2011年普通高等学校招全国统一考试湖南卷

2011年普通高等学校招生全国统一考试（湖南卷）数学（理工农医类）本试题卷包括选择题、填空题和解答题三部分，共6页，时量120分钟，满分150分。

参考公式：（1）()()()P AB P B A P A =，其中,A B 为两个事件，且()0P A >， （2）柱体体积公式V Sh =，其中S 为底面面积，h 为高。

（3）球的体积公式343V R π=，其中R 为求的半径。

一选择题：本大题共8小题，每小题5分，共40分，在每小题给出的四个选项中，只有一项符合题目要求的。

1.若,a b R ∈，i 为虚数单位，且()a i i b i +=+，则（ ）A ．1,1a b ==B ．1,1a b =-=C ．1,1a b =-=-D ．1,1a b ==- 答案：D解析：因()1a i i ai b i +=-+=+，根据复数相等的条件可知1,1a b ==-。

2.设{1,2}M =，2{}N a =，则“1a =”是“N M ⊆”则（ ）A ．充分不必要条件B ．必要不充分条件C ．充分必要条件 D ．既不充分又不必要条件 答案：A解析：因“1a =”，即{1}N =，满足“N M ⊆”，反之“N M ⊆”，则2{}={1}N a =，或2{}={2}N a =，不一定有“1a =”。

3.设图一是某几何体的三视图，则该几何体的体积为（ ）A ．9122π+B ．9182π+C ．942π+D ．3618π+答案：B解析：有三视图可知该几何体是一个长方体和球构成的组合体，其体积3439+332=18322V ππ=⨯⨯+（）。

4.通过随机询问110名性别不同的大学生是否爱好某项运动，得到如下的列联表： 男 女 总计 爱好 40 20 60 不爱好 20 30 50 总计 60 50 110由22()()()()()n ad bc K a b c d a c b d -=++++算得22110(40302020)7.860506050K ⨯⨯-⨯=≈⨯⨯⨯ 附表：正视图侧视图俯视图图12()P K k ≥ 0.0500.010 0.001 k3.8416.63510.828参照附表，得到的正确结论是（ ）A ．在犯错误的概率不超过0.1%的前提下，认为“爱好该项运动与性别有关”B ．在犯错误的概率不超过0.1%的前提下，认为“爱好该项运动与性别无关”C ．有99%以上的把握认为“爱好该项运动与性别有关”D ．有99%以上的把握认为“爱好该项运动与性别有关” 答案：C解析：由27.8 6.635K ≈>，而2( 6.635)0.010P K ≥=，故由独立性检验的意义可知选C.5.设双曲线2221(0)9x y a a -=>的渐近线方程为320x y ±=，则a 的值为（ ） A ．4 B ．3 C ．2 D ．1答案：C解析：由双曲线方程可知渐近线方程为3y x a=±，故可知2a =。

2011年普通高等学校招生全国统一考试（湖南卷）理科综合物理部分试题解析二、选择题：本大题共8小题，每小题6分，在每小题给出的四个选项中，有的只有一项符合题目要求，有的有多项符合题目要求。

全部选对的得6分，选对但不全的得3分，有选错的得0分。

14.为了解释地球的磁性，19世纪安培假设：地球的磁场是由绕过地心的轴的环形电流I引起的。

在下列四个图中，正确表示安培假设中环形电流方向的是（B）解析：主要考查安培定则和地磁场分布。

根据地磁场分布和安培定则判断可知正确答案是B。

15.一质点开始时做匀速直线运动，从某时刻起受到一恒力作用。

此后，该质点的动能可能（ABD）A. 一直增大B. 先逐渐减小至零，再逐渐增大C. 先逐渐增大至某一最大值，再逐渐减小D. 先逐渐减小至某一非零的最小值，再逐渐增大解析：主要考查力和运动关系。

当恒力方向与速度在一条直线上，质点的动能可能一直增大，也可能先逐渐减小至零，再逐渐增大。

当恒力方向与速度不在一条直线上，质点的动能可能一直增大，也可能先逐渐减小至某一非零的最小值，再逐渐增大。

所以正确答案是ABD。

16.一蹦极运动员身系弹性蹦极绳从水面上方的高台下落，到最低点时距水面还有数米距离。

假定空气阻力可忽略，运动员可视为质点，下列说法正确的是（ABC）A. 运动员到达最低点前重力势能始终减小B. 蹦极绳张紧后的下落过程中，弹性力做负功，弹性势能增加C. 蹦极过程中，运动员、地球和蹦极绳所组成的系统机械能守恒D. 蹦极过程中，重力势能的改变与重力势能零点的选取有关解析：主要考查功和能的关系。

运动员到达最低点过程中，重力做正功，所以重力势能始终减少，A项正确。

蹦极绳张紧后的下落过程中，弹性力做负功，弹性势能增加，B项正确。

蹦极过程中，运动员、地球和蹦极绳所组成的系统，只有重力和弹性力做功，所以机械能守恒，C项正确。

重力势能的改变与重力势能零点选取无关，D项错误。

17.如图，一理想变压器原副线圈的匝数比为1：2；副线圈电路中接有灯泡，灯泡的额定电压为220V，额定功率为22W；原线圈电路中接有电压表和电流表。

2011年普通高等学校招生全国统一考试（湖南卷）英语试题Part Ⅱ Language Knowledge(45 marks）Section A (15 marks)Directions：for each of the following unfinished sentences there are four choices marked A,B,C and D. Choose the one that best completes the sentence.Example:The wild flowers looked like a soft orange blanket _______ the desert.A. coveringB. coveredC. coverD. to coverThe answer is A.21. The ability _______ an idea is as important as the idea itself.A. expressingB. expressedC. to expressD. to be expressed22. -----Joan, what _______ in your hand?-----Look! It‟s a birthday gift for my grandma.A. had you heldB. are you holdingC. do you holdD. will you hold23. The players _______ from the whole country are expected to bring us honor in thissummer game.A. selectingB. to selectC. selectedD. having selected24. I knew that would over discourage him, he would never give up wanting to be adirectorA. somethingB. anythingC. everythingD. nothing25. Julia was good at German, French and Russian, all of _______ she spoke fluently.A. whoB. whomC. whichD. that26. One-third of the country _______ covered with trees and the majority of the citizens_______ black people.A. is; areB. is; isC. are; areD. are; is27. In 1492, Columbus _______ on one of the Bahama Islands, but the mistook is for an islandoffIndia.A. landsB. landedC. has landedD. had landed28. -----No one _______ be compared with Yao Ming in playing basketball.----Oh, you are really his big fan.A. canB. needC. mustD. might29. Do you wake up every morning _______ energetic and ready to start a new day?A. feelB. to feelC. feelingD. felt30. It is most instructive lecture that I _______ since I came to this school.A. attendedB. had attendedC. am attendingD. have attended31. Before a problem can be solved, it must be obvious _______ the problem itself is.A. whatB. thatC. whichD. why32. Only after they had discussed the matter for several hours _______ a decision.A. they reachedB. did they reachC. they reachD. do they reach33. Jack wasn‟t saying anything, but the teacher smiled at him _______ he had donesomething very clever.A. as ifB. in caseC. whileD. though34. In the near future, more advances in the robot technology _______ by science.A. are makingB. are madeC. will makeD. will be made35. It‟s not what we do once in a while _______ shapes our lives, but what we doconsistently.A. whichB. thatC. howD. whenSection B (18 marks)Directions：For each blank in the following passages there are four words or phrases markedA,B,C and D. Fill in each blank with the words or phrases that best fits the context.People in communities have slowly been pushed apart through the years, mostly becausepeople simply aren‟t taking the time to say a simple “ hello. ” After considering this phenomenon, I decided I was going to 36 the way I was doing things.My 37 came one morning when I was in the community library. I passed by a girl who38 her books out of her locker. Thinking like most that someone else would help her pick them up,I continued my way. However, when I had to 39 because I stupidly forgot my book, I noticed she had just finished packing them up by herself. No one h ad stopped to 40 her.“OK,” I thought to myself, “this is where I should have changed.”My best opportunity came a few days later when I saw a man 41 by himself waiting for the library to open, so I sat down next to him and began a 42 . It was difficult to get started, and even when I had to say goodbye, almost every 43 from my new friend had a tone (语气) of doubt in it. And who could blame him?People aren‟t used to making an 44 chat with a stranger. But a change, no matter how 45 it is needed, doesn‟t just happen. It takes people like us to make it possible. I 46 you to take a small step out of your comfort zone and try to make someone‟s day a little brighter. Together, we can really make society come 47 as a whole.36. A. change B. explain C. learn D. show37. A. trouble B. doubt C. wish D. opportunity38. A. took B. dropped C. got D.pulled39. A. come out B. stand by C. go back D. turn up40. A. please B. greet C. help D. praise41. A. sitting B. walking C. riding D. running42. A. discussing B. lesson C. report D. conversation43. A. joke B. response C. cry D. story44. A. unchangeable B. unprepared C. unforgettable D. unfinished45. A. desperately B. frequently C. simply D. widelySection C (12marks)Directions: Complete the following passage by filling in each black with one word thatbest fits the context.Does going to college really pay off? Certainly!I remember taking 48 English class in college on the short story. Our first assignment was to read 49 short stories and then discuss which one was better. After read ing both, I wasn‟t sure. Over the 50 several months, my professor taught me 51 one story was so much better than the other.52 was rich in metaphor（隐喻）and character development, while the other was humorous 53 too shallow. I couldn‟t see this at first. Yet, in a few months, my brain got reeducated and 54could see the difference between good and bad writing and could appreciate literature at a whole new level.Going to college helps build a strong mind, which leads 55 greater success in one‟s life.Part Ⅲ Reading Comprehension (30marks)Directions: Read the following passages. Each passage is followed by several questions or unfinished statements .For each of them there are four choices marked A, B,C, and D .Choose the one that fits best according to the information given in the passage.AWhen first entered, Vanak Restaurant does not look like much of a restaurant, but once the pleasant smells of kabob （烤肉串）hit the senses, you are incapable of calling it anything less.Owned by a local couple, this Persian restaurant has an inviting, homelike atmosphere that many restaurants lack.The space is small with only a few dining tables and nearly no decoration, but the environment is truly chaiming.Lying in a hardly noticeable street corner, the restaurant still attracts all customer especially those experienced in the delights of Middle Easrern cooking.A common sight is that of old Persian men sitting in the corner talking loudly about world topics, wathcing news events on TV, drinking a black tea known as Persian chai, an reading local Persian nespapers all the while trying to finish off their plates piled wit food.The variety of food at the restaurant is limited, but the amount of each dish is fairly large. Most of the meals can serve two people and are under $10, so not only is it affordably but practical as well.The food, especially appeals to health-conscious eaters because each dish is very healthy, made with limited fat and o il and served straight off the grill（烤肉架）.The main dish that the restaurant is popular for is its kabobs, which are different style of grilled meat.One delicious and extemely healthy dish is the Jooieh Kabob, which is made of grille chichen picccs served with either rice or bread. Another great kabob is the Chelo Kabob, kabob consinting of grilled beef.Although the restaurant is samall, the atmosphere and the food is delicious. It is a plan that should not be overlooked.56.When first entering the restaurant ,one can find that itA. is splendidly decorated.B. has pleasant smells of kabobs.C. is crowded with dining table.D. looks like a common restaurant.57.What activity is also mentioned apart from dining in the restaurant?A. Watching news events on TV.B. Drinking a kind of black coffee.C. Reading local English newspaper.D. Discussing world topics in loe voices.58.The food of the restaurantA. is served in small amounts.B. is rather expensive.C. is rich in varity.D. is very heslthy59.What is the dish Joojeh Kabob mainly made of ？A. RiceB. ChickenC. BreadD. Beef60. It can be inferred from the passage that restaurant .A. occupiesB. owns a favorable locationC. is popular for its special foodD. has a quiet environment insideBMy father was chief engineer of a merchant ship ，which was sunk in world war ？？？the book night of the U-boats told the story。

