2012年高考(湖北A卷)
2012年高考文科数学湖北卷(含详细答案)

数学试卷 第1页(共26页) 数学试卷 第2页(共26页)绝密★启用前2012年普通高等学校招生全国统一考试(湖北卷)数学(文史类)本试卷共4页,共22题.满分150分.考试用时120分钟.★祝考试顺利★考生注意:1.答卷前,考生务必将自己的姓名、准考证号填写在试题卷和答题卡上,并将准考证号条形码粘贴在答题卡上的指定位置.用统一提供的2B 铅笔将答题卡上试卷类型后的方框涂黑.2.选择题的作答:每小题选出答案后,用统一提供的2B 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.答在试题卷、草稿纸上无效.3.填空题和解答题的作答:用统一提供的签字笔将答案直接答在答题卡上对应的答题区域内.答在试题卷、草稿纸上无效.4.考生必须保持答题卡的整洁.考试结束后,请将本试题卷和答题卡一并上交. 一、选择题:本大题共10小题,每小题5分,共50分.在每小题给出的四个选项中,只有一项是符合题目要求的.1.已知集合23 20,|} {A x x x x -+=∈R ,05 {|}B x x x =∈<<,N ,则满足条件A CB ⊆⊆的集合C 的个数为( ) A .1B .2C .3D .42.容量为20的样本数据,分组后的频数如下表:则样本数据落在区间[10,40)的频率为( )A .0.35B .0.45C .0.55D .0.65 3.函数s ()co 2f x x x =在区间[0,2π]上的零点的个数为 ( ) A .2B .3C .4D .54.命题“存在一个无理数,它的平方是有理数”的否定是( )A .任意一个有理数,它的平方是有理数B .任意一个无理数,它的平方不是有理数C .存在一个有理数,它的平方是有理数D .存在一个无理数,它的平方不是有理数 5.过点)(1,1P 的直线,将圆形区域22{()|+4}x y x y ,≤分为两部分,使得这两部分的面积差最大,则该直线的方程为( )A .20x y +-=B .10y -=C .0x y -=D .340x y +-=6.已知定义在区间[0,2]上的函数()y f x =的图象如图所示,则()2y f x =--的图象为( )ABCD7.定义在()(),00,-∞+∞上的函数)(f x ,如果对于任意给定的等比数列{}n a ,{)(}n f a 仍是等比数列,则称)(f x 为“保等比数列函数”.现有定义在()(),00,-∞+∞上的如下函数:①2()f x x =;②()2x f x =;③()f x =;④()ln ||f x x =.则其中是“保等比数列函数”的)(f x 的序号为( ) A .①②B .③④C .①③D .②④8.设ABC △的内角A ,B ,C 所对的边分别为a ,b ,c .若三边的长为连续的三个正整 数,且A B C >>,320b acosA =,则sin :sin :sin A B C 为 ( ) A .4∶3∶2B .5∶6∶7C .5∶4∶3D .6∶5∶49.设a b c ∈,,R ,则“1abc =++a b c ”的()--------在--------------------此--------------------卷--------------------上--------------------答--------------------题--------------------无--------------------效----------------姓名________________ 准考证号_____________数学试卷 第3页(共26页) 数学试卷 第4页(共26页)A .充分条件但不是必要条件B .必要条件但不是充分条件C .充分必要条件D .既不充分也不必要的条件10.如图,在圆心角为直角的扇形OAB 中,分别以OA ,OB 为直径作两个半圆.在扇形OAB 内随机取一点,则此点取自阴影部分的概率是( )A .112π-B .1πC .21π-D .2π二、填空题:本大题共7小题,每小题5分,共35分.请将答案填在答题卡对应题号的位置上.答错位置,书写不清,模棱两可均不得分.11.一支田径运动队有男运动员56人,女运动员42人.现用分层抽样的方法抽取若干人,若抽取的男运动员有8人,则抽取的女运动员有 人.12.若3+i=+i 1ib a b -(a ,b 为实数,i 为虚数单位),则a b += . 13.已知向量0)(1,=a ,1)(1,=b ,则(Ⅰ)与2+a b 同向的单位向量的坐标表示为 ;(Ⅱ)向量3-b a 与向量a 夹角的余弦值为 .14.若变量x ,y 满足约束条件1,1,33,x y x y x y --⎧⎪+⎨⎪-⎩≥≥≤则目标函数23z x y =+的最小值是 .15.已知某几何体的三视图如图所示,则该几何体的体积为 .16.阅读如图所示的程序框图,运行相应的程序,输出的结果s = .17.传说古希腊毕达哥拉斯学派的数学家经常在沙滩上画点或用小石子表示数.他们研究过如图所示的三角形数:将三角形数1,3,6,10,记为数列{}n a ,将可被5整除的三角形数按从小到大的顺序组成一个新数列{}n b .可以推测: (Ⅰ)2012b 是数列{}n a 中的第 项; (Ⅱ)21k b =- .(用k 表示)三、解答题:本大题共5小题,共65分.解答应写出文字说明、证明过程或演算步骤. 18.(本小题满分12分)设函数22()sin cos cos ()f x x x x x x ωωωωλ-∈++=R 的图象关于直线π=x 对称,其中ω,λ为常数,且)11(2ω∈,. (Ⅰ)求函数()f x 的最小正周期;(Ⅱ)若()y f x =的图象经过点π()40,,求函数()f x 的值域. 19.(本小题满分12分)某个实心零部件的形状是如图所示的几何体,其下部是底面均是正方形,侧面是全等的等腰梯形的四棱台1111A B C D ABCD -,上部是一个底面与四棱台的上底面重合,侧面是全等的矩形的四棱柱2222ABCD A B C D -. (Ⅰ)证明:直线11B D ⊥平面22ACC A ;(Ⅱ)现需要对该零部件表面进行防腐处理.已知10=AB ,1120=A B ,20=3A ,113=AA (单位:厘米),每平方厘米的加工处理费为0.20元,需加工处理费多少元? 20.(本小题满分13分)已知等差数列{}n a 前三项的和为,前三项的积为.(Ⅰ)求等差数列{}n a 的通项公式;(Ⅱ)若2a ,3a ,1a 成等比数列,求数列{||}n a 的前n 项和.21.(本小题满分14分)设A 是单位圆221x y +=上的任意一点,l 是过点A 与x 轴垂直的直线,D 是直线l 与x 轴的交点,点M 在直线l 上,且满足|(|)|01DM m DA m m ≠=>,且.当点A 在圆上运动时,记点M 的轨迹为曲线C .(Ⅰ)求曲线C 的方程,判断曲线C 为何种圆锥曲线,并求其焦点坐标;3-8数学试卷 第5页(共26页) 数学试卷 第6页(共26页)(Ⅱ)过原点斜率为k 的直线交曲线C 于P ,Q 两点,其中P 在第一象限,且它在y 轴上的射影为点N ,直线QN 交曲线C 于另一点H .是否存在m ,使得对任意的0k >,都有PQ PH ⊥?若存在,求m 的值;若不存在,请说明理由.22.(本小题满分14分)设函数()(1)()0n f x ax x b x =-+>,n 为正整数,a ,b 为常数.曲线()y f x =在(1)(1)f ,处的切线方程为1x y +=.(Ⅰ)求a ,b 的值;(Ⅱ)求函数()f x 的最大值; (Ⅲ)证明:1()ef x n <.数学试卷第7页(共26页)数学试卷第8页(共26页)5 / 13数学试卷 第11页(共26页)数学试卷 第12页(共26页)3S ,4S 。
2012年湖北省高考英语真题(附详细解析)

2012年湖北省高考英语试卷一、听力(共两节,满分30分)1. 第一节听下面5段对话.每段对话后有一个小题,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.1.What is the problem for the man?A.He has to meet many people.B.He has to leave his friends.C.He has to travel a lot.2.How does the man think of the book?A.Humorous. B.Scientific. C.Popular.3.What's the matter with the woman?A.She has caught a bad cold.B.She stayed online too long.C.She is allergic to paint smell.4.What does the man suggest the woman do?A.Consult a repair shop. B.Purchase another car. C.Fix the car herself.5.In which year is the man in college now?A.The first year. B.The second year. C.The third year.听下面5段对话或独白.每段对话或独白后有几个小题,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.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6、7题.6.What has the woman ordered for herself?A.Milk. B.Juice. C.Coffee.7.Why does the man recommend strawberry juice?A.It's sweeter. B.It's fresher. C.It's colder.听第7段材料,回答第8、9题.8.Why is Jane upset?A.David fell in love with her.B.Kevin made up stories about her.C.She made a mistake in calculation.9.What is the probable relationship between the speakers?A.Teacher and student.B.Father and daughter.C.Employer and employee.听第8段材料,回答第10至12题.10.How far away is Hill Farm?A.Nearly a mile. B.Just one mile. C.More than a mile.11.Which is the route to Hill Farm?A.Left track→bridge→road.B.Road→left track→bridge.C.Bridge→road→left track.12.What would the man like the woman to do towards the end of the conversation?A.Give him a ride.B.Repeat what she said.C.Walk him to Hill Farm.听第9段材料,回答第13至16题.13.What is the woman doing?A.Hosting a TV show.B.Giving a lecture on poetry.C.Conducting a radio debate.14.How did the man's mother contribute to his success in poetry?A.She sent him to poetry classes.B.She taught him to write business plans.C.She asked him to read from early childhood.15.What does the man find most difficult in writing?A.Choosing the right words.B.Describing real experiences.C.Getting an appropriate opportunity.16.What does the man say about his own writing?A.Creative. B.Successful. C.Encouraging.听第10段材料,回答第17至20题.17.How do students enter the library?A.With a library account. B.With a student card. C.With a password.18.What is the maximum number of books current students can borrow?A.12.B.11.C.9.19.What kind of books have to be returned within one week?A.Books borrowed by local residents.B.Books liked by a lot of people.C.Books published recently.20.What will the speaker do next?A.Tell the students where to get bottled water.B.Take the students on a campus tour.C.Show the students around the library.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.1.What is the problem for the man?A.He has to meet many people.B.He has to leave his friends.C.He has to travel a lot.2.How does the man think of the book?A.Humorous. B.Scientific. C.Popular.3.What's the matter with the woman?A.She has caught a bad cold.B.She stayed online too long.C.She is allergic to paint smell.4.What does the man suggest the woman do?A.Consult a repair shop. B.Purchase another car. C.Fix the car herself.5.In which year is the man in college now?A.The first year. B.The second year. C.The third year.听下面5段对话或独白.每段对话或独白后有几个小题,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.听每段对话或独白前,你将有时间阅读各个小题,每小题5秒钟;听完后,各小题将给出5秒钟的作答时间.每段对话或独白读两遍.听第6段材料,回答第6、7题.6.What has the woman ordered for herself?A.Milk. B.Juice. C.Coffee.7.Why does the man recommend strawberry juice?A.It's sweeter. B.It's fresher. C.It's colder.听第7段材料,回答第8、9题.8.Why is Jane upset?A.David fell in love with her.B.Kevin made up stories about her.C.She made a mistake in calculation.9.What is the probable relationship between the speakers?A.Teacher and student.B.Father and daughter.C.Employer and employee.听第8段材料,回答第10至12题.10.How far away is Hill Farm?A.Nearly a mile. B.Just one mile. C.More than a mile.11.Which is the route to Hill Farm?A.Left track→bridge→road.B.Road→left track→bridge.C.Bridge→road→left track.12.What would the man like the woman to do towards the end of the conversation?A.Give him a ride.B.Repeat what she said.C.Walk him to Hill Farm.听第9段材料,回答第13至16题.13.What is the woman doing?A.Hosting a TV show.B.Giving a lecture on poetry.C.Conducting a radio debate.14.How did the man's mother contribute to his success in poetry?A.She sent him to poetry classes.B.She taught him to write business plans.C.She asked him to read from early childhood.15.What does the man find most difficult in writing?A.Choosing the right words.B.Describing real experiences.C.Getting an appropriate opportunity.16.What does the man say about his own writing?A.Creative. B.Successful. C.Encouraging.听第10段材料,回答第17至20题.17.How do students enter the library?A.With a library account. B.With a student card. C.With a password.18.What is the maximum number of books current students can borrow?A.12.B.11.C.9.19.What kind of books have to be returned within one week?A.Books borrowed by local residents.B.Books liked by a lot of people.C.Books published recently.20.What will the speaker do next?A.Tell the students where to get bottled water.B.Take the students on a campus tour.C.Show the students around the library.二、词汇知识运用(共两节,满分10分)多项选择(共10小题;每小题1分,满分10分)从A、B、C、D四个选项中,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.2. Two lawyers have donated $50,000 to ________ our school’s campaign“Help the Needy”,which was started by our former headmaster three years ago.()A.sponsorunchanizeD.plan3. Finally,my thanks go to my tutor,who has offered a lot of suggestions and comments on my paper and ________ every page of my draft.()A.approvedB.quotedC.polishedD.folded4. Walking alone in the dark,the boy whistled to ________ his courage.()A.hold upB.keep upC.set upD.take up5. I’m so glad you’ve come here to ________ this matter in person.