2001 年

Find the mean deviation of the five numbers $0,3,4,6$ and $7$.

For $0^\circ\le x\le360^\circ$, how many roots does the equation $\cos^3x=\cos x$ have?

If $\tan(90^\circ-\theta)=2$, then $\dfrac{\sin^3\theta+\sin\theta\cos^2\theta}{\cos\theta}=$

The figure shows the graph of the function

In the figure, $O$ is the centre of the circle, $AOB$ is a straight line and $BCD$ is the tangent to the circle at $C$. Find $x$.

In the figure, $\widehat{AB}=\widehat{BC}=\dfrac{1}{2}\widehat{CD}$. Find $\angle ABC$.

$\dfrac{1-x}{x^2+4x-5}+\dfrac{x-1}{x+1}=$

Let $\mathrm{f}(x)=x^3+2x^2+ax+b$. If $\mathrm{f}(x)$ is divisible by $x+1$ and $x-2$, $\mathrm{f}(x)$ can be factorized as

The shaded region in the figure represents the solution of one of the following systems of inequalities. Which is it?

In the figure, $ADB$, $BEC$ and $CFA$ are straight lines. If the area of $\triangle ABC$ is $225\text{ cm}^2$, find the area of the parallelogram $DECF$.