问题 解答题

已知直线l:y=ax+b,其中实数a,b∈{-1,1,2}.

(Ⅰ)求可构成的不同的直线l的条数;

(Ⅱ)求直线l:y=ax+b与圆x2+y2=1没有公共点的概率.

答案

(Ⅰ)∵实数a,b∈{-1,1,2},直线l:y=ax+b,

∴可构成的不同的直线l的条数有:

a=-1,b=-1,1,2;a=1,b=-1,1,2;a=2,b=-1,1,2.

故可构成的不同的直线l的条数共9条.

(Ⅱ)直线l:y=ax+b与圆x2+y2=1没有公共点,

是指圆心(0,0)到直线ax-y+b=0的距离d=

|b|
a2+1
>圆的半径1,

|b|
a2+1
>1,即a2+1<b2

∵构成直线l:y=ax+b的(a,b)的值有(-1,-1),(-1,1),(-1,2),(1,-1),

(1,1),(1,2),(2,-1),(2,1),(2,2),

满足a2+1<b2的(a,b)的值有(-1,2),(1,2),

∴直线l:y=ax+b与圆x2+y2=1没有公共点的概率P=

2
9

单项选择题
完形填空
完形填空(20 分)
阅读下面短文,掌握其大意,然后从下列各题所给的A、B、C和D四个选项中,选出最佳选项。
Many people of my generation(代,一代) say that there is no hope for the future because of the way that 11  people behave today.
Their first argument(论点) is that when we were young we used to look after the  12  people in our community and help them. They also say that young people today don’t  13  about anything or anyone. However, I think the reason why we looked after older people was that we had no 14  . People had to live with their  15  and grandparents because they had no money. Young people today earn more and have more  16   to live where they want.
Their second argument is that in our day we didn’t expect (盼望,期待)to be given jobs -----and that young people now don’t look for jobs, but just complain(抱怨) about  17   . On the other hand, things were easier in the past and it was always easy to get a job if you had friends and contacts(关系). It is really   18 today.
In conclusion I think there is hope for the  19  . This generation, like generations before them, has new  20  as well as old problems. If they learn from our mistakes the world will be a better place in future.
小题1:
A.youngB.oldC.otherD.our
小题2:
A.oldB.olderC.elderD.eldest
小题3:
A.knowB.careC.complainD.look
小题4:
A.moneyB.freedom C.choiceD.help
小题5:
A.friendsB.childrenC.grandchildrenD.parents
小题6:
A.freedomB.moneyC.reasonsD.hope
小题7:
A.futureB.wagesC.work D.unemployment(失业)
小题8:
A.easierB.harderC.impossibleD.possible
小题9:
A.youngB.oldC.futureD.generation
小题10:
A.opportunitiesB.hopes C.futureD.world