2011 年

The length of a rectangle is decreased by $20\%$ but its breadth is increased by $k\%$. If the area of the rectangle remains unchanged, find the value of $k$.

Let $m$ and $n$ be non-zero numbers. If $\dfrac{2m-n}{m-2n}=3$, then $m:n=$

It is given that $a$ varies directly as $b$ and inversely as $c^2$. When $b=6$ and $c=3$, $a=-2$. When $a=-9$ and $c=4$, $b=$

The figure shows the positions of four real numbers $p$, $q$, $r$ and $s$ on the number line. Which of the following is the best estimate of $(p-q)(r+s)$?

In the figure, the bearing of $B$ from $A$ is

If the radius and the area of a sector are $12\text{ cm}$ and $48\pi\text{ cm}^2$ respectively, find the perimeter of the sector correct to the nearest $0.1\text{ cm}$.

In the figure, the total surface area of the solid right triangular prism is

If the volume of a solid hemisphere of radius $r$ is equal to the volume of a solid right circular cylinder of height $h$ and base radius $r$, then $r:h=$

In the figure, $ABCD$ is a parallelogram. $E$ is the mid-point of $AB$. $F$ and $G$ are points lying on $CD$ such that $DF=FG=GC$. $BG$ and $CE$ intersect at $H$. If the area of $\triangle BCH$ is $6\text{ cm}^2$, then the area of the quadrilateral $EFGH$ is

If $x$, $y$ and $z$ are the angles of a triangle with $x+y=90^\circ$, which of the following are true? I. $\tan x\tan y=\sin z$ II. $\cos y+\cos z=\sin x$ III. $\sin^2 x+\sin^2 y=\sin^2 z$