2007 年

A sum of $\$30\,000$ is deposited at an interest rate of $12\%$ per annum for $4$ years, compounded monthly. Find the amount correct to the nearest dollar.

Express $\sqrt{2007}$ as a decimal correct to 5 significant figures.

Let $a$ and $b$ be non-zero numbers. If $7a+5b=3a+8b$, then $a:b=$

It is given that $y$ is partly constant and partly varies directly as $x$. When $x=2$, $y=17$ and when $x=4$, $y=11$. Find the value of $x$ when $y=5$.

$A$ and $B$ are two points on a map. If the bearing of $A$ from $B$ is $110^\circ$, then the bearing of $B$ from $A$ is

In the figure, $OAB$ is a sector with centre $O$. If the perimeter of the sector $OAB$ is $12\text{ cm}$, find $OA$ correct to the nearest $0.01\text{ cm}$.

In the figure, the volume of the right prism is

If a solid metal hemisphere of radius $r$ is melted and recast into $3$ identical solid right circular cones of height $h$ and base radius $r$, then $r:h=$

In the figure, $ABCD$ is a parallelogram. $E$ is a point lying on $AB$. If $EC$ and $BD$ intersect at $F$, then the ratio of the area of $\triangle DEF$ to the area of $\triangle CBF$ is

If $x$ and $y$ are acute angles such that $x+y=90^\circ$, which of the following must be true? I. $\sin x=\cos y$ II. $\sin(90^\circ-x)=\cos(90^\circ-y)$ III. $\tan x\tan y=1$