1992 年

The mid-points of the sides of a triangle are $(3,4)$, $(2,0)$ and $(4,2)$. Which of the following points is a vertex of the triangle?

The table shows the mean marks of two classes of students in a mathematics test. | | Number of students | Mean mark | |---|---|---| | Class $A$ | 38 | 72 | | Class $B$ | 42 | 54 | A student in Class $A$ scored $91$ marks. It is found that his score was wrongly recorded as $19$ in the calculation of the mean mark for Class $A$ in the above table. Find the correct mean mark of the $80$ students in the two classes.

Two cards are drawn randomly from five cards $A$, $B$, $C$, $D$ and $E$. Find the probability that card $A$ is drawn while card $C$ is not.

The figure shows the cumulative frequency curves of three distributions. Arrange the three distributions in the order of their standard deviations, from the smallest to the largest.

If the quadratic equation $ax^2-2bx+c=0$ has two equal roots, which of the following is/are true? I. $a,b,c$ form an arithmetic sequence. II. $a,b,c$ form a geometric sequence. III. Both roots are $\dfrac{b}{a}$.

Which of the following intervals must contain a root of $2x^3-x^2-x-3=0$? I. $-1<x<1$ II. $0<x<2$ III. $1<x<3$

How many integers $x$ satisfy the inequality $6x^2-7x-20\le 0$?

From the figure, if $\alpha\le x\le\beta$, then

Under which of the following conditions must the mean of $n$ consecutive positive integers also be an integer?

The L.C.M. of $P$ and $Q$ is $12ab^3c^2$. The L.C.M. of $X$, $Y$ and $Z$ is $30a^2b^3c$. What is the L.C.M. of $P$, $Q$, $X$, $Y$ and $Z$?