the map is $2\text{ cm}^2$, then the actual area of the park is

In the figure, $PA=QA$. If the bearings of $P$ and $Q$ from $A$ are $\text{N}42^\circ\text{E}$ and $\text{S}28^\circ\text{E}$ respectively, then the bearing of $P$ from $Q$ is

In the figure, the area of the trapezium $ABCD$ is

In the figure, the solid consists of a hemisphere of radius $3\text{ cm}$ joined to the bottom of a right circular cylinder of height $8\text{ cm}$ and base radius $3\text{ cm}$. Find the volume of the solid.

In the figure, $O$ is the centre of the circle. $B$ and $C$ are points lying on the circle. If $OC=2\text{ cm}$ and $OA=1\text{ cm}$, then the area of the shaded region $OABC$ is

In the figure, sector $OXY$ is a thin metal sheet. By joining $OX$ and $OY$ together, which of the following right circular cones can be folded?