第二节　听取信息(共5小题；每小题1分，满分5分)

第一节　 听力理解(共15小题；每小题2分，满分30分)

每段播放两遍。各段后有几个小题，各段播放前每小题有5秒钟的阅题时间。请根据各段播放内容及其相关小题，在5秒钟内从题中所给的ABC项中，选出最佳选项，并在该答题卡上将该项涂黑。

听下面一段对话，回答第1~3三个小题。

1．Where does the talk take place?

A．At a radio station.

B．At a concert.C．At a Music Club.

2．What does the woman think of her experience in America?

A．It is boring.

B．It is relaxing.

C．It is crazy.

3．Why will the woman go back to America next year?

A．To give more shows.

B．To meet local fans.

C．To record some songs.

听下面一段对话，回答第4~6三个小题。

4．What does the man think of the woman’s new hairstyle?

A．It is very nice.

B．It doesn’t look good.

C．It is the same as his.

5．What did the woman want to do with her hair at first?

A．Wash it .

B．Grow it.

C．Oil it.

6．What do we know about the man?

A．He has a new hairstyle.

B．He wants a hair cut.

C．He has no hair.

　　 听下面一段独白，回答第7~9三个小题。

7．What is giving the girl the most trouble?

A．Homework from teachers.

B．Pressure from friends.

C．Speaking in front of others.

8．How did the girl’s mother try to help her?

A．She bought a book for the girl.

B．She suggested the girl practice in front of her.

C．She asked the girl to think about Fruit and vegetables.

9．Which word best describes the girl?

A．Friendly.

B．Angry.

C．Nervous.

听下面一段对话，回答第10~12三个小题。

10．Where will the boy stay during summer?

A．At his mother’s home.

B．At his grandparents’ house.

C．At his friend’s place.

11．How does the boy usually spend most of his time there?

A．Swimming in the sea.

B．Playing with the neighbours’ kids.

C．Staying in his room.

12．What is the talk mainly about?

A．School exams.

B．Summer fun.

C．Unhappy relationships.

　　 听下面一段独白，回答第13~15三个小题。

13．Who is the speaker?

A．A teacher.

B．A theatre manager.

C．A customer.

14．Why will the listeners visit the theatre?

A．To watch a film.

B．To practice their English.

C．To prepare a report.

15．How does the speaker want the listeners to work?

A．Alone.

B．With a partner.

C．With the secretary.

22.(本小题满分12分)

已知圆C:问是否存在斜率为1的直线,使得被圆C截得的弦AB为直径的圆经过原点,若存在,写出直线的方程;若不存在,说明理由. (若存在写出直线的一般式)

21. (本题满分12分)

已知数列是等差数列， ；数列的前n项和是，且．

(Ⅰ) 求数列的通项公式；　

(Ⅱ) 求证：数列是等比数列；

20. 已知点在圆上运动.

(1)求的最大值与最小值；

(2)求的最大值与最小值.

19.(12分)如图： PA⊥平面ABCD，ABCD是矩形,PA=AB=1，

AD=，点F是PB的中点，点E在边BC上移动.

(Ⅰ)求三棱锥E-PAD的体积;

(Ⅱ)当点E为BC的中点时，

试判断EF与平面PAC的位置关系，并说明理由；

(Ⅲ)证明：无论点E在边BC的何处，都有PE⊥AF.

18. (本小题满分12分) 已知函数.

(1)求的值域和最小正周期；

(2)设，且，求的值。

17. (本小题满分10分)已知两条直线与的交点，

分别求满足下列条件的直线方程　

(1)过点且过原点的直线方程；

　 　　(2)过点且垂直于直线的直线的方程。

16．函数的部分图象如图所示，

则=　　　　　 ．

15．某公司一年购某种货物400吨，每次都购买x吨，运费为4万元／次，

一年的总存储费用为4x万元，要使一年的总运费与总存储费用之和最小，

则x为　　 　　　吨。