()A.lead toB.see toC.turn toD.refer to6. The furniture,with its modern style and bright colors,suits modern houses and their gardens,but looks _______ in the garden of a traditional home.()A.out of questionB.out of orderC.out of sightD.out of place7.“Perhaps we need to send for Dr.Smith to see what we can do about it,”Father suggested ________ to his neighbor who had come to discuss the problem.()A.tentativelyB.thoughtlesslyC.definitelyD.rudely8. Can you tell the ________ difference between the words“require”and“request”?I sometimes get puzzled by their meanings.()A.dramaticB.regionalC.apparentD.subtle9. Whether the buildings in this area should be pulled down has remained ________;people are still looking for other possible solutions.()A.unchallengedB.relevantC.controversialD.contradictory10. It is important to have your eyes examined regularly to check for any sign of eye disease that may not have any ________.()A.shadowB.similarityC.sampleD.symptom11.The officer insisted that Michael did not follow the correct ________ in applying for a visa.()A.patternB.procedureC.programD.perspective三、完形填空(共1小题;每小题20分,满分20分)12. I tend to accept any idea put forward by experts on TV.One day,a sociologist proposed that the (31)________ society has been consuming modern humans little by little.For fear that I would become a victim of the consumer society,I (32)________ hurried to a bicycle shop in my neighborhood.(33)________ the shopkeeper Mr.Johnson was selling me the bicycle,he said,“This is the best thing you (34)________ have done.Life has become hopelessly (35)________.A bicycle is simple,and it brings to you (36)________ things:fresh air,sunshine and exercise.”I agreed.Happy as a child,I got on the bicycle and headed out onto the streets.After some time,I (37)________ at the other end of the town.I was (38)________ that this simple vehicle could let me (39)________ long distances in a fairly short time.But how (40)________ did I really go?Since I hated to be (41)________,I went back to Mr.Johnson and asked him to (42)________ an odometer (里程表) on my bicycle.He agreed,but (43)________,“An odometer without a speedometer (速度计) is like a (44)________ without a knife.”I admitted he was right and in a few minutes,the two devices (装置) were (45)________ to the handlebars of my bicycle.“What about a horn?”he then asked.“Look,this horn is no larger than a matchbox and has many (46)________.”Attracted by these functions,I bought the horn.“You can’t leave the back part (47)________,”n oted Mr.Johnson.He fixed a metal box with buttons (48)________ the seat,and said,“Is there anything better than this oven when you f8el (49)________ on your way?I can give you a special discount.”I was not strong enough to (50)________ the offer.“I congratulate you once more; this is the best thing you could have done,”said Mr.John son in the end.31.A.adult B.human C.consumer D.bachelor32.A.eventually B.immediately C.reluctantly D.gratefully 33.A.Although B.Because C.As D.Unless34.A.would B.should C.must D.could35.A.boring B.complicated C.stressful D.tough36.A.natural B.mysterious C.complex D.unique37.A.gave up B.broke down C.calmed down D.ended up 38.A.amazed B.amused C.confused D.concerned39.A.march B.drive C.cover D.measure40.A.far B.long C.fast D.deep41.A.unreliable B.impractical C.unprepared D.inaccurate42.A.fix B.check C.repair D.lay43.A.swore B.added C.replied D.concluded44.A.pencil B.fork C.box D.cake45.A.distributed B.converted C.applied D.attached46.A.shapes B.sizes C.functions D.models47.A.loose B.blank C.bare D.incomplete48.A.beside B.before C.below D.behind49.A.sick B.hungry C.hot D.thirsty50.A.consider B.withdraw C.make D.resist.四、阅读理解(共5小题;每小题8分,满分40分)阅读下列短文,从每篇短文后所给各题的四个选项(A、B、C和D)中,选出最佳选项.13. You’ve just come home, after living abroad for a few years.Since you’ve been away, h as this country changed for the better-or for the worse?If you’ve just arrived back in the UK after a fortnight’s holiday, small changes have probably surprised you-anything from a local greengrocer suddenly being replaced by a mobile-phone shop to someone in your street moving house.So how have things changed to people coming back to Britain after seven, ten or even 15y ears living abroad? What changes in society can they see that the rest of us have hardly notic ed-or now take for granted? To find out, we asked some people who recently returned.Debi: When we left, Cheltenham, my home town, was a town of white, middle-class families-all very conservative (保守的).The town is now home to many eastern Europeans and lots of Australians, who come here mainly to work in hotels and tourism.There are even several shops only for foreigners. Having been an immigrant (移民) myself, I admire people who go overseas to find a job.Maybe if I lived in an inner city where unemployment was high, I’d think differently, but I believe foreign settlers have impro ved this country because they’re more open-minded and often work harder than the natives. Christine: As we flew home over Britain, both of us remarked how green everything looked .But the differences between the place we’d left behind and the one we returned to were brought sharply into focus as soon as we landed.To see policemen with guns in the airport for the first time was frightening-in Cyprus, they’re very relaxed-and I got pulled over by customs officers just for taking a woolen sweater with some metal-made buttons out of my case in the arrivals hall.Everyone seemed to be on guard.Even th e airport car-hire firm wanted a credit card rather than cash because they said their vehicles had been use d by bank robbers.But anyway, this is still a green, beautiful country.I just wish more people would apprecia te what they’ve got.(1)After a short overseas holiday,people tend to________.A.notice small changesB. C.welcome small changes D.(2)How does Debi look at the foreign settlers?________A.Cautiously.B.Positively.C.Sceptically.D.Critically.(3)When arriving at the airport in Britain,Christine was shocked by________.A.the relaxed policemenB. C.the tight security.D.the bank robbers.(4)Which might be the best title for the passage?________A.Life in Britain.B.Back in Britain.C.Britain in Future.D.Britain in Memory.14. When my brother and I were young, my mom would take us on Transportation Days. It goes like this: You can’t take any means of transportation more than once.We would st art from home, walking two blocks to the rail station.We’d take the train into the city cente r, then a bus, switching to the tram, then maybe a taxi.We always considered taking a hors e carriage in the historic district, but we didn’t like the way the horses were treated, so we n ever did.At the end of the day, we took the subway to our closest station, where Mom’s fri end was waiting to give us a ride home-our first car ride of the day.The good thing about Transportation Days is not only that Mom taught us how to get arou nd.She was born to be multimodal (多方式的).She understood that depending on cars only was a failure of imagination and, above al l, a failure of confidence-the product of a childhood not spent exploring subway tunnels. Once you learn the route map and step with certainty over the gap between the train and the platform, nothing is frightening anymore.New cities are just light-rail lines to be explored.And your personal car, if you have one, becomes just one more too l in the toolbox-and often an inadequate one, limiting both your mobility and your wallet. On Transportation Days, we might stop for lunch on Chestnut Street or buy a new book ortoy, but the transportation was the point.First, it was exciting enough to watch the world s peed by from the train window.As I got older, my mom helped me unlock the mysteries tha t would otherwise have paralyzed my first attempts to do it myself: How do I know where to get off? How do I know how much it costs? How do I know when I need tickets, and where to get them? What track, what line, which direction, where’s the stop, and will I get wet when we go under the river?I’m writing this right now on an airplane, a means we didn’t try on our Transportation Days and, we now know, the dirtiest and most polluting of them all.My flight routed me throug h Philadelphia.My multimodal mom met me for dinner in the airport.She took a train to meet me.(1)Which was forbidden by Mom on Transportation Days?________A.Having a car ride.B.Taking the train twice.C.Buying more than one toy.D.Touring the historic district.(2)According to the writer,what was the greatest benefit of her Transportation Days?________A.Building confidence in herself.B.Reducing her use of private cars.C.Developing her sense of direction.D.Giving her knowledge about vehicles.(3)The underlined word“paralyzed”(in Para.5)is closest in meaning to“________”.A.displayedB. C.ignored D.(4)Which means of transportation does the writer probably disapprove of?