2001 年

Ship $A$ is $8\text{ km}$ due north of a light house $L$ and ship $B$ is $6\text{ km}$ due east of $L$. Find the bearing of $B$ from $A$.

In the figure, $ABCD$ is a semicircle, $AB:BD=4:3$. Find $AB$ correct to the nearest $0.1\text{ cm}$.

If the straight lines $x-2y+5=0$ and $ax-y+1=0$ intersect at $(1,b)$, find $a$ and $b$.

In the figure, $A$, $B$ and $C$ are points on a rectangular coordinate plane. $AC$ and $BC$ are parallel to the $x$-axis and $y$-axis respectively. If the coordinates of $C$ are $(2,1)$ and the equation of the straight line $AB$ is $y=2x+3$, find the distance between $A$ and $B$.

Two cards are drawn randomly from five cards numbered $1,2,3,4$ and $4$ respectively. Find the probability that the sum of the two numbers drawn is even.

A bag contains $2$ black balls and $3$ white balls. A boy randomly draws balls from the bag one at a time (without replacement) until a white ball appears. Find the probability that he will make at least $2$ draws.

If $\log x^2=(\log x)^2$, then $x=$

If $a>b$, which of the following must be true? I. $-a<-b$ II. $a+b>b$ III. $a^2>b^2$

If $a$, $b$ are distinct real numbers and $\begin{cases}a^2+4a+1=0\\ b^2+4b+1=0\end{cases}$, find $a^2+b^2$.

Suppose the graph of $y=x^2-2x-3$ is given. In order to solve the quadratic equation $2x^2-6x-3=0$, which of the following straight lines should be added to the given graph?