1998 年

If $b<0$ and $c<0$, which of the following shaded regions may represent the solution of $x+by+c\ge 0$?

In the figure, a right pyramid with a square base is divided into three parts $A$, $B$ and $C$ by two planes parallel to the base such that the lengths of their slant edges are $1\text{ cm}$, $2\text{ cm}$ and $3\text{ cm}$ respectively. Find volume of $A$ : volume of $B$ : volume of $C$.

Find the sum to infinity of the geometric sequence $-1,\dfrac{1}{x},-\dfrac{1}{x^2},\dfrac{1}{x^3},\dots$, where $x>1$.

$\dfrac{1+\sin\theta}{\cos\theta}+\dfrac{\cos\theta}{1+\sin\theta}=$

The figure shows the graph of the function

In the figure, $ABC$ is a semicircle. Find the area of the shaded part.

For $0^\circ\le x\le 360^\circ$, how many roots does the equation $3\sin^2x+2\sin x-1=0$ have?

The figure shows a right pyramid with a square base $ABCD$. Let $\theta$ be the angle between the planes $VAB$ and $VCD$. Find $\sin\dfrac{\theta}{2}$.

In the figure, $CE$ is tangent to the circle at $C$. Find $\angle DCE$.

In the figure, $ABCD$, $AFE$, $CGE$ and $FGD$ are straight lines. If $AB=BC=2CD$, then $CG:GE=$