________ A.Airplane. B.Subway. C.Tram. D.Car.15. It was a simple letter asking for a place to study at Scotland’s oldest university which h elped start a revolution in higher education.A 140-year-old letter written by a lady calling for her to be allowed to study medicine at St Andrews Univ ersity has been discovered by researchers.Written by Sophia Jex-Blake in 1873, the seven-page document, which urged the university to allow women to study medicine at the institut ion, was released yesterday on International Women’s Day.The document was discovered buried in the university archives (档案) by part-time history student Lis Smith, who is completing her PhD at St Andrews Institute of Scottish Historical Research.She said: “We knew that Sophia Jex-Blake and her supporters, in their effort to open up university medical education for women, had written to the Senatus Academicus (校评议委员会) at St Andrews in an attempt to gain permission to attend classes there, but we didn’t k now documentary evidence existed.While searching the archives for information about the university’s higher certificate for women, I was astonished to come across what must be the very letter Jex-Blake wrote.”In the letter, Sophia and her supporters offered to hire teachers or build suitable buildings for a medical school and to arrange for lectures to be delivered in the subjects not already co vered at St Andrews.Although her letter was not successful, it eventually led to the establis hment of the Ladies Literate in Arts at St Andrews, a distance-learning degree for women.The qualification, which ran from 1877until the 1930s, gave wo men access to university education in the days before they were admitted as students.It w as so popular that it survived long after women were admitted as full students to St Andrews in 1892.Ms Jex-Blake went on to help establish the London School of Medicine for Women in 1874.She wa s accepted by the University of Berne, where she was awarded a medical degree in January 1 877.Eventually, she moved back to Edinburgh and opened her own practice.(1)Sophia wrote a letter to St Andrews University because she wanted________.A.to carry out a research project there.B.to set up a medical institute there.C.to study medicine there.D.to deliver lectures there.(2)Lis Smith found Sophia’s letter to St Andrews University________.A.by pure chance.B.in the school office.C.with her supporters’helpD.(3)Sophia’s letter resulted in the establishment of________.A.the London School of Medicine for Women.B.a degree programme for women.C.a system of medical education .D.the University of Berne.(4)When did St Andrews University begin to take full-time women students?________ A.In 1873. B.In 1874. C.In 1877. D.In 1892.16. How is it that siblings (兄弟姐妹) can turn out so differently? One answer is that in fact each sibling grows up in a differe nt family.The firstborn is, for a while, an only child, and therefore has a completely different experience of the parents than those born later.The next child is, for a while, the younges t, until the situation is changed by a new arrival.The mother and father themselves are cha nging and growing up too.One sibling might live in a stable and close family in the first few years; another might be raised in a family crisis, with a disappointed mother or an angry fath er.Sibling competition was identified as an important shaping force as early as in 1918.But more recently, researchers have found many ways in which brothers and sisters are a lasting force in each others’lives.Dr.Annette Henderson says firstborn children pick up vocabular y more quickly than their siblings.The reason for this might be that the later children aren’t getting the same one-on-one time with parents.But that doesn’t mean that the younger children have problems wit h language development.Later-borns don’t enjoy that much talking time with parents, but instead they harvest lessons from bigger brothers and sisters, learning entire phrases and getting an understanding of social co ncepts such as the difference between“I”and“me”.A Cambridge University study of 140children found that siblings created a rich world of pla y that helped them grow socially.Love-hate relationships were common among the children.Even those siblings who fought the m ost had just as much positive communication as the other sibling pairs.One way children seek more attention from parents is by making themselves different fro m their siblings, particularly if they are close in age.Researchers have found that the first t wo children in a family are typically more different from each other than the second and thir d.Girls with brothers show their differences to a maximum degree by being more feminine than girls with sisters.A 2003research paper studied adolescents from 185families over two years, finding that those who changed to make themselves different from their siblings were successful in increasing the amount of warmth they gained from their parents.(1)The underlined part“in a different family”(in Para.1)means“________”.A.in a different family environment B.C.in different family crises.D.in different families.(2)In terms of language development,later-borns________.A.get their parents’individual guidance.B.learn a lot from their elder siblings.C.experience a lot of difficulties.D.pick up words more quickly.(3)What was found about fights among siblings?________A.Siblings hated fighting and loved playing.B.Siblings in some families fought frequently.C.Sibling fights led to bad sibling relationships.D.Siblings learned to get on together from fights.(4)The w ord“feminine”(in Para.4)means“________”.A.having qualities of parentsB. C.having defensive qualities.D.having extraordinary qualities.17. Brrriiinnng.The alarm clock announces the start of another busy weekday in the mor ning.You jump out of bed, rush into the shower, into your clothes and out the door with ha rdly a moment to think.A stressful journey to work gets your blood pressure climbing.On ce at the office, you glance through the newspaper with depressing stories or reports of disa sters.In that sort of mood, who can get down to work, particularly some creative, original p roblem-solving work?The way most of us spend our mornings is exactly opposite to the conditions that promote flexible, open-minded thinking.Imaginative ideas are most likely to come to us when we're unfocused.If you are one of those energetic morning people, your most inventive time comes in the early evening when you are relaxed.Sleepy people's lack of focus leads to an increase in creative problem solving.By not giving yourself time to tune into your wandering mind, you're missi ng out on the surprising solutions it may offer.The trip you take to work doesn't help, either.The stress slows down the speed with whi ch signals travel between neurons (神经细胞), making inspirations less likely to occur.And while we all should read a lot about what 's going on in the world, it would not make you feel good for sure, so put that news websiteor newspaper aside until after the day's work is done.So what would our mornings look like if we wanted to start them with a full capacity for cr eative problem solving? We'd set the alarm a few minutes early and lie awake in bed, followi ng our thoughts where they lead.We'd stand a little longer under the warm water of the sh ower, stopping thinking about tasks in favor of a few more minutes of relaxation.We'd take some deep breaths on our way to work, instead of complaining about heavy traffic.And on ce in the office-after we get a cup of coffee-we'd click on links not to the news of the day but to the funniest videos the web has to offer.(1)According to the author,we are more creative when we are________.A.focused B. C.awake D.(2)What does the author imply about newspapers?________A.They are solution providers.B.They are a source of inspiration.C.They are normally full of bad news.D.They are more educational than websites.(3)By"tune into your wandering mind"(in Para.2),the author means"________".A.wander into the wild.B.listen to a beautiful tune.C.switch to the traffic channel D.(4)The author writes the last paragraph in order to________.A.offer practical suggestions.B.summarize past experiences.C.advocate diverse ways of life D.五、书面表达(共两节,满分20分)第一节:完成句子(共10小题;每小题2分,满分20分)阅读下列各小题,根据汉语提示,用句末括号内的英语单词完成句子,并将答案写在答题卡上的相应题号后.18. With________,some animals are facing the danger of dying out.(cut)由于越来越多的森林被砍伐,一些动物正面临着灭绝的危险.19. Popularly________ American films ever made,The Godfather is a milestone of cinema.(regard)《教父》被普遍认为是美国有史以来最好的影片之一,是电影界的一个里程碑.20. I don’t know________ in the novel that made him burst into tears.(what)我不知道是小说中的什么东西使他突然泪如泉涌.21. Little________ what she looks like; all she cares about is her job performance.(care)她不在乎外表,她在乎的是自己的工作表现.22. Had we not used an out﹣of﹣date train schedule,we________ the train.(miss)要不是用了一张过期的列车时刻表,我们就不会误了火车.23. However________,I could not read his handwriting.(try)不论我怎样努力,还是没法看清他写的字.24. In response to the audience’s great demand,the play________ in the theatre twice a week.(put)应观众的强烈要求,这部戏将会在这个剧院每周上演两次.25. The soldier was absent from his camp for three days without________.(ask)这个士兵没有请假就离开营地三天.26. Our understanding of education,work and society is________ of the earlier generation.