1986 年

In the figure, $ABC$, $ACD$, $ADE$ and $AEF$ are right angled isosceles triangles. If $AB=BC=1$, how long is $AF$?

In the figure, $A$, $B$, $C$, $D$ and $E$ lie on a circle. $AC$ intersects $BE$ at $K$. $\angle ACD=100^\circ$ and $\angle CDE=130^\circ$. If $BE\parallel CD$, then $\angle ACB=$

In a shooting game, the probabilities for John and Mary to hit a target are $\dfrac{4}{5}$ and $\dfrac{3}{5}$ respectively. When both shoot at the target, what is the probability that they both miss?

Given two groups of numbers $a+1,\ a+2,\ a+3$ and $b+1,\ b+2,\ b+3$, where $a>b$. $m_1$ and $m_2$ are respectively the means of the two groups, and $s_1$ and $s_2$ are respectively their standard deviations. Which of the following is true?

The figure shows the frequency curve of a certain distribution. Which of the following can be the distribution's cumulative frequency curve?

If $(10^x)^y=(2^z)(5^z)$, then which of the following must be true?

$\left(\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}}\right)^2=$

The L.C.M. of $12a^2b$ and $18ab^3c$ is

Let $p=2x+3y$. Under the following constraints $x\ge0$ $y\ge0$ $x\le4$ $y\le3$ $x+y\le6$ what is the greatest value of $p$?

If $\log x^2+\log y^2=\log z^2$, where $x$, $y$ and $z$ are positive numbers, which of the following must be true? I. $x^2+y^2=z^2$. II. $\log x+\log y=\log z$ III. $x^2y^2=z^2$