2012年普通高等学校招生全国统一考试（湖南卷）数学（理工农医类）一、选择题：本大题共8小题，每小题5分，共40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.设集合M={-1,0,1}，N={x|x 2≤x}，则M ∩N=A.{0}B.{0,1}C.{-1,1}D.{-1,0,0} 【答案】B 【解析】{}0,1N = M={-1,0,1} ∴M ∩N={0,1}.【点评】本题考查了集合的基本运算，较简单，易得分. 先求出{}0,1N =,再利用交集定义得出M ∩N. 2.命题“若α=4π，则tan α=1”的逆否命题是 A.若α≠4π，则tan α≠1B. 若α=4π，则tan α≠1C. 若tan α≠1，则α≠4πD. 若tan α≠1，则α=4π【答案】C【解析】因为“若p ，则q ”的逆否命题为“若p ⌝，则q ⌝”，所以 “若α=4π，则tan α=1”的逆否命题是 “若tan α≠1，则α≠4π”. 【点评】本题考查了“若p ，则q ”形式的命题的逆命题、否命题与逆否命题，考查分析问题的能力.3.某几何体的正视图和侧视图均如图1所示，则该几何体的俯视图不可能是 【答案】D【解析】本题是组合体的三视图问题，由几何体的正视图和侧视图均如图1所示知，原图下面图为圆柱或直四棱柱，上面是圆柱或直四棱柱或下底是直角的三棱柱，Ａ，Ｂ，Ｃ都可能是该几何体的俯视图，Ｄ不可能是该几何体的俯视图，因为它的正视图上面应为如图的矩形.【点评】本题主要考查空间几何体的三视图，考查空间想象能力.是近年高考中的热点题型.4.设某大学的女生体重y （单位：kg ）与身高x （单位：cm ）具有线性相关关系，根据一组样本数据（x i ，y i ）（i=1，2，…，n ），用最小二乘法建立的回归方程为yA.y 与x 具有正的线性相关关系B.回归直线过样本点的中心（x ，y ）C.若该大学某女生身高增加1cm ，则其体重约增加D.若该大学某女生身高为170cm ，则可断定其体重比为 【答案】D【解析】由回归方程为y y 随x 的增大而增大，所以y 与x 具有正的线性相关关系，由最小二乘法建立的回归方程得过程知ˆ()y bx a bx y bx a y bx =+=+-=-，所以回归直线过样本点的中心（x ，y ），利用回归方程可以预测估计总体，所以D 不正确.【点评】本题组要考查两个变量间的相关性、最小二乘法及正相关、负相关的概念，并且是找不正确的答案，易错.5. 已知双曲线C ：22x a -22y b=1的焦距为10 ，点P （2,1）在C 的渐近线上，则C 的方程为A ．220x -25y =1 B.25x -220y =1 C.280x -220y =1 D.220x -280y =1【答案】A【解析】设双曲线C ：22x a -22y b=1的半焦距为c ，则210,5c c ==.又C 的渐近线为b y x a =±，点P （2,1）在C 的渐近线上，12ba∴=，即2a b =.又222c a b =+，a ∴==，∴C 的方程为220x -25y =1.【点评】本题考查双曲线的方程、双曲线的渐近线方程等基础知识，考查了数形结合的思想和基本运算能力，是近年来常考题型. 6. 函数f （x ）=sinx-cos(x+6π)的值域为A ． [ -2 ,2] C.[-1,1 ] , ] 【答案】B【解析】f （x ）=sinx-cos(x+6π)1sin cos sin )226x x x x π=-+=-，[]sin()1,16x π-∈-，()f x ∴值域为].【点评】利用三角恒等变换把()f x 化成sin()A x ωϕ+的形式，利用[]sin()1,1x ωϕ+∈-，求得()f x 的值域.7. 在△ABC 中，AB=2，AC=3，AB BC = 1则___BC =.C.【答案】A【解析】由下图知AB BC = cos()2(cos )1AB BC B BC B π-=⨯⨯-=.1cos 2B BC∴=-.又由余弦定理知222cos 2AB BC AC B AB BC +-=⋅，解得BC =. 【点评】本题考查平面向量的数量积运算、余弦定理等知识.考查运算能力，考查数形结合思想、等价转化思想等数学思想方法.需要注意,AB BC 的夹角为B ∠的外角. 8．已知两条直线1l ：y =m 和2l ： y=821m +(m ＞0)，1l 与函数2log y x =的图像从左至右相交于点A ，B ，2l 与函数2log y x =的图像从左至右相交于C,D .记线段AC 和BD 在X 轴上的投影长度分别为a ,b ,当m变化时，ba的最小值为 A．B. C. D. 【答案】B【解析】在同一坐标系中作出y=m ，y=821m +(m ＞0)，2log y x =图像如下图，由2log x = m ，得122,2m mx x -==，2log x = 821m +，得821821342,2m m x x +-+==.依照题意得8218218218212222,22,22m m m mmm m m b a b a++--+--+-=-=-=-821821222m m mm +++==.8141114312122222m m m m +=++-≥-=++，min ()b a ∴=【点评】在同一坐标系中作出y=m ，y=821m +(m ＞0)，2log y x =图像，结合图像可解得.二 、填空题： 本大题共8小题，考生作答7小题，每小题5分 ，共35分，把答案填在答题卡中对应题号后的横线上.（一）选做题（请考生在第9、10、 11三题中任选两题作答，如果全做，则按前两题记分 ）9. 在直角坐标系xOy 中，已知曲线1C ：1,12x t y t =+⎧⎨=-⎩ (t 为参数)与曲线2C ：sin ,3cos x a y θθ=⎧⎨=⎩(θ为参数，0a >) 有一个公共点在X 轴上，则__a =.【答案】32【解析】曲线1C ：1,12x t y t=+⎧⎨=-⎩直角坐标方程为32y x =-，与x 轴交点为3(,0)2；曲线2C ：sin ,3cos x a y θθ=⎧⎨=⎩直角坐标方程为22219x y a +=，其与x 轴交点为(,0),(,0)a a -， 由0a >，曲线1C 与曲线2C 有一个公共点在X 轴上，知32a =. 【点评】本题考查直线的参数方程、椭圆的参数方程，考查等价转化的思想方法等.曲线1C 与曲线2C 的参数方程分别等价转化为直角坐标方程，找出与x 轴交点，即可求得.10.不等式|2x+1|-2|x-1|>0的解集为_______. 【答案】14x x ⎧⎫>⎨⎬⎩⎭【解析】令()2121f x x x =+--，则由()f x 13,()2141,(1)23,(1)x x x x ⎧-<-⎪⎪⎪=--≤≤⎨⎪>⎪⎪⎩得()f x 0>的解集为14x x ⎧⎫>⎨⎬⎩⎭.【点评】绝对值不等式解法的关键步骤是去绝对值，转化为代数不等式（组）.11.如图2，过点P 的直线与圆O 相交于A ，B 两点.若PA=1，AB=2，PO=3，则圆O 的半径等于_______.【解析】设PO 交圆O 于C ，D ，如图，设圆的半径为R ，由割线定理知【点评】本题考查切割线定理，考查数形结合思想，由切割线定理知PA PB PC PD ⋅=⋅，从而求得圆的半径. (二)必做题（12~16题）12.已知复数2(3)z i =+ (i 为虚数单位)，则|z|=_____. 【答案】10【解析】2(3)z i =+=29686i i i ++=+，10z ==.【点评】本题考查复数的运算、复数的模.把复数化成标准的(,)a bi a b R +∈形式，利用z =求得.13.(6的二项展开式中的常数项为 .（用数字作答） 【答案】-160 【解析】()6的展开式项公式是663166C (C 2(1)r r r r rr r r T x ---+==-.由题意知30,3r r -==，所以二项展开式中的常数项为33346C 2(1)160T =-=-.【点评】本题主要考察二项式定理，写出二项展开式的通项公式是解决这类问题的常规办法. 14.如果执行如图3所示的程序框图，输入1x =-,n =3,则输出的数S = . 【答案】4-【解析】输入1x =-,n =3,，执行过程如下：2:6233i S ==-++=-；1:3(1)115i S ==--++=；0:5(1)014i S ==-++=-，所以输出的是4-.【点评】本题考查算法流程图，要明白循环结构中的内容，一般解法是逐步执行，一步步将执行结果写出，特别是程序框图的执行次数不能出错.15.函数f （x ）=sin (x ωϕ+)的导函数()y f x '=的部分图像如图4所示，其中，P 为图像与y 轴的交点，A,C 为图像与x 轴的两个交点，B 为图像的最低点. （1）若6πϕ=，点P 的坐标为（0），则ω= ; （2）若在曲线段ABC 与x 轴所围成的区域内随机取一点，则该点在△ABC 内的概率为 . 【答案】（1）3；（2）4π【解析】（1）()y f x '=cos()x ωωϕ=+，当6πϕ=，点P 的坐标为（0，2）时cos36πωω=∴=； （2）由图知222T AC ππωω===，122ABCS AC πω=⋅=，设,A B 的横坐标分别为,a b . 