(different)我们对教育、工作和社会的认识和我们上一代人的不同.27. Things aren’t always________.(appear)事情往往不是它们看上去的那样.第二节:短文写作(共1题;满分30分)28. 请根据以下提示,并结合事例,用英语写一篇短文.You cannot choose what you are given,but you can choose how you make use of it.注意:①无须写标题,不得照抄英语提示语;②除诗歌外,文体不限;③文中不得透露个人姓名和学校名称;④词数为120左右.参考答案与试题解析2012年湖北省高考英语试卷一、听力(共两节,满分30分)1.【答案】1.B 2.C 3.A 4.B 5.A 6.A 7.B 8.B 9.C 10.A11.A 12.C 13.C &am;,p;nb,sp; 14.A 15.C 16.A 17.B 18.C 19.B 20.B【解析】略二、词汇知识运用(共两节,满分10分)多项选择(共10小题;每小题1分,满分10分)从A、B、C、D四个选项中,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.2.【答案】D【解析】句意:两位律师捐赠了5,0000美元赞助我校“帮助贫困生”活动,该活动是由三年前我们的前任校长发起的.3.【答案】C【解析】句意:最后,我要感谢我的辅导老师,他给我的论文提出了很多批评和建议,并对每张稿件作了推敲.4.【答案】B【解析】句意:独自在黑暗中行走,男孩吹口哨保持勇气.5.【答案】B【解析】句意:很高兴你能来亲自负责这件事情.6.【答案】D【解析】句意:有现代风格和明亮颜色的家具很适合现代的房子和花园,但是在一个传统花园里看起来很不协调.7.【答案】D【解析】句意:父亲突然对来讨论问题的邻居建议:“也许我们应该派人去请Dr.Smith来看看我们能够做什么”.8.【答案】D【解析】句意:你能告诉我“require”和“request”两个词之间的细微区别吗?我有时候对他们的意思感到困惑.9.【答案】C【解析】句意:是否要推倒这些建筑仍然有争议,人们还在寻找其它可行的解决方法.10.【答案】D【解析】定期对眼睛检查是很重要的,以便检查出任何可能的眼部疾病的征兆,这些疾病可能是没有症状的.11.【答案】B【解析】句意:这位官员坚持认为麦克尔Michael没有按照正确的程序申请签证.三、完形填空(共1小题;每小题20分,满分20分)12.【答案】bachelor,eventually,Because,must,tough,mysterious,calmeddown,concerned,drive,deep,unp repared,check,replied,cake,converted,shapes,incomplete,beside,hot,consider【解析】本文是一篇记叙文,讲述了“我”接受了社会学家在电视节目中提出的消费观点,担心成为现代消费社会的受害者,便去邻家商店买了自行车.老板推荐了自行车上的多种装置,甚至烤炉,我无法拒绝,一一购买.实际上我仍然是现代消费社会的受害者.本文旨在说明:无论做什么事都要有自己的立场,不能被别人左右.四、阅读理解(共5小题;每小题8分,满分40分)阅读下列短文,从每篇短文后所给各题的四个选项(A、B、C和D)中,选出最佳选项.13.【答案】ABCB【解析】文章大意:本文主要讲述的是一些人在离开英国以后再回来的时候,对于故乡发生的变化,自己是怎么理解的.为此,作者询问了一些从国外回到英国的人(Debi和Christine).Debi认为,原来的故乡是保守的,但是现在很多东欧国家和澳大利亚的人来到这里工作,他们的到来改善了英国的一些情况;Christine认为,回国之后发现这儿的一切看起来充满了绿色,但是和Christine之前呆过的地方相比,这里的机场很严格.14.【答案】CDAD【解析】我和我弟弟小时,在交通运输日,母亲总带着我们乘坐火车、公共汽车、出租车等,让我们感受到了自信与快乐.15.【答案】CABD【解析】本文向人们介绍了一封尘封了140年信,该信被研究人员偶然发现,那是一位女士向圣安德鲁斯大学写的学医申请信.只是要求在苏格兰最古老的大学里能有一席之地学习.这封由名叫索菲亚•杰克斯•布莱克的女性于1873年写的信在昨天的国际妇女节上被发布出来,整整七页的信敦促大学允许女性在医学研究机构学习.从而促使了妇女学位课程的创立.16.【答案】ABDB【解析】同一家庭出身的兄弟姐妹性格为何不同?那是因为他们生活于不同的家庭环境:对于父母的体验,第一个出生的孩子与以后出生的孩子会迥然不同;在语言发展上,后出生的孩子更喜欢向哥哥姐姐学习而不是向父母学习.17.【答案】BCDA。
2013-年高考辨析并修改病句”六种类型(学案)

高三“辨析并修改病句”六种类型对应练习学案课时安排:共7课时第一课时一、【真题体验】(广东卷)下列句子中,没有语病的一项是A.中国科学院最近研究发现,喜马拉雅山冰川退缩,湖泊的面积扩张,冰湖溃决危险性增大,引起了研究者的广泛关注。
B.长江中的江豚被誉为“水中大熊猫”,是国家二级保护动物,也是《华盛顿公约》确定的全球濒危物种之一,再不加以保护,15年后将会灭绝。
C.专家认为,我国人均饮茶量每天不足10克,加之大部分农药不溶于水,茶叶中即使有少量的农药残留,泡出的茶汤中也会农药含量极低,对人体健康影响不大。
D.今年广东天气形势复杂,西江、北江可能出现五年一遇的洪水;省政府要求各地要立足防大汛、抢大险、抗大旱,做到排查在前、排险在前、预警在前,确保群众的生命财产安全。
第二课时【一】“语序不当”病句类型(相关理论P19)一、经典例题1.如果人们连续看上四五个小时的电视节目,就会感到十分疲劳。
2.网络语言的泛滥,不仅影响了我国语言文字的纯洁化建设,而且误导了孩子,使之无法正确使用规范化语言。
3.可怜的小狗躺在地上,奄奄一息,满身伤痕,这时它已无力叫唤了。
4.作为一种助学贷款的消费信贷,市场需求的潜力很大。
大力发展这项贷款业务,为商业银行开拓信贷市场、培育业务增长点提供了契机。
5.夜深人静,张亮想起今天一连串发生的事情,仍然懊悔不已。
6.几位手足口病康复患者昨天在医院里在医护人员陪同下都十分高兴地同家人见了面。
7.托尔斯泰的记忆力和观察力是十分惊人的,他能迅速捕捉形象并将之长久地储存在头脑中,创作需要时,一“呼”即出。
8.至于我报考信息类专业是既定方向,哪所院校放在第一志愿,还在考虑中。
二、方法总结关于语序不当的语病要特别注意以下几种情况:★1.望见句中有关联词语,检查是否患关联词位置失当症。
★3.望见句中有数量词语,检查是否患数量词位置不当症。
★4.望见分句较多的复句,检查是否患分句间语序不当症。
三、演练高考(2012年题)1.我国首座自主建造、设计、开发的第六代深水半潜式钻井平台,在我国南海海域正式开钻,标志着我国海洋石油工业深水战略迈出了实质性步伐。
2012年湖北高考试题(文数,word解析版)

*归海木心*工作室 QQ:634102564感谢您对 *归海木心*工作室的支持!敬请收藏:2012年普通高等学校招生全国统一考试(湖北卷)数学(文科)【整理】佛山市三水区华侨中学 骆方祥(lbylfx @ )本试题卷共4页,共22题。
满分150分。
考试用时120分钟。
★祝考试顺利★注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在试题卷和答题卡上,并将准考证号条形码粘贴在答题卡上的指定位置。
用统一提供的2B 铅笔将答题卡上试卷类型A 后的方框涂黑。
2.选择题的作答:每小题选出答案后,用统一提供的2B 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。
答在试题卷、草稿纸上无效。
3.填空题和解答题的作答:用统一提供的签字笔将答案直接答在答题卡上对应的答题区域内。
答在试题卷、草稿纸上无效。
4.考生必须保持答题卡的整洁。
考试结束后,请将本试题卷和答题卡一并上交。
一、选择题:本大题共10小题,每小题5分,共50分. 在每小题给出的四个选项中,只有一项是符合题目要求的. 1.已知集合2{|320,}A x x x x =-+=∈R ,{|05,}B x x x =<<∈N ,则满足条件A C B ⊆⊆的集合C 的个数为A .1B .2C .3D .42.容量为20的样本数据,分组后的频数如下表:则样本数据落在区间[10,40)的频率为A .0.35B .0.45C .0.55D .0.65 3.函数()cos2f x x x =在区间[0,2π]上的零点的个数为A .2B .3C .4D .54.命题“存在一个无理数,它的平方是有理数”的否定是A .任意一个有理数,它的平方是有理数B .任意一个无理数,它的平方不是有理数C .存在一个有理数,它的平方是有理数D .存在一个无理数,它的平方不是有理数 5.过点(1,1)P 的直线,将圆形区域22{(,)|4}x y x y +≤分为两部分,使得这两部分的面积之差最大,则该直线的方程为A .20x y +-=B .10y -=C .0x y -=D .340x y +-=*归海木心*工作室6.已知定义在区间[0,2]上的函数()y f x =的图象如图所示,则(2)y f x =--的图象为7.定义在(,0)(0,)-∞+∞U 上的函数()f x ,如果对于任意给定的等比数列{}n a ,{()}n f a 仍是等比数列,则称()f x 为“保等比数列函数”. 现有定义在(,0)(0,)-∞+∞U 上的如下函数:①2()f x x =; ②()2x f x =; ③()||f x x =; ④()ln ||f x x =. 则其中是“保等比数列函数”的()f x 的序号为 A .① ②B .③ ④C .① ③D .② ④8.设△ABC 的内角A ,B ,C 所对的边分别为a ,b ,c . 若三边的长为连续的三个正整数,且A B C >>,320cos b a A =,则sin :sin :sin A B C 为 A .4:3:2B .5:6:7C .5:4:3D .6:5:49.设,,a b c +∈R ,则“1abc =”是“a b c a b c++≤++”的A .充分条件但不是必要条件B .必要条件但不是充分条件C .充分必要条件D .既不充分也不必要的条件10.如图,在圆心角为直角的扇形OAB 中,分别以OA ,OB 为直径作两个半圆. 在扇形OAB内随机取一点,则此点取自阴影部分的概率是A .112π- B .1πC .21π- D .2π第6题图O 1 2 x1-1yAO 1 2 x1-1 yBO 1 2 x1-1 y C O 12 x1-1 y DO 1 2x1-1y第10题图*归海木心*工作室侧视图正视图4 4 2俯视图11第15题图二、填空题:本大题共7小题,每小题5分,共35分. 请将答案填在答题卡对应题号的位置上. 答错位置,书写不清,模棱两可均不得分.11.一支田径运动队有男运动员56人,女运动员42人. 现用分层抽样的方法抽取若干人,若抽取的男运动员有8人,则抽取的女运动员有 人. 12.若3ii 1ib a b +=+-(a ,b 为实数,i 为虚数单位),则a b += . 13.已知向量(1,0)=a ,(1,1)=b ,则(Ⅰ)与2+a b 同向的单位向量的坐标表示为 ; (Ⅱ)向量3-b a 与向量a 夹角的余弦值为 .14.若变量,x y 满足约束条件1,1,33,x y x y x y -≥-⎧⎪+≥⎨⎪-≤⎩ 则目标函数23z x y =+的最小值是 .15.已知某几何体的三视图如图所示,则该几何体的体积为 .16.阅读如图所示的程序框图,运行相应的程序,输出的结果s = .17.传说古希腊毕达哥拉斯学派的数学家经常在沙滩上画点或用小石子表示数. 他们研究过如图所示的三角形数:将三角形数1,3,6,10,L 记为数列{}n a ,将可被5整除的三角形数按从小到大的顺序组成一个新数列{}n b . 可以推测: (Ⅰ)2012b 是数列{}n a 中的第________项; (Ⅱ)21k b -=________.(用k 表示)第16题图第17题图 10 6 3 1 ···*归海木心*工作室三、解答题:本大题共5小题,共65分. 解答应写出文字说明、证明过程或演算步骤. 18.(本小题满分12分)设函数22()sin cos cos f x x x x x ωωωωλ=+⋅-+()x ∈R 的图象关于直线πx =对称,其中ω,λ为常数,且1(,1)2ω∈.(Ⅰ)求函数()f x 的最小正周期;(Ⅱ)若()y f x =的图象经过点π(,0)4,求函数()f x 的值域.19.(本小题满分12分)某个实心零部件的形状是如图所示的几何体,其下部是底面均是正方形,侧面是全等的等腰梯形的四棱台1111A B C D ABCD -,上部是一个底面与四棱台的上底面重合,侧面是全等的矩形的四棱柱2222ABCD A B C D -. (Ⅰ)证明:直线11B D ⊥平面22ACC A ;(Ⅱ)现需要对该零部件表面进行防腐处理. 已知10AB =,1120A B =,230AA =,113AA =(单位:厘米),每平方厘米的加工处理费为0.20元,需加工处理费多少元?20.(本小题满分13分)已知等差数列{}n a 前三项的和为3-,前三项的积为8.(Ⅰ)求等差数列{}n a 的通项公式;(Ⅱ)若2a ,3a ,1a 成等比数列,求数列{||}n a 的前n 项和. 21.(本小题满分14分)设A 是单位圆221x y +=上的任意一点,l 是过点A 与x 轴垂直的直线,D 是直线l 与x 轴的交点,点M 在直线l 上,且满足||||(0,1)DM m DA m m =>≠且. 当点A 在圆上运动时,记点M 的轨迹为曲线C .(Ⅰ)求曲线C 的方程,判断曲线C 为何种圆锥曲线,并求其焦点坐标;(Ⅱ)过原点斜率为k 的直线交曲线C 于P ,Q 两点,其中P 在第一象限,且它在y 轴上的射影为点N ,直线QN 交曲线C 于另一点H . 是否存在m ,使得对任意的0k >,都有PQ PH ⊥?若存在,求m 的值;若不存在,请说明理由.22.(本小题满分14分)设函数()(1) (0)n f x ax x b x =-+>,n 为正整数,a ,b 为常数. 曲线()y f x =在(1,(1))f 处的切线方程为1x y +=. (Ⅰ)求a ,b 的值;(Ⅱ)求函数()f x 的最大值; (Ⅲ)证明:1()ef x n <. A 2B 2C 2D 2 CB ADA 1B 1C 1D 1第19题图*归海木心*工作室2012年普通高等学校招生全国统一考试(湖北卷)数学(文史类)试题参考答案一、选择题:A 卷:1.D 2.B 3.D 4.B 5.A 6.B 7.C 8.D 9.A 10.C 二、填空题:11. 6 12. 3 13.(Ⅰ);(Ⅱ) 14. 2 15.12π 16. 9 17.(Ⅰ)5030;(Ⅱ)()5512k k -三、解答题:18.解:(Ⅰ)因为22()sin cos cos f x x x x x ωωωωλ=-+⋅+cos 22x x ωωλ=-+π2sin(2)6x ωλ=-+.由直线πx =是()y f x =图象的一条对称轴,可得πsin(2π)16ω-=±,所以ππ2ππ()62k k ω-=+∈Z ,即1()23k k ω=+∈Z . 又1(,1)2ω∈,k ∈Z ,所以1k =,故56ω=.所以()f x 的最小正周期是6π5. (Ⅱ)由()y f x =的图象过点π(,0)4,得π()04f =,即5πππ2sin()2sin 6264λ=-⨯-=-=,即λ=故5π()2sin()36f x x =-()f x的值域为[22-.19.解:(Ⅰ)因为四棱柱2222ABCD A B C D -的侧面是全等的矩形,所以2AA AB ⊥,2AA AD ⊥. 又因为AB AD A =I ,所以2AA ⊥平面ABCD . 连接BD ,因为BD ⊂平面ABCD ,所以2AA BD ⊥.*归海木心*工作室因为底面ABCD 是正方形,所以AC BD ⊥. 根据棱台的定义可知,BD 与B 1 D 1共面.又已知平面ABCD ∥平面1111A B C D ,且平面11BB D D I 平面ABCD BD =, 平面11BB D D I 平面111111A B C D B D =,所以B 1 D 1∥BD . 于是由2AA BD ⊥,AC BD ⊥,B 1 D 1∥BD ,可得211AA B D ⊥,11AC B D ⊥. 又因为2AA AC A =I ,所以11B D ⊥平面22ACC A .(Ⅱ)因为四棱柱2222ABCD A B C D -的底面是正方形,侧面是全等的矩形,所以2221222()410410301300(cm )S S S A B AB AA =+=+⋅=+⨯⨯=四棱柱上底面四棱柱侧面.又因为四棱台1111A B C D ABCD -的上、下底面均是正方形,侧面是全等的等腰梯形,所以2211111()42S S S A B AB A B h =+=+⨯+四棱台下底面四棱台侧面等腰梯形的高()221204(101120(cm )2=+⨯+=.于是该实心零部件的表面积为212130*********(cm )S S S =+=+=, 故所需加工处理费为0.20.22420484S =⨯=(元).20.解:(Ⅰ)设等差数列{}n a 的公差为d ,则21a a d =+,312a a d =+,由题意得1111333,()(2)8.a d a a d a d +=-⎧⎨++=⎩ 解得12,3,a d =⎧⎨=-⎩或14,3.a d =-⎧⎨=⎩所以由等差数列通项公式可得23(1)35n a n n =--=-+,或43(1)37n a n n =-+-=-.故35n a n =-+,或37n a n =-. (Ⅱ)当35n a n =-+时,2a ,3a ,1a 分别为1-,4-,2,不成等比数列;当37n a n =-时,2a ,3a ,1a 分别为1-,2,4-,成等比数列,满足条件. 故37,1,2,|||37|37, 3.n n n a n n n -+=⎧=-=⎨-≥⎩记数列{||}n a 的前n 项和为n S .当1n =时,11||4S a ==;当2n =时,212||||5S a a =+=; 当3n ≥时,*234||||||n n S S a a a =++++L 5(337)(347)(37)n =+⨯-+⨯-++-L2(2)[2(37)]311510222n n n n -+-=+=-+. 当2n =时,满足此式.综上,24,1,31110, 1.22n n S n n n =⎧⎪=⎨-+>⎪⎩21.解:(Ⅰ)如图1,设(,)M x y ,00(,)A x y ,则由||||(0,1)DM m DA m m =>≠且,可得0x x =,0||||y m y =,所以0x x =,01||||y y m=. ① 因为A 点在单位圆上运动,所以22001x y +=. ②将①式代入②式即得所求曲线C 的方程为222 1 (0,1)y x m m m+=>≠且.因为(0,1)(1,)m ∈+∞U ,所以当01m <<时,曲线C 是焦点在x 轴上的椭圆, 两焦点坐标分别为(0),0); 当1m >时,曲线C 是焦点在y 轴上的椭圆, 两焦点坐标分别为(0,,(0,.(Ⅱ)解法1:如图2、3,0k ∀>,设11(,)P x kx ,22(,)H x y ,则11(,)Q x kx --,1(0,)N kx , 直线QN 的方程为12y kx kx =+,将其代入椭圆C 的方程并整理可得 222222211(4)40m k x k x x k x m +++-=.依题意可知此方程的两根为1x -,2x ,于是由韦达定理可得 21122244k x x x m k -+=-+,即212224m x x m k =+. 因为点H 在直线QN 上,所以2121222224km x y kx kx m k -==+.于是11(2,2)PQ x kx =--u u u r ,22112121222242(,)(,)44k x km x PH x x y kx m k m k =--=-++u u u r .而PQ PH ⊥等价于2221224(2)04m k x PQ PH m k -⋅==+u u u r u u u r ,即220m -=,又0m >,得m ,故存在m =2212y x +=上,对任意的0k >,都有PQ PH ⊥.图2 (01)m <<图3 (1)m >图1*归海木心*工作室解法2:如图2、3,1(0,1)x ∀∈,设11(,)P x y ,22(,)H x y ,则11(,)Q x y --, 1(0,)N y ,因为P ,H 两点在椭圆C 上,所以222211222222,,m x y m m x y m ⎧+=⎪⎨+=⎪⎩ 两式相减可得 222221212()()0m x x y y -+-=. ③依题意,由点P 在第一象限可知,点H 也在第一象限,且P ,H 不重合, 故1212()()0x x x x -+≠. 于是由③式可得212121212()()()()y y y y m x x x x -+=--+. ④又Q ,N ,H 三点共线,所以QN QH k k =,即1121122y y y x x x +=+. 于是由④式可得211212121121212()()12()()2PQ PHy y y y y y y m k k x x x x x x x --+⋅=⋅=⋅=---+. 而PQ PH ⊥等价于1PQ PHk k ⋅=-,即212m -=-,又0m >,得m ,故存在m =2212y x +=上,对任意的0k >,都有PQ PH ⊥.22.解:(Ⅰ)因为(1)f b =,由点(1,)b 在1x y +=上,可得11b +=,即0b =.因为1()(1)n n f x anx a n x -'=-+,所以(1)f a '=-.又因为切线1x y +=的斜率为1-,所以1a -=-,即1a =. 故1a =,0b =. (Ⅱ)由(Ⅰ)知,1()(1)n n n f x x x x x +=-=-,1()(1)()1n nf x n x x n -'=+-+.*归海木心*工作室令()0f x '=,解得1n x n =+,即()f x '在(0,)+∞上有唯一零点01n x n =+. 在(0,)1nn +上,()0f x '>,故()f x 单调递增; 而在(,)1nn +∞+上,()0f x '<,()f x 单调递减. 故()f x 在(0,)+∞上的最大值为1()()(1)111(1)nn n n n n n f n n n n +=-=++++. (Ⅲ)令1()ln 1+(0)t t t t ϕ=->,则22111()= (0)t t t t t tϕ-'=->. 在(0,1)上,()0t ϕ'<,故()t ϕ单调递减; 而在(1,)+∞上()0t ϕ'>,()t ϕ单调递增.故()t ϕ在(0,)+∞上的最小值为(1)0ϕ=. 所以()0(1)t t ϕ>>,即1ln 1(1)t t t >->.令11t n =+,得11ln 1n n n +>+,即11ln()ln e n n n++>, 所以11()e n n n++>,即11(1)e n n n n n +<+. 由(Ⅱ)知,11()(1)en n n f x n n +≤<+,故所证不等式成立.。
