1995 年

In a shooting game, the probability that A will hit a target is $\dfrac35$ and the probability that B will hit it is $\dfrac23$. If each fires once, what is the probability that they will both miss the target ?

The figure shows that Mr. Chan has 3 ways to leave town X and Mr. Lee has 2 ways to leave town Y. Mr. Chan and Mr. Lee leave town X and town Y respectively at the same time. If they select their ways randomly, find the probability that they will meet on their way.

The mean of a set of 9 numbers is 12. If the mean of the first 5 numbers is 8, the mean of the other four numbers is

The figure shows the frequency curves of two symmetric distributions $A$ and $B$. Which of the following is/are true ? I. The mean of $A$ = the mean of $B$. II. The inter-quartile range of $A$ > the inter-quartile range of $B$. III. The standard deviation of $A$ > the standard deviation of $B$.

If $\mathrm{f}(x)=\dfrac{x}{1-x}$, then $\mathrm{f}\!\left(\dfrac1x\right)\mathrm{f}(-x)=$

Factorize $2a^{n+1}-7a^n-30a^{n-1}$.

Simplify $\dfrac{\left(\dfrac yx-1\right)\left(1-\dfrac xy\right)}{\dfrac xy-\dfrac yx}$.

If $5^a=2^b=10^c$ and $a,b,c$ are non-zero, then $\dfrac ca+\dfrac cb=$

If $\alpha,\beta$ are the roots of the equation $x^2-4x-3=0$, then $\alpha^2+\alpha\beta+\beta^2=$

Find the range of values of $k$ such that the equation $x^2+(k-2)x+1=0$ has real roots.