2013年高考英语(福建卷)WORD解析版

2012年普通高等学校招生全国统一考试(福建卷)英语第I卷（选择题共115分）第一部分听力（共两节,满分30分）第一节例：How much is the shirt？A．￡19.15 B. ￡9.15 C. ￡9.181. Where does this conversation probably take place?A. In a bookstore.B. In a classroom.C. In a library.2. At what time will the film begin?A. 7:20.B. 7:15.C. 7:00.3. What are the two speakers mainly talking about?A. Their friend Jane.B. A weekend trip.C. A radio programme.4. What will the woman probably do?A. Catch a train.B. See the man off.C. Go shopping.5. Why did the woman apologize?A. She made a late delivery.B. She went to the wrong place.C. She couldn't take the cake back.笫二节（共15小题;每小题1.5分,满分22.5分）听第6段材料,回答第6、7题。

6. Whose CD is broken?A. Kathy's.B. Mum’sC. Jack's.7. What does the boy promise to do for the girl?A. Buy her a new CD.B. Do some cleaningC. Give her 10 dollars.听第7段材料,回答第8、9题。

2013年高考福建卷语文试题解析一、古代诗文阅读（27分）（一）默写常见的名句名篇（6分）1、补写出下列名句名篇中的空缺部分。

（6分）【答案】（6分）（1）鸡鸣桑树颠（2）烟光凝而暮山紫（3）此情可待成追忆（4）烽火扬州路（5）惶恐滩头说惶恐（6）援疑质理【考点定位】本题考查考生默写常见的名句名篇的能力，能力层次为A级。

