问题 解答题

命题p:关于x的不等式x2+(a-1)x+a2≤0的解集为φ,命题q:函数y=(2a2-a)x为增函数,若p或q为真,p且q为假,求实数a的取值范围.

答案

命题p为真时,△=(a-1)2-4a2<0,即a<-1或a>

1
3

命题q为真时,2a2-a>1,解得 a<-

1
2
,或 a>1.

∵p或q为真,p且q为假,∴p和q一真一假.

当p真q假时,则

a<-1 或a>
1
3
-
1
2
≤ a ≤ 1
,即
1
3
<a ≤1

当p假q真时,则

-1≤a≤
1
3
a<-
1
2
或a> 1
,-1≤a<-
1
2

综上所述:实数a的取值范围为 {a|

1
3
<a≤1 或-1≤a <-
1
2
}.

阅读理解

阅读理解。

     Ron is ten years old. He loves to watch TV. But for one full year he did not watch TV at all. What was

the reason? Ron's parents said they would give him $ 600 if he didn't watch TV for a year.

     Ron's parents thought he watched too much TV. One day his mother saw a news- paper story about a

boy who didn't watch TV for a year. She showed the story to Ron. Ron liked the idea. He turned off the

TV right away, and said, "It doesn't bother me not to watch TV. I just want the money."

     At first, Ron's parents were very happy. Ron read books and newspapers, played outside, played

computer games, and played cards with his mother. But after some time, he got bored. Every morning,

he asked his parents,"What are we doing tonight?" Sometimes his mother and father wished he would

watch TV just for one evening. Ron always said, "No, it would cost me money!"

      Finally the year was over. Then Ron started watching his favourite TV shows all day long again. Ron

got the money from his parents. What does he plan to do with the $ 600? "I want to buy myself a TV set!"

he said.

1. Ron didn't watch TV for one year because _____. [ ]

A. he wanted the money

B. watching TV too much is bad

C. he wanted to study harder

D. he wanted to learn from the boy

2. "It doesn't bother me not to watch TV" means "It's _____ to watch TV". [ ]

A. waste time

B. important for me

C. not use

D. not important for me

3. The best title for the story is _____. [ ]

A. A Funny Story

B. A Year without TV

C. A Good Boy

D. Buying a TV Set

选择题