1．解析：，故选A。

2．解析：抽取回族学生人数是，故选B。

3．解析：由，得，此时，所以，，故选C。

4．解析：∵∥，∴，∴，故选C。

5．解析：设公差为，由题意得，；，解得或，故选C。

6．解析：∵双曲线的右焦点到一条渐近线的距离等于焦距的，∴，又∵，∴，∴双曲线的渐近线方程是,故选D.

7.解析：∵、为正实数，∴，∴；由均值不等式得恒成立，，故②不恒成立，又因为函数在是增函数，∴，故恒成立的不等式是①③④。故选C.

8．解析：∵，∴在区间上恒成立，即在区间上恒成立，∴，故选D。

9．解析：∵

，∴此函数的最小正周期是，故选C。

10．解析：如图，∵正三角形的边长为，∴，∴，又∵，∴，故选D。

11．解析：∵在区间上是增函数且，∴其反函数在区间上是增函数，∴，故选A

12．解析：如图，①当或时，圆面被分成2块，涂色方法有20种；②当或时，圆面被分成3块，涂色方法有60种；

③当时，圆面被分成4块，涂色方法有120种，所以m的取值范围是，故选A。

13．解析：将代入结果为，∴时，表示直线右侧区域，反之，若表示直线右侧区域，则，∴是充分不必要条件。

14.解析：∵，∴时，，又时，满足上式，因此，。

15．解析：设正四面体的棱长为，连，取的中点，连，∵为的中点，∴∥，∴或其补角为与所成角，∵，，∴，∴，又∵，∴，∴与所成角的余弦值为。

16．解析：∵，∴，∵点为的准线与轴的交点，由向量的加法法则及抛物线的对称性可知，点为抛物线上关于轴对称的两点且做出图形如右图，其中为点到准线的距离，四边形为菱形，∴，∴，∴，∴，∴，∴向量与的夹角为。

17．(10分)解析：（Ⅰ）由正弦定理得，，，…2分

∴，，………4分

（Ⅱ）∵，，∴，∴，………………………6分

又∵，∴，∴，………………………8分

∴。………………………10分

18.解析：（Ⅰ）∵，∴；……………………理3文4分

（Ⅱ）∵三科会考不合格的概率均为，∴学生甲不能拿到高中毕业证的概率；……………………理6文8分

（Ⅲ）∵每科得A，B的概率分别为，∴学生甲被评为三好学生的概率为。……………………12分

19．(12分)解析：（Ⅰ）∵，∴，

 ，，……………3分

（Ⅱ）∵，∴，

∴，

又，∴数列自第2项起是公比为的等比数列，………………………6分

∴，………………………8分

（Ⅲ）∵，∴，………………10分

∴。………………………12分

20．解析：（Ⅰ）∵∥，，∴，∵底面，∴，∴平面，∴，又∵平面，∴，∴平面，∴。………………………4分

（Ⅱ）∵平面，∴，，∴为二面角的平面角，………………………6分

，，∴，又∵平面，，∴，∴二面角的正切值的大小为。………………………8分

（Ⅲ）过点做∥，交于点，∵平面，∴为在平面内的射影，∴为与平面所成的角，………………………10分

∵，∴，又∵∥，∴和与平面所成的角相等，∴与平面所成角的正切值为。………………………12分

解法2：如图建立空间直角坐标系，（Ⅰ）∵，，∴点的坐标分别是，，，∴，，设，∵平面，∴，∴，取，∴，∴。………………………4分

（Ⅱ）设二面角的大小为，∵平面的法向量是，平面的法向量是，∴，∴，∴二面角的正切值的大小为。………………………8分

（Ⅲ）设与平面所成角的大小为，∵平面的法向量是，，∴，∴，∴与平面所成角的正切值为。………………………12分

21.解析：（Ⅰ）设抛物线方程为，将代入方程得

所以抛物线方程为。………………………2分

由题意知椭圆的焦点为、。

设椭圆的方程为，

∵过点，∴，解得，，，

∴椭圆的方程为。………………………5分

（Ⅱ）设的中点为，的方程为：，

以为直径的圆交于两点，中点为。

设，则

∵  

………………………8分

∴

………………………10分

当时，，，

此时，直线的方程为。………………………12分

22．(12分)解析：（Ⅰ）∵是偶函数，∴，

又∵∴，，………………………2分

由得，，

∵时，；时，；时，；∴时，函数

根据短文内容，从下框的A---F选项中选出能概括每一段主题的最佳选项。选项中有一项为多余项。
Bill，Emy，Ben，Brigitte和Susan五个人想购买杂志。阅读下面六本杂志(A、B、C、D、E和F ) 的介绍，选出符合各人需要的最佳选项。选项中有一项是多余选项。
注意： 该题要求做在答题卡上。选择E，则涂黑A+B, 选择F，则涂黑A+C
【小题1】Bill travels a lot when he was younger．Now that he has stopped his work，he enjoys reading about foreign people，places and customs even if he has already visited that part of the world．
【小题2】 
Emy is a university student studying Italian and Politics．She doesn’t have much time to read anything very detailed but she is looking for something with plenty of news and information．
【小题3】Ben serves as an assistant to the general manager of an American company in Los Angeles．He is very interested in management and the use of high technology．
【小题4】
Up till now Brigitte has never traveled far so this year she has decided to go abroad for the first time．The travel agent suggests that she should read about various countries first before choosing her holiday．
【小题5】Susan likes shopping．She is interested in buying clothes and she needs to be offered advice on clothes．

A．Discover News magazine of science devoted to the wonders and stories of modem science，written for the educated general reader．Published by Disney Magazine Publishing CO．，Discover tells many of the same stories professionals read in Scientific American．A truly delightful family science magazine，each issue brings to light new and newsworthy topics to make dinnertime and water-cooler conversations interesting．

B．World Travel This weekly magazine can bring the world to your home．Have you ever wondered what the Chinese eat for breakfast? Did you know that the Sahara Desert is getting bigger every year? This fascinating magazine，full of color photographs，is your window to the world．

C．Self Published by Conde Nast Publications Inc．，Self is a handbook devoted to women’s overall physical and mental health．Every issue contains usable articles such as “Style Lab”．in which wearable clothes are mixed and matched on non—models and the “Eat—Right Road Map”．with tips on how to eat properly．

D．Foreign Parts

The weekly magazine tells what you need to know if you’re thinking of traveling．Helpful advice on what to pack and what to buy once you’re there．Lots of color photos to help you choose the best hotel, the cheapest flights and a special guide to different climates each week．
E．Wired
This magazine is designed for leaders in the field of information engineering including top managers and professionals in the computer，business，design and education industries．Published by Conde Nast Publications Inc，Wired often carries articles on how technology changes people’s lives．
F．Europe News
The weekly magazine keeps you in touch with what’s happening．Filled with facts and figures about almost everything you can think of, plus articles by our regular writers on the week’s most interesting news stories．Special back page sums up the news for the busy readers．

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