2001 年

If the mean of the ten numbers $8,6,6,6,7,4,10,9,9,x$ is $7$, find the median of the ten numbers.

Which of the following is a factor of $2(a-b)^2-a^2+b^2$?

In the figure, the graph of $y=2x^2-9x+4$ cuts the $x$-axis at $A$ and $B$, and the $y$-axis at $C$. Find the area of $\triangle ABC$.

In the figure, a solid right circular cone of height $12\text{ cm}$ is put into a cylinder which has the same internal radius as the base radius of the cone. Water is then poured into the cylinder until the water level just reaches the tip of the cone. If the cone is removed, what is the height of the water in the cylinder?

In the figure, $OABC$ is a sector. Find the length of the arc $ABC$.

In the figure, $A$, $B$ and $C$ are the centres of three equal circles, each of radius $1\text{ cm}$. Find the area of the shaded region.

$40\%$ of the students in a class failed in a test. They had to sit for another test in which $70\%$ of them failed again. Find the percentage of students who failed in both tests.

If $\dfrac{x+3y}{2x-y}=\dfrac{2}{3}$, then $\dfrac{x-y}{x+y}=$

Suppose $y$ is partly constant and partly varies inversely as $x$. When $x=1$, $y=7$ and when $x=3$, $y=3$. Find $y$ when $x=2$.

In the figure, find $x$ correct to 3 significant figures.