2004 年

Let $a_n$ be the $n$th term of an arithmetic sequence. If $a_1=10$ and $a_2=13$, then $a_{21}+a_{22}+\cdots+a_{30}=$

The marked price of a book is $20\%$ above the cost. If the book is sold at a $10\%$ discount on the marked price, then the percentage profit is

If $(a-b):(b-2a)=2:3$, then $a:b=$

A box contains two kinds of coins: $\$5$ and $\$2$. The ratio of the number of $\$5$ coins to the number of $\$2$ coins is $4:5$. If the total value of the coins is $\$90$, then the total number of coins in the box is

The scale of a map is $1:20\,000$. If two buildings are $3.8\text{ cm}$ apart on the map, then the actual distance between the two buildings is

It is known that $y$ varies partly as $x$ and partly as $\sqrt{x}$. When $x=1$, $y=4$ and when $x=4$, $y=10$. Find $y$ when $x=16$.

In the figure, $ABCD$ is a parallelogram and $E$ is a point on $AD$ such that $AE:ED=1:3$. If the area of $\triangle ABE$ is $3\text{ cm}^2$, then the area of the shaded region is

In the figure, $AD$ and $BC$ meet at $E$. If $CE:EB=3:1$, then area of $\triangle ABD$ : area of $\triangle CDE=$

If the area of a regular 10-sided polygon is $123\text{ cm}^2$, find the length of the side of the 10-sided polygon. Give the answer correct to the nearest $0.1\text{ cm}$.

For $0^\circ\le x\le 90^\circ$, the least value of $\dfrac{4}{2-\cos x}$ is