问题 填空题
给出下列命题:
①3≥3
x+
1
x
≥2(x∈R)

③“若x>3,则x2>9”的否命题
④“若a≤1,则方程ax2+2x+1=0至少有一个负根”的逆否命题.
则其中正确的命题序号是______.
答案

对于①,∵3=3成立,

∴3≥3成立.∴命题①正确;

对于②,x=0时不等式左边无意义,且当x<0时,x+

1
x
=-[-x+
1
-x
]≤-2,

∴命题②不正确;

对于③,命题“若x>3,则x2>9”的否命题为:“若x≤3,则x2≤9”.

-4≤3,但(-4)2=16>9,∴命题③的否命题为假命题;

对于④“若a≤1,则方程ax2+2x+1=0至少有一个负根”的逆否命题的正误判断如下:

当a=1时,方程ax2+2x+1=0有一个根-1,a=0时,方程ax2+2x+1=0有一个根-

1
2

当0<a<1时,△=4-4a>0,x1+x2=-

2
a
<0,方程ax2+2x+1=0至少有一个负根,

当a<0时,△=4-4a>0,x1x2=

1
a
<0,方程ax2+2x+1=0有一个负根,

∴命题④为真命题,则命题④的逆否命题为真命题.

∴正确命题的序号为①④.

故答案为:①④

阅读理解

In the past, when people had problems, they went to their families or friends to get advice. Today, it is possible to get advice from radio show, TV programmer and telephone hot lines, too. Most telephone hot lines are completely anonymous-callers, they do not have to say their names or telephone numbers. Most hot lines are usual free(免费的)too, even if the calls are long distance(距离).Other hot lines pay their advisers for their work. Usually the advisers are professional with years of education and experience, but sometimes, the advisers have only taken a short class before starting to work on the hot lines. All the advisers listen to people and help them solve their problems.

小题1:Today when people have problems, ____________________.

A.they can only ask their families for help

B.they can only get help from their friends

C.they can get help from telephone hot lines

D.they go to the advisers to get help小题2:The word “anonymous” probably means _____________________.

A.telling a name

B.without telling a name

C.free of charge

D.interesting小题3:Callers _____________ the hot line for the advice or the phone calls.

A.pay much

B.have to pay

C.don’t have to pay

D.get money from小题4:The advisers working at the hot line _______________.

A.are usually professionals

B.have all taken a short class

C.can solve any problem

D.are not all paid小题5:How do the hot line advisers work?

A.They do what the callers tell them to do

B.They go to the callers to help them

C.They give advice to the callers by phone.

D.They ask people to come to see him

单项选择题