设曲线段ABC与x 轴所围成的区域的面积为S则()()sin()sin()2bbaaS f x dx f x a b ωϕωϕ'===+-+=⎰，由几何概型知该点在△ABC 内的概率为224ABCSP Sππ===. 【点评】本题考查三角函数的图像与性质、几何概型等，（1）利用点P 在图像上求ω， （2）几何概型，求出三角形面积及曲边形面积，代入公式即得. 16.设N =2n （n ∈N *，n ≥2），将N 个数x 1,x 2,…，x N 依次放入编号为1,2，…，N 的N 个位置，得到排列P 0=x 1x 2…x N .将该排列中分别位于奇数与偶数位置的数取出，并按原顺序依次放入对应的前2N 和后2N个位置，得到排列P 1=x 1x 3…x N-1x 2x 4…x N ，将此操作称为C 变换，将P 1分成两段，每段2N 个数，并对每段作C 变换，得到2p ；当2≤i ≤n-2时，将P i 分成2i 段，每段2i N个数，并对每段C 变换，得到P i+1，例如，当N=8时，P 2=x 1x 5x 3x 7x 2x 6x 4x 8，此时x 7位于P 2中的第4个位置. （1）当N=16时，x 7位于P 2中的第___个位置；（2）当N=2n （n ≥8）时，x 173位于P 4中的第___个位置. 【答案】（1）6；（2）43211n -⨯+【解析】（1）当N=16时,012345616P x x x x x x x =,可设为(1,2,3,4,5,6,,16), 113571524616P x x x x x x x x x =,即为(1,3,5,7,9,2,4,6,8,,16),2159133711152616P x x x x x x x x x x x =,即(1,5,9,13,3,7,11,15,2,6,,16), x 7位于P 2中的第6个位置,；（2）方法同（1）,归纳推理知x 173位于P 4中的第43211n -⨯+个位置.【点评】本题考查在新环境下的创新意识，考查运算能力，考查创造性解决问题的能力. 需要在学习中培养自己动脑的习惯，才可顺利解决此类问题.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.（本小题满分12分）某超市为了解顾客的购物量及结算时间等信息，安排一名员工随机收集了在该超市购物的100位已知这100位顾客中的一次购物量超过8件的顾客占55％.（Ⅰ）确定x ，y 的值，并求顾客一次购物的结算时间X 的分布列与数学期望；（Ⅱ）若某顾客到达收银台时前面恰有2位顾客需结算，且各顾客的结算相互独立，求该顾客结算前的等候时间不超过．．．分钟的概率. （注：将频率视为概率）【解析】（1）由已知,得251055,35,y x y ++=+=所以15,20.x y ==该超市所有顾客一次购物的结算时间组成一个总体，所以收集的100位顾客一次购物的结算时间可视为总体的一个容量随机样本，将频率视为概率得X 的分布为X 的数学期望为 33111()1 1.52 2.53 1.920104510E X =⨯+⨯+⨯+⨯+⨯=. （Ⅱ）记A 为事件“该顾客结算前的等候时间不超过分钟”，(1,2)i X i =为该顾客前面第i 位顾客的结算时间，则121212()(11)(1 1.5)( 1.51)P A P X X P X X P X X ===+==+==且且且. 由于顾客的结算相互独立，且12,X X 的分布列都与X 的分布列相同，所以 333333920202010102080=⨯+⨯+⨯=. 故该顾客结算前的等候时间不超过分钟的概率为980. 【点评】本题考查概率统计的基础知识，考查分布列及数学期望的计算，考查运算能力、分析问题能力.第一问中根据统计表和100位顾客中的一次购物量超过8件的顾客占55％知251010055%,35,y x y ++=⨯+=从而解得,x y ，计算每一个变量对应的概率，从而求得分布列和期望；第二问，通过设事件，判断事件之间互斥关系，从而求得 该顾客结算前的等候时间不超过．．．分钟的概率. 18.（本小题满分12分）如图5，在四棱锥P-ABCD 中，PA ⊥平面ABCD ，AB=4，BC=3，AD=5，∠DAB=∠ABC=90°，E 是CD 的中点.（Ⅰ）证明：CD ⊥平面PAE ； （Ⅱ）若直线PB 与平面PAE 所成的角和PB 与平面ABCD 所成的角相等，求四棱锥P-ABCD 的体积. 【解析】解法1（Ⅰ如图（1）），连接AC ，由AB=4，3BC =，90 5.ABC AC ∠==,得5,AD =又Ｅ是ＣＤ的中点，所以.CD AE ⊥,,PA ABCD CD ABCD ⊥⊂平面平面所以.PA CD ⊥而,PA AE 是平面PAE 内的两条相交直线，所以CD ⊥平面PAE. （Ⅱ）过点Ｂ作,,,,.BG CD AE AD F G PF //分别与相交于连接由（Ⅰ）CD ⊥平面PAE 知，ＢＧ⊥平面PAE.于是BPF ∠为直线ＰＢ与平面PAE 所成的角，且BG AE ⊥.由PA ABCD ⊥平面知，PBA ∠为直线PB 与平面ABCD 所成的角.4,2,,AB AG BG AF ==⊥由题意，知,PBA BPF ∠=∠因为sin ,sin ,PA BF PBA BPF PB PB∠=∠=所以.PA BF = 由90//,//,DAB ABC AD BC BG CD ∠=∠=知，又所以四边形BCDG 是平行四边形，故3.GD BC ==于是 2.AG =在Rt ΔBAG 中，4,2,,AB AG BG AF ==⊥所以于是PA BF ==又梯形ABCD 的面积为1(53)416,2S =⨯+⨯=所以四棱锥P ABCD -的体积为 解法2：如图（2），以A 为坐标原点，,,AB AD AP 所在直线分别为x y z 轴，轴，轴建立空间直角坐标系.设,PA h =则相关的各点坐标为：（Ⅰ）易知(4,2,0),(2,4,0),(0,0,).CD AE AP h =-==因为8800,0,CD AE CD AP ⋅=-++=⋅=所以,.CD AE CD AP ⊥⊥而,AP AE 是平面PAE 内的两条相交直线，所以.CD PAE ⊥平面(Ⅱ)由题设和（Ⅰ）知，,CD AP 分别是PAE 平面，ABCD 平面的法向量，而PB 与PAE 平面所成的角和PB 与ABCD 平面所成的角相等，所以由（Ⅰ）知，(4,2,0),(0,0,),CD AP h =-=-由(4,0,),PB h =-故解得5h =. 又梯形ABCD 的面积为1(53)4162S =⨯+⨯=，所以四棱锥P ABCD -的体积为111633515V S PA =⨯⨯=⨯⨯=. 【点评】本题考查空间线面垂直关系的证明，考查空间角的应用，及几何体体积计算.第一问只要证明PA CD ⊥即可，第二问算出梯形的面积和棱锥的高，由13V S PA =⨯⨯算得体积，或者建立空间直角坐标系，求得高几体积. 19.（本小题满分12分）已知数列{a n }的各项均为正数，记A （n ）=a 1+a 2+……+a n ，B （n ）=a 2+a 3+……+a n +1，C （n ）=a 3+a 4+……+a n +2，n =1,2，……（1） 若a 1=1，a 2=5，且对任意n ∈N ﹡，三个数A （n ），B （n ），C （n ）组成等差数列，求数列{ a n }的通项公式. （2） 证明：数列{ a n }是公比为q 的等比数列的充分必要条件是：对任意N n *∈，三个数A （n ），B （n ），C （n ）组成公比为q 的等比数列. 【解析】解（１）对任意N n *∈,三个数(),(),()A n B n C n 是等差数列，所以 即112,n n a a a ++-=亦即2121 4.n n a a a a +--=-=故数列{}n a 是首项为１，公差为４的等差数列.于是1(1)44 3.n a n n =+-⨯=- （Ⅱ）（１）必要性：若数列{}n a 是公比为ｑ的等比数列，则对任意N n *∈，有1.n nq a a -=由0n a >知，(),(),()A n B n C n 均大于０，于是即()()B n A n ＝()()C n B n ＝q ，所以三个数(),(),()A n B n C n 组成公比为q 的等比数列. （２）充分性：若对于任意N n *∈，三个数(),(),()A n B n C n 组成公比为q 的等比数列， 则()(),()()B n qA n C n qB n ==，于是[]()()()(),C n B n q B n A n -=-得2211(),n n a a q a a ++-=-即 由1n =有(1)(1),B qA =即21a qa =，从而210n n a qa ++-=. 因为0n a >，所以2211n n a a q a a ++==，故数列{}n a 是首项为1a ，公比为q 的等比数列， 综上所述，数列{}n a 是公比为q 的等比数列的充分必要条件是：对任意n ∈N ﹡，三个数(),(),()A n B n C n 组成公比为q 的等比数列.【点评】本题考查等差数列、等比数列的定义、性质及充要条件的证明.第一问由等差数列定义可得；第二问要从充分性、必要性两方面来证明，利用等比数列的定义及性质易得证. 