2002 年

For $0^\circ\le\theta\le90^\circ$, the maximum value of $\dfrac{2}{3+\sin^2\theta}$ is

If $45^\circ<\theta<90^\circ$, which of the following must be true? I. $\tan\theta>\sin\theta$ II. $\tan\theta>\cos\theta$ III. $\cos\theta>\sin\theta$

In the figure, find $x$ correct to 3 significant figures.

In the figure, $AB$ and $CD$ are the heights of two buildings on the same level ground. If $AB=9\text{ m}$, $AC=20\text{ m}$ and the angle of depression of $A$ from $D$ is $50^\circ$, find the angle of elevation of $D$ from $B$ correct to the nearest $0.1^\circ$.

In the figure, $AC=3AB$. Find $AB$ correct to 3 significant figures.

In the figure, $ABC$ and $AFED$ are straight lines. $\angle ABF=\angle CDE$ and $BE/\!/CD$. Which of the following triangles are similar? I. $\triangle ABF$ II. $\triangle AEB$ III. $\triangle ADC$

In the figure, $ABCDEFGH$ is a regular octagon. $x+y+z=$

In the figure, $O$ is the centre of the semicircle $ABCD$ and $BC/\!/AD$. If $\angle COD=42^\circ$, then $x=$

In the figure, $\widehat{AED}=1$ and $\widehat{CFD}=4$. If $\angle ABC=100^\circ$, then $\angle ABD=$

If the length of the line segment joining the points $(2,3)$ and $(k,\ 1-k)$ is $4$, then $k=$