2004 年

It is known that the equation $2x^3=12x-9$ has only one root in the interval $-3\le x\le-2$. The method of bisection is used to find the root starting with the interval $-3\le x\le-2$. After the first approximation, the interval which contains the root becomes $-3\le x\le-2.5$. Find the interval which contains the root after the third approximation.

If $\alpha\ne\beta$ and $\begin{cases}\alpha^2=4\alpha+3\\\beta^2=4\beta+3\end{cases}$, then $(\alpha+1)(\beta+1)=$

Which of the following shaded regions may represent the solution of $x\le y-2$ ?

If $81,\ a,\ b,\ 3$ is a geometric sequence, then $b-a=$

In the figure, $OAB$ is a sector. The perimeter and the area of the sector are $x\text{ cm}$ and $y\text{ cm}^2$ respectively. If $x=y$, then $\widehat{AB}=$

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

If $A+B=\pi$, which of the following must be true? I. $\sin A=\sin B$ II. $\cos A=\sin B$ III. $\cos A=\cos B$

The figure shows the cube $ABCDEFGH$ of side $2\text{ cm}$. $X$ and $Y$ are the mid-points of $AB$ and $GH$ respectively. Find $XY$.

In the figure, $ABCDEFGH$ is a rectangular block. $EG$ and $FH$ meet at $X$. $M$ is the mid-point of $EH$. Which of the following makes the greatest angle with the plane $ABCD$ ?

In the figure, $ABCD$ is a circle. If $\widehat{CD}=2\widehat{DA}=2\widehat{AB}=2\widehat{BC}$, then $x=$