2012年普通高考学校招生全国统一考试(湖北卷)及答案

2012年普通高等学校招生全国统一考试（湖北卷）数学（文科）本试题卷共4页，共22题。

满分150分。

考试用时120分钟。

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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 +-=数学（文史类）试卷A型 第2页（共10页） 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,)-∞+∞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,)-∞+∞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 ．① ②B ．③ ④C ．① ③D ．② ④ 8．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 =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ABCD第10题图数学（文史类）试卷A型 第3页（共10页） 侧视图正视图俯视图第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，记为数列{}n a ，将可被5整除的三角形数按从小到大的第16题图第17题图 10 6 3 1 ···数学（文史类）试卷A型 第4页（共10页） 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）数学（文史类）试卷A型 第5页（共10页） 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题图数学（文史类）试卷A型 第6页（共10页） 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=-⨯-=-=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ABAD A =，所以2AA ⊥平面ABCD .连接BD ，因为BD ⊂平面ABCD ，所以2AA BD ⊥.数学（文史类）试卷A型 第7页（共10页） 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 DD 平面ABCD BD =，平面11BB D D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 =，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 nS S a a a=++++5(337)(347)(37)n=+⨯-+⨯-++-2(2)[2(37)]311510222n nn n-+-=+=-+. 当2n=时，满足此式.综上，24,1,31110, 1.22nnSn 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x x=，||||y m y=，所以x x=，1||||y ym=. 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2221 (0,1)yx m mm+=>≠且.因为(0,1)(1,)m∈+∞，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 xx xm k-+=-+，即212224m xxm k=+.因为点H在直线QN上，所以2121222224km xy kx kxm k-==+.于是11(2,2)PQ x kx=--，22112121222242(,)(,)44k x km xPH x x y kxm k m k=--=-++.而PQ PH⊥等价于2221224(2)4m k xPQ PHm k-⋅==+，即220m-=，又0m>，得m，故存在m=2212yx+=上，对任意的0k>，都有PQ PH⊥.数学（文史类）试卷A型 第9页（共10页）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 =.数学（文史类）试卷A型 第10页（共10页） （Ⅱ）由（Ⅰ）知，1()(1)n n n f x x x x x +=-=-，1()(1)()1n nf x n x x n -'=+-+. 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。

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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年普通高等学校招生全国统一考试（湖北卷）本试题卷共16页，81题。

全卷满分150分。

考试用时120分钟。

（听力部分略）第二部分：选择题（共两节，满分30分）第一节：单项选择（每小题1分，满分10分）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.A. lead toB. see toC. turn toD. refer to25. The furniture, with its modern style and bright colors, suits modern houses and their gardens, butlooks 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. Could you tell the difference between “require” and “request”? I sometimes get puzzled by their meanings.A. dramaticB. regionalC. apparentD. subtle28. Whether building in this area should be pull down has remained ; people are still looking for other possible solutions.contradictoryA. unchallengedB. relevantC. controversialD.29. It is important to have your eyes examined regularly to check for any sign of eye disease that may not have any .A. symptomB. similaritiesC. sampleD. shadow30. The officer insisted that Michael did not follow the correct in applying for a visa.A. patternB. procedureC. programD. perspective第二节：完形填空（每小题1分，满分20分）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 ask 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 aknife.” 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 ,” 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 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.bachelor31. A. adult B. human C. consumer D.32. 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. inaccuraterepair D.lay42. A. fix B. check C.43. 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（每小题2分，满分40）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. The town is now home to many eastern Europeans and lots of Australia, 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 aninner 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. 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 certainly 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, ifyou 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 now when I need tickets, and where to get them? What track, what line, which direction, where’s the stop, and will I get 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 greateds benefit of her TransportationDays?A. Building confidence in herself.B. Reducing her use of private cars.C. Developing her senses 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. Train.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 now documentary evidence existed. While searching thearchives 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 teachears or build suitable buildings for 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 ot 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 Medicines 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 Edingburgh and opened her own pracitce.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 the 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 brother 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’tenjoy that much talking time with parents, but instead they harvest lessons from bigger brother 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 sibling 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 sibling 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 different family traditionC. in a 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. Siblings 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 are one of those energetic morning people, your most inventive time come in the early evening when you are relaxed. Sleepy people’s lack of focus leads to an increase in creative problem solving. By not givingyourself 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 inspiratins 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 newpaper 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 thingking 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第四部分：书面表达（共两节，满分50分）第一节：完成句子（共10小题：每小题2分，满分20分）71. 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。

