1、绝密*启用前2012年普通高等学校招生全国统一考试理科数学注息事项: 1.本试卷分第卷（选择题）和第卷(非选择题)两部分。答卷前，考生务必将自己的姓名、准考证号填写在本试卷和答题卡相应位置上。 2.问答第卷时。选出每小题答案后，用铅笔把答题卡上对应题目的答案标号涂黑。如需改动.用橡皮擦干净后，再选涂其它答案标号。写在本试卷上无效.3.回答第卷时。将答案写在答题卡上.写在本试卷上无效4.考试结束后.将本试卷和答且卡一并交回。第一卷一 选择题：本大题共12小题，每小题5分，在每小题给同的四个选项中，只有一项是符合题目要求的。（1）已知集合；,则中所含元素的个数为（ ） 【解析】选 ，共10个（2）
2、将名教师，名学生分成个小组，分别安排到甲、乙两地参加社会实践活动，每个小组由名教师和名学生组成，不同的安排方案共有（ ）种 种 种 种【解析】选 甲地由名教师和名学生：种（3）下面是关于复数的四个命题：其中的真命题为（ ） 的共轭复数为 的虚部为 【解析】选 ，的共轭复数为，的虚部为（4）设是椭圆的左、右焦点，为直线上一点， 是底角为的等腰三角形，则的离心率为（ ） 【解析】选 是底角为的等腰三角形（5）已知为等比数列，则（ ） 【解析】选，或来源:Zxxk.Com（6）如果执行右边的程序框图，输入正整数和实数，输出，则（ ）为的和为的算术平均数和分别是中最大的数和最小的数和分别是中最小的数和
3、最大的数【解析】选来源:Zxxk.Com（7）如图，网格纸上小正方形的边长为，粗线画出的是某几何体的三视图，则此几何体的体积为（ ） 【解析】选 该几何体是三棱锥，底面是俯视图，高为 此几何体的体积为（8）等轴双曲线的中心在原点，焦点在轴上，与抛物线的准线交于两点，；则的实轴长为（ ） 【解析】选设交的准线于得：（9）已知，函数在上单调递减。则的取值范围是（ ） 【解析】选 不合题意 排除 合题意 排除来源:Zxxk.Com另：， 得：（10） 已知函数；则的图像大致为（ ）【解析】选 得：或均有 排除（11）已知三棱锥的所有顶点都在球的求面上，是边长为的正三角形，为球的直径，且；则此棱锥的体
4、积为（ ） 【解析】选 的外接圆的半径，点到面的距离 为球的直径点到面的距离为 此棱锥的体积为 另：排除（12）设点在曲线上，点在曲线上，则最小值为（ ） 【解析】选 函数与函数互为反函数，图象关于对称 函数上的点到直线的距离为 设函数 由图象关于对称得：最小值为第卷 本卷包括必考题和选考题两部分。第13题第21题为必考题，每个试题考生都必须作答，第22-第24题为选考题，考生根据要求做答。二填空题：本大题共4小题，每小题5分。（13）已知向量夹角为 ，且；则【解析】(14) 设满足约束条件：；则的取值范围为 【解析】的取值范围为 约束条件对应四边形边际及内的区域： 则（15）某个部件由三个元
5、件按下图方式连接而成，元件1或元件2正常工作，且元件3正常工作，则部件正常工作，设三个电子元件的使用寿命（单位：小时）均服从正态分布，且各个元件能否正常相互独立，那么该部件的使用寿命超过1000小时的概率为 新 课 标第 一网【解析】使用寿命超过1000小时的概率为 三个电子元件的使用寿命均服从正态分布得：三个电子元件的使用寿命超过1000小时的概率为超过1000小时时元件1或元件2正常工作的概率 那么该部件的使用寿命超过1000小时的概率为（16）数列满足，则的前项和为 【解析】的前项和为 可证明： 三、解答题：解答应写出文字说明，证明过程或演算步骤。 （17）（本小题满分12分）已知分别为
6、三个内角的对边，（1）求 （2）若，的面积为；求。【解析】（1）由正弦定理得： （2） 解得：（l fx lby）18.（本小题满分12分）新课 标 第 一网某花店每天以每枝元的价格从农场购进若干枝玫瑰花，然后以每枝元的价格出售，如果当天卖不完，剩下的玫瑰花作垃圾处理。（1）若花店一天购进枝玫瑰花，求当天的利润(单位：元)关于当天需求量（单位：枝，）的函数解析式。 （2）花店记录了100天玫瑰花的日需求量（单位：枝），整理得下表：以100天记录的各需求量的频率作为各需求量发生的概率。（i）若花店一天购进枝玫瑰花，表示当天的利润（单位：元），求的分布列，数学期望及方差；（ii）若花店计划一天购进
7、16枝或17枝玫瑰花，你认为应购进16枝还是17枝？请说明理由。【解析】（1）当时， 当时， 得： （2）（i）可取， 的分布列为 （ii）购进17枝时，当天的利润为 得：应购进17枝（19）（本小题满分12分）如图，直三棱柱中，是棱的中点，（1）证明：（2）求二面角的大小。来源:Z*xx*k.Com【解析】（1）在中， 得： 同理：来源:学科网 得：面 （2）面 取的中点，过点作于点，连接 ，面面面 得：点与点重合 且是二面角的平面角 设，则， 既二面角的大小为（20）（本小题满分12分）设抛物线的焦点为，准线为，已知以为圆心，为半径的圆交于两点；（1）若，的面积为；求的值及圆的方程；（2）