【解析】要严格按规定默写，要求写几句就写几句。

注意：这道题目的字迹一定要工整清楚，严禁潦草，要像小学生一样写字。

严禁空白！错一字、漏一字这道小题均不得分。

（二）文言文阅读（15分）阅读下面的文言文，完成2-5题。

龙洞山记【元】张养浩历下多名山水，龙洞尤为胜。

洞距城东南三十里，旧名禹登山。

按《九域志》，禹治水至其上，故云。

中有潭，时出云气，旱祷辄雨，胜国①尝封其神曰灵惠公。

其前，层峰云矗，曰锦屏，曰独秀，曰三秀，释家者流居之。

由锦屏抵佛刹山，巉岩环合，飞鸟劣②及其半。

即山有龛屋，深广可容十数人，周镌佛象甚夥。

世兵，逃乱在多此焉。

依上下有二穴，下者居傍，可逶迤东出，其曰龙洞，即此穴也。

望之窅然。

未几，俯首焉；未几，磐折③焉；又未几，膝行焉；又未几，则蒲伏焉；又未几，则全体覆地蛇进焉。

会所导火灭，烟郁勃满洞中。

欲退，身不容；引进，则其前隘，且重以烟，遂缄吻、抑鼻、潜息。

心骇乱恐甚，自谓命当尽死此，不复出矣。

余强呼使疾进，众以烟故，无有出声应者，心尤恐然。

余适居前，倏得微明，意其穴竟于是，极力奋身，若鱼纵焉者，始获脱然以出。

如是，仅里所。

既会，有泣者，恚者，诟者，相讥笑者，顿足悔者，提肩喘者，喜幸生手其额者，免冠科首具陈其狼狈状者。

惟导者一人年稚，形瘠小，先出，若无所苦，见众皆病，亦阳慑力殆。

其宴于外者，即举酒酌穴者，人二杯。

虽雅不酒，必使之酹，名曰定心饮。

疑许事未必有。

由今观之，则韩文公之号为非妄矣。

呜呼，不登高、不临深，前圣之训较然④，而吾辈为细娱，使父母遗体几同压没不吊⑤。

其为戒，讵止殁身不可忘！窃虞嗣至者或不知，误及此，故记其事以告焉。

2013年福建高考口试题第一套：1.How many people are there in your family?2.Do you like English class ? Why or why not ?3.Can you say something about your school?第二套：1.What does your father/mother do ?2.Do you like ti be a volunteer ? why or why not ?3.Do you like your English teacher ? Why or why not ?第三套：1. Which school do you study in ?2. Who does most of the housework in your home ?3. when were you born?第四套：1.Who doyou like better ,your mother or father ?2.Can you say something about your family members ?3.Do you like your English teacher? Why or why not ?第五套：1.How much time do you spend in reading every day ?2.How do you celebrate your birhtday?3.Can you say something about your table manners?第六套：1.Do you want to be a volunteer ? Why or why not ?2.How will you spend your summer vacation?3.What kind of weather do you like best ?第七套：1.How do you feel about your middle school life ?2.Can you cook ?3.Do you like your school ? Why or why not ？第八套:1.Do you like Chinese food or western food ?2.What kind of music do you like best ?3.What do your parents do in your birthday ?第九套:1.Do you like sports ?2.What's your most unforgettable experience in your life? Why ?3.Can you say something about the season you like ?第十套:1.What's the weather like in summer in your home town?2.How do you spend your pocket money ?3.Can you say something about one of the sports you like ?第11套:1.Do you like music ?2.Do you often eat out ?3.What do you usually do in your spare time ?第12套:1.Which pop star do you like best ?2.What is your favourite food ?3.Can you say something about one of famous places of interest ?第13套:1.Do you have any good friends ?2.Can you say something about one of your family members?3.Do you help your parents do the housework ? Why or why not ?第14套:1. Do your like English songs ? Why or why not ?2.Do you like travelling ?3.Can you say something about one of your favourite stars ?第15套:1.Which sport do you like best ?2.What do you think of the Internet ? Can you say something about its advantages and disadvantages?3.What do you think of your high school life ?第16套：1.How do your spend your spare time ?2.Do you like to go shopping alone or with others ?3.Can yousay something about one of your best friends ?第17套：1.What job do you want to do in the future?2.What subject do you like best in senior high school ? Why or why not ?3.What do you usually do when you feel happy or sad ?第18套：1.what sport do you like best ?2.Who is your favourite teacher ? Why ?3.What do you think of cooperation and competition ? Which is more important ? Why？。