2012年普通高考学校招生全国统一考试(湖北卷)及答案

2012年普通高考学校招生全国统一考试(湖北卷)语文一、语文基础知识(共15分,共5小题,每小题3分)1.下列各组词语中加点的字,读音全都相同的一组是A.灵.秀磷.光玲.珑剔透聆.听教诲B.诞.生旦.角淡.泊明志担.当重任C.宿.营诉.说夙.兴夜寐素.昧平生D.咨.询滋.生芝.兰之室孜.孜不倦2.下列各组词语中,没有错别字的一组是A.羞涩袅娜歌声渺茫荷塘薄雾B.霜天廖廓峥嵘岁月浪遏飞舟C.细腻萧索落蕊残叶秋蝉嘶叫D.嫩黄葱茏婆娑起舞繁茂苍翠3.依次填入下列横线处的词语,最恰当的是说到底,世上风景闲流水,端的还是咬人慢下来。
中国这如诗的城市中,最是江城得了个中,且将它地挥洒出来。
这江城街头巷尾,湖畔公园里数不胜数的茶馆,茶铺,一个人在清晨的不慌不忙的起来,到茶馆里,一坐就是一天,那叫一个悠闲!A.趣味痛痛快快当是溜B.滋味淋漓尽致便是走C.意味兴致勃勃自是逛D.韵味尽情尽兴恰是晃4.下列各项中,没有语病的是A.坐上画舫游清江,如行画卷之中,江水清澈,绿树蓊郁,自然与人,相遇相依,随风生长,好一派如诗如画的风光。
B.游览三峡大瀑布时,我们从倾泻而下的水帘中狂奔而过,尖叫声,嬉笑中响声一片,真是充满刺激的难忘体验。
C.当今已经很少有人回想以前那样闲情逸致,拿出一本小说,从头到尾阅读一遍,欣赏其委婉动人的故事。
D.现代文明不仅带来了理性化、工业化、市场化、都市化、民主化和法制化这些美好的社会制度,而却创造了前所未有的物质财富。
5.下列有关文学常识的表述,有错误...的一项是A.《孔乙己》描写了科举考试失意者的命运。
作者对孔乙己的穷困潦倒和因窃书而被赶出鲁镇的悲惨遭遇,寄予了同情。
B.已知杀父娶母的实情却迟迟不采取复仇行动,这一情节构成《哈姆莱特》中著名的“延宕”,体现了主人公复杂、矛盾的心理。
C.宋词至苏轼,让人耳目一新,苏轼拓宽了词的题材,提升了词的格调,丰富了词的表现手法,开创了具有革新意义的豪放词派。
2012湖北省高考试卷含解析(必备资料)

1、依次填入下列各句横线处的成语,最恰当的一组是(3分)①他是一个心地善良的人,但性格懦弱、谨小慎微,做起事来总是,从来不敢越雷池一步。
②当今世界科技突飞猛进,我们更要勇于开拓,不断进取,如果,就会落后甚至被时代潮流所淘汰。
③要想让中国传统戏曲焕发出新的生命力,决不能满足于现状,,唯有创新才是弘扬戏曲文化的康庄大道.A.故步自封墨守成规抱残守缺B.墨守成规故步自封抱残守缺C.抱残守缺故步自封墨守成规D.墨守成规抱残守缺故步自封2、下列各句中,没有语病的一句是(3分)A.“地坛书市”曾经是北京市民非常喜爱的一个文化品牌,去年更名为“北京书市”并落户朝阳公园后,依旧热情不减。
B.“丝绸之路经济带”横跨亚、非、欧三大洲,其形成与繁荣必将深刻影响世界政治、经济格局,促进全球的和平与发展。
C.在那个民族独立和民族解放斗争风起云涌的时代,能激发人们的爱国热情是评判一部文学作品好坏的非常重要的标准。
D.父亲住院期间,梅兰每天晚上都陪伴在他身旁,听他讲述一生中经历的种种苦难和幸福,她就算再忙再累,也不例外。
3、在下面一段文字横线处填入语句,衔接最恰当的一项是(3分)自宋元至明清,清明节除了要祭扫家墓,还要在门楣、窗户上插上柳条。
,。
,,,。
①达到人丁兴旺、身体健康的目的②于是在郊游踏青时③它便成了人类文化中生命力的象征④人们企盼将这种生命力转移到自家门庭和家庭成员身上⑤不会忘记顺便折一些柳条回来⑥由于柳树最先送来春的消息并且具有旺盛的生殖力A.⑥③④①②⑤ B.②⑤①④⑥③ C.②④⑥③①⑤ D.⑥④②⑤③①4、依次填入下面语段横线处的词语,最恰当的一组是散文能够真正地见出一位作家的个性和__________。
阅读散文,我们能体味到鲁迅的________,冰心的________,梁实秋的幽默机智,丰子恺的清雅淡泊。
“情”是散文的命脉和灵魂,对于散文的“情”来说,真挚_________。
A.情趣冷峻深沉温和娴雅至关重要B.情趣冷峭深沉冲淡平和至关重要C.情调冷峭阴沉温和娴雅举足轻重D.情调冷峻深沉冲淡平和举足轻重5、下列诗句中,没有使用比拟手法的一项是(3分)A.东风便试新刀尺,万叶千花一手裁。
2012年湖北省高考数学试卷(理科)附送答案
2012年湖北省高考数学试卷(理科)一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的1.(5分)方程x2+6x+13=0的一个根是()A.﹣3+2i B.3+2i C.﹣2+3i D.2+3i2.(5分)命题“∃x0∈∁R Q,x03∈Q”的否定是()A.∃x0∉∁R Q,x03∈Q B.∃x0∈∁R Q,x03∉QC.∀x0∉∁R Q,x03∈Q D.∀x0∈∁R Q,x03∉Q3.(5分)已知二次函数y=f(x)的图象如图所示,则它与x轴所围图形的面积为()A. B.C.D.4.(5分)已知某几何体的三视图如图所示,则该几何体的体积为()A. B.3πC.D.6π5.(5分)设a∈Z,且0≤a≤13,若512012+a能被13整除,则a=()A.0 B.1 C.11 D.126.(5分)设a,b,c,x,y,z是正数,且a2+b2+c2=10,x2+y2+z2=40,ax+by+cz=20,则=()A.B.C.D.7.(5分)定义在(﹣∞,0)∪(0,+∞)上的函数f(x),如果对于任意给定的等比数列{a n},{f(a n)}仍是等比数列,则称f(x)为“保等比数列函数”.现有定义在(﹣∞,0)∪(0,+∞)上的如下函数:①f(x)=x2;②f(x)=2x;③f(x)=;④f(x)=ln|x|.则其中是“保等比数列函数”的f(x)的序号为()A.①②B.③④C.①③D.②④8.(5分)如图,在圆心角为直角的扇形OAB中,分别以OA,OB为直径作两个半圆.在扇形OAB内随机取一点,则此点取自阴影部分的概率是()A.1﹣B.﹣C.D.9.(5分)函数f(x)=xcosx2在区间[0,4]上的零点个数为()A.4 B.5 C.6 D.710.(5分)我国古代数学名著《九章算术》中“开立圆术”曰:置积尺数,以十六乘之,九而一,所得开立方除之,即立圆径,“开立圆术”相当于给出了已知球的体积V,求其直径d的一个近似公式d≈.人们还用过一些类似的近似公式.根据π=3.14159…..判断,下列近似公式中最精确的一个是()A.d≈B.d≈ C.d≈D.d≈二、填空题:(一)必考题(11-14题)本大题共4小题,考试共需作答5小题,每小题5分,共25分.请将答案填在答题卡对应题号的位置上.答错位置,书写不清,模棱两可均不得分.11.(5分)设△ABC的内角A,B,C,所对的边分别是a,b,c.若(a+b﹣c)(a+b+c)=ab,则角C=.12.(5分)阅读如图所示的程序框图,运行相应的程序,输出的结果s=.13.(5分)回文数是指从左到右与从右到左读都一样的正整数.如22,11,3443,94249等.显然2位回文数有9个:11,22,33…,99.3位回文数有90个:101,111,121,…,191,202,…,999.则:(Ⅰ)4位回文数有个;)位回文数有个.(Ⅱ)2n+1(n∈N+14.(5分)如图,双曲线﹣=1(a,b>0)的两顶点为A1,A2,虚轴两端点为B1,B2,两焦点为F1,F2.若以A1A2为直径的圆内切于菱形F1B1F2B2,切点分别为A,B,C,D.则:(Ⅰ)双曲线的离心率e=;(Ⅱ)菱形F1B1F2B2的面积S1与矩形ABCD的面积S2的比值=.二、填空题:(二)选考题(请考生在第15、16两题中任选一题作答,请先在答题卡指定位置将你所选的题目序号后的方框用2B铅笔涂黑,如果全选,则按第15题作答结果计分.)15.(5分)如图,点D在⊙O的弦AB上移动,AB=4,连接OD,过点D作OD 的垂线交⊙O于点C,则CD的最大值为.16.(选修4﹣4:坐标系与参数方程):在直角坐标系xOy中,以原点O为极点,x轴的正半轴为极轴建立极坐标系,已知射线θ=与曲线(t为参数)相交于A,B来两点,则线段AB的中点的直角坐标为.三、解答题:本大题共6小题,共75分.解答应写出文字说明、证明过程或演算步骤.17.(12分)已知向量=(cosωx﹣sinωx,sinωx),=(﹣cosωx﹣sinωx,2cosωx),设函数f(x)=•+λ(x∈R)的图象关于直线x=π对称,其中ω,λ为常数,且ω∈(,1)(1)求函数f(x)的最小正周期;(2)若y=f(x)的图象经过点(,0)求函数f(x)在区间[0,]上的取值范围.18.(12分)已知等差数列{a n}前三项的和为﹣3,前三项的积为8.(1)求等差数列{a n}的通项公式;(2)若a2,a3,a1成等比数列,求数列{|a n|}的前n项和.19.(12分)如图1,∠ACB=45°,BC=3,过动点A作AD⊥BC,垂足D在线段BC上且异于点B,连接AB,沿AD将△ABD折起,使∠BDC=90°(如图2所示),(1)当BD的长为多少时,三棱锥A﹣BCD的体积最大;(2)当三棱锥A﹣BCD的体积最大时,设点E,M分别为棱BC,AC的中点,试在棱CD上确定一点N,使得EN⊥BM,并求EN与平面BMN所成角的大小.20.(12分)根据以往的经验,某工程施工期间的将数量X(单位:mm)对工期的影响如下表:降水量X X<300300≤X<700700≤X<900X≥90002610工期延误天数Y历年气象资料表明,该工程施工期间降水量X小于300,700,900的概率分别为0.3,0.7,0.9,求:(I)工期延误天数Y的均值与方差;(Ⅱ)在降水量X至少是300的条件下,工期延误不超过6天的概率.21.(13分)设A是单位圆x2+y2=1上的任意一点,l是过点A与x轴垂直的直线,D是直线l与x轴的交点,点M在直线l上,且满足丨DM丨=m丨DA丨(m>0,且m≠1).当点A在圆上运动时,记点M的轨迹为曲线C.(I)求曲线C的方程,判断曲线C为何种圆锥曲线,并求焦点坐标;(Ⅱ)过原点且斜率为k的直线交曲线C于P、Q两点,其中P在第一象限,它在y轴上的射影为点N,直线QN交曲线C于另一点H,是否存在m,使得对任意的k>0,都有PQ⊥PH?若存在,求m的值;若不存在,请说明理由.22.(14分)(I)已知函数f(x)=rx﹣x r+(1﹣r)(x>0),其中r为有理数,且0<r<1.求f(x)的最小值;(II)试用(I)的结果证明如下命题:设a1≥0,a2≥0,b1,b2为正有理数,若b1+b2=1,则a1b1a2b2≤a1b1+a2b2;(III)请将(II)中的命题推广到一般形式,并用数学归纳法证明你所推广的命题.注:当α为正有理数时,有求导公式(xα)r=αxα﹣1.2012年湖北省高考数学试卷(理科)参考答案与试题解析一、选择题:本大题共10小题,每小题5分,共50分,在每小题给出的四个选项中,只有一项是符合题目要求的1.(5分)(2012•湖北)方程x2+6x+13=0的一个根是()A.﹣3+2i B.3+2i C.﹣2+3i D.2+3i【分析】由方程x2+6x+13=0中,△=36﹣52=﹣16<0,知=﹣3±2i,由此能求出结果.【解答】解:∵方程x2+6x+13=0中,△=36﹣52=﹣16<0,∴=﹣3±2i,故选A.2.(5分)(2012•湖北)命题“∃x0∈∁R Q,x03∈Q”的否定是()A.∃x0∉∁R Q,x03∈Q B.∃x0∈∁R Q,x03∉QC.∀x0∉∁R Q,x03∈Q D.∀x0∈∁R Q,x03∉Q【分析】根据特称命题“∃x∈A,p(A)”的否定是“∀x∈A,非p(A)”,结合已知中命题,即可得到答案.【解答】解:∵命题“∃x0∈C R Q,∈Q”是特称命题,而特称命题的否定是全称命题,∴“∃x0∈C R Q,∈Q”的否定是∀x0∈C R Q,∉Q故选D3.(5分)(2012•湖北)已知二次函数y=f(x)的图象如图所示,则它与x轴所围图形的面积为()A. B.C.D.【分析】先根据函数的图象求出函数的解析式,然后利用定积分表示所求面积,最后根据定积分运算法则求出所求.【解答】解:根据函数的图象可知二次函数y=f(x)图象过点(﹣1,0),(1,0),(0,1)从而可知二次函数y=f(x)=﹣x2+1∴它与X轴所围图形的面积为=()=(﹣+1)﹣(﹣1)=故选B.4.(5分)(2012•湖北)已知某几何体的三视图如图所示,则该几何体的体积为()A. B.3πC.D.6π【分析】通过三视图判断几何体的特征,利用三视图的数据,求出几何体的体积即可.【解答】解:由三视图可知几何体是圆柱底面半径为1高为6的圆柱,被截的一部分,如图所求几何体的体积为:=3π.故选B.5.(5分)(2012•湖北)设a∈Z,且0≤a≤13,若512012+a能被13整除,则a=()A.0 B.1 C.11 D.12【分析】由二项式定理可知512012+a=(52﹣1)2012+a的展开式中的项含有因数52,要使得能512012+a能被13整除,只要a+1能被13整除,结合已知a的范围可求【解答】解:∵512012+a=(52﹣1)2012+a=+…++a由于含有因数52,故能被52整除要使得能512012+a能被13整除,且a∈Z,0≤a≤13则可得a+1=13∴a=12故选D6.(5分)(2012•湖北)设a,b,c,x,y,z是正数,且a2+b2+c2=10,x2+y2+z2=40,ax+by+cz=20,则=()A.B.C.D.【分析】根据所给条件,利用柯西不等式求解,利用等号成立的条件即可.【解答】解:由柯西不等式得,(a2+b2+c2)(x2+y2+z2)≥(ax+by+cz)2,当且仅当时等号成立∵a2+b2+c2=10,x2+y2+z2=40,ax+by+cz=20,∴等号成立∴∴=故选C.7.(5分)(2012•湖北)定义在(﹣∞,0)∪(0,+∞)上的函数f(x),如果对于任意给定的等比数列{a n},{f(a n)}仍是等比数列,则称f(x)为“保等比数列函数”.现有定义在(﹣∞,0)∪(0,+∞)上的如下函数:①f(x)=x2;②f(x)=2x;③f(x)=;④f(x)=ln|x|.则其中是“保等比数列函数”的f (x)的序号为()A.①②B.③④C.①③D.②④【分析】根据新定义,结合等比数列性质,一一加以判断,即可得到结论.【解答】解:由等比数列性质知,①=f2(a n),故正确;+1),故不正确;②≠=f2(a n+1),故正确;③==f2(a n+1④f(a n)f(a n+2)=ln|a n|ln|a n+2|≠=f2(a n+1),故不正确;故选C8.(5分)(2012•湖北)如图,在圆心角为直角的扇形OAB中,分别以OA,OB 为直径作两个半圆.在扇形OAB内随机取一点,则此点取自阴影部分的概率是()A.1﹣B.﹣C.D.【分析】求出阴影部分的面积即可,连接OC,把下面的阴影部分平均分成了2部分,然后利用位移割补的方法,分别平移到图中划线部分,那么阴影部分的面积就是图中扇形的面积﹣直角三角形AOB的面积.【解答】解:设扇形的半径为r,则扇形OAB的面积为,连接OC,把下面的阴影部分平均分成了2部分,然后利用位移割补的方法,分别平移到图中划线部分,则阴影部分的面积为:﹣,∴此点取自阴影部分的概率是.故选A.9.(5分)(2012•湖北)函数f(x)=xcosx2在区间[0,4]上的零点个数为()A.4 B.5 C.6 D.7【分析】令函数值为0,构建方程,即可求出在区间[0,4]上的解,从而可得函数f(x)=xcosx2在区间[0,4]上的零点个数【解答】解:令f(x)=0,可得x=0或cosx2=0∴x=0或x2=,k∈Z∵x∈[0,4],则x2∈[0,16],∴k可取的值有0,1,2,3,4,∴方程共有6个解∴函数f(x)=xcosx2在区间[0,4]上的零点个数为6个故选C10.(5分)(2012•湖北)我国古代数学名著《九章算术》中“开立圆术”曰:置积尺数,以十六乘之,九而一,所得开立方除之,即立圆径,“开立圆术”相当于给出了已知球的体积V,求其直径d的一个近似公式d≈.人们还用过一些类似的近似公式.根据π=3.14159…..判断,下列近似公式中最精确的一个是()A.d≈B.d≈ C.d≈D.d≈【分析】根据球的体积公式求出直径,然后选项中的常数为,表示出π,将四个选项逐一代入,求出最接近真实值的那一个即可.【解答】解:由V=,解得d=设选项中的常数为,则π=选项A代入得π==3.375;选项B代入得π==3;选项C代入得π==3.14;选项D代入得π==3.142857由于D的值最接近π的真实值故选D.二、填空题:(一)必考题(11-14题)本大题共4小题,考试共需作答5小题,每小题5分,共25分.请将答案填在答题卡对应题号的位置上.答错位置,书写不清,模棱两可均不得分.11.(5分)(2012•湖北)设△ABC的内角A,B,C,所对的边分别是a,b,c.若(a+b﹣c)(a+b+c)=ab,则角C=.【分析】利用已知条件(a+b﹣c)(a+b+c)=ab,以及余弦定理,可联立解得cosB 的值,进一步求得角B.【解答】解:由已知条件(a+b﹣c)(a+b+c)=ab可得a2+b2﹣c2+2ab=ab即a2+b2﹣c2=﹣ab由余弦定理得:cosC==又因为0<C<π,所以C=.故答案为:12.(5分)(2012•湖北)阅读如图所示的程序框图,运行相应的程序,输出的结果s=9.【分析】用列举法,通过循环过程直接得出S与n的值,得到n=3时退出循环,即可.【解答】解:循环前,S=1,a=3,第1次判断后循环,n=2,s=4,a=5,第2次判断并循环n=3,s=9,a=7,第3次判断退出循环,输出S=9.故答案为:9.13.(5分)(2012•湖北)回文数是指从左到右与从右到左读都一样的正整数.如22,11,3443,94249等.显然2位回文数有9个:11,22,33…,99.3位回文数有90个:101,111,121,…,191,202,…,999.则:(Ⅰ)4位回文数有90个;(Ⅱ)2n+1(n∈N)位回文数有9×10n个.+【分析】(I)利用回文数的定义,四位回文数只需从10个数字中选两个可重复数字即可,但要注意最两边的数字不能为0,利用分步计数原理即可计算4位回文数的个数;(II)将(I)中求法推广到一般,利用分步计数原理即可计算2n+1(n∈N)位+回文数的个数【解答】解:(I)4位回文数的特点为中间两位相同,千位和个位数字相同但不能为零,第一步,选千位和个位数字,共有9种选法;第二步,选中间两位数字,有10种选法;故4位回文数有9×10=90个故答案为90(II)第一步,选左边第一个数字,有9种选法;第二步,分别选左边第2、3、4、…、n、n+1个数字,共有10×10×10×…×10=10n 种选法,)位回文数有9×10n个故2n+1(n∈N+故答案为9×10n14.(5分)(2012•湖北)如图,双曲线﹣=1(a,b>0)的两顶点为A1,A2,虚轴两端点为B1,B2,两焦点为F1,F2.若以A1A2为直径的圆内切于菱形F1B1F2B2,切点分别为A,B,C,D.