20.（本小题满分13分）某企业接到生产3000台某产品的A ，B ，Ｃ三种部件的订单，每台产品需要这三种部件的数量分别为２,２,１（单位：件）.已知每个工人每天可生产Ａ部件６件，或Ｂ部件３件，或Ｃ部件２件.该企业计划安排２００名工人分成三组分别生产这三种部件，生产Ｂ部件的人数与生产Ａ部件的人数成正比，比例系数为k （k 为正整数）.（１）设生产Ａ部件的人数为ｘ，分别写出完成Ａ，Ｂ，Ｃ三种部件生产需要的时间；（２）假设这三种部件的生产同时开工，试确定正整数k 的值，使完成订单任务的时间最短，并给出时间最短时具体的人数分组方案. 【解析】 解：（Ⅰ）设完成A,B,C 三种部件的生产任务需要的时间（单位：天）分别为123(),(),(),T x T x T x 由题设有期中,,200(1)x kx k x -+均为1到200之间的正整数.（Ⅱ）完成订单任务的时间为{}123()max (),(),(),f x T x T x T x =其定义域为2000,.1x x x N k *⎧⎫<<∈⎨⎬+⎩⎭易知，12(),()T x T x 为减函数，3()T x 为增函数.注意到212()(),T x T x k=于是（1）当2k =时，12()(),T x T x = 此时 {}1310001500()max (),()max ,2003f x T x T x x x ⎧⎫==⎨⎬-⎩⎭， 由函数13(),()T x T x 的单调性知，当100015002003x x=-时()f x 取得最小值，解得 4009x =.由于 134002503004445,(44)(44),(45)(45),(44)(45)91113f T f T f f <<====<而.故当44x =时完成订单任务的时间最短，且最短时间为250(44)11f =.（2）当2k >时，12()(),T x T x > 由于k 为正整数，故3k ≥，此时{}1375(),()max (),()50T x x T x T x xϕ==-易知()T x 为增函数，则 1000375()max ,50x x x ϕ⎧⎫==⎨⎬-⎩⎭.由函数1(),()T x T x 的单调性知，当100037550x x =-时()x ϕ取得最小值，解得40011x =.由于14002502503752503637,(36)(36),(37)(37),119111311T T ϕϕ<<==>==>而此时完成订单任务的最短时间大于25011.（3）当2k <时，12()(),T x T x < 由于k 为正整数，故1k =，此时{}232000750()max (),()max ,.100f x T x T x x x ⎧⎫==⎨⎬-⎩⎭由函数23(),()T x T x 的单调性知， 当2000750100x x=-时()f x 取得最小值，解得80011x =.类似（1）的讨论.此时 完成订单任务的最短时间为2509，大于25011. 综上所述，当2k =时完成订单任务的时间最短，此时生产Ａ，Ｂ，Ｃ三种部件的人数 分别为44,88,68.【点评】本题为函数的应用题，考查分段函数、函数单调性、最值等，考查运算能力及用数学知识分析解决实际应用问题的能力.第一问建立函数模型；第二问利用单调性与最值来解决，体现分类讨论思想.21.（本小题满分13分）在直角坐标系xOy 中，曲线C 1的点均在C 2：（x-5）2＋y 2=9外，且对C 1上任意一点M ，M 到直线x=﹣2的距离等于该点与圆C 2上点的距离的最小值.（Ⅰ）求曲线C 1的方程；（Ⅱ）设P(x 0,y 0)（y 0≠±3）为圆C 2外一点，过P 作圆C 2的两条切线，分别与曲线C 1相交于点A ，B 和C ，D.证明：当P 在直线x=﹣4上运动时，四点A ，B ，C ，D 的纵坐标之积为定值.【解析】（Ⅰ）解法1 ：设M 的坐标为(,)x y ，由已知得23x +=，易知圆2C 上的点位于直线2x =-的右侧.于是20x +>，所以5x =+.化简得曲线1C 的方程为220y x =.解法2 ：由题设知，曲线1C 上任意一点M 到圆心2C (5,0)的距离等于它到直线5x =-的距离，因此，曲线1C 是以(5,0)为焦点，直线5x =-为准线的抛物线，故其方程为220y x =. （Ⅱ）当点P 在直线4x =-上运动时，P 的坐标为0(4,)y -，又03y ≠±，则过P 且与圆 2C 相切得直线的斜率k 存在且不为0，每条切线都与抛物线有两个交点，切线方程为0(4),y y k x -=+0即kx-y+y +4k=0.于是整理得2200721890.k y k y ++-= ①设过P 所作的两条切线,PA PC 的斜率分别为12,k k ，则12,k k 是方程①的两个实根，故001218.724y y k k +=-=- ② 由101240,20,k x y y k y x -++=⎧⎨=⎩得21012020(4)0.k y y y k -++= ③ 设四点A,B,C,D 的纵坐标分别为1234,,,y y y y ，则是方程③的两个实根，所以0112120(4).y k y y k +⋅=④ 同理可得 0234220(4).y k y y k +⋅=⑤ 于是由②，④，⑤三式得 22001212400166400y y k k k k ⎡⎤-+⎣⎦=.所以，当P 在直线4x =-上运动时，四点A ，B ，C ，D 的纵坐标之积为定值6400.【点评】本题考查曲线与方程、直线与曲线的位置关系，考查运算能力，考查数形结合思想、函数与方程思想等数学思想方法.第一问用直接法或定义法求出曲线的方程；第二问设出切线方程，把直线与曲线方程联立，由一元二次方程根与系数的关系得到,,,A B C D 四点纵坐标之积为定值，体现“设而不求”思想.22.（本小题满分13分）已知函数()f x =ax e x =-，其中a ≠0.（1） 若对一切x ∈R ，()f x ≥1恒成立，求a 的取值集合.（2）在函数()f x 的图像上取定两点11(,())A x f x ，22(,())B x f x 12()x x <，记直线AB 的斜率为K ，问：是否存在x 0∈（x 1，x 2），使0()f x k '>成立？若存在，求0x 的取值范围；若不存在，请说明理由.【解析】（Ⅰ）若0a <，则对一切0x >，()f x 1ax e x =-<，这与题设矛盾，又0a ≠， 故0a >.而()1,ax f x ae '=-令11()0,ln .f x x a a '==得 当11ln x a a <时，()0,()f x f x '<单调递减；当11ln x a a>时，()0,()f x f x '>单调递增，故当11ln x a a =时，()f x 取最小值11111(ln )ln .f a a a a a=- 于是对一切,()1x R f x ∈≥恒成立，当且仅当111ln 1a a a-≥. ① 令()ln ,g t t t t =-则()ln .g t t '=-当01t <<时，()0,()g t g t '>单调递增；当1t >时，()0,()g t g t '<单调递减.故当1t =时，()g t 取最大值(1)1g =.因此，当且仅当11a=即1a =时，①式成立. 综上所述，a 的取值集合为{}1. （Ⅱ）由题意知，21212121()() 1.ax ax f x f x e e k x x x x --==--- 令2121()(),ax ax axe e xf x k ae x x ϕ-'=-=--则 令()1t F t e t =--，则()1t F t e '=-.当0t <时，()0,()F t F t '<单调递减；当0t >时，()0,()F t F t '>单调递增.故当0t =，()(0)0,F t F >=即10.t e t -->从而21()21()10a x x e a x x ---->，12()12()10,a x x e a x x ---->又1210,ax e x x >-2210,ax e x x >- 所以1()0,x ϕ<2()0.x ϕ>因为函数()y x ϕ=在区间[]12,x x 上的图像是连续不断的一条曲线，所以存在012(,)x x x ∈使0()0,x ϕ=2()0,()axx a e x ϕϕ'=>单调递增，故这样的c 是唯一的，且21211ln ()ax ax e e c a a x x -=-.故当且仅当212211(ln ,)()ax ax e e x x a a x x -∈-时， 0()f x k '>. 综上所述，存在012(,)x x x ∈使0()f x k '>成立.且0x 的取值范围为212211(ln ,)()ax ax e e x a a x x --. 【点评】本题考查利用导函数研究函数单调性、最值、不等式恒成立问题等，考查运算能力，考查分类讨论思想、函数与方程思想，转化与划归思想等数学思想方法.第一问利用导函数法求出()f x 取最小值11111(ln )ln .f a a a a a=-对一切x ∈R ，f(x) ≥1恒成立转化为min ()1f x ≥，从而得出a的取值集合；第二问在假设存在的情况下进行推理，通过构造函数，研究这个函数的单调性及最值来进行分析判断.。