2013高考英语：二轮单项选择+with复合结构专练（答案、解析）(2011全国卷I) 22. Try____ she might, Sue couldn’t get the door open.A. ifB. whenC. sineD. as(2011全国卷I) 28. Only when he reached the tea-house ______it was the same place he’d been in last year.A. he realizedB. he did realizeC. realized heD. did he realize（2011福建卷）29.-It’s nice. Never before____ such a special drink!-I’m glad you like it.A.I have hadB. I hadC. have I hadD. had I(2011湖南卷)32. Only after they had discussed the matter for a few hours _______a decisionA. they reachedB. did they reachC. they reachD. do they reach强调句：（2011四川卷）15. Was it on a lonely island ______ he was saved one month after the boat went down?A. whereB. thatC. whichD. what（2011陕西卷）23.It is not how much we do but how much love we put into what we do______benefits our work most.A. whoB. whichC. thatD. what（2011重庆卷）32.—Have you seem the film Under the Hawthorn Tree?— Of course, I have. It was in our village _______ it was made.A.thatB.whereC.whenD.which(2011湖南卷)35 It’s not what we do once in a while ______ shapes our lives, bu t what we do consistentlyA .which B. that C. how D. when省略句：（2011全国卷II）13. Jane won’t join us for dinner tonight and .A. neither won’t TomB. Tom won’t eitherC. Tom will tooD. so will Tom（2011江苏卷）33. It sounds like something is wrong with the car’s engine._______ , we’d better take it to the garage immediately.A. OtherwiseB. If notC. But for thatD. If so感叹句：（2011辽宁卷）33. _____ a strange plant! I've never seen it before.A. WhichB. WhatC. HowD. Whetherwhere反意问句(2011上海卷) 30. It doesn’t matter if they want to come to your party, _______?A. doesn’t itB. does itC. don’t theyD. do they（2011重庆卷）28.I told them not everybody could run as fast as you did, ______ ?A. could heB. didn’t IC. didn’t youD. could they独立主格（2011浙江卷）3. Bats are surprisingly long lived creatures some ______a life span of around20 years.A. havingB. hadC. haveD. to have*****************************************************结束*********************************************************结束第六讲非谓语动词与with复合结构1.Thesenioryearlifeinhighschoolisamazeofpossibilities,sodon'thavethosemythsaboutitslife______. (2012·师大附中月考二)A.gettingyoudownB.gotyoudownC.togetyoudownD.getyoudown2.BocaiMiddleSchool, whichisreported______justtwoyearsago, isnowrenownedthroughoutHunanprovince.(2012·师大附中月考一)A.havingestablishedB.tobeestablishedC.beingestablishedD.tohavebeenestablished3.WithFather'sDayaroundthecorner,Ihavetakensomemoneyoutofthebank______presentsformydad.A.buyB.tobuyC.buyingD.tohavebought4.Thetrafficrulesaysyoungchildrenundertheageoffourand______lessthan40poundsmustbeinachil dsafetyseat.A.beingweighedB.toweighC.weighedD.weighing5.______fromthetopofthetower, thesouthfootofthemountainisaseaoftrees.A.SeenB.SeeingC.HaveseenD.Tosee6.Thelawyerlistenedwithfullattention, ______tomissanypoint.A.nottryingB.tryingnotC.totrynotD.nottotry7.______totoomuchsunlight, asisgenerallyconsidered, willaddtothepotentialofcatchingskincancer.(2012·雅礼中学月考五)A.ExposedB.BeingexposedC.ExposingD.Toexpose8.______fromendlesshomeworkonweekends, thestudentsnowfindtheirownactivities, suchastakingaridetogethertowatchthesunrise.(2012·雅礼中学月考五)A.FreedB.FreeingC.TofreeD.Havingfreed9.Youshouldn'tmind______，solongasitishelpfulinhavingyourwork______.(2012·师大附中月考五)A.criticizing; improvingB.beingcriticized; improvedC.tocriticizing; improvedD.beingcriticized; tobeimproved10.Toturnoffmycellphonebeforegoingtobedseemstomearule______.(2012·师大附中月考五)A.toneverbreakB.nevertohavebrokenC.nevertobebrokenD.nevertobebreaking11.Thespeech______tomorrowinourschoolhasbeencancelledduetotheterribleweather.(2012·长郡中学月考五)A.todeliverB.deliveredC.beingdeliveredD.tobedelivered12.Tomakebelievethattherewasstillsomeoneinthehouse, thehousewifewentdownstairs, ______thelights______inthelivingroom.(2012·长郡中学月考五)A.left; burntB.leaving; burningC.left; beingburntD.leaving; burnt13.Lydiadoesn'tfeellike______abroad.Herparentsareold.A.studyB.studyingC.studiedD.tostudy14.PoorChinesetestscoresmakeithardforthem______tothesecondaryschools.A.toadmitB.tobeadmittingC.tobeadmittedD.tohavebeenadmitted15.When______primaryschools, ChinesechildrenarealreadyabletoreadandwritesomeChinese.A.toattendB.attendedC.attendingD.beingattended16.Whiletalkingabouthisownhappychildhood, ______onhisface.A.asmileappearedB.hewaswearingasmileC.asmilewasseenD.wesawasmile17.Asafatheroftwoyounggirls, heknowsthedifficultiesofkeepingkids______.A.toentertainB.entertainingC.entertainedD.entertain18.Duringthetestweweresupposedtostayinourseats, keepoureyesonourwork, ______toanyone.A.andnotspeakB.insteadofspeakingC.ratherthanspeakD.butcouldnottalk19.Nancywasbornwithagreatsenseoflecturingandisalwayskeepingtheaudience______inherspeec hes.(2012·长郡中学月考六)A.absorbingB.absorbedC.toabsorbD.tobeabsorbed20.Manychildrenhaveformedthehabitofreadingbut______efficientnotesmeanwhile.A.nottakeB.nottotakeC.nottotakingD.nottaking21.Hestoodupandlookedforwardto______whatwashappeningoverthereandfoundtherewasacinem aaround______hecouldseeafilmbeingshown.A.seeing; whichB.see; whereC.see; whichD.seeing; that22.Aftertheywonthefinaltonighttheteamtouredaroundthecity,______bytheirenthusiasticsupporters.(2011·浙江卷改编)A.beingcheeredB.becheeredC.tobecheeredD.cheered23.—Canourwallnewspapercomeoutasrequired?—Sure, ______itcompletedintime, weneedanotherhelpinghand.(2012·师大附中月考七)A.havinggotB.togetC.gettingD.get24.______thathemightlosehisjob, Peteralwaysworksextrahourstopleasehisboss.(2012·雅礼月考六)A.WorryingB.HavingworriedC.HavingbeenworriedD.Worried25.Asaresultoftheheavysnow，two-thirdsofthebuildingsinthearea______.(2012·雅礼月考六)A.needtorepairB.needstorepairC.needsrepairingD.needrepairing26.Hotelswereaslimitedastheuniversitydormitories______specificallyforforeignersin1995.A.meaningB.meantC.tomeanD.tobemeant27.______tocampisagreatwaytoprovidefunandahealthyphysicalactivityforthekids.A.GoB.GoneC.WentD.Going28.Today, thecommonChinesestillfinditamusing______thepresenceofforeigners.A.tobeseeingB.toseeC.seeingD.tohaveseen29.ItisatraditionforChineseparentstopayhighcostsfortheirchildren'seducation,______themtobesuccessfuloneday.A.tobeexpectedB.expectingC.expectedD.havingexpected30.Thepolicywillcertainlyhelpindealingwiththedifficulties______aboutbyhavinganolderpopulati on.A.tobringB.bringingC.broughtD.beingbrought答案第六讲非谓语动词与with复合结构1．选D。