8、若三点在同一直线上，直线与平行，且与只有一个公共点，求坐标原点到距离的比值。【解析】（1）由对称性知：是等腰直角，斜边 点到准线的距离 圆的方程为 （2）由对称性设，则 点关于点对称得： 得：，直线 切点 直线坐标原点到距离的比值为。（lfx lby）（21）（本小题满分12分）已知函数满足满足；（1）求的解析式及单调区间；（2）若，求的最大值。【解析】（1） 令得： 得： 在上单调递增 得：的解析式为 且单调递增区间为，单调递减区间为 （2）得 当时，在上单调递增 时，与矛盾 当时， 得：当时， 令；则 当时， 当时，的最大值为请考生在第22,23,24题中任选一题做答，如果多做，则按所做的
9、第一题计分，做答时请写清题号。（22）（本小题满分10分）选修4-1：几何证明选讲如图，分别为边的中点，直线交的外接圆于两点，若，证明：（1）；（2）【解析】（1）， （2） （23）本小题满分10分)选修44；坐标系与参数方程已知曲线的参数方程是，以坐标原点为极点，轴的正半轴为极轴建立坐标系，曲线的坐标系方程是，正方形的顶点都在上，且依逆时针次序排列，点的极坐标为（1）求点的直角坐标；（2）设为上任意一点，求的取值范围。【解析】（1）点的极坐标为 点的直角坐标为 （2）设；则 （lfxlby）（24）（本小题满分10分）选修：不等式选讲已知函数（1）当时，求不等式的解集；（2）若的解集包含，
10、求的取值范围。【解析】（1）当时， x kb1. co m 或或 或 （2）原命题在上恒成立在上恒成立在上恒成立2012年6月8日15：00前 绝 密2012年普通高等学校招生全国统一考试英 语本试题卷分第I卷(选择题）和第II卷(非选择题)两部分。考生作答时，将答案答在答题卡上(答题注意事项见答题卡)，在本试题卷上答题无效。考试结束后，将本试题卷和答题卡一并交回。第I卷第一部分 听力(共两节，满分30分) 做题时，先将答案标在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。第一节(共5小题:每小题1.5分，满分7.5分）听下面5段对话。每段对话后有一个小题，从题中所给
11、的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题每段对话仅读一遍。例：How much is the shirt?A.19.15.B. 9.15C. 9.18答案是B。1. Where does this conversation probably take place?A. In a bookstore. B. In a classroom C. In a library.2. At what time will the film begin?A. 7:20. B. 7:15. C. 7:00.3. What are
12、the two speakers mainly talking about?A.Their friend Jane. B. A weekend trip. C. A radio programme.4. What will the woman probably do?A. Catch a train. B. See the man off. C. Go shopping.5. Why did the woman apologize?A. She made a late delivery.B. bne went to the wrong place.C. She couldnt take the
13、 cake back.第二节(共15小题:每小题1.5分，满分22.5分) 听下面5段对话。每段对话后有几个小题，从题中所给的A. B. C三个选项中选出最佳选项，并标在试卷的相应位置。听每段对话前，你将有时间阅读各个小题，每小题5秒钟;听完后，各小题给出5秒钟的作答时间。每段对话读两遍。听第6段材料，回答第6. 7题。6.Whose CD is broken?A. Kathys. B. Mums. C. Jacks.7.What does the boy promise to do for the girl?A. Buy her a new CD.B. Do some cleaning.C.
