上海市崇明中学2010届高三第一次月考试卷

嘉定区2010学年高三年级第一次质量调研数学试卷（文）参考答案与评分标准一．填空题（本大题满分56分）本大题共有14题，考生必须在答题纸相应编号的空格内直接填写结果，每个空格填对得4分，否则一律得零分．1．答案：1．因i a a ai i )1(1)1)(1(-++=-+是实数，所以=a 1．2．答案：]2,0[．由022≥-x x ，得022≤-x x ，所以]2,0[∈x ．3．答案：1．112+=a a ，314+=a a ，由已知得4122a a a =，即)3()1(1121+=+a a a ，解得11=a ． 4．答案：257-． 由532sin =⎪⎭⎫ ⎝⎛+θπ，得53cos =θ，所以2571cos 22cos 2-=-=θθ． 5．答案：2-． 解法一：函数x x f -=)(的反函数为21)(x x f =-（0≤x ），由4)(1=-x f 得42=x ，因为0<x ，故2-=x ．解法二：由4)(1=-x f ，得2)4(-==f x ． 6．答案：5arctan ．因为BC ∥AD ，所以BC D 1∠就是异面直线1BD 与AD 所成的角，连结C D 1，在直角三角形BC D 1中，0190=∠BCD ，1=BC ，51=C D ，所以5tan 11==∠BCC D BC D ． 7．答案：3π（或060）． 设a 与b 的夹角为θ，由2)(=+⋅b a a ，得22=⋅+b a a ，即2cos 21=+θ，21cos =θ． 8．答案：2．9)21(x -展开式的第3项为288)2(2293=-=x C T ，解得23=x ， 所以232132132lim 323232lim 111lim 22=-⎥⎥⎦⎤⎢⎢⎣⎡⎪⎭⎫ ⎝⎛-=⎥⎥⎦⎤⎢⎢⎣⎡⎪⎭⎫ ⎝⎛++⎪⎭⎫ ⎝⎛+=⎪⎭⎫ ⎝⎛+++∞→∞→∞→n n n n n n x x x ． 9．答案：1．三阶行列式x a x 1214532+中元素3的余子式为x a x x f 21)(+=，由0)(<x f 得022<-+ax x ，由题意得a b -=+-1，所以1=+b a ．10．答案：16．1=a ，满足3≤a ，于是4211==+b ；2=a ，满足3≤a ，8212==+b ；3=a ，满足3≤a ，则16213==+b ；4=a ，不满足3≤a ，则输出b ，16=b ．11．答案：21． 21210105)(3101337===C C C A P ． 12．答案：32π． 由题意，61cos 2>θ且21sin 2>θ，⎩⎨⎧==+2cos 34ab b a θ，⎪⎪⎩⎪⎪⎨⎧=⋅-=+2111sin 211a b a b θ， 所以θθsin 2cos 32-=，3tan -=θ，因⎪⎭⎫ ⎝⎛∈ππθ,2，32πθ=． 13．答案：1±．因为)(x f 是奇函数，所以0)()(=-+x f x f ，即0212212=⋅+-+⋅+---xxx x k k k k ， 0212212=+-⋅+⋅+-x x x x k k k k ，0)2)(21()12)(1(22=+⋅++-x x x k k k ，所以12=k ，1±=k ． 14．答案：100．])1[()1()1()1()1()1()(22221n n n n n f n f a n n n n -+-=+⋅-+⋅-=++=-， )12()1(+-=n n ，所以201)199(9)7(5)3(100321+-+++-++-=++++ a a a a 100502=⨯=．二．选择题（本大题满分20分）本大题共有4题，每题有且只有一个正确答案，考生必须在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分．15．C ．16．A ．17．D ．18．B ．15．因为A 、B 是三角形内角，所以A 、),0(π∈B ，在),0(π上，x y cos =是减函数．16．①错．不在同一直线上的三点才能确定一个平面；②错．四边相等的四边形也可以是空间四边形；③错．如果三棱锥的底面是等边三角形，一条侧棱垂直于底面且长度等于底面边长，则三个侧面都是等腰三角形；④错．若这两点是球的直径的两个端点，过这两点可作无数个大圆．17．作出函数x y 2=与2x y =，可发现两函数图像在第二象限有一个交点，在第一象限有两个交点（第一象限的两个交点是)4,2(和)16,4(）．18．若取1x 、2x 为区间]4,2[的两个`端点，则22)()(21=x f x f ． 若22>C ，取21=x ，2)(1=x f ，对任意]4,2[2∈x ，4)(2≤x f ，于是22)(2)()(221≤=x f x f x f ； 若22<C ，取41=x ，4)(1=x f ，对任意]4,2[2∈x ，2)(2≥x f ，于是 22)(4)()(221≥=x f x f x f ．所以22=C ．三．解答题（本大题满分74分）本大题共有5题，解答下列各题必须在答题纸相应编号的规定区域内写出必要的步骤．19．（本题满分12分） 解：设半圆的半径为r ，在△ABC 中，090=∠ACB ，030=∠ABC ，3=BC ，连结OM ，则AB OM ⊥，……（2分） 设r OM =，则r OB 2=，…………（4分）因为OB OC BC +=，所以r BC 3=， 即33=r ．………………（6分） 130tan 0=⋅=BC AC ．阴影部分绕直线BC 旋转一周所得旋转体为底面半径1=AC ，高3=BC 的圆锥中间挖掉一个半径33=r 的球．………………（8分） 所以，圆锥V V =球V -πππ27353334313132=⎪⎪⎭⎫ ⎝⎛⋅⋅-⋅⋅⋅=．