2011年普通高等学校夏季招生全国统一考试数学(湖南卷)一、选择题：本大题共8小题，每小题5分，共40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．若a，b∈R，i为虚数单位，且(a＋i)i＝b＋i，则()A．a＝1，b＝1 B．a＝－1，b＝1C．a＝－1，b＝－1 D．a＝1，b＝－12．设集合M＝{1，2}，N＝{a2}，则“a＝1”是“N M”的()A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分又不必要条件3．如图是某几何体的三视图，则该几何体的体积为…()A．92π＋12 B．92π＋18C．9π＋42 D．36π＋184．通过随机询问110名性别不同的大学生是否爱好某项运动，得到如下的列联表：男女总计爱好402060不爱好203050总计6050110由22()()()()()n ad bcKa b c d a c b d-=++++算得，22110(40302020)7.860506050K⨯⨯-⨯=≈⨯⨯⨯.附表：P(K2≥k)0.0500.0100.001k 3.841 6.63510.828参照附表，得到的正确结论是()A．在犯错误的概率不超过0.1%的前提下，认为“爱好该项运动与性别有关”B．在犯错误的概率不超过0.1%的前提下，认为“爱好该项运动与性别无关”C．有99%以上的把握认为“爱好该项运动与性别有关”D．有99%以上的把握认为“爱好该项运动与性别无关”5．设双曲线2221(0)9x yaa-=>的渐近线方程为3x±2y＝0，则a的值为()A．4 B．3 C．2 D．16．由直线ππ,,033x x y=-==与曲线y＝cos x所围成的封闭图形的面积为()A．12B．1 C．32D．37．设m ＞1，在约束条件1y x y mx x y ≥⎧⎪≤⎨⎪+≤⎩下，目标函数z ＝x ＋my 的最大值小于2，则m 的取值范围为( )A ．(1,12)+B ．(12,)++∞C ．(1，3)D ．(3，＋∞)8．设直线x ＝t 与函数2(),()ln f x x g x x ==的图象分别交于点M ，N ，则当|MN |达到最小时t 的值为( )A ．1B ．12 C ． 52 D ． 22 二、填空题：本大题共8小题，考生作答7小题，每小题5分，共35分．(一)选做题(请考生在第 9，10，11三题中任选两题作答，如果全做，则按前两题记分．)9．在直角坐标系xOy 中，曲线C 1的参数方程为cos ,1sin x y αα=⎧⎨=+⎩，(α为参数)．在极坐标系(与直角坐标系xOy 取相同的长度单位，且以原点O 为极点，以x 轴正半轴为极轴)中，曲线C 2的方程为ρ(cos θ－sin θ)＋1＝0，则C 1与C 2的交点个数为______．10．设x ，y ∈R ，且xy ≠0，则222211()(4)x y y x++的最小值为______． 11．如图，A ，E 是半圆周上的两个三等分点，直径BC ＝4，AD ⊥BC ，垂足为D ，BE 与AD 相交于点F ，则AF 的长为______．(二)必做题(12～16题)12．设S n 是等差数列{a n }(n ∈N *)的前n 项和，且a 1＝1，a 4＝7，则S 5＝______.13．若执行如图所示的框图，输入1231,2,3,2x x x x ====，则输出的数等于______． 14．在边长为1的正三角形ABC 中，设2,3BC BD CA CE == ，则AD BE ⋅= ______.15．如图，EFGH 是以O 为圆心、半径为1的圆的内接正方形．将一颗豆子随机地扔到该圆内，用A 表示事件“豆子落在正方形EFGH 内”，B 表示事件“豆子落在扇形OHE (阴影部分)内”，则。