XX年全国高考英语试题及答案福建卷做题时，先将答案标在试卷上。

录音内容完毕后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。

第一节(共5小题;每题1.5分，总分值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三个选项巾选出最正确选项，并标在试卷的相应位置。

听完每段对话后，你都有10秒钟的时间来答复有关小题和阅读下一小题。

每段对话仅读一遍。

例：How much is the shirt?A.￡19. 15.B.￡9.18.C.￡9.15.答案是C。

1. What does the woman want to do?A. Find a place.B. Buy a map.C. Get an address.2. What will the man do for the woman?A. Repair her car.B. Give her a ride.C. Pick up her aunt.3. Who might Mr. Peterson be?A.A new professor.B.A department head.C.A pany director.4. What does the man think of the book?A. Quite difficult.B. Very interesting.C. Too simple.5. What are the speakers talking about?A. Weather.B. Clothes.C. News.第二节(共15小题;每题1.5分，总分值22.5分)听下面5段对话或独白。

每段对话或独白后有几个小题，从题巾所给的A.B.C三个选项巾选m最正确选项，并标在试卷的相应位置。

听每段对话或独向前，你将有时间阅读各个小题，每题5秒钟;听完后，各小题给t 5秒钟的作答时间。

每段对话或独白读两遍。

听第6段材料，答复第6、7题。

2013年高考英语试题分类汇编之书面表达【2013年高考陕西卷】书面表达（满分30分）假定你是李华。

请根据写作要点用英语写一篇周记，记述你周末帮助家人做家务的一次经历。

写作要点：1.做家务的理由；2.做家务的过程；3.你的感受。

注意：1.短文词数不少于100；2.开头部分已写好，不计入总词数；3.不能使用真实姓名和学校名称。

I am an 18-year-old middle school student,【参考范文】I’m an 18-year old middle school student. I have been busy with my study and seldom helped my parents with the housework. Feeling quite sorry for that, I begin to think about what to do to help.Last Sunday, when my parents went out shopping, I suddenly got an idea: why not give the rooms a thorough cleaning? Firstly I collected all the books, newspapers and other things scattered in the rooms and put them in place. Then I wiped the dust off all the furniture. After that, I swept and mopped the floors.At this very moment, my parents came back and were quite surprised to see all the rooms tidy and floors shining. My mother gave me a hug and I could see satisfaction in her eyes. Tired as I was, I never felt so happy.【2013•课标全国卷Ⅰ】书面表达(满分25分)假定你是李华。