…………（12分） 20．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 解：（1）由a ∥b 的充要条件知，存在非零实数λ，使得a b ⋅=λ，即⎩⎨⎧=⋅=λλx x cos sin 1，所以1cos sin =x x ，212sin =x ，…………（3分） 6)1(2ππ⋅-+=k k x ，Z k ∈． 所以x 的集合是⎭⎬⎫⎩⎨⎧∈⋅-+=Z k k x x k ,12)1(2ππ．………………（6分） （也可写成⎭⎬⎫⎩⎨⎧∈+=⎭⎬⎫⎩⎨⎧∈+=Z k k x x Z k k x x ,125,12ππππ ） （2）2)cos (sin 2cos sin )1(cos )1(sin ||)(22222++++=+++=+=x x x x x x b a x f3)cos (sin 2++=x x 34sin 22+⎪⎭⎫ ⎝⎛+=πx ，…………（9分） 因为⎥⎦⎤⎢⎣⎡-∈2,2ππx ，所以⎥⎦⎤⎢⎣⎡-∈+43,44πππx ，……（10分） 所以⎥⎦⎤⎢⎣⎡-∈⎪⎭⎫ ⎝⎛+1,224sin πx ，……………（12分） 所以函数)(x f 的值域为]223,1[+．………………（14分）21．（本题满分14分）本题共有2个小题，第1小题满分6分，第2小题满分8分． 解：（1）由已知，当0=x 时，8)(=x C ，即85=k ，所以40=k ，……（1分） 所以5340)(+=x x C ，…………（2分） 又加装隔热层的费用为x x C 6)(1=．所以5380066534020)()(20)(1++=++⨯=+⋅=x x x x x C x C x f ，…………（5分） )(x f 定义域为]10,0[．…………（6分）（2）10380062103538003563538006538006)(-⨯≥-⎪⎭⎫ ⎝⎛++⎪⎭⎫ ⎝⎛+=⎪⎭⎫ ⎝⎛++=++=x x x x x x x f 70=，…………（10分） 当且仅当⎪⎭⎫ ⎝⎛+=⎪⎭⎫ ⎝⎛+353800356x x ， 18800352=⎪⎭⎫ ⎝⎛+x ，32035=+x ，即5=x 时取等号．…………（13分） 所以当隔热层加装厚度为5厘米时，总费用)(x f 最小．最小总费用为70万元．…（14分）22．（本题满分16分）本题共有3个小题，第1小题满分3分，第2小题满分7分，第3小题满分6分．解：（1）1=m 时，1)(2+=x x f ，因为01=a ，所以1)0()(12===f a f a ，2)(23==a f a ，5)(34==a f a ．…………（3分，每求对一项得1分）（2）m x x f +=2)(，则m a =2，m m a +=23，m m m m m m m a +++=++=2342242)(，…………（5分）如果2a ，3a ，4a 成等差数列，则)()2(22342m m m m m m m m m +-+++=-+，02234=-+m m m ，……（6分）若0=m ，则0432===a a a ，不合题意，故0≠m ．所以，0122=-+m m ，所以21282±-=±-=m ．…………（8分） 当21+-=m 时，公差==-+=-=2223m m m m a a d 223-，…………（9分） 当21--=m 时，公差2232+==m d ．………………（10分）（3）11=b ，n n n b m m b b 22)(21=-+=+，…………（12分）所以}{n b 是首项为1，公比为2的等比数列，12-=n n b ，…………（13分） 201012>-=n n S ，20112>n ，10>n ．…………（15分）所以，使2010>n S 成立的最小正整数n 的值为11．…………（16分）23．（本题满分18分）本题共有3个小题，第1小题满分5分，第2小题满分6分，第3小题满分7分．23．解：（1）设),(y x P 为图像2C 上任意一点，P 关于点A 对称的点为),(y x P '''，则12='+x x ，22='+y y ，于是x x -='2，y y -='4，…………（2分） 因为),(y x P '''在1C 上，所以x a x y '+'='，即x a x y -+-=-224，22-++=x a x y ．所以22)(-++=x a x x g ．…………（5分） （2）由a x g =)(得a x a x =-++22，整理得0)43(2=-+-a ax x ① ………（7分） 若2=x 是方程①的解，则0=a ，此时方程①有两个实数解2=x 和2-=x ，原方程有且仅有一个实数解2-=x ；…………（8分）若2=x 不是方程①的解，则由△016122=+-=a a ，解得526±=a ．……（9分）所以，当0=a 时，方程的解为2-=x ； …………（10分）当=a 526+时，方程的解为53+=x ； …………（11分） 当=a 526-时，方程的解为53-=x ． …………（12分）（3）设1x 、),2[2∞+∈x ，且21x x <，因为函数)(x f 在区间),2[∞+上是增函数，所以0)()(12>-x f x f ．……（14分） 0)()()()(212112212112112212>-⋅-=-+-=--+=-x x a x x x x x x x x a x x x a x x a x x f x f ， 因为012>-x x ，021>x x ，所以021>-a x x ，即21x x a <，…………（16分） 而421>x x ，所以4≤a ． …………（17分）因此a 的取值范围是]4,(-∞．…………（18分）。