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湖北高考语文试卷AB答案2012年普通高等学校招生全国统一考试（湖北卷）语文试题参考答案一、语文基础知识（共15分，共5小题，每小题3分）A卷：1．B 2．C 3．D 4．A 5．CB卷：1．C 2．D 3．B 4．B 5．A二、现代文（论述类文本）阅读（共9分，共3小题，每小题3分）A卷：6．A 7．B 8．CB卷：6．A 7．C 8．D三、古代诗文阅读（共34分，共7小题）A卷：9．（3分）C 10．（3分）A 11．（3分）AB卷：9．（3分）C 10．（3分）A 11．（3分）A12．（9分）（1）（3分）王湛于是和王济一起谈论《周易》，（王湛）分析精微，王济从来没听说过，感叹（叔父）深不可测。

（2）（3分）王浑问他这样说的缘故，王济感慨地把此事如此这般详尽地叙述（一遍）。

（3）（3分）武帝每次见到王济，总是拿王湛来调侃他。

13．（3分）不修常人近事/少工射/入山泽/每猎大获/为后将军钟毓长史/毓与参佐射戏/舒常为坐画筹。

14．（8分）（1）（4分）诗中邹明府形象的主要特点是: 清正廉洁。

三年县令任满离去，马依旧瘦弱，随身相伴的还是那些书。

如今冒雪远游朔方，前程艰险，单薄的衣衫哪抵得住透骨寒风。

正是通过这些细节的刻画，展现了邹明府至清至廉的形象。

（2）（4分）①“藏”字，运用拟人手法，描绘人行之迹很快便为大雪覆盖的边塞雪景，写景生动，颇有画意；一个“藏”字，已包含大雪纷飞、道路莫辨、行人稀少等多重意蕴。

②“透”字，极为传神地展现了林间朔风砭人肌骨的穿透力，同时还隐含风急、天寒、衣单等内容，富有想象力和感染力。

15．（5分）（1）君子好逑（2）空山凝云颓不流（3）故国不堪回首月明中（4）休说鲈鱼堪脍（5）则其负大翼也无力（6）外无期功强近之亲（7）有良田美池桑竹之属（8）此后汉所以倾颓也（8个小题，从中任选5个小题作答即可）四、现代文（文学类、实用类文本）阅读（共20分，共4小题）16．（4分）A卷：B CB卷：B C17．（4分）①相对诗词、传说的片段引用，“姑嫂鸟”这一民间故事则为完整叙述，丰富了文章内容，增添了杜鹃鸟传说的美好意义。

