第一节　 听力理解(5段共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A、B、C项中，选出最佳选项，并在答题卡上将该项涂黑。

听第1段对话，回答第1-3题。

1．What does the woman say about the house?

A．It is located in the city centre.

B．The transportation is convenient.

C．Parking around it is a problem for her.

2．What does the man think of the bathroom?

A．It is made full use of.

B．It looks very popular.

C．It is in good condition.

3．Why does the man come to the woman’s house?

A．Because he will rent it.

B．Because he plans to buy it.

C．Because he wants to help her rent it out.

听第2段对话，回答第4-6题。

4．What do we know about the man?

A．He has a full-time job.

B．He lives in his parents’ house.

C．He and his wife earn less than $5,000 a year.

5．What advice does the woman give the man?

A．He should include his parents’ income.

B．He should go to her office and fill out forms.

C．He should give her his information in more detail.

6．What day is it today?

A．Thursday.　　　　　 B．Friday.　　　　　　 C．Saturday.

听第3段对话，回答第7-9题。

7．How many objects will the woman choose for an academic year?

A．Four.　　　　　　　 B．Eight.　　　　　　 C．Twelve.

8．What does the woman think of completing the registration form?

A．It will be a time-consuming work.

B．It is unnecessary to complete it by hand.

C．There seems to be something wrong with it.

9．What does the man advise the woman to do with the registration form?

A．Go back home to finish it.

B．Fill it out online in the computer lab.

C．Go to the teaching building and ask for more information.

听第4段对话，回答第10-12题。

10．Where does the conversation probably take place?

A．In a garage.　　　　　 B．In a shop.　　　　　　 C．In a restaurant.

11．What advice does the man give the woman about fixing her car?

A．She should get familiar with her car.

B．She should avoid being overcharged.

C．She should look for a person she can trust.

12．What does the woman say about the mechanic?

A．He has fixed her car before.

B．He is one of her neighbours.

C．He will drive her home today.

听第5段对话，回答第13-15题。

13．What is the probable relationship between the speakers?

A．Engaged couple.　　　　　 B．Mother and son.　　　　 C．Wife and husband.

14．Why do people want to protect their money and property according to the man?

A．Because marriages don’t last long nowadays.

B．Because they don’t believe each other at all.

C．Because they don’t plan on being together forever.

15．What can we learn from the conversation?

A．The man wants to protect his money.

B．The woman is thinking about a divorce.

C．The man wants to have many children.

20．(本小题共14分)已知函数().

　　 (1)若函数的图象在点处的切线的倾斜角为，求；

(2)若存在，使，求的取值范围.

19. (本小题满分14分)已知函数的图象上。

(1)求数列的通项公式；

(2)令求数列

　　 (3)令证明：。

18．(本小题满分14分)在直角坐标系中，以为圆心的圆与直线相切．

(Ⅰ)求圆的方程；

(Ⅱ)如果圆上存在两点关于直线对称,求的值.

(Ⅲ)已知、，圆内的动点满足，求的取值范围．

17．(本题满分12分)为了解某班学生喜爱打篮球是否与性别有关，对本班50人进行了问卷调查得到了如下的列联表：

已知在全部50人中随机抽取1人抽到喜爱打篮球的学生的概率为。

(1)请将上面的列联表补充完整；

(2)是否有99.5%的把握认为喜爱打篮球与性别有关？说明你的理由；

(3)已知喜爱打篮球的10位女生中，还喜欢打羽毛球，还喜欢打乒乓球，还喜欢踢足球，现再从喜欢打羽毛球、喜欢打乒乓球、喜欢踢足球的女生中各选出1名进行其他方面的调查，求和不全被选中的概率．

下面的临界值表供参考：

	0.15	0.10	0.05	0.025	0.010	0.005	0.001
	2.072	2.706	3.841	5.024	6.635	7. 879	10.828

　(参考公式：，其中)

16．(本题满分14分)右图为一简单组合体，其底面ABCD为正方形，平面，

，且=2 .

(1)求四棱锥B－CEPD的体积；

(2)求证：平面．

15．(本题满分12分)已知复数,,且．

(1)若且，求的值；

(2)设＝，求的最小正周期和单调减区间．

14．随机抽取某中学甲、乙两个班各10名同学，测量他们的身高(单位：cm)获得身高数据的茎叶图如下图甲，在样本的20人中，记身高在，的人数依次为、、、．图乙是统计样本中身高在一定范围内的人数的算法流程图，由图甲可知甲、乙两班中平均身高较高的是　　　 班；图乙输出的　　　　　 ．(用数字作答)

　　　　　　　　　　　　　 图甲　　　　　　　　　　　　　　　　　 图乙

13．已知点M(1，0)是圆C:内的一点，那么过点M的最短弦所在的直线方程是　　　 。

12．复数的虚部是　　　　　　　　　 .