第I卷(共105分)I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. At 5:00. B. At 5:15. C. At 5:30. D. At 5:45.2. A. In Washington. B. In New York. C. In Michigan. D. In Boston.3. A. He is careful. B. He is nervous. C. He is humorous. D. He is brave.4. A. He is ready to stay for another cup of coffee. B. He is unwilling to stay longer for lack ofmoney.C. He can’t stay longer for lack of time.D. He doesn’t enjoy the coffee.5. A. 18. B. 38. C. 30. D. 48.6. A. Look for the pen. B. Write the letter. C. Paint the shelf. D. Fix the shelf.7. A. She doesn’t like to work with Mr. Clinton at all. B. She thinks Mr. Clinton is the best person.C. She thinks she’d better work alone.D. She’d like Mr. Clinton to work with her at last.8. A. It will take about one month to repair the camera. B. It costs too much to have the camerarepaired.C. The camera is no longer worth repairing.D. He doesn’t have the ability to repair the camera.9. A. Teacher and student. B. Nurse and patient. C. Boss and secretary. D. Father anddaughter.10. A. Professor Smith is going to speak some other night.B. He’s never heard of Professor Smith.C. He didn’t know Professor Smith was speaking tonight.D. Professor Smith is giving his speech in this room.Section BDirections: In Section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. A record of the school year. B. A book that is just for seniors.C. A book designed specially to print students’ titles.D. A record of students’ development.12. A. Students’ photos. B. Teachers’ photos.C. Descriptions of students’ academic results.D. Descriptions of after-school activities.13. A. All the students and teachers vote. B. Students sign each other’s yearbooks.C. Students in a yearbook club choose.D. Students who are soon graduating vote. Questions 14 through 16 are based on the following report.14. A. Chinese. B. Mathematics. C. English. D. Physics.15. A. Four hours. B. Seven hours. C. Eight hours. D. Nine hours.16. A. Homework, especially in mathematics, leads to high school students’ lack of sleep.B. Mathematics is the most difficult subject in high schools.C. Mathematics courses in China are more difficult than those in the USA.D. Mathematics is one of the three most important subjects for Chinese students.Section CDirections: In Section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.II. Grammar and VocabularySection ADirections: Read the following passage. For some blanks, there is a word given in the brackets. Fill in each of these blanks with the proper form of the given word. Fill in the other blanks with words that are correct in structure and proper in meaning.(A)One day, when I was working as a psychologist in England, an adolescent boy showed up in my office. It was David. He kept 25 (walk) up and down restlessly, his face pale, and his hands shaking slightly. His head teacher had referred him to me. “This boy has lost his family,” he wrote. “He is understandably very sad and refuses to talk to others, 26 I’m very worried about him. Can you help?”I looked at David and showed him to a chair. How could I help him? There are problems psychology doesn’t have the answer 27 , and which no words can describe. Sometimes thebest thing one can do is to listen openly and sympatheticallyThe fir st two times we met, David didn’t say a word. He sat there, only 28 (look) up to look at the children’s drawings on the wall behind me. I suggested we play a game of chess. He nodded. After that he played chess with me every Wednesday afternoon—in complete silence and without looking at me. It’s not easy to cheat in chess, but I admit I made sure David won once or twice.Usually, he arrived 29 than agreed, took the chess board and pieces from the shelf and began setting them up before I even got a chance to sit down. It seemed as if he enjoyed my company. But why did he never look at me?“Perhaps he simply needs someone 30 (share) his pain with,” I thought. “Perhaps he senses that I respect his suffering.” Some months later, when we were playing chess, he looked up at me suddenly.