2010 年

If $a$ and $b$ are real numbers such that $ab>0$, which of the following must be true? I. $\dfrac{a}{b}>0$ II. $a+b>0$ III. $a^2+b^2>0$

Which of the following may represent the $n$th term of the sequence $0,\ \dfrac{-1}{4},\ \dfrac{2}{5},\ \dfrac{-3}{6},\ \dfrac{4}{7},\ \dots$ ?

If the price of a magazine is $60\%$ higher than the price of a newspaper, then the price of the newspaper is

A sum of $\$40\,000$ is deposited at an interest rate of $4\%$ per annum for $3$ years, compounded quarterly. Find the amount correct to the nearest dollar.

If tea of brand $A$ costs $\$80/\text{kg}$ and tea of brand $B$ costs $\$40/\text{kg}$, then a mixture of $4\ \text{kg}$ of tea of brand $A$ and $6\ \text{kg}$ of tea of brand $B$ costs

It is given that $z$ varies directly as $x$ and directly as $y^2$. If $x$ is decreased by $20\%$ and $y$ is increased by $15\%$, then $z$

If the length and the breadth of a rectangle are measured as $12\ \text{cm}$ and $10\ \text{cm}$ respectively and all the measurements are correct to the nearest cm, then the least possible area of the rectangle is

The volume of a right circular cylinder of radius $R$ is twice the volume of another right circular cylinder of radius $r$. If the heights of these two circular cylinders are the same, then $R:r=$

In the figure, the total surface area of the solid right prism is

In the figure, $ABCD$ is a semicircle of diameter $26\ \text{cm}$. It is given that $CDEF$ is a rectangle such that $E$ and $F$ are points lying on $AB$. If $AE=1\ \text{cm}$, find the area of the rectangle $CDEF$.