准考证号_＿_＿____姓名＿_____＿＿_(在此卷上答题无效)绝密★启用前２０1１年普通高等学校招生全国统一考试理科综合能力测试本试卷分第Ⅰ卷(选择题)和第Ⅱ卷（非选择题)两部分。

第Ⅰ卷１至5页,第Ⅱ卷6至12页。

共300分考生注意：1.答题前，考生务必将自己的准考证号、姓名填写在答题卡上。

考生要认真核对答题卡上粘贴的条形码中“准考证号、姓名、考试科目”与考生本人准考证号、姓名是否一致。

２.第Ⅰ卷每小题选出答案后,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。

第Ⅱ卷用黑色墨水签字笔在答题卡上书写作答，在试题卷上作答，答案无效。

3.考试结束，监考员将试题卷、答题卡一并收回。

第Ⅰ卷(选择题共120分)本卷共２1小题,每小题6分,共1２6分。

以下数据可供解题时参考：可能用到的相对原子质量：H 1B11 C 12 N １4 O 16 Na2３Ｓ3２Cｌ35.5 Ca40 Cｕ64一、选择题：本大题共１3小题,每小题６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．将人的红细胞放入4℃蒸馏水中,一段时间后红细胞破裂，主要原因是Ａ.红细胞具有水溶性 B.红细胞的液泡体积增大C．蒸馏水大量进入红细胞Ｄ.低温时红细胞膜流动性增大2．甲、乙两种酶用同一种蛋白酶处理，酶活性与处理时间的关系如下图所示。

