1991 年

In the figure, $O$ is the centre of the circle $BCD$. $ABC$ and $EDC$ are straight lines, $BC=DC$ and $\angle AED=70^\circ$. Find $\angle BOD$.

In the figure, $ABCDE$ and $ABXYZ$ are two identical regular pentagons. Find $\angle AEZ$.

In the figure, $TPA$ and $TQB$ are tangents to the circle at $P$ and $Q$ respectively. If $PQ=PR$, which of the following must be true?

I. $\angle APR=\angle QRP$ II. $\angle QTP=\angle QPR$ III. $\angle QPR=\angle APR$

In the figure, $E$ and $F$ are the mid-points of $AB$ and $AC$ respectively. $G$ and $H$ divide $DB$ and $DC$ respectively in the ratio $1:3$. If $EF=12$, find $GH$.

The circle $x^2+y^2+4x+ky+4=0$ passes through the point $(1,3)$. The radius of the circle is

Let $A$ and $B$ be the points $(4,-7)$ and $(-6,5)$ respectively. The equation of the line passing through the mid-point of $AB$ and perpendicular to $3x-4y+14=0$ is

$PQRS$ is a parallelogram with vertices $P=(0,0)$, $Q=(a,b)$ and $S=(-b,a)$. Find $R$.

In the figure, $A$ and $B$ are the positions of two boats. The bearing of $B$ from $A$ is

The mean and standard deviation of a distribution of test scores are $m$ and $s$ respectively. If $4$ marks are added to each score of the distribution, what are the mean and standard deviation of the new distribution?

The graph shows the frequency curves of two symmetric distributions $P$ and $Q$. Which of the following is/are true?

I. The mean of $P<$ the mean of $Q$. II. The mode of $P>$ the mode of $Q$. III. The inter-quartile range of $P<$ the inter-quartile range of $Q$.