14、 Give her 10 dollars.听第7段材料，回答第8、9题。8. What did the man think of the meal?A. Just so-soB. Quite satisfactory.C. A bit disappointing.9. What was the 15% on the bill paid for?A. The food. B. The drinks. C. The service.听第8段材料，回答第10至12题。10. Why is the man at the shop?A. To order a camera for his wifeB.
15、To have a camera repairedC. To get a camera changed.11. What colour does the man want?A. Pink. B. Black. C. Orange.12. What will the man do afterwards?A. Make a phone call.B. Wait until further notice.C. Come again the next day.听第9段材料,回答第13至16题。13. What would Joe probably do during the Thanksgiving
16、holiday?A. Go to a play. B. Stay at home. C. Visit Kingston.14. What is Ariel going to do in Toronto?A. Attend a party. B. Meet her aunt. C. See a car show.15. Why is Ariel in a hurry to leave?A. To call up Betty.B. To buy some DVDs.C. To pick up Daniel.16. What might be the relationship between the
17、 speakers?A. Classmates .B. Fellow workers. C. Guide and tourist.听第10段材料，回答第17至20题。17. Where does Thomas Manning work?A. In the Guinness Company.B. At a radio station.C. In a museum.18. Where did the idea of a book of records come from?A. A bird-shooting trip.B. A visit to Europe.C. A television tal
18、k show.19. When did Sir Hughs first book of records appear?A. In 1875. B. In 1950. C. In 1955.20. What are the two speakers going to talk about next?A. More records of unusual facts.B. The founder of the company.C. The oldest person in the world.第二部分 英语知识运用 （共两节，满分45分）第一节 单项琪空(共15小题:每小题1分，满分15分)从A.
19、B. C. D四个选项中，选出可以填入空白处的最佳选硕，并在答题卡上将该项涂黑。例: It is generally considered unwise to give a child he or she wants.A. however B. whatever C. whichever D. whenever答案是B.21. - Which one of these do you want? -_.Either will do.A. I dont mind B. Im sure C. No problem D. Go ahead22. Sarah looked at finished pai
20、nting with satisfaction.A.不填; a B. a; the C. the;不填 D. the; a23. Life is like walking in the snow, Granny used to say, because every step A. has shown B. is showingC. shows D. showed24. It is by no means clear the president can do to end the strike.A. how B. which C.that D. what25. I dont believe we
21、ve met before, I must say you do look familiar.A. therefore B. althoughC. since D. unless26. The result is not very important to us, but if we do win, then so much A. the best B. bestC. better D. the better27. Mary is really good at taking notes in class. She can almost every word her teacher says.A
22、. put out B. put down C. put away D. put together28. The party will be held in the garden, weather A. permitting B. to permit C. permitted D. permit29. This restaurant wasnt that other restaurant we went to.A. half as good as B. as half good as C as good as half D. good as half as30.1 use a clock to
23、 wake me up because at six oclock each morning the train comes by my house. -A. couldnt B. mustnt C. shouldnt D. neednt31. Larry asks Bill and Peter to go on a picnic with him, but of them wants to,because they have work to do.-A. either B. any C. neither D none32. Film has a much shorter history, e
24、specially when such art forms as music and painting.A. having compared to B. comparing toC. compare to D. compared to33.1 had been working on math for the whole aftersoon and the numbers before my eyes.A. swim B. swum C. swam D. had swum34. You have to move out of the way the truck cannot get past y
25、ouA. so B.or C and D. but35. If she doesnt want to go, nothing you can say will her.A persuade B. promise C. invite D. support第二节 完形填空 （共20小题；每小题1.5分，满分30分）阅读下面短文，从短文后各题所给的四个选项(A, B, C和D)中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。Body language is the quiet, secret and most powerful language of all ！It speaks 36 t