下列分析错误．．的是A．甲酶能够抗该种蛋白酶降解B. 甲酶是不可能具有催化功能的ＲNＡＣ.乙酶的化学本质为蛋白质D.乙酶活性的改变是因为其分子结构的改变３.番茄幼苗在缺镁的培养液中培养一段时间后，与对照组相比,其叶片光合作用强度下降，原因是Ａ．光反应强度升高,暗反应强度降低 B.光反应强度降低，暗反应强度降低C.反应强度不变,暗反应强度降低D．光反应强度降低,暗反应强度不变4.撕取紫色洋葱外表皮,分为两份，假定两份外表皮细胞的大小、数目和生理状态一致,一份在完全营养液中浸泡一段时间,浸泡后的外表皮称为甲组;另一份在蒸馏水中浸泡相同的时间，浸泡后的外表皮称为乙组。

总题数：22 题第1题(2011年普通高等学校夏季招生考试英语(湖南卷))题目Directions：Readthefollowingpassage.Answerthequestionsaccordingtotheinformationgiveninthepassage.My First Long RunTwo weeks ago，I had a quarrel with my husband.After he had driven off in anger，I realized that I wasn't going to feel any better just sitting there.Feeling abandoned and guilty，I put on my gym shoes to get some fresh air.Our driveway has a slope（斜坡） that is easier just to jog down if you are lazy，taking advantage of gravity.Instead of stopping at the end of the slope，I decided to see if I could just jog to the end of the street.I had tried a few months ago and failed miserably.Since that first attempt I had been jogging regularly and was significantly fitter，but still very lazy.However this time around I managed to reach the stop sign with ease and I figured I would go a little further.After about one kilometer，however，I noticed that my upper body was tense.To make the movement easier I had to relax my body，and tried to take deep breaths of fresh air.I kept giving myself the excuse to stop.No one would be disappointed.No one would even know.But I didn't stop.I wanted to keep going harder，better，faster，stronger.To my great surprise，I ran 4.9 km in 31 minutes.When I got back，I had tears in my eyes.I did something I thought I could never do.It was the first long run of my life.Since then，I have improved my stride（步幅） and time.After every run I feel fitter，happier and motivated to keep progressing.I love the runner's high.I normally jog because I want to look good.I want to run because it makes me feel good.（1）Why did the author feel guilty?（No more than 9 words）（2 marks）________________________________________________________________________（2）What did the author fail to do miserably a few months ago?（No more than 11 words）（2 marks）________________________________________________________________________（3）What excuses did the author keep giving herself to stop?（No more than 9 words）（3 marks）________________________________________________________________________（4）How is running different from jogging to the author?（No more than 14 words）（3 marks）________________________________________________________________________答案（1）Because she had a quarrel with her husband.（2）She failed to jog to the end of the street.（3）No one would be disappointed or even know.（4）Running makes her feel good while jogging makes her look good.第2题(2009年普通高等学校夏季招生考试英语（全国Ⅰ卷）)题目阅读下面短文，从短文后各题所给的四个选项(A、B、C和D)中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。

古诗春暮西园翻译赏析《春暮西园》作者为唐朝文学家高启。

其古诗全文如下：绿池芳草满晴波，春色都从雨里过。

知是人家花落尽，菜畦今日蝶来多。

【前言】这首《春暮西园》诗是“明初诗文三大家”之一、并有“明代诗人之冠”美誉的诗人高启的作品。

此诗曾作为诗歌鉴赏题的材料出现在2011年普通高等学校招生全国统一考试湖南卷的语文试题中。

【注释】满：指水满晴波：阳光下的水波。

释”阳光“，误【翻译】在绿水盈盈、芳草萋萋的美景里，春天的美丽的光景仿佛快要从春雨中走过的样子，而在这暮春时节里虽然农人家的花快要落尽了，但菜畦地里今天来的蝴蝶分外的多。

【鉴赏】池塘里满漾着的粼粼春波，池面上倒映着的晴朗天空，池周围缭绕着的嫩绿芳草——这一切，你或许会想起谢灵运笔下“池塘生春草”（《登池上楼》的初春美景。

然而，你可不必为晴空的一碧如洗而欢欣，那是潇潇春雨过后的景象，这雨洗净了天空，可也带走了春色！至于那池畔的芳草，若你读过谢灵运的另两句诗“首夏犹清和，芳草亦未歇”（《游赤石进帆海》），怕也不能把它们只看成是春天正盛的象征吧？本诗的前两句，诗人为你写了春景，但却提醒你：现在是暮春了。

暮春了，你该首先想到春花的凋谢，想赶快来几句惋叹之词，去作一番凭吊，然而，这千年的陈规旧习，高明的诗人是无心再去追逐的。

他的心里，当然也在惦念残红狼藉的花圃；而他的目光，却投向了平常无奇、司空见惯、毫不足珍的菜畦。

菜畦？你会说，那可是农人野夫的躬耕之处，有何风雅气息能从其间飘逸出来？你会举出无数例子证明，文人骚客向来只留连于月下花前，何尝为油菜黄瓜而徘徊不舍？可是，就是这最俗、最不起眼的所在，诗人的慧眼，却偏要使它放出光彩、生出诗意；你没见那畦上纷纷扰扰的粉蝶儿么？它们为何今日来得如许之多？不就是邻家的花朵给春雨摧折得零落满地，才使这儿的菜花大增了招蜂引蝶的魅力？你要直待面见了落花才知春尽，难道不自惭反应迟钝缺乏生活的灵性？就凭这畦上的蝶阵，不也能升起同样的悟念？你若见了落花便忙着伤春，岂不是太嫌俗套？请看看这蝶舞蜂狂、飞得正欢，这暮春时节，不也别有一番盎然情趣，可供你赏玩，令你欣悦？你要想做一个诗人，怎能没点自己的眼光？此诗又题作《西园即事》。

2011年普通高等学校招生全国统一考试(湖南卷)数学(文史类)本试题卷包括选择题、填空题、解答题三部分,共6页,时量120分钟,满分150分参考公式:(1)()(|)()P AB P B A P A =,其中,A B 为两个基本事件,且()0P A >. (2)柱体体积公式V Sh =,其中S 为底面面积,h 为高. (3)球的体积公式343V R π=,其中R 为球的半径. 一、选择题:本大题共8小题,每小题5分,满分40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. 设全集{1,2,3,4,5},{2,4},U U M N M C N ===U I 则N =（ ）A .{1,2,3}B .{1,3,5}C .{1,4,5}D . {2,3,4} 2. 若,,a b R i ∈为虚数单位,且()a i i b i +=+,则( )A .1,1a b ==B . 1,1a b =-=C . 1,1a b ==-D . 1,1a b =-=-3. “1x >”是“||1x >”的( )A .充分不必要条件B . 必要不充分条件C . 充分必要条件D . 既不充分也不必要条件 4. 设图1是某几何体的三视图,则该几何体的体积为 ( )A .942π+B .3618π+C .9122π+ D .9182π+ 5. 通过询问110名性别不同的的大学生是否爱好某项运动,得到如下的列联表.由22()()()()()n ad bc K a b c d a c b d -=++++算得,22110(40302020)7.860506050K ⨯-⨯=≈⨯⨯⨯,附表如右下,参照附表,得到的正确结论( )A .有99%以上的把握认为“爱好该项运动与性别有关”B .有99%以上的把握认为“爱好该项运动与性别无关”C .在犯错误的概率不超过0.1%的前提下,认为“爱好该项运动与性别有关”D .在犯错误的概率不超过0.1%的前提下,认为“爱好该项运动与性别无关”6. 设双曲线2221(0)9x y a a -=>的渐近线方程为320x y =±,则a 的值为( ) A .4 B .3 C .2 D .1 7. 曲线sin 1sin cos 2x y x x =-+在点(,0)4M π处的切线的斜率为( )A .-12B . 12C . -22D . 228. 已知函数2()1,()4 3.x f x e g x x x =-=-+-若有()()f a g b =,则b 的取值范围为( )A .[2-2,2+2]B .(2-2,2+2)C . [1,3]D .(1,3)二、填空题:本大题共8小题,考生作答7小题,每小题5分,共35分.把答案填在答题卡中对应题号后的横线上.(一)选做题(请考生在第9、10两题中任选一题作答,如果全做,则按前一题记分)9. 在直角坐标系xOy 中,曲线1C的参数方程为2cos (x y ααα=⎧⎪⎨=⎪⎩为参数),在极坐标系(与直角坐标系xOy 取相同的长度单位,且以原点O 为极点,以x 轴正半轴为极轴)中,曲线2C 的方程为(cos sin )10ρθθ-+=,则1C 与2C 的交点个数为 .10. 已知某试验范围为[10,90],若用分数法进行4次优选试验,则第二次试点可以是 （只写出其中一个也正确）. (二)必做题(11～16题)11. 若执行如图2所示的框图,输入12341,2,4,8,x x x x ==== 则输出的数等于 .12. 已知()f x 为奇函数,()()9g x f x =+,(2)3g -=,则(2)f = .13. 设向量a ,b 满足|a|=25,b =(2,1),且a 与b 的方向相反,则a 的坐标为 .14. 设1m >,在约束条件,,1y x y mx x y ≥⎧⎪≤⎨⎪+≤⎩下,目标函数5z x y =+的大值为4,则m 的值为 。

