2010 年

In the figure, $D$ is a point lying on $BC$ such that $AD$ is perpendicular to $BC$. Find $\dfrac{AC}{BD}$.

If $\theta$ is an acute angle, then $\tan\theta+\tan(90^\circ-\theta)=$

Which of the following statements about a cube must be true? I. The number of planes of reflection is $9$. II. All the axes of rotational symmetry intersect at the same point. III. The angle between any two intersecting axes of rotational symmetry is $90^\circ$.

If the plane figure above is rotated anticlockwise about the point $O$ through $270^\circ$, which of the following is its image?

In the figure, $C$ is a point lying on $AB$ such that $AC=AD$. If $AB\,/\!/\,ED$, find $\angle ADE$.

In the figure, $ABCD$ is a rectangle. If $M$ is a point lying on $AC$ such that $DM$ is perpendicular to $AC$, then $AM:MC=$

Each interior angle of a regular $24$-sided polygon is

In the figure, $AD$ is a vertical pole standing on the horizontal ground $BCD$. If $E$ is a point lying on $BC$ such that $DE$ and $AE$ are perpendicular to $BC$, then the angle between the plane $ABC$ and the horizontal ground is

If the point $R(-4,-3)$ is reflected with respect to the straight line $y+7=0$ to the point $S$, then the coordinates of $S$ are

If the polar coordinates of a point are $(6,\ 210^\circ)$, then the rectangular coordinates of the point are