则:(Ⅰ)双曲线的离心率e=;(Ⅱ)菱形F1B1F2B2的面积S1与矩形ABCD的面积S2的比值=.【分析】(Ⅰ)直线B2F1的方程为bx﹣cy+bc=0,所以O到直线的距离为,根据以A1A2为直径的圆内切于菱形F1B1F2B2,可得,由此可求双曲线的离心率;(Ⅱ)菱形F1B1F2B2的面积S1=2bc,求出矩形ABCD的长与宽,从而求出面积S2=4mn=,由此可得结论.(Ⅰ)直线B2F1的方程为bx﹣cy+bc=0,所以O到直线的距离为【解答】解:∵以A1A2为直径的圆内切于菱形F1B1F2B2,∴∴(c2﹣a2)c2=(2c2﹣a2)a2∴c4﹣3a2c2+a4=0∴e4﹣3e2+1=0∵e>1∴e=(Ⅱ)菱形F1B1F2B2的面积S1=2bc设矩形ABCD,BC=2n,BA=2m,∴∵m2+n2=a2,∴,∴面积S2=4mn=∴==∵bc=a2=c2﹣b2∴∴=故答案为:,二、填空题:(二)选考题(请考生在第15、16两题中任选一题作答,请先在答题卡指定位置将你所选的题目序号后的方框用2B铅笔涂黑,如果全选,则按第15题作答结果计分.)15.(5分)(2012•湖北)如图,点D在⊙O的弦AB上移动,AB=4,连接OD,过点D作OD的垂线交⊙O于点C,则CD的最大值为2.【分析】由题意可得CD2=OC2﹣OD2,故当半径OC最大且弦心距OD最小时,CD取得最大值,故当AB为直径、且D为AB的中点时,CD取得最大值,为AB的一半.【解答】解:由题意可得△OCD为直角三角形,故有CD2=OC2﹣OD2,故当半径OC最大且弦心距OD最小时,CD取得最大值.故当AB为直径、且D为AB的中点时,CD取得最大值,为AB的一半,由于AB=4,故CD的最大值为2,故答案为2.16.(2012•湖北)(选修4﹣4:坐标系与参数方程):在直角坐标系xOy中,以原点O为极点,x轴的正半轴为极轴建立极坐标系,已知射线θ=与曲线(t为参数)相交于A,B来两点,则线段AB的中点的直角坐标为(2.5,2.5).【分析】化极坐标方程为直角坐标方程,参数方程为普通方程,联立可求线段AB的中点的直角坐标.【解答】解:射线θ=的直角坐标方程为y=x(x≥0),曲线(t为参数)化为普通方程为y=(x﹣2)2,联立方程并消元可得x2﹣5x+4=0,∴方程的两个根分别为1,4∴线段AB的中点的横坐标为2.5,纵坐标为2.5∴线段AB的中点的直角坐标为(2.5,2.5)故答案为:(2.5,2.5)三、解答题:本大题共6小题,共75分.解答应写出文字说明、证明过程或演算步骤.17.(12分)(2012•湖北)已知向量=(cosωx﹣sinωx,sinωx),=(﹣cosωx ﹣sinωx,2cosωx),设函数f(x)=•+λ(x∈R)的图象关于直线x=π对称,其中ω,λ为常数,且ω∈(,1)(1)求函数f(x)的最小正周期;(2)若y=f(x)的图象经过点(,0)求函数f(x)在区间[0,]上的取值范围.【分析】(1)先利用向量数量积运算性质,求函数f(x)的解析式,再利用二倍角公式和两角差的余弦公式将函数f(x)化为y=Asin(ωx+φ)+k型函数,最后利用函数的对称性和ω的范围,计算ω的值,从而得函数的最小正周期;(2)先将已知点的坐标代入函数解析式,求得λ的值,再求内层函数的值域,最后将内层函数看做整体,利用正弦函数的图象和性质即可求得函数f(x)的值域.【解答】解:(1)∵f(x)=•+λ=(cosωx﹣sinωx)×(﹣cosωx﹣sinωx)+sinωx ×2cosωx+λ=﹣(cos2ωx﹣sin2ωx)+sin2ωx+λ=sin2ωx﹣cos2ωx+λ=2sin(2ωx﹣)+λ∵图象关于直线x=π对称,∴2πω﹣=+kπ,k∈z∴ω=+,又ω∈(,1)∴k=1时,ω=∴函数f(x)的最小正周期为=(2)∵f()=0∴2sin(2××﹣)+λ=0∴λ=﹣∴f(x)=2sin(x﹣)﹣由x∈[0,]∴x﹣∈[﹣,]∴sin(x﹣)∈[﹣,1]∴2sin(x﹣)﹣=f(x)∈[﹣1﹣,2﹣]故函数f(x)在区间[0,]上的取值范围为[﹣1﹣,2﹣]18.(12分)(2012•湖北)已知等差数列{a n}前三项的和为﹣3,前三项的积为8.(1)求等差数列{a n}的通项公式;(2)若a2,a3,a1成等比数列,求数列{|a n|}的前n项和.【分析】(I)设等差数列的公差为d,由题意可得,,解方程可求a1,d,进而可求通项(II)由(I)的通项可求满足条件a2,a3,a1成等比的通项为a n=3n﹣7,则|a n|=|3n ﹣7|=,根据等差数列的求和公式可求【解答】解:(I)设等差数列的公差为d,则a2=a1+d,a3=a1+2d由题意可得,解得或由等差数列的通项公式可得,a n=2﹣3(n﹣1)=﹣3n+5或a n=﹣4+3(n﹣1)=3n ﹣7(II)当a n=﹣3n+5时,a2,a3,a1分别为﹣1,﹣4,2不成等比当a n=3n﹣7时,a2,a3,a1分别为﹣1,2,﹣4成等比数列,满足条件故|a n|=|3n﹣7|=设数列{|a n|}的前n项和为S n当n=1时,S1=4,当n=2时,S2=5当n≥3时,S n=|a1|+|a2|+…+|a n|=5+(3×3﹣7)+(3×4﹣7)+…+(3n﹣7)=5+=,当n=2时,满足此式综上可得19.(12分)(2012•湖北)如图1,∠ACB=45°,BC=3,过动点A作AD⊥BC,垂足D在线段BC上且异于点B,连接AB,沿AD将△ABD折起,使∠BDC=90°(如图2所示),(1)当BD的长为多少时,三棱锥A﹣BCD的体积最大;(2)当三棱锥A﹣BCD的体积最大时,设点E,M分别为棱BC,AC的中点,试在棱CD上确定一点N,使得EN⊥BM,并求EN与平面BMN所成角的大小.【分析】(1)设BD=x,先利用线面垂直的判定定理证明AD即为三棱锥A﹣BCD 的高,再将三棱锥的体积表示为x的函数,最后利用导数求函数的最大值即可;(2)由(1)可先建立空间直角坐标系,写出相关点的坐标和相关向量的坐标,设出动点N的坐标,先利用线线垂直的充要条件计算出N点坐标,从而确定N 点位置,再求平面BMN的法向量,从而利用夹角公式即可求得所求线面角【解答】解:(1)设BD=x,则CD=3﹣x∵∠ACB=45°,AD⊥BC,∴AD=CD=3﹣x∵折起前AD⊥BC,∴折起后AD⊥BD,AD⊥CD,BD∩DC=D∴AD⊥平面BCD=×AD×S△BCD=×(3﹣x)××x(3﹣x)=(x3﹣6x2+9x)∴V A﹣BCD设f(x)=(x3﹣6x2+9x)x∈(0,3),∵f′(x)=(x﹣1)(x﹣3),∴f(x)在(0,1)上为增函数,在(1,3)上为减函数∴当x=1时,函数f(x)取最大值∴当BD=1时,三棱锥A﹣BCD的体积最大;(2)以D为原点,建立如图直角坐标系D﹣xyz,由(1)知,三棱锥A﹣BCD的体积最大时,BD=1,AD=CD=2∴D(0,0,0),B(1,0,0),C(0,2,0),A(0,0,2),M(0,1,1),E (,1,0),且=(﹣1,1,1)设N(0,λ,0),则=(﹣,λ﹣1,0)∵EN⊥BM,∴•=0即(﹣1,1,1)•(﹣,λ﹣1,0)=+λ﹣1=0,∴λ=,∴N(0,,0)∴当DN=时,EN⊥BM设平面BMN的一个法向量为=(x,y,z),由及=(﹣1,,0)得,取=(1,2,﹣1)设EN与平面BMN所成角为θ,则=(﹣,﹣,0)sinθ=|cos<,>|=||==∴θ=60°∴EN与平面BMN所成角的大小为60°20.(12分)(2012•湖北)根据以往的经验,某工程施工期间的将数量X(单位:mm)对工期的影响如下表:降水量X X<300300≤X<700700≤X<900X≥900工期延误天数02610Y历年气象资料表明,该工程施工期间降水量X小于300,700,900的概率分别为0.3,0.7,0.9,求:(I)工期延误天数Y的均值与方差;(Ⅱ)在降水量X至少是300的条件下,工期延误不超过6天的概率.【分析】(I)由题意,该工程施工期间降水量X小于300,700,900的概率分别为0.3,0.7,0.9,结合某程施工期间的降水量对工期的影响,可求相应的概率,进而可得期延误天数Y的均值与方差;(Ⅱ)利用概率的加法公式可得P(X≥300)=1﹣P(X<300)=0.7,P(300≤X <900)=P(X<900)﹣P(X<300)=0.9﹣0.3=0.6,利用条件概率,即可得到结论【解答】(I)由题意,P(X<300)=0.3,P(300≤X<700)=P(X<700)﹣P(X <300)=0.7﹣0.3=0.4,P(700≤X<900)=P(X<900)﹣P(X<700)=0.9﹣0.7=0.2,P(X≥900)=1﹣0.9=0.1Y的分布列为Y02610P0.30.40.20.1∴E(Y)=0×0.3+2×0.4+6×0.2+10×0.1=3D(Y)=(0﹣3)2×0.3+(2﹣3)2×0.4+(6﹣3)2×0.2+(10﹣3)2×0.1=9.8∴工期延误天数Y的均值为3,方差为9.8;(Ⅱ)P(X≥300)=1﹣P(X<300)=0.7,P(300≤X<900)=P(X<900)﹣P (X<300)=0.9﹣0.3=0.6由条件概率可得P(Y≤6|X≥300)=.21.(13分)(2012•湖北)设A是单位圆x2+y2=1上的任意一点,l是过点A与x 轴垂直的直线,D是直线l与x轴的交点,点M在直线l上,且满足丨DM丨=m 丨DA丨(m>0,且m≠1).当点A在圆上运动时,记点M的轨迹为曲线C.(I)求曲线C的方程,判断曲线C为何种圆锥曲线,并求焦点坐标;(Ⅱ)过原点且斜率为k的直线交曲线C于P、Q两点,其中P在第一象限,它在y轴上的射影为点N,直线QN交曲线C于另一点H,是否存在m,使得对任意的k>0,都有PQ⊥PH?若存在,求m的值;若不存在,请说明理由.【分析】(I)设M(x,y),A(x0,y0),根据丨DM丨=m丨DA丨,确定坐标之间的关系x0=x,|y0|=|y|,利用点A在圆上运动即得所求曲线C的方程;根据m∈(0,1)∪(1,+∞),分类讨论,可确定焦点坐标;(Ⅱ)∀x1∈(0,1),设P(x1,y1),H(x2,y2),则Q(﹣x1,﹣y1),N(0,y1),利用P,H两点在椭圆C上,可得,从而可得可得.利用Q,N,H三点共线,及PQ⊥PH,即可求得结论.【解答】解:(I)如图1,设M(x,y),A(x0,y0)∵丨DM丨=m丨DA丨,∴x=x0,|y|=m|y0|∴x0=x,|y0|=|y|①∵点A在圆上运动,∴②①代入②即得所求曲线C的方程为∵m∈(0,1)∪(1,+∞),∴0<m<1时,曲线C是焦点在x轴上的椭圆,两焦点坐标分别为(),m>1时,曲线C是焦点在y轴上的椭圆,两焦点坐标分别为(),(Ⅱ)如图2、3,∀x1∈(0,1),设P(x1,y1),H(x2,y2),则Q(﹣x1,﹣y1),N(0,y1),∵P,H两点在椭圆C上,∴①﹣②可得③∵Q,N,H三点共线,∴k QN=k QH,∴∴k PQ•k PH=∵PQ⊥PH,∴k PQ•k PH=﹣1∴∵m>0,∴故存在,使得在其对应的椭圆上,对任意k>0,都有PQ⊥PH22.(14分)(2012•湖北)(I)已知函数f(x)=rx﹣x r+(1﹣r)(x>0),其中r 为有理数,且0<r<1.求f(x)的最小值;(II)试用(I)的结果证明如下命题:设a1≥0,a2≥0,b1,b2为正有理数,若b1+b2=1,则a1b1a2b2≤a1b1+a2b2;(III)请将(II)中的命题推广到一般形式,并用数学归纳法证明你所推广的命题.注:当α为正有理数时,有求导公式(xα)r=αxα﹣1.【分析】(I)求导函数,令f′(x)=0,解得x=1;确定函数在(0,1)上是减函数;在(0,1)上是增函数,从而可求f(x)的最小值;(II)由(I)知,x∈(0,+∞)时,有f(x)≥f(1)=0,即x r≤rx+(1﹣r),分类讨论:若a1,a2中有一个为0,则a1b1a2b2≤a1b1+a2b2成立;若a1,a2均不为0,,可得a1b1a2b2≤a1b1+a2b2成立(III)(II)中的命题推广到一般形式为:设a1≥0,a2≥0,…,a n≥0,b1,b2,…,b n为正有理数,若b1+b2+…+b n=1,则a1b1a2b2…a n bn≤a1b1+a2b2+…a n b n;用数学归纳法证明:(1)当n=1时,b1=1,a1≤a1,推广命题成立;(2)假设当n=k时,推广命题成立,证明当n=k+1时,利用a1b1a2b2…a k bk a k+1bk+1=(a1b1a2b2…a k bk)a k+1bk+1=a k+1bk+1,结合归纳假设,即可得到结论.【解答】(I)解:求导函数可得:f′(x)=r(1﹣x r﹣1),令f′(x)=0,解得x=1;当0<x<1时,f′(x)<0,所以f(x)在(0,1)上是减函数;当x>1时,f′(x)>0,所以f(x)在(0,1)上是增函数所以f(x)在x=1处取得最小值f(1)=0;(II)解:由(I)知,x∈(0,+∞)时,有f(x)≥f(1)=0,即x r≤rx+(1﹣r)①若a1,a2中有一个为0,则a1b1a2b2≤a1b1+a2b2成立;若a1,a2均不为0,∵b1+b2=1,∴b2=1﹣b1,∴①中令,可得a1b1a2b2≤a1b1+a2b2成立综上,对a1≥0,a2≥0,b1,b2为正有理数,若b1+b2=1,则a1b1a2b2≤a1b1+a2b2;②(III)解:(II)中的命题推广到一般形式为:设a1≥0,a2≥0,…,a n≥0,b1,b2,…,b n为正有理数,若b1+b2+…+b n=1,则a1b1a2b2…a n bn≤a1b1+a2b2+…a n b n;③用数学归纳法证明(1)当n=1时,b1=1,a1≤a1,③成立(2)假设当n=k时,③成立,即a1≥0,a2≥0,…,a k≥0,b1,b2,…,b k为正有理数,若b1+b2+…+b k=1,则a1b1a2b2…a k bk≤a1b1+a2b2+…a k b k.当n=k+1时,a1≥0,a2≥0,…,a k+1≥0,b1,b2,…,b k+1为正有理数,若b1+b2+…+b k+1=1,>0则1﹣b k+1于是a1b1a2b2…a k bk a k+1bk+1=(a1b1a2b2…a k bk)a k+1bk+1=a k+1bk+1∵++…+=1∴…≤++…+=bk+1≤•(1∴a k+1﹣b k)+a k+1b k+1,+1∴a1b1a2b2…a k b ka k+1bk+1≤a1b1+a2b2+…a k b k+a k+1b k+1.∴当n=k+1时,③成立由(1)(2)可知,对一切正整数,推广的命题成立.。
2012年湖北省高考试卷语文试卷及答案湖北高考
2012年湖北省高考试卷语文试卷及答案湖北高考2012年湖北省高考试卷 B(尽管2月9日美日韩达成了美国向朝鲜提供0页,七大题23小题。
全卷满分150分。
万吨粮食,朝鲜停止核试验,但由于朝鲜本试题卷共124考试用时150分钟。
与美日韩的矛盾由来已久,很难在短期内消注意事项: 除双方敌对的情结。
1(答卷前,考生务必将自己的姓名、准考证号填 C(少林寺寺务处工作人员告诉记者,这个讲解写在试题卷和答题卡上,并将准考证号条形码粘贴在团由近20名延字辈僧人组成,上岗之前还进答题卡上的指定位置。
用2B铅笔将答题卡上试卷类型行了专门的培训,主要是介绍寺院里边的一A后的方框涂黑。
些人文景观、典故等,为游客服务。
2(选择题的作答:每小题选出答案后,用2B铅D(此次震中位于南部瓦哈卡州附近地区,震源深笔把答题卡上对应题目的答案标号涂黑。
如需改动,度17(5公里,震中距首都墨西哥城300多公用橡皮擦干净后,再选涂其他答案标号。
答在试题卷、。
震区格雷罗州的官员称,有约800余栋房里草稿纸上无效。
屋受损约60余栋房屋倒塌。
3(非选择题的作答:用0.5毫米黑色墨水签字笔5(下面有关文学常识的表述,有错误的一项是直接答在答题卡上对应的答题区域内。
答在试题卷、 A(莎士比亚是十六世纪英国杰出的戏剧家,雨果草稿纸上无效。
是十九世纪法国浪漫主义文学代表作家,川端康4(考生必须保持答题卡的整洁。
考试结束后,请成是日本著名作家,曾获诺贝尔文学奖。
他们的将本试题卷和答题卡一并上交。
代表作分别是喜剧《威尼斯商人》、小说《悲惨世界》和《雪国》。
一、语文基础知识(共15分,共5小题,每小题3分) B(《红楼梦》的情节主线是贾宝玉与林黛玉、薛1(下列各组词语中加点字的读音全都不相同的一项宝钗的爱情悲剧。
贾宝玉鄙弃功名富贵,追求率是性自然,公然声称“女儿是水做的骨肉,男人是A(酒馔,撰写孤僻,癖好讥诮,峻峭泥做的骨肉”;林黛玉与贾宝玉情趣相投,从不忌妒,殚精竭虑对宝玉说读书求功名的“混账话”,不像薛宝钗那样做封建社会标准的“名媛淑女”B(搅拌,绊倒祈祷,乞求枝柯,舸舰。
2012年湖北省高考试卷语文试卷及答案湖北高考
2012年湖北省高考试卷本试题卷共10页,七大题23小题。
全卷满分150分。
考试用时150分钟。
注意事项:1.答卷前,考生务必将自己的姓名、准考证号填写在试题卷和答题卡上,并将准考证号条形码粘贴在答题卡上的指定位置。
用2B铅笔将答题卡上试卷类型A后的方框涂黑。
2.选择题的作答:每小题选出答案后,用2B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,再选涂其他答案标号。
答在试题卷、草稿纸上无效。
3.非选择题的作答:用0.5毫米黑色墨水签字笔直接答在答题卡上对应的答题区域内。
答在试题卷、草稿纸上无效。
4.考生必须保持答题卡的整洁。
考试结束后,请将本试题卷和答题卡一并上交。
一、语文基础知识(共15分,共5小题,每小题3分)1.下列各组词语中加点字的读音全都不相同的一项是 A.酒馔/撰写孤僻/癖好讥诮/峻峭忌妒/殚精竭虑B.搅拌/绊倒祈祷/乞求枝柯/舸舰赢弱/果实累累C.搠倒/溯流掂量/惦记洗漱/咳嗽玷辱/拈轻怕重D.端倪/睥睨挑衅/体恤棕榈/闾阎提防/金榜题名2.下列各组词语中,没有错别字.....的一组是A.跳槽邻界点醍醐灌顶树倒猢狲散B.心扉协奏曲骨鲠在喉时世造英雄C.像素副食品不记前嫌家书抵万金D.饯行热烘烘先发制人蚍蜉撼大树3.在下列各句中,加点的成语使用不恰当...的一项是()A.柯达有过这样自豪的口号:“你只要按下快门,其他的交给我们。
”但对于今日的柯达而言,那些曾经的辉煌都已是明日黄花....。
B.酒家又切了二斤熟牛肉,再筛了三碗酒。
武松吃得荡气回肠....,只顾要吃;去身边取些碎银子,叫道:“主人家,你且来看我银子!还你酒肉钱够么?”C.全球经济波谲云诡....,资本市场动荡不安。
在货币政策紧缩、国内资金面紧张的大背景下,今年以来国内A股不断下跌,很多普通投资者或深度套牢,或忍痛割肉出场,令人扼腕叹息。
D.虽然美联储三位高层都表示反对美联储未来两年维持利率不变的举动,但他们的言论也显示,美联储内部对此问题莫衷一是....。
2012湖北省高考语文试卷及参考答案知识大全_图文
1、阅读下文,完成22—26题。
(12分)治学(东汉)徐幹①昔之君子成德立行,身没而名不朽,其故何□?学也。
②学也者,所以疏神达思,怡情理性,圣人之上务也。
民之初载,其矇未知。
譬如宝在于玄室①,有所求而不见,白日照焉,则群物斯辩矣。
学者,心之白日也。
③学犹饰也,器不饰则无以为美观,人不学则无以有懿德。
有懿德,故可以经人伦;为美观,故可以供神明。
④夫听黄钟之声,然后知击缶之细;视衮龙之文,然后知被褐之陋;涉庠序之教,然后知不学之困。
故学者如登山焉,动而益高;如寤寐焉,久而愈足。
顾所由来,则杳然其远,以其难而懈之,误且非矣。
⑤倚立而思远,不如速行之必至也;矫首而徇飞,不如修翼之必获也;孤居而愿智,不如务学之必达也。
故君子心不苟愿,必以求学;身不苟动,必以从师;言不苟出,必以博闻。
⑥君子之于学也,其不懈,犹上天之动,犹日月之行,终身亹亹②,没而后已。
故虽有其才而无其志,亦不能兴其功也。
志者,学之帅也;才者,学之徒也。
学者不患才之不赡,而患志之不立。
是以为之者亿兆,而成之者无几,故君子必立其志。
【注】①玄室:暗室。
②亹亹:勤勉不倦的样子。
22、可填入第①段方框处的虚词是()(1分)A、兮B、哉C、夫D、矣23、第②段使用了比喻论证的手法,请结合该段内容加以分析。
(3分)24、对第④段画线句理解正确的一项是()(2分)A、治学不能因为目标过远而松懈。
B、人疏于学习,会犯错而招来批评。
C、治学要回顾走过的路,并加以总结。
D、人不能因为害怕困难而放松学习。
25、赏析第⑤段运用整句的表达效果。
(3分)26、分析第⑥段作者论述治学的思路。
(3分)2、依次填入下列各句横线处的成语,最恰当的一组是(3分)①他是一个心地善良的人,但性格懦弱、谨小慎微,做起事来总是,从来不敢越雷池一步。
②当今世界科技突飞猛进,我们更要勇于开拓,不断进取,如果,就会落后甚至被时代潮流所淘汰。
③要想让中国传统戏曲焕发出新的生命力,决不能满足于现状,,唯有创新才是弘扬戏曲文化的康庄大道.A.故步自封墨守成规抱残守缺B.墨守成规故步自封抱残守缺C.抱残守缺故步自封墨守成规D.墨守成规抱残守缺故步自封3、下列词语中加点字的读音,全都正确的一组是A.寂寥(liáo)雾霾(mái)瞋(chēng)目潜(qián)移默化B.氛(fēn)围吝啬(sâ)熹(xī)微束(shù)之高阁C.发酵(jiào)徘徊(huái)滂(pāng)沱叱咤(chà)风云D.模(mó)板怯(qiâ)懦签(qiān)署断壁颓垣(yuán)4、依次填入下列横线处的词语,最恰当的一组是研究伊始,该团队选取了华北、西北地区生产的几十种马铃薯进行分析,从营养成分、、硬度等方面多次试验,确定了适合加工马铃薯面条的两个品种。
