2008 年

In the figure, the 1st pattern consists of $10$ dots. For any positive integer $n$, the $(n+1)$th pattern is formed by adding $(2n+5)$ dots to the $n$th pattern. Find the number of dots in the 7th pattern.

The marked price of a bag is $\$900$. If the bag is sold at the marked price, then the percentage profit is $50\%$. If the bag is sold at a $20\%$ discount on the marked price, then the profit is

The costs of rice of brand $A$ and rice of brand $B$ are $\$8/\mathrm{kg}$ and $\$4/\mathrm{kg}$ respectively. If $x\ \mathrm{kg}$ of rice of brand $A$ and $y\ \mathrm{kg}$ of rice of brand $B$ are mixed so that the cost of the mixture is $\$5/\mathrm{kg}$, find $x:y$.

Suppose that $y$ varies directly as $x$ and inversely as $z^2$. If $x$ and $z$ are both decreased by $20\%$, then $y$

It is known that $\mathrm{f}(x)$ varies partly as $x$ and partly as $x^2$. If $\mathrm{f}(1)=5$ and $\mathrm{f}(2)=16$, then $\mathrm{f}(3)=$

If the radius of a sphere is measured as $8\text{ cm}$ correct to the nearest cm, then the least possible surface area of the sphere is

$0.0498765=$

The figure shows a solid right circular cone of height $12\text{ cm}$. The circumference of the base is $18\pi\text{ cm}$. Find the total surface area of the circular cone.

In the figure, the volume of the right prism is

In the figure, $OAB$ and $OCD$ are sectors with centre $O$. It is given that the area of the shaded region $ABDC$ is $54\pi\text{ cm}^2$. If $AC=6\text{ cm}$, then $OA=$