2007 年

Find the equation of the straight line which is perpendicular to the straight line $x+2y+3=0$ and passes through the point $(1,3)$.

The figure shows the graph of the straight line $ax+by+1=0$. Which of the following is true?

Two numbers are randomly drawn at the same time from five cards numbered $1$, $2$, $3$, $4$ and $5$ respectively. Find the probability that the sum of the numbers drawn is a multiple of $3$.

If the mode of the seven numbers $8$, $7$, $1$, $3$, $7$, $a$ and $b$ is $8$, then the median of the seven numbers is

In the figure, $B_X$ and $B_Y$ are the box-and-whisker diagrams for the distributions $X$ and $Y$ respectively. Let $\mu_1$, $q_1$ and $r_1$ be the mean, the interquartile range and the range of $X$ respectively while $\mu_2$, $q_2$ and $r_2$ be the mean, the interquartile range and the range of $Y$ respectively. Which of the following must be true? I. $\mu_1<\mu_2$ II. $q_1<q_2$ III. $r_1<r_2$

The stem-and-leaf diagram below shows the distribution of the weights (in kg) of some students.

Which of the following frequency curves may represent the distribution of their weights?

If $a>0$, then $\dfrac{3\sqrt{a}}{2}-\dfrac{a}{\sqrt{4a}}=$

Which of the following may represent the graph of $y=f(x)$ and the graph of $y=f(x+1)$ on the same rectangular coordinate system?

Which of the following is the greatest?

Let $f(x)$ be a polynomial. If $f(x)$ is divisible by $x-1$, which of the following must be a factor of $f(2x+1)$?