2013·福建卷(理科数学)1． 已知复数z 的共轭复数z ＝1＋2i(i 为虚数单位)，则z 在复平面内对应的点位于( ) A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限1．D [解析] z ＝1－2i ，对应的点为P (1，－2)，故选D.2． 已知集合A ＝{1，a }，B ＝{1，2，3}，则“a ＝3”是“A ⊆B ”的( ) A ．充分而不必要条件 B ．必要而不充分条件 C ．充分必要条件D ．既不充分也不必要条件2．A [解析] 当a ＝3时，A ＝{1，3}，A ⊆B ；当A ⊆B 时，a ＝2或a ＝3，故选A. 3． 双曲线x 24－y 2＝1的顶点到其渐近线的距离等于( )A.25B.45C.2 55D.4 553．C [解析] 取一顶点(2，0)，一条渐近线x ＋2y ＝0，d ＝212＋22＝255，故选C. 4． 某校从高一年级学生中随机抽取部分学生，将他们的模块测试成绩分成6组：[40，50)，[50，60)，[60，70)，[70，80)，[80，90)，[90，100]加以统计，得到如图1－1所示的频率分布直方图．已知高一年级共有学生600名，据此估计，该模块测试成绩不少于60分的学生人数为( )图1－1A ．588B ．480C ．450D ．1204．B [解析] 成绩在[40，60)的频率P 1＝(0.005＋0.015)×10＝0.2，成绩不少于60分的频率P 2＝1－0.2＝0.8，所以成绩不少于60分的学生人数约为600×0.8＝480人，故选B.5． 满足a ，b ∈{－1，0，1，2}，且关于x 的方程ax 2＋2x ＋b ＝0有实数解的有序数对(a ，b )的个数为( )A ．14B ．13C ．12D ．105．B [解析] 当a ＝0时，2x ＋b ＝0⇒x ＝－b2，有序数对(0，b )有4个；当a ≠0时，Δ＝4－4ab ≥0⇒ab ≤1，有序数对(－1，b )有4个，(1，b )有3个，(2，b )有2个，综上共有4＋4＋3＋2＝13个，故选B.6． 阅读如图1－2所示的程序框图，若输入的k ＝10，则该算法的功能是( )图1－2A ．计算数列{2n －1}的前10项和B ．计算数列{2n －1}的前9项和 C ．计算数列{2n －1}的前10项和 D ．计算数列{2n －1}的前9项和6．A [解析] S ＝0，i ＝1→S ＝1，i ＝2→S ＝1＋2，i ＝3→S ＝1＋2＋22，i ＝4→…→S ＝1＋2＋22＋…＋29，i ＝11>10，故选A.7． 在四边形ABCD 中，AC →＝(1，2)，BD →＝(－4，2)，则该四边形的面积为( ) A. 5 B ．2 5 C ．5 D ．107．C [解析] ∵AC →·BD →＝1×(－4)＋2×2＝0，∴AC →⊥BD →，面积S ＝12|AC →|·|BD →|＝12×12＋22×（－4）2＋22＝5，故选C.8． 设函数f (x )的定义域为，x 0(x 0≠0)是f (x )的极大值点，以下结论一定正确的是( )A ．∀x ∈，f (x )≤f (x 0)B ．－x 0是f (－x )的极小值点C ．－x 0是－f (x )的极小值点D ．－x 0是－f (－x )的极小值点 8．D [解析] 根据极值点是函数局部的性质可排除A 选项，根据函数f (x )的图像与f (－x )、－f (x )、－f (－x )的图像分别关于y 轴、x 轴、原点对称，可排除B 、C 选项，故选D.9． 已知等比数列{a n }的公比为q ，记b n ＝a m (n －1)＋1＋a m (n －1)＋2＋…＋a m (n －1)＋m ，c n ＝a m (n －1)＋1·a m (n －1)＋2·…·a m (n －1)＋m (m ，n ∈)，则以下结论一定正确的是( ) A ．数列{b n }为等差数列，公差为q m B ．数列{b n }为等比数列，公比为q 2m C ．数列{c n }为等比数列，公比为qm 2 D ．数列{c n }为等比数列，公比为qm m9．