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2012年全国高考英语试卷(湖北A卷)21. Two lawyers have donated $50,000 to ________ our school’s campaign “Help the Needy”, which was started by our former headmaster three years ago.A. sponsorB. launchC. organizeD. plan22. Finally, my thanks go to my tutor, who has offered a lot of suggestions and comments on my paper and ________ every page of my draft.A. approvedB. quotedC. polishedD. folded23. Walking alone in the dark, the boy whistled to ________ his courage.A. hold upB. keep upC. set upD. take up24. I’m so glad you’ve come here to ________ this matter in person.tick to /look fore to _________neutralA. lead to B. see to C. turn to D. refer to25. The furniture, with its modern style and bright colors, suits modern houses and their gardens, but looks _______ in the garden of a traditional home.A. out of questionB. out of orderC. out of sightD. out of place26. “Perhaps we need to send for Dr. Smith to see what we can do about it,”Father suggested ________ to his neighbor who had come to discuss the problem.A. tentativelyB. thoughtlesslyC. definitelyD. rudely27. Can you tell the ________ difference between the words “require”and “request”? I sometimes get puzzled by their meanings.A. dramaticB. regionalC. apparentD. subtle28. Whether the buildings in this area should be pulled down has remained ________; people are still looking for other possible solutions.A. unchallengedB. relevantC. controversialD. contradictory29. It is important to have your eyes examined regularly to check for any sign of eye disease that may not have any ________.A. symptomB. similarityC. sampleD. shadow30. The officer insisted that Michael did not follow the correct ________ in applying for a visa.A. patternB. procedureC. programD. perspectiveI tend to accept any idea put forward by experts on TV. One day, a sociologist proposed that the 31 society has been consuming modern humans little by little. For fear that I would become a victim of the consumer society, I 32 hurried to a bicycle shop in my neighborhood. 33 the shopkeeper Mr. Johnson was selling me the bicycle, he said, “This is the best thing you 34 have done. Life has become hopelessly 35 . A bicycle issimple, and it brings to you 36 things: fresh air, sunshine and exercise.”I agreed. Happy as a child, I got on the bicycle and headed out onto the streets. After some time, I 37 at the other end of the town. I was 38 that this simple vehicle could let me 39 long distances in a fairly short time. But how 40 did I really go? Since I hated to be 41 , I went back to Mr. Johnson and asked him to 42 an odometer (里程表) on my bicycle. He agreed, but 43 , “An odometer without a speedometer (速度计) is like a 44 without a knife.”I admitted he was right and in a few minutes, the two devices were 45 to the handlebars of my bicycle. “What about a horn?”he then asked. “Look, this horn is no larger than a matchbox and has many 46 .”Attracted by these functions, I bought the horn.“You can’t leave the back part 47 ,”noted Mr. Johnson. He fixed a metal box with buttons 48 the seat, and said, “Is there anything better than this oven when you feel 49 on your way? I can give you a special discount.”I was not strong enough to 50 the offer.“I congratulate you once more; this is the best thing you could have done,”said Mr. Johnson in the end.31. A. adult B. human C. consumer D. bachelor32. A. eventually B. immediately C. reluctantly D. gratefully33. A. Although B. Because C. As D. Unless34. A. would B. should C. must D. could35. A. boring B. complicated C. stressful D. tough36. A. natural B. mysterious C. complex D. unique37. A. gave up B. broke down C. calmed down D. ended up38. A. amazed B. amused C. confused D. concerned39. A. march B. drive C. cover D. measure40. A. far B. long C. fast D. deep41. A. unreliable B. impractical C. unprepared D. inaccurate42. A. fix B. check C. repair D. lay43. A. swore B. added C. replied D. concluded44. A. pencil B. fork C. box D. cake45. A. distributed B. converted C. applied D. attached46. A. shapes B. sizes C. functions D. models47. A. loose B. blank C. bare D. incomplete48. A. beside B. before C. below D. behind49. A. sick B. hungry C. hot D. thirsty50. A. consider B. withdraw C. make D. resist第三部分:阅读理解(共20小题;每小题2分,满分40分)AYou’ve just come home, after living abroad for a few years. Since you’ve been away, has this country changed for the better—or for the worse?If you’ve just arrived back in the UK after a fortnight’s holiday, small changes have probably surprised you—anything from a local greengrocer suddenly being replaced by a mobile-phone shop to someone in your street moving house.So how have things changed to people coming back to Britain after seven, ten or even 15 years living abroad? What changes in society can they see that the rest of us have hardly noticed—or now take for granted? To find out, we asked some people who recently returned.Debi: When we left, Cheltenham, my home town, was a town of white, middle-class families—all very conservative (保守的). The town is now home to many eastern Europeans and lots of Australians, who come here mainly to work in hotels and tourism. There are even several shops only for foreigners.Having been an immigrant myself, I admire people who go overseas to find a job. Maybe if I lived in an inner city where unemployment was high, I’d think differently, but I believe foreign settlers have improved this country because they’re more open-minded and often work harder than the natives.Christine: As we flew home over Britain, both of us remarked how green everything looked. But the differences between the place we’d left behind and the one we returned to were brought sharply into focus as soon as we landed.To see policemen with guns in the airport for the first time was frightening—in Cyprus, they’re very relaxed—and I got pulled over by customs officers just for taking a woolen sweater with some metal-made buttons out of my case in the arrivals hall. Everyone seemed to be on guard. Even the airport car-hire firm wanted a credit card rather than cash because they said their vehicles had been used by bank robbers.But anyway, this is still a green, beautiful country. I just wish more people would appreciate what they’ve got.51. After a short overseas holiday, people tend to _______.A. notice small changesB. expect small changesC. welcome small changesD. exaggerate small changes52. How does Debi look at the foreign settlers?A. Cautiously.B. Positively.C. Skeptically.D. Critically.53. When arriving at the airport in Britain, Christine was shocked by _______.A. the relaxed policemenB. the messy arrivals hallC. the tight securityD. the bank robbers54. Which might be the best title for the passage?A. Life in Britain.B. Back in Britain.C. Britain in Future.D. Britain in Memory.BWhen my brother and I were young, my mom would take us on Transportation Days.It goes like this: You can’t take any means of transportation more than once. We would start from home, walking two blocks to the rail station. We’d take the train into the city center, then a bus, switching to the tram, then maybe a taxi. We always considered taking a horse carriage in the historic district, but we didn’t like the way the horses were treated, so we never did. At the end of the day, we took the subway to our closest station, where Mom’s friend was waiting to give us a ride home—our first car ride of the day. The good thing about Transportation Days is not only that Mom taught us how to get around. She was born to be multimodal (多方式的). She understood that depending on cars only was a failure of imagination and, above all, a failure of confidence—the product of a childhood not spent exploring subway tunnels.Once you learn the route map and step with certainty over the gap between the train and the platform, nothing is frightening anymore. New cities are just light-rail lines to be explored. And your personal car, if you have one, becomes just one more tool in the toolbox—and often an inadequate one, limiting both your mobility and your wallet.On Transportation Days, we might stop for lunch on Chestnut Street or buy a new book or toy, but the transportation was the point. First, it was exciting enough to watch the world speed by from the train window. As I got older, my mom helped me unlock the mysteries that would otherwise have paralyzed my first attempts to do it myself: How do I know where to get off? How do I know how much it costs? How do I know when I need tickets, and where to get them? What track, what line, which direction, where’s the stop, and will I get wet when we go under the river?I’m writing this right now on an airplane, a means we didn’t try on our Transportation Days and, we now know, the dirtiest and most polluting of them all. My flight routed me through Philadelphia. My multimodal mom met me for dinner in the airport. She took a train to meet me.55. Which was forbidden by Mom