1989 年

In the figure, $ABCD$ is a square and $AE=BE$. $\dfrac{\text{Area of }AED}{\text{Area of }ABCD}=$

A right conical vessel placed on horizontal ground contains some water as shown in the figure. If $AD:DB=2:3$, then $\dfrac{\text{volume of empty space}}{\text{volume of water}}=$

If $A$ is greater than $B$ by $20\%$ and $B$ is smaller than $C$ by $30\%$, then

At the beginning of a year, a man borrows $\$1000$ from a bank at $5\%$ per annum, compounded yearly. He promises to repay $\$300$ at the end of each year. How much will he still owe the bank just after the second repayment?

The least value of $9\cos^2\theta-6\cos\theta+1$ is

$\dfrac{1}{\dfrac{1}{\cos\theta}-1}-\dfrac{1}{\dfrac{1}{\cos\theta}+1}=$

The figure shows the graph of $y=\cos 2x$, where $0\le x\le\pi$. The area of the rectangle $ABCD$ is

Given that $0^\circ\le\theta\le180^\circ$, how many roots has the equation $(\sin\theta+1)(\tan\theta+3)=0$?

In the figure, $AD\perp BC$. Find $\dfrac{x}{y}$.

Referring to the figure, find $y$.