C [解析] 取a n ＝1，q ＝1，则b n ＝m ，c n ＝1，排除A ，取a 1＝1，q ＝－1，m 取正偶数，则b n ＝0，排除B ，c n ＋1c n ＝a mn ＋1·a mn ＋2·…·a mn ＋ma m （n －1）＋1·a m （n －1）＋2·…·a m （n －1）＋m ＝q m ·q m ·…·q m ,\s \do 4(共m 个))＝qm 2，故选C.10．， 设S ，T 是的两个非空子集，如果存在一个从S 到T 的函数y ＝f (x )满足：(1)T ＝{f (x )|x ∈S }；(2)对任意x 1，x 2∈S ，当x 1<x 2时，恒有f (x 1)<f (x 2)，那么称这两个集合“保序同构”．以下集合对不是“保序同构”的是( )A ．A ＝，B ＝B ．A ＝{x |－1≤x ≤3}，B ＝{x |x ＝－8或0<x ≤10}C ．A ＝{x |0<x <1}，B ＝D ．A ＝，B ＝10．D [解析] 函数f (x )为定义域S 上的增函数，值域为T .构造函数f (x )＝x －1，x ∈*， 如图①，则f (x )值域为，且为增函数，A 选项正确；构造函数f (x )＝⎩⎪⎨⎪⎧－8，x ＝－1，52（x ＋1），－1<x ≤3，如图②，满足题设条件，B 选项正确；构造函数f (x )＝tan x －12π，0<x <1，如图③，满足题设条件，C 选项正确；假设存在函数f (x )，f (x )在定义域上是增函数，值域为，则存在a <b 且a 、b ∈，使得f (a )＝0，f (b )＝1，因为区间(a ，b )内的整数至多有有限个，而区间(0，1)内的有理数有无数多个，所以必存在有理数m ∈(0，1)，方程f (x )＝m 在区间(a ，b )内无整数解，这与f (x )的值域为矛盾，因此满足题设条件的函数f (x )不存在，D 选项错误，故选D.11． 利用计算机产生0～1之间的均匀随机数a ，则事件“3a －1>0”发生的概率为________．11.23 [解析] 13<a <1，概率P ＝1－131＝23.图1－3 12．， 已知某一多面体内接于球构成一个简单组合体，如果该组合体的正视图、侧视图、俯视图均如图1－3所示，且图中的四边形是边长为2的正方形，则该球的表面积是__________．12．12π [解析] 该多面体是棱长为2的正方体，设球的半径为R ，则2R ＝2 3⇒R ＝3，所以S 球＝4πR 2＝12π.13． 如图1－4所示，在△ABC 中，已知点D 在BC 边上，AD ⊥AC ，sin ∠BAC ＝2 23，AB ＝32，AD ＝3，则BD 的长为__________．图1－413.3 [解析] 设∠BAD ＝θ，则∠BAC ＝θ＋π2，sin θ＋π2＝23 2，所以cos θ＝23 2，△ABD 中，由余弦定理得BD ＝AB 2＋AD 2－2AB ·AD ·cos θ＝ 3.14．， 椭圆Γ：x 2a 2＋y 2b 2＝1(a >b >0)的左、右焦点分别为F 1，F 2，焦距为2c .若直线y ＝3(x ＋c )与椭圆Γ的一个交点M 满足∠MF 1F 2＝2∠MF 2F 1，则该椭圆的离心率等于__________．14.3－1 [解析] 如图，△MF 1F 2中，∵∠MF 1F 2＝60°，∴∠MF 2F 1＝30°，∠F 1MF 2＝90°，又|F 1F 2|＝2c ，∴|MF 1|＝c ，|MF 2|＝3c ，∴2a ＝|MF 1|＋|MF 2|＝c ＋3c ，得e ＝c a ＝23＋1＝3－1.15．，， 当x ∈，|x |<1时，有如下表达式：1＋x ＋x 2＋…＋x n ＋…＝11－x. 两边同时积分得：∫1201dx ＋∫120xd x ＋∫120x 2d x ＋…＋∫120x n d x ＋…＝∫12011－x d x ，从而得到如下等式：1×12＋12×⎝⎛⎭⎫122＋13×⎝⎛⎭⎫123＋…＋1n ＋1×⎝⎛⎭⎫12n ＋1＋…＝ln 2.请根据以上材料所蕴含的数学思想方法，计算： C 0n ×12＋12C 1n ×122＋13C 2n ×123＋…＋1n ＋1C n n ×⎝⎛⎭⎫12n ＋1＝__________． 