2012年普通高等学校招生全国统一考试（湖北卷）数学（文科）本试题卷共4页，共22题。

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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2A x x x x=-+=∈R，{|05,}{|320,}⊆⊆B x x x=<<∈N，则满足条件A C B 的集合C的个数为A．1 B．2 C．3 D．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 +-=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,)-∞+∞ 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,)-∞+∞ 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 ．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 为第6题图ABCDA ．4:3:2B ．5:6:7C ．5:4:3D ．6:5:49．设,,a b c+∈R ，则“1abc =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10题图侧视图正视图二、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， 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17题图 10 6 3 1 ···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；A 2B 2C 2D 2 CB A DA 1B 1C 1D 1第19题图（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 <.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=-+⋅+cos22x 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 = ，所以2AA ⊥平面ABCD . 连接BD ，因为BD ⊂平面ABCD ，所以2AA BD ⊥.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 平面ABCD BD =， 平面11BB D D 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 = ，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 =++++ 5(337)(347)(37)n =+⨯-+⨯-++-2(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 ∈+∞ ，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 =-- ，22112121222242(,)(,)44k x km x PH x x y kx m k m k =--=-++ . 而PQ PH ⊥等价于2221224(2)04m k x PQ PH m k -⋅==+ ， 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 第21题解答图解法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 -'=+-+. 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年普通高等学校招生全国统一考试（湖北A卷）数学（理工类）数学（理工类）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题目要求的1. 方程2+6+13=0x x 的一个根是的一个根是A -3+2iB 3+2iC -2 + 3iD 2 + 3i()()222+6+13=+3+4=0+3=-4,+3=2x x x x x i ∴±，所以=-32x i ±，故选A2. 命题“命题“300,R x C Q x Q ∃∈∈”的否定是”的否定是A 300,R x C Q x Q ∃∉∈ B 300,R x C Q x Q ∃∈∉ C300,R x C Q x Q ∀∉∈ D 300,R x C Q x Q ∀∈∉存在性命题的否定为“∃”改为“∀”，后面结论加以否定，故为300,R x C Q x Q ∀∈∉，选D 3. 已知二次函数()=y f x 的图像如图所示的图像如图所示， 则它与x 轴所围图形的面积为轴所围图形的面积为A.25πB.43C.32D.2π 由图像可知，二次函数解析式为()2=1-f x x设面积为S ，则()()111223-10014=1-=21-=2-=33Sx dx x dx x x ⎛⎫ ⎪⎪⎝⎭⎰⎰，故选B4.4.已知某几何体的三视图如图所示，则该几何体的体积为已知某几何体的三视图如图所示，则该几何体的体积为已知某几何体的三视图如图所示，则该几何体的体积为 A.83π B.3π C. 103πD.6π 此几何体为一个圆柱切去了一部分，此圆柱底面半径为此几何体为一个圆柱切去了一部分，此圆柱底面半径为 1 1，高为，高为，高为 4 4，现，现在此几何体上方补上一个和此几何体完全一样的几何体在此几何体上方补上一个和此几何体完全一样的几何体，从而构成一个底面半径为1，高为6的圆柱，这个圆柱的体积为=6V π，要求几何体的体积为圆柱体积的一半，为3π，故选B5.5.设设a Z ∈，且013a ≤≤，若201251+a 能被13整除，则=a A.0 B.1 C.11 D.12()()2012201220121201120112012201220122012201251+=52-1+=52-52++-52++a a CCCC a L ，显然上式除了+1a 外，其余各个因式都能被13整除，所以201251+a 能被13整除，只需=12a ，故选，故选 DD 6.6.设设,,,,,a b c x y z 是正数，且222222++=10,++=40,++=20a b c x y z ax by cz ，则++=++a b cx y z A. 14 B. 13 C.12 D.34 由柯西不等式知()()()22222222222++++++=400a b cx y zax by cz ≥，而此时()()222222++++=400a b cx y z 恰好满足取等条件==a b c x y z ，令===,=,=,=a b ck a kx b yk c zk x y z代入到222++=10a b c 中得中得()2222211++=10,=,>0=42k x y z k k k ∴∴，所以由合比定理得++1=====++2a b c a b ck x y z x y z ，故选C7.7.定义在（定义在（定义在（--∞，∞，00）∪（）∪（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”。

2012年普通高等学校招生全国统一考试（湖北卷）英语本试题卷共16页，81题。

全卷满分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。

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考试结束后，请将本试题卷和答题卡一并上交。

第一部分：听力（共两节，满分30分）做题时，先将答案划在试卷上。

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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。

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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.第二节（共15小题；每小题1.5分，满分22.5分)听下面5段对话或独白。

2012年普通高等学校招生全国统一考试（湖北卷）语文答案详解一、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【答案】C【解析】A项读líng lín ling líng；B项读dàn dàn dàn dān；C项都读sù；D项读zīzīzhīzī。

2．下列各组词语中，没有错别字的一组是A.羞涩袅娜歌声缈茫荷塘薄雾B.霜天廖廓峥嵘岁月浪遏飞舟C.细腻箫索落蕊残叶秋蝉嘶叫D.嫩黄葱茏婆娑起舞繁茂苍翠【答案】D【解析】A项“歌声渺茫”；B项“寥廓”；C项“萧索”；D项全都正确。

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，端的还是要人慢下来。

中国这如许的城市中，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，一个人在清晨里不慌不忙的起来，到茶馆里，一坐就是一天，那叫一个悠闲！A．趣味痛痛快快当是遛B．滋味淋漓尽致便是踱C．意味兴致勃勃自是逛D．韵味尽情尽兴恰是晃【答案】B【解析】第一空“个中滋味”是固定搭配，可以排除A、C、D三项。

第四个空要与“悠闲”照应，“逛”“遛”“晃”都不及“踱”效果好。

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，和谐相依，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、嬉笑声响成一片，那真是充满刺激的难忘体验！C．当今已经很少有人会像以前那样的闲情逸致，拿出一本小说，从头到尾地阅读一遍，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。