问题 选择题
对于函数y=f(x),有下 * * 个命题:
①若y=f(x)存在反函数,且与反函数图象有公共点,则公共点一定在直线y=x上;
②若y=f(x)在R上有定义,则y=f(|x|)一定是偶函数;
③若y=f(x)是偶函数,且f(x)=0有解,则解的个数一定是偶数;
④若T(T≠0)是函数y=f(x)的周期,则nT(n∈N),也是函数y=f(x)的周期;
⑤f(0)=0是函数y=f(x)为奇函数的充分也不必要条件.
从中任意抽取一个,恰好是真命题的概率为(  )
A.
1
5
B.
2
5
C.
3
5
D.
4
5
答案

①若y=f(x)存在反函数,且与反函数图象有公共点,则公共点不一定在直线y=x上,如函数f(x)=

1
x
,反函数是其本身,公共点是整个函数图象;

②若y=f(x)在R上有定义,则y=f(|x|)一定是偶函数,因f(|-x|)=f(|x|)对于任意x恒成立,故正确;

③若y=f(x)是偶函数,且f(x)=0有解,则解的个数一定是偶数不正确,如y=x2,是偶函数,x2=0的解只有一个,不是偶数个;

④若T(T≠0)是函数y=f(x)的周期,则f(x+T)=f(x),从而f(x+nT)=f(x),则nT(n∈N),也是函数y=f(x)的周期;

⑤f(0)=0是函数y=f(x)为奇函数的充分也不必要条件,不正确,f(x)=x2时,f(0)=0,而f(x)=x2是偶函数.

故正确的命题有2个,

则从中任意抽取一个,恰好是真命题的概率为

2
5

故选B.

阅读理解

Boys at the top of the pecking order(长幼次序) either by birth or because their older brothers died score higher on IQ tests than their younger brothers. 

Norwegian researchers now report that it’s a matter of what they call social rank in the family that gives the first born the highest scores or, if the first born had died young, the next oldest. 

Kristensen and Bjerkedal studied the IQ test results of 241,310 Norwegian men drafted(征兵) into the armed forces between 1967 and 1976. All were aged 18 or 19 at the time. 

The average IQ of first-born men was 103.2, they found second-born men averaged 101.2, but second-born men whose older brother died young scored 102.9. And for third-borns, the average was 100.0. But if both older brothers died young,the third-born score rose to 102.6.

The findings provide “evidence that the relation between birth order and IQ score is dependent on the social rank in the family and not birth order as such.” they concluded.

It’s an issue that has been hotly discussed since at least 1874,when Sir Francis Galton reported that men in noticeable positions tended to be firstborns more often than would have been statistically (统计) expected.

Since then, several studies have reported higher intelligence scores for firstborns, while other analyses have questioned those findings and the methods of those reports.

“These two researchers prove that how study participants(参与者) were raised, not how they were born, is what actually influences their IQs,” said Sulloway, an American professor, who was not part of the research team.

“The elder child pulls ahead,” he said, “perhaps as a result of learning gained through the process of tutoring younger brothers and sisters”. 

“The older child benefits by having to organize and express its thoughts to tutor youngsters”, he said, “while the later born children may have no one to tutor.”

小题1:According to Norwegain researchers’ finding, which of the following is linked to boys’ IQ?

A.Birth order

B.Position in the family

C.Parents’ social rank

D.Educational experience小题2:What does the sentence “It’s an issue that has been hotly discussed” underlined in Paragraph 6 mean?

A.Many people take interest in IQ study.

B.IQ study has gone further and further.

C.Many people do research on boys’ IQ.

D.Opinions are divided on the conclusion.小题3:According to Kristensen and Bjerkedal’s test results, parents can make youngsters smarter by ________.

A.treating them as the oldest child

B.teaching them as the oldest child

C.talking to them as much as possible

D.encouraging them to express thoughts

不定项选择