2014年普通高等学校招生全国统一考试（湖南卷) 英语Part I Listening Comprehension (30 marks)Section A (22.5 marks)Directions: In this section,you will hear six conversations between two speakers. For each conversation, there are several questions and each question is followed by three choices marked A, B and C. Listen carefully and then choose the best answer for each question.You will hear each conversation TWICE.Example:When will the magazine probably arrive?A. Wednesday.B. Thursday.C. Friday.The answer is B.Conversation 11. What will the woman do first?A. Take a shower.B. Go camping.C. Set up a time.2. When will the man probably call the woman?A. Thursday.B. Friday.C. Sunday.Conversation 23. What is the man going to do?A, Have a coffee break. B. See a doctor. C. Buy a pet.4. What happened to the man?A. He fell ill.B. He lost his dog.C. He slept badly.Conversation 35. What is the woman?A. A bus driver.B. A waitress.C. A tour guide.6. What does the man want to get?A. Some gifts.B. A menu.C. A bus schedule.Conversation 47. What did the man do yesterday?A. He saw a movie.B. He watched TV.C. He visited some friends.8. What time will the speakers probably meet this Saturday evening?A. At 6:30.B. At 7:00.C. At 7:30.9. Which of the following will the man buy?A. Some drinks.B. A birthday cake.C. Concert tickets.Conversation 510. What is the woman doing now?A. She is serving a customer.B. She is conducting an interview.C. She is doing some recording.11 .When does the man go to the nursing home?A. Tuesdays.B. Thursdays.C. Sundays.12. Where will the man probably be working next Monday?A. At the airport nearby.B. In the studio next door.C. At the store downtown. Conversation 613. Why does the woman call the man?A. The oven doesn’t work.B. The heater won’t start.C. The plug is broken.14. Who will handle the problem first tomorrow evening?A. The woman.B. The man. C A worker.15. Who is the woman speaking to?A. Her husband.B. Her house owner.C. Her boss.Section B (7.5 marks)Directions: In this section, you will hear a short passage. Listen carefully and then Jill in the numbered blanks with the information you have heard. Fill in each blank with NO MORE THAN THREE WORDS.You will hear the short passage TWICE.Part II Language Knowledge (45 marks)Section A (15 marks)Directions: For each of the following unfinished sentences there are four choices marked A, B, C and D. Choose the one that best completes the sentence.Example:The wild flowers looked like a soft orange blanket the desert,A. coveringB. coveredC. coverD. to coverThe answer is A.21. Children, when by their parents, are allowed to enter the stadium.A. to be accompaniedB. to accompanyC. accompanyingD. accompanied22. If Mr. Dewey _____ present, he would have offered any possible assistance to the people there.A. wereB. had beenC. should beD. was23. ____your own needs and styles of communication is as important as learning to convey your affection and emotions.A. UnderstandingB. To be understoodC. Being understoodD. Having understood24. As John Lennon once said, life is_____ happens to you while you are busy making other plans.A. whichB. thatC. whatD. where25. —I’ve prepared all kinds of food for the picn ic.—Do you mean we_____ bring anything with us?A. can’tB. mustn’tC. shan’tD. needn't26. You will never gain success you are fully devoted to your work.A. whenB. becauseC. afterD. unless27. There is no greater pleasure than lying on my back in the middle of the grassland, _____at the night sky.A. to stareB. staringC. stared D, having stared28. Since the time humankind started gardening, we _____to make our environment more beautiful.A. tryB. have been tryingC. are tryingD. will try29. Only when you can find peace in your heart _____good relationships with others.A. will you keepB. you will keepC. you keptD. did you keep30. What you’re doing today important, because you’re trading a day of your life for itA. MakeB. To makeC. MakingD. Made31.1 am looking forward to the day_____ my daughter can read this book and know my feelings for her.A. asB. whyC. whenD. where32. All we need _____ a small piece of land where we can plant various kinds of fruit trees throughout the growing seasons of the year.A. areB. wasC. isD. were33. It’s not doing the things we like, but liking the things we have to do makes life happy.A. thatB. whichC. whatD. who34. Whenever you _____ a present, you should think about it from the receiver’s point of view.A. boughtB. have boughtC. will buyD. buy35. _____ ourselves from the physical and mental tensions, we each need deep thought and inner quietness.A. Having freedB. FreedC. To freeD. FreeingSection B (18 marks)Directions: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.The summer before I went off to college, Mom stood me in her usual spot behind the ironing board (烫衣板)and said, “Pay attention: I’m going to teach you to iron.”Mom clearly explained her 36 for this lesson. I was going to be 37 and needed to learn this vital skill. Also, I would be meeting new people, and properly ironed clothes would help me make a good 38 .“Learn to iron a shirt,” Mom said, “and you can iron anything.”But ironing shirts was not 39 work. I t didn’t make use of long muscles we used to throw a baseball, and it wasn’t a40 operation like ice-skating. Ironing was like driving a car on a street that has a stop sign every 10 feet, Moreover, an iron produced steam and it carried an element of 41 .If you touched the wrong part of it, you’d get burnt. If you forgot to turn it off when you 42 ,you might bum down the house.As for technique, Mom 43 me to begin with the flat spaces outward, always pushing the iron forward into wrinkled (有褶皱的）parts. Collars had to be done right. Mom said they were close to your face, where everyone would 44 them.Over the years, I’ve learned to iron shirts skillfully, which gives me a sense of 45 Whatever failures I suffer in my life, an ironed shirt tells me I am good at something. 46 ,through ironing I’ve learned the method for solving even the most troublesome problems. “47 wrinkles one at a time,” as Mom might have said, “and before long everything will get ironed out.”36. A. reasons B. rules C. emotions D. methods37. A. helpful B. confident C. powerful D. independent38. A. conclusion B. suggestion C. impression D. observation39. A. useful B. easy C. special D. suitable40. A. direct B. single C. smooth D. strange41. A. doubt B. pressure C. surprise D. danger42. A. went away B. fell down C. jumped off D. looked up43. A. taught B. chose C. forced D. sent44. A. touch B. design C. see D. admire45. A. honesty B. freedom C. justice D. pride46. A. Instead B. Besides C. Otherwise D. However47. A. Make up B. Deal with C Ask for D. Rely onSection C (12 marks)Directions: Complete the following passage by filling in each blank with one word that best fits the contextWe can choose our friends, but usually we cannot choose our neighbors. However, to get a happy home life, we have to get along with 48 as well as possible.An important quality in a neighbor is consideration for 49 . People should not do things 50 will disturb their neighbors unnecessarily. For example, television sets need not be played at full volume (音量）51 loud pop music should not be played very late at night. By avoiding things likely to upset your neighbors, you can enjoy 52 friendly relationship with them.An equally important quality is tolerance. Neighbors should do all they can to avoid disturbing other people, 53 there are times when some level of disturbance is unavoidable. 54 neighbors want to get along well with each other, they have to show their tolerance. In this way, everyone will live 55 peace.Part Ⅲ Reading Comprehension (30 marks)Directions: Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C andD. Choose the one that fits best according to the information given in the passage.AWant to improve your writing skills? New Writing South is directing the way!· Towner Writer Squad (班组）for kids aged 13-17Led by comedy and TV writer, Marian Kilpatrick, Towner Writer Squad will meet once a month at the contemporary art museum for 11 months, starting 12 October, 2014.The FREE squad sessions will include introductions to a wide range of writing styles, from poetry to play writing and lyrics (抒情诗）to flash fiction, to support the development of young writers.Application & SelectionIf you would like to apply to be part of the Towner Writer Squad, please send a sample piece of your writing (about 500 words), responding to the title ‘LUNCH,’ with your name, age, address and e-mail address to: debo@.Once all applications are in, you will be invited to an open selection event on 17 September,4-5pm, at the gallery of Towner. This will be an informal opportunity to meet the Squad Leader, Squad Associate and other young people.You will also have a chance to get to know the fantastic gallery space and get a taste of what’s to come.Deadline for applications: 8 September, 2014For further information go to: /towner or or Any questions 一feel free to send your e-mail to Towner Writer Squad Associate: whame@﹡﹡﹡﹡﹡﹡﹡﹡﹡· Beginner Writing Project for kids aged 10-13Due to popular demand, a writing project will be started for eager beginners.Start time: 6 September, 2014Meet every other Saturday, 2-4 pm, at the Towner Study Centre.Study and write at your own pace—you do not have to rush—as you have a year to go through the project. Practise under the guidance of some experienced writers and teachers who can help you with basic writing skills. Most importantly, build confidence and have fun while writing!No previous experience or special background is required. Many others have been successful this way. Ifthey can do it, why can’t you?Fee: £179For more information go to: or 56. Towner Writer Squad will be started _______.A. to train comedy and TV writersB. to explore the fantastic gallery spaceC. to introduce a contemporary art museumD. to promote the development of young writers57. To join the Writer Squad, each applicant should first _______.A. provide a piece of their writingB. meet the Writer Squad LeaderC. offer their family informationD. complete an application form58. Applications for the Writer Squad should be e-mailed no later than _______.A. 6 September, 2014B. 8 September, 2014C. 17 September, 2014D. 12 October, 201459. What is most important for the beginners?A. Practising as much as possible.B. Gaining confidence and having fun.C. Studying and writing at their own pace.D. Learning skills from writers and teachers.60. More information about Beginner Writing Project can be found at _______.A. /townerB. C. D. BIn the mid-1950s, I was a somewhat bored early-adolescent male student who believed that doing any more than necessary was wasted effort. One day, this approach threw me into embarrassment In Mrs. Totten’s eighth-grade math class at Central Avenue School in Anderson, Indiana, we were learning to add and subtract decimals (小数).Our teacher typically assigned daily homework, which would be recited in class the following day. On most days, our grades were based on our oral answer to homework questions.Mrs. Totten usually walked up and down the rows of desks requesting answers from student after student in the order the questions had appeared on our homework sheets. She would start either at the front or the back of the classroom and work toward the other end.Since I was seated near the middle of about 35 students, it was easy to figure out which questions I might have to answer. This particular time, I had completed my usual two or three problems according to my calculations.What I failed to expect was that several students were absent, which threw off my estimate. As Mrs. Totten made her way from the beginning of the class, I desperately tried to determine which math problem I would get.I tried to work it out before she got to me, but I had brain freeze and couldn’t function.When Mrs. Totten reached my desk, she asked what answer I’d got for problem No. 14. “I…I didn’t get anything,” I answered, and my face felt warm.“Correct,” she said.It turned out that the correct answer was zero.What did I learn that day? First, always do all your homework. Second, in real life it isn’t always what you say but how you say it that matters. Third, I would never make it as a mathematician.If I could choose one school day that taught me the most, it would be that one.61. What does the underlined part in Paragraph 1 indicate?A. It is wise to value one’s time.B. It is important to make an effortC. It is right to stick to one’s belief.D. It is enough to do the necessary.62. Usually, Mrs. Totten asked her students to _______.A. recite their homework togetherB. grade their homework themselvesC. answer their homework questions orallyD. check the answers to their homework questions63. The author could work out which questions to answer since the teacher always _______.A. asked questions in a regular wayB. walked up and down when asking questionsC. chose two or three questions for the studentsD. requested her students to finish their usual questions64. The author failed to get the questions he had expected because _______.A. the class didn’t begin as us ualB. several students didn’t come to schoolC. he didn’t try hard to make his estimateD. Mrs. Totten didn’t start from the back of the class65. Which of the following can be the best title for the passage?A. An Unforgettable TeacherB. A Future MathematicianC. An Effective ApproachD. A V aluable LessonCThe behaviour of a building’s users may be at least as important as its design when it comes to energy use, according to new research from the UK Energy Research Centre (UKERC). The UK promises to reduce its carbon emissions (排放）by 80 percent by 2050, part of which will be achieved by all new homes being zero-carbon by 2016. But this report shows that sustainable building design on its own — though extremely important- is not enough to achieve such reductions: the behaviour of the people using the building has to change too.The study suggests that the ways that people use and live in their homes have been largely ignored by existing efforts to improve energy efficiency (效率), which instead focus on architectural and technological developments.‘Technology is going to assist but it is not going to do everything,’ explains Katy Janda, a UKERC senior researcher, ‘consumption patterns of building users can defeat the most careful design.’In other words, old habits die hard, even in the best-designed eco-home.Another part of the problem is information. Households and bill-payers don’t have the knowledge they need to change their energy-use habits. Without specific information, it’s hard to estimate the costs and benefits of making different choices. Feedback (反馈）facilities, like smart meters and energy monitors, could help bridge this information gap by helping people see how changing their behaviour directly affects their energy use; some studies have shown that households can achieve up to 15 percent energy savings using smart meters.Social science research has added a further dimension (方面）,suggesting that individuals’ behaviour in the home can be personal and cannot be predicted 一whether people throw open their windows rather than turn down the thermostat (恒温器) , for example.Janda argues that education is the key. She calls for a focused programme to teach people about buildings and their own behaviour in them.66. As to energy use, the new research from UKERC stresses the importance of________.A. zero-carbon homesB. the behaviour of building usersC. sustainable building designD. the reduction of carbon emissions67. The underlined word “which” in Paragraph 2 refers to”________.”A. the waysB. their homesC. developmentsD. existing efforts68. What are Katy Janda’s words mainly about?A. The importance of changing building users, habits.B. The necessity of making a careful building design.C. The variety of consumption patterns of building users.D. The role of technology in improving energy efficiency.69. The information gap in energy use _______.A. can be bridged by feedback facilitiesB. affects the study on energy monitorsC. brings about problems for smart metersD. will be caused by building users’ old habits70. What does the dimension added by social science research suggest?A. The social science research is to be furthered.B. The education programme is under discussion.C. The behaviour of building users is unpredictable.D. The behaviour preference of building users is similar. Part IV Writing (45 marks)Section A (10 marks)Directions: Read the following passage. Fill in the numbered blanks by using the information from the passage.Write NO MORE THAN THREE WORDS for each answer.Many of us invest valuable time, energy and money planning our vacations. We do this because we know for sure that going on vacations must be good for us. Research proves this feeling without a doubt. Vacations help us perform better at work, improve our sleep quality and cushion us against depression.Yet, despite these benefits, many of us return home with a feeling that our last vacation was OK - but not great. In order to change this, some mistakes should be avoided. A classic one for vacation planners is attempting to maximize value for money by planning trips that have too many components (组成部分)• Perhaps you’re planning a trip to Europe, seven cities in 10 days, and you realize it will cost only a little more to add two more destinations to the list Sounds fine in theory, but hopping from one place to the next hardly gives an opportunity to experience what psychologists call mindfulness - time to take in our new surroundings, time to be present and absorb our travel experiences. Another mistake is that we worry too much about strategic issues such as how to find a good flight deal, how to get from A to B, or which destinations to add or subtract from our journey. These issues may seem important, but our psychological state of mind is far more important.Actually, vacation happiness is based on the following top rules. First, choose your travel companions wisely, because nothing co ntributes more significantly to a trip than the right companions. Second, don’t spend your vacation time in a place where everything is too expensive so as to maintain a positive mood. Third, shop wisely, for meaningful experiences provide more long-term happiness than physical possessions.Section B (10 marks)Directions: Read the following passage. Answer the questions according to the information given in the passage.Kids and PondsYears ago there was a group of kids who would hang around at some local ponds in the woods near theirhouses in Warwick, Rhode Island. In summer they caught frogs and fish. When winter arrived they couldn’t wait to go skating. Time passed, and the ponds became the only open space for the kids to enjoy themselves in that neighborhood.One day, a thirteen-year-old boy from this group of kids read in the local newspaper that a developer wanted to fill in the ponds and build over a hundred small houses called condominiums. So the boy went door to door and gathered more than two hundred signatures (签名）to stop the development A group of citizens met and decided to support him.At the meeting of the town planning board (委员会),the boy was quite nervous at first and spoke very softly. But when he saw the faces of his friends and neighbors in the crowd and thought about what was happening to their favorite ponds, his voice grew louder. He told the town officials that they should speak for the citizens. He also insisted that they should leave enough space for children. A few days later, the developer stopped his plan.Nine years later, when that teen was a senior in college, he was informed that the developer was back with his proposal to build condominiums. Now twenty-two years old, he was studying wetlands ecology. He again appeared before the town planning board. This time as an expert witness, he used environmental protection laws to explain restrictions on development in and around wetlands and the knowledge of wetlands ecology to help improve the development. Finally some condominiums were built, but less than half the number the developer wanted. The ponds where those kids used to hang around were protected by a strip of natural land, and are still there today.81. What did the kids like to do at the local ponds in winter?(No more than 6 words) (2 marks)_______________________________________________________________________________82. How did the boy win the citizens’ support?(No more than 10 words) (2 marks)_______________________________________________________________________________83. What did the boy tell the town officials?(No more than 16 words) (3 marks)_______________________________________________________________________________84. What helped the boy to protect the ponds successfully nine years later?(No more than 12 words) (3 marks)_______________________________________________________________________________Section C (25 marks)Directions: Write an English composition according to the instructions given below.学校正在组织科技创新大赛,你想为日常生活中某件物品（如钢笔、书包、鞋子……)设计添加新功能来参赛。