“31 ’s your turn,” he said.After that day, David started talking. He got friends in school and joined a bicycle club. He wrote to me a few times about his biking with some friends, and about his plan to get into university. Now he had really started to live his own life.Maybe I gave David something. But I also learned that one—without any words—can reach out to32 person. All it takes is a hug, a shoulder to cry on, a friendly touch, and an ear that listens【解析】试题分析：文章介绍作者和一个有心理问题的男孩David的故事，作者通过和David下象棋，分担(B)Some years ago, writing in my diary used to be a usual activity. I would return from school and 33(spend) the expected half hour recording the day’s events, feelings, and impressions in my little blue diary. I did not really need to express my emotions by way of words, but I gained a certain satisfaction from seeing my experiences forever 34 (record) on paper. Aft er all, isn’t accumulating memories a way of preserving the past?When I was thirteen years old, I went on a long journey on foot in a great valley, 35 (well-equip) with pens, a diary, and a camera. During the trip, I was busy recording every incident, name and place I came across. I felt proud to be spending my time 36 (productive), dutifully preserving for future generations a detailed description of my travels. On my last night there, I wandered out of my tent, diary in hand. The sky was clear and lit by the glare of themoon, and the walls of the valley looked threatening behind their screen of shadows. I automatically took out my pen….At that point, I understood that nothing I 37 (write) could ever match or replace the few seconds I allowed myself to experience the dramatic beauty of the valley. All I remembered of the previous few days were the dull characterizations I 38 (set) down in my diary.Now, I only write in my diary when I need to write down a special thought or feeling. I still love to record ideas and quotations that strike me in books, or observations that are particularly meaningful. I take pictures, but not very often—only of objects 39 I find really beautiful. I’m no longer blindly satisfied with having something to remember when I grow old. I realize that life will simply pass me by if I stay behind the camera, busy 40 (preserve) the present so as to live it in the future.I don’t want to wake up one day and have nothing but a pile of pictures and notes. Mayb e I won’t have as many exact representations of people and places; maybe I’ll forget certain facts, but at least the experiences will always remain inside me. I don’t live to make memories—I just live, and the memories form themselves.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. psychologicalB. proportionC. suspectedD. confessedE. kidnappedF. minorsG. strivingH. IntermediateI. transformedJ. mysteriouslyK. remainedTeen killers spur discussion on youth crimeNANNING—A high school student who was sentenced to life in prison for killing a 9-year-old girl has sparked discussions on juvenile delinquency (少年犯罪) in China.The defendant, surnamed Lyu, 41 the victim in December 2012, molested(骚扰)her, and beat her to death, according to a statement released by the 42 People’s Court in the city of Xinzhou in North China’s Shanxi province on Saturday.The court said the crimes committed were so horrible that no mitigation (减轻) was offered.The case was just one more in a series of similar cases committed by 43 .Back in February of this year, the son of a famous Chinese singer was detained in Beijing along with four others for their alleged involvement in a gang rape.Beijing police refused to disclose the name of the 44 minor, but police insiders who requested anonymity said he is the son of Li Shuangjiang, dean of the music department of the People’s Lib eration Army Academy of Arts.In April, a 12-year-old boy killed a 76-year-old woman in Guiping City in south China’s Guangxi Zhuang Autonomous Region. The boy, who is currently in custody, 45 to police that he never wanted to kill the woman, and that he only wanted to steal money from her.Many have expressed concern on the Internet about the 46 conditions of China’s underage population, wondering what 47 these little “flowers of the motherland” into “carnivorous plants” in a country 48 for a harmonious society.These cases are not rare, said Xia Xueluan, professor with the Department of Sociology at Peking University, adding that juvenile crimes in China, which have decreased in recent years, are still large in number.From 2002 to 2011, the rate of recidivism of China’s juvenile offenders 49 at 1 percent to 2 percent, according to a white paper on judicial reform published in October of last year, which also reported drops in juvenile delinquency cases and the 50 of juvenile offenders among the total criminal population.However, China’s juvenile offender number is still high, standing at around 67,000 in 2011, according to the white paper.“The national average rate of juvenile delinquency may have fallen, but in many parts of the country, youth crimes are still on the rise,” Xia said.【答案】【小题1】E【小题2】H【小题3】F【小题4】C【小题5】D【小题6】A【小题7】I【小题8】G【小题9】K【小题10】B【解析】【小题9】中国的少年犯的比例还保持在1%-2%，remain保持，做连系动词，选K【小题10】在整个的犯罪的人里面少年犯的比例在下降。