26、han words. According to specialists, our bodies send out more 37 than we realize. In fact, non-verbal(非言语)communication takes up about 50% of what we really 38 .And body language is particularly _ 39 when we attempt to communicate across cultures. Indeed, what is called body language is so 40 a part
27、 of us that its actually often unnoticed. And misunderstandings occur as a result of it. 41 ，different societies treat the 42 between people differently. Northern Europeans usually do not like having 43 contact(接触)even with friends, and certainly not with 44 . People from Latin American countries, 4
28、5 ，touch each other quite a lot. Therefore, its possible that in 46 . It may look like a Latino is 47 a Norwegian all over the room. The Latino, trying to express friendship, will keep moving 48 .The Norwegian, very probably seeing this as pushiness, will keep 49 which the Latino will in return rega
29、rd as 50 .Clearly , a great deal is going on when people 51 . And only a part of it is in the words themselves. And when parties are from 52 cultures, theres a strong possibility of 53 .But whatever the situation, the best 54 is to obey the Golden Rule: treat others as you would like to be 55 36. A.
30、 straighter B. louder C. harder D. further37. A. sounds B. invitations C. feelings D. messages38. A. hope B. receive C. discover D. mean39. A. immediate B. misleading C. important D. difficult40. A. well B. far C. much D. long41. A. For example B. Thus C. However D. In short42. A. trade B. distance
31、C. connection D. greetings43. A. eye B. verbal C. bodily D. telephone44. A. strangers B. relatives C. neighbour D. enemies45. A. in other words B. on the other hand C. in a similar way D. by all means46. A. trouble B. conversation C. silence D. experiment47. A. disturbing B. helping C. guiding D. fo
32、llowing48. A. closer B. faster C. in D. away49. A. stepping forward B. going onC. backing away D. coming out50. A. weakness B. carelessness C. friendliness D. coldness51. A. talk B. travel C. laugh D. think52. A. different B. European C. Latino D. rich 53. A. curiosity B. excitement C. misunderstand
33、ing D. nervousness54. A. chance B. time C. result D. advice55. A. noticed B. treated C. respected D. pleased第三部分 阅读理解(共两节，满分40分)第一节(共15小题:每小题2分，满分30分) 阅读下列短文，从每题所给的四个选项(A. B. C和D)中，选出最佳选项，并在答题卡上将该项涂黑。AAre you looking for some new and exciting places to take your kids to? Try some ofthese places:Visi
34、t art museums. They offer a variety of activities to excite your kids interest. Many offer workshops for making hand-made pieces, traveling exhibits, book signings(签名) by childrens favorite writers, and even musical performances and other arts.Head to a natural history museum. This is where kids can
35、 discover the past from dinosaur models to rock collections and pictures of stars in the sky. Also, ask what kind of workshops and educational programs are prepared for kids and any special events that are coming up.Go to a Youtheater. Look for one in your area offering plays for child and family vi
36、sitors. Pre-show play shops are conducted by area artists and educators where kids can discover the secret about performing arts. Puppet (木偶) making and stage make-up are just a couple of the special offerings you might find. Try hands-on science. Visit one of the many hands-on science museums aroun
37、d the country. These science play-lands are great fun for kids and grown-ups alike. Theyll keep your child mentally and physically active the whole day through while pushing buttons, experimenting, and building. When everyone is tired, enjoy a fun family science show, commonly found in these museums.56. If a child is interested in the universe, he probably will visit .A. a YoutheaterB. an art museum -C. a natural history museumD. a hands-on science museum57. What can kids do at a Yout
