1997 年

In the figure, find the coordinates of the mid-point of $AB$.

Find the values of $x$ which satisfy both $-2x<3$ and $(x+3)(x-2)<0$.

If $a<b<0$, then which of the following must be true? I. $a^2<b^2$ II. $ab<a^2$ III. $\dfrac{1}{a}<\dfrac{1}{b}$

The figure shows the graph of a quadratic function $\mathrm{f}(x)$. If the vertex of the graph is $(1,3)$, then $\mathrm{f}(x)=$

The $n$-th term of an arithmetic sequence is $3+2n$. Find the sum of the first $50$ terms of the sequence.

The first term of a geometric sequence is $a$. If the sum to infinity of the sequence is $\dfrac{3}{4}a$, then its common ratio is

$a$, $b$, $c$, $d$ are $4$ consecutive terms of a geometric sequence. Which of the following must be true? I. $b^2=ac$ II. $\dfrac{b}{a}=\dfrac{d}{c}$ III. $\dfrac{d}{a}=\left(\dfrac{c}{b}\right)^3$

Find the interest on $\$10\,000$ at $16\%$ per annum for $2$ years, compounded half-yearly. Give the answer correct to the nearest dollar.

Suppose $x$ varies directly as $y$ and inversely as $z$. When $y=2$ and $z=3$, $x=7$. When $y=6$ and $z=7$, $x=$

$\dfrac{\cos(90^\circ-A)\sin(180^\circ-A)}{\tan(360^\circ-A)}=$