上海市部分重点中学2009—2010学年高三年级第一次联考语文试题一、80分阅读下文，完成下面小题一杯烧开水里盛放的历史赵瑜①不知从哪一年始，中国阅读市场突然被一群游戏历史的水煮派作家占领，历史读物的泛滥已经达到了让人不太愉悦的地步。

历史的竹简被熬成了一锅粥，大众文化的传播像《三国演义》的流传一样，具有清洗底牌的功效。

历史在被消费的同时，也被破坏，真正历史学者的文字被这些花哨的文字淹没。

②我一直渴望读到一份具有人文意味的读史作品。

这册毛边的《重现——韩少功读史笔记》就让我大开眼界，它虽然片断、拼凑，但却充满着韩少功印记的智慧。

他不是在翻译历史趣事和后宫秘史，而是在解释历史是如何在时间的河流里一点点风化，成为今天的固态。

③历史不仅仅是朝代更替和血雨腥风的战争，也是文字的成长史，礼仪习俗的渐变史，更是大众如何在时间的河流里找到自己位置的具体罗列史。

④在《夷俗》一文中，韩少功淘洗了通俗历史中的一些琐碎列举，归纳出我们阅读时时常忽略的理路：文字的成长与历史习俗和地缘关系密切。

远离了印刷术和造纸术的时代，人们用音乐符号，用舞蹈，用肩膀和臀胯的肢体动作来表达内里的想法。

然而，随着印刷术和造纸术的出现，这种习俗长期延续下来的结果是，中原地区的人们习惯用诗书来表达喜乐，对酒当歌，人生几何？而边远地区的少数民族则用歌舞来庆祝自己的丰沛和收获。