on Transportation Days?A. Having a car ride.B. Taking the train twice.C. Buying more than one toy.D. Touring the historic district.56. According to the writer, what was the greatest benefit of her Transportation Days?A. Building confidence in herself.B. Reducing her use of private cars.C. Developing her sense of direction.D. Giving her knowledge about vehicles.57. The underlined word “paralyzed”(in Para. 5) is closest in meaning to “_______”.A. displayedB. justifiedC. ignoredD. ruined58. Which means of transportation does the writer probably disapprove of?A. Airplane.B. Subway.C. Tram.D. Car.CIt was a simple letter asking for a place to study at Scotland’s oldest university which helped start a revolution in higher education. A 140-year-old letter written by a lady calling for her to be allowed to study medicine at St Andrews University has been discovered by researchers. Written by Sophia Jex-Blake in 1873, the seven-page document, which urged the university to allow women to study medicine at the institution, was released yesterday on International Women’s Day.The document was discovered buried in the university archives (档案) by part-time history student Lis Smith, who is completing her PhD at St Andrews Institute of Scottish Historical Research. She said: “We knew that Sophia Jex-Blake and her supporters, in their effort to open up university medical education for women, had written to the Senatus Academicus (校评议委员会) at St Andrews in an attempt to gain permission to attend classes there, but we didn’t know documentary evidence existed. While searching the archives for information about the university’s higher certificate for women, I was astonished to come across what must be the very letter Jex-Blake wrote.”In the letter, Sophia and her supporters offered to hire teachers or build suitable buildings for a medical school and to arrange for lectures to be delivered in the subjects not already covered at St Andrews. Although her letter was not successful, it eventually led to the establishment of the Ladies Literate in Arts at St Andrews, a distance-learning degree for women. The qualification, which ran from 1877 until the 1930s, gave women access to university education in the days before they were admitted as students. It was so popular that it survived long after women were admitted as full students to St Andrews in 1892.Ms Jex-Blake went on to help establish the London School of Medicine for Women in 1874. She was accepted by the University of Berne, where she was awarded a medical degree in January 1877. Eventually, she moved back to Edinburgh and opened her own practice.59. Sophia wrote a letter to St Andrews University because she wanted _______.A. to carry out a research project thereB. to set up a medical institute thereC. to study medicine thereD. to deliver lectures there60. Lis Smith found Sophia’s letter to St Andrews University _______.A. by pure chanceB. in the school officeC. with her supporters’helpD. while reading history books61. Sophia’s letter resulted in the establishment of _______.A. the London School of Medicine for WomenB. a degree programme for womenC. a system of medical educationD. the University of Berne62. When did St Andrews University begin to take full-time women students?A. In 1873.B. In 1874.C. In 1877.D. In 1892.DHow is it that siblings (兄弟姐妹) can turn out so differently? One answer is that in fact each sibling grows up in a different family. The firstborn is, for a while, an only child, and therefore has a completely different experience of the parents than those born later. The next child is, for a while, the youngest, until the situation is changed by a new arrival. The mother and father themselves are changing and growing up too. One sibling might live in a stable and close family in the first few years; another might be raised in a family crisis, with a disappointed mother or an angry father.Sibling competition was identified as an important shaping force as early as in 1918. But more recently, researchers have found many ways in which brothers and sisters are a lasting force in each others’lives. Dr. Annette Henderson says firstborn children pick up vocabulary more quickly than their siblings. The reason for this might be that the later children aren’t getting the same one-on-one time with parents. But that doesn’t mean that the younger children have problems with language development. Later-borns don’t enjoy that much talking time with parents, but instead they harvest lessons from bigger brothers and sisters, learning entire phrases and getting an understanding of social concepts such as the difference between “I”and “me”.A Cambridge University study of 140 children found that siblings created a rich world of play that helped them grow socially. Love-hate relationships were common among the children. Even those siblings who fought the most had just as much positive communication as the other sibling pairs.One way children seek more attention from parents is by making themselves different from their siblings, particularly if they are close in age. Researchers have found that the first two children in a family are typically more different from each other than the second and third. Girls with brothers show their differences to a maximum degree by being more feminine than girls with sisters. A 2003 research paper studied adolescents from 185 families over two years, finding that those who changed to make themselves different from their siblings were successful in increasing the amount of warmth they gained from their parents.63. The underlined part “in a different family”(in Para. 1) means “_______”.A. in a different family environmentB. in a different family traditionC. in different family crisesD. in different families64. In terms of language development, later-borns ________.A. get their parents’individual guidanceB. learn a lot from their elder siblingsC. experience a lot of difficultiesD. pick up words more quickly65. What was found about fights among siblings?A. Siblings hated fighting and loved playing.B. Siblings in some families fought frequently.C. Sibling fights led to bad sibling relationships.D. Siblings learned to get on together from fights.66. The word “feminine”(in Para. 4) means “_______”.A. having qualities of parentsB. having qualities of womenC. having defensive qualitiesD. having extraordinary qualitiesEBrrriiinnng. The alarm clock announces the start of another busy weekday in the morning. You jump out of bed, rush into the shower, into your clothes and out the door with hardly a moment to think. A stressful journey to work gets your blood pressure climbing. Once at the office, you glance through the newspaper with depressing stories or reports of disasters. In that sort of mood, who can get down to work, particularly some creative, original problem-solving work?The way most of us spend our mornings is exactly opposite to the conditions that promote flexible,open-minded thinking. Imaginative ideas are most likely to come to us when we’re unfocused. If you areone of those energetic morning people, your most inventive time comes in the early evening when you are relaxed. Sleepy people’s lack of focus leads to an increase in creative problem solving. By not giving yourself time to tune into your wandering mind, you’re missing out on the surprising solutions it may offer. The trip you take to work doesn’t help, either. The stress slows down the speed with which signals travel between neurons (神经细胞), making inspirations less likely to occur. And while we all should read a lot about what’s going on in the world, it would not make you feel good for sure, so put that news website or newspaper aside until after the day’s work is done.So what would our mornings look like if we wanted to start them with a full capacity for creative problem solving? We’d set the alarm a few minutes early and lie awake in bed, following our thoughts where they lead. We’d stand a little longer under the warm water of the shower, stopping thinking about tasks in favor of a few more minutes of relaxation. We’d take some deep breaths on our way to work, instead of complaining about heavy traffic. And once in the office—after we get a cup of coffee—we’d click on links not to the news of the day but to the funniest videos the web has to offer.67. According to the author, we are more creative when we are _______.A. focusedB. relaxedC. awakeD. busy68. What does the author imply about newspapers?A. They are solution providers.B. They are a source of inspiration.C. They are normally full of bad news.D. They are more educational than websites.69. By “tune into your wandering mind”(in Para. 2), the author means “_______”.A. wander into the wildB. listen to a beautiful tuneC. switch to the traffic channelD. stop concentrating on anything70. The author writes the last paragraph in order to _______.A. offer practical suggestionsB. summarize past experiencesC. advocate diverse ways of lifeD. establish a routine for the future第一节:完成句子(共10小题;每小题2分,满分20分)阅读下列各小题,根据汉语提示,用句末括号内的英语单词完成句子,并将答案写在答题卡上的相应题号后。