2000 年

In the figure, $CAB$ is a semicircle and $ABCD$ is a parallelogram. Find the area of $ABCD$.

The figure shows a square, a triangle and a sector with areas $a\text{ cm}^2$, $b\text{ cm}^2$ and $c\text{ cm}^2$ respectively.

Which of the following is true?

In the figure, a solid wooden sphere of radius $r$ cm is to be cut into a cube of side $3\text{ cm}$. Find the smallest possible value of $r$.

If $9a^2-b^2=0$ and $ab<0$, then $\dfrac{a-b}{a+b}=$

$y$ varies directly as $x^2$ and inversely as $\sqrt{z}$. If $y=1$ when $x=2$ and $z=9$, find $y$ when $x=1$ and $z=4$.

Tea $A$ and tea $B$ are mixed in the ratio $x:y$ by weight. $A$ costs $\$80$/kg and $B$ costs $\$100$/kg. If the cost of $A$ is increased by $10\%$ and that of $B$ is decreased by $12\%$, the cost of the mixture per kg remains unchanged. Find $x:y$.

Simplify $\dfrac{a}{a+b}+\dfrac{b}{b-a}+\dfrac{2ab}{a^2-b^2}$.

If $\log(x-a)=3$, then $x=$

Which of the following may represent the graph of $y=-x^2+2x-3$ ?

If $\left(\dfrac{\sqrt{5}}{2}+1\right)x=\sqrt{2}$, then $x=$