⑤《楚辞》是中国传统文化继《诗三百》之后又一个高峰，然而它的古奥难懂难倒了后世一代又一代的儒生。

直到后来有一个叫林河的学者在研究的过程中发现，《楚辞》中的《九歌》竟然脱胎于侗族的民歌《歌（嘎）九》，于是，《楚辞》中那些深奥的含义一一找到了巫辞的对应。

历史在延续中丢失了直接的注释，却又在另外的习俗和风物里有暗道相通。

⑥除了屈原的《楚辞》是历史，在韩少功的解读中，即使是一个地方的人走路的姿势也是历史。

直到现在，在楚地生活人们走路仍然喜欢背着手弯腰走路，有上年纪的人说，这是他们的先人被捆绑惯了的动作，直接影响了一代又一代人。

上海市崇明县2010届高三上学期期末考试试卷高三数学（理科）（满分150分，答题时间120分钟）注意：在本试卷纸上答题无效，必须在答题纸上的规定位置按照要求答题．一、填空题（每小题4分，共56分）1、设}5,4,3,2,1{=U ，{}1)43(log 22=+-=x x x M ，那么=M C U .2、若函数)(x f y =是函数xy alog=（1,0≠>a a ）的反函数，且2)1(=-f ，则=)(x f . 3、一个三阶行列式按某一列展开等于22113311332232　ba b a ba b a ba b a ++，那么这个三阶行列式可能是 .（答案不唯一） 4、已知6π-=x 是方程3)tan(3=+αx 的一个解，)0(，πα-∈，则=α ．5、右图是一个算法的流程图，最后输出的 =W．6、若圆锥的侧面积为π20，且母线与底面所成的角的余弦值为54，则该圆锥的体积为.7、已知二项展开式5522105)1(x a x a x a a ax +⋯+++=-中，803=a ，则5210a a a a +⋯+++等于 . 8、复数2)2321(i z -=是实系数方程012=++bx ax 的根，则=⨯b a .9、已知n S 是数列{}n a 前n 项和，2,111+==+n n a a a （*N n ∈）,则limn n nna S →∞= 。

10、定义在R 上的函数)(x f 满足⎩⎨⎧---=+)1()()4(log )1(2x f x f x x f,0,>≤x x，计算)2010(f 的值等于 .·A BCO11、如图，在半径为3的球面上有A 、B 、C 三点，︒=∠90ABC ，BCBA =，球心O 到平面ABC 的距离是223，则B 、C 两点的球面距离是 .12、若命题p ：34-x ≤1；命题q :)2)((---m x m x ≤0，且p 是q 的充分不必要条件，则实数m 的取值范围是 .13、给定两个长度为1的平面向量OA 和OB ，它们的夹角为︒120.如图所示，点C 在以O 为圆心的圆弧AB 上变动.若OB y OA x OC +=，其中R y x ∈,，则y x + 的取值范围是 .14、已知函数1)(-=x x f ，关于x 的方程0)()(2=+-k x f x f ，给出下列四个命题：① 存在实数k ，使得方程恰有2个不同的实根； ② 存在实数k ，使得方程恰有4个不同的实根； ③ 存在实数k ，使得方程恰有5个不同的实根； ④ 存在实数k ，使得方程恰有8个不同的实根. 其中真命题的序号为 .二、选择题（每小题4分，共16分）15、公差不为零的等差数列{}n a 的前n 项和为n S . 若31-=a 且4a 是3a 与7a 的等比中项，则10S 等于…………………………………………………………………………………（ ） （A ）18 （B ）24 （C ）60 （D ）90 16、函数⎪⎭⎫ ⎝⎛+⎪⎭⎫⎝⎛+=4cos 12sin 2ππx x y 的最大值、最小值分别为 …………………………（ ）（A ）2，2-（B ）21,23- （C ）21,23 （D ）23,21-17、投掷两颗骰子，得到其向上的点数分别为m 和n ，则复数))((mi n ni m -+为实数的概率为 …………………………………………………………………………………………（ ） （A ）31 （B ）41 （C ）61 （D ）12118、定义在R 上的偶函数)(x f 满足：对任意的]0,(,21-∞∈x x )(21x x ≠，（有0))()()((1212>--x f x f x x 恒成立. 则当*N n ∈时，有……………………………（ ）（A ）)1()()1(-<-<+n f n f n f（B ）)1()()1(+<-<-n f n f n f （C ）)1()1()(+<-<-n f n f n f（D ）)()1()1(n f n f n f -<-<+三、解答题（本大题共有5题，满分78分，解答下列各题必须写出必要的步骤） 19、（本题满分14分，第1小题6分，第2小题8分） 设函数xx x f 2sin)32cos()(++=π.（1）求函数)(x f 的最大值和最小正周期； （2）设C B A ,,为∆ABC 的三个内角，41)2(-=Cf ，且C 为锐角，35=∆ABC S ，4=a ，求c 边的长．20、（本题满分14分，第1小题6分，第2小题8分）如图，在直四棱柱D C B A ABCD ''''-中，底面ABCD 为等腰梯形，AB ∥CD ，4=AB ，2==CD BC ，21=AA ，E 、F 、G 分别是棱11B A 、AB 、11D A 的中点.（1）证明：直线GE ⊥平面1FCC ； （2）求二面角C FC B --1的大小.ABFCDEGA 1D 1 C 1B 121、（本题满分16分，第1小题3分，第2小题5分，第3小题8分）某学校数学兴趣小组有10名学生，其中有4名女同学；英语兴趣小组有5名学生，其中有3名女学生，现采用分层抽样方法（层内采用不放回简单随机抽样）从数学兴趣小组、英语兴趣小组中共抽取3名学生参加科技节活动。