15.1n ＋1⎣⎡⎦⎤⎝⎛⎭⎫32n ＋1－1 [解析] (1＋x)n ＝C 0n ＋C 1n x ＋C 2n x 2＋…＋C n n x n， 两边同时积分得C 0n ∫1201d x ＋C 1n ∫120xd x ＋C 2n ∫120x 2d x ＋…＋C n n ∫120x n d x ＝∫120(1＋x )n d x ， 得C 0n ×12＋12C 1n ×122＋13C 2n ×123＋…＋1n ＋1C n n ×12n ＋1＝1n ＋132n ＋1－1. 16．， 某联欢晚会举行抽奖活动，举办方设置了甲、乙两种抽奖方案，方案甲的中奖率为23，中奖可以获得2分；方案乙的中奖率为25，中奖可以获得3分；未中奖则不得分．每人有且只有一次抽奖机会，每次抽奖中奖与否互不影响，晚会结束后凭分数兑换奖品．(1)若小明选择方案甲抽奖，小红选择方案乙抽奖，记他们的累计得分为X ，求X ≤3的概率；(2)若小明、小红两人都选择方案甲或都选择方案乙进行抽奖，问：他们选择何种方案抽奖，累计得分的数学期望较大？16．解：方法一：(1)由已知得，小明中奖的概率为23，小红中奖的概率为25，且两人中奖与否互不影响．记“这2人的累计得分X ≤3”的事件为A ，则事件A 的对立事件为“X ＝5”，因为P (X ＝5)＝23×25＝415，所以P (A )＝1－P (X ＝5)＝1115，即这两人的累计得分X ≤3的概率为1115.(2)设小明、小红都选择方案甲抽奖中奖次数为X 1，都选择方案乙抽奖中奖次数为X 2，则这两人选择方案甲抽奖累计得分的数学期望为E (2X 1)，选择方案乙抽奖累计得分的数学期望为E (3X 2)．由已知可得，X 1～B ⎝⎛⎭⎫2，23，X 2～B ⎝⎛⎭⎫2，25， 所以E (X 1)＝2×23＝43，E (X 2)＝2×25＝45，从而E (2X 1)＝2E (X 1)＝83，E (3X 2)＝3E (X 2)＝125.因为E (2X 1)>E (3X 2)，所以他们都选择方案甲进行抽奖时，累计得分的数学期望较大．方法二：(1)由已知得，小明中奖的概率为23，小红中奖的概率为25，且两人中奖与否互不影响．记“这两人的累计得分X ≤3”的事件为A ，则事件A 包含有“X ＝0”“X ＝2”“X ＝3”三个两两互斥的事件，因为P (X ＝0)＝⎝⎛⎭⎫1－23×⎝⎛⎭⎫1－25＝15，P (X ＝2)＝23×⎝⎛⎭⎫1－25＝25，P (X ＝3)＝⎝⎛⎭⎫1－23×25＝215， 所以P (A )＝P (X ＝0)＋P (X ＝2)＋P (X ＝3)＝1115，即这两人的累计得分X ≤3的概率为1115.(2)设小明、小红都选择方案甲所获得的累计得分为X 1，都选择方案乙所获得的累计得分为X 2，则X 1，X 2的分布列如下：X 1 0 2 4 P194949X 2 0 3 6 P9251225425所以E (X 1)＝0×19＋2×49＋4×49＝83，E (X 2)＝0×925＋3×1225＋6×425＝125.因为E (X 1)>E (X 2)，所以他们都选择方案甲进行抽奖时，累计得分的数学期望较大． 17． 已知函数f (x )＝x －a ln x (a ∈)．(1)当a ＝2时，求曲线y ＝f (x )在点A (1，f (1))处的切线方程； (2)求函数f (x )的极值．17．解：函数f (x )的定义域为(0，＋∞)，f ′(x )＝1－ax .(1)当a ＝2时，f (x )＝x －2ln x ，f ′(x )＝1－2x(x >0)，因而f (1)＝1，f ′(1)＝－1，所以曲线y ＝f (x )在点A (1，f (1))处的切线方程为y －1＝－(x －1)， 即x ＋y －2＝0.(2)由f ′(x )＝1－a x ＝x －ax，x >0知：①当a ≤0时，f ′(x )>0，函数f (x )为(0，＋∞)上的增函数，函数f (x )无极值；②当a >0时，由f ′(x )＝0，解得x ＝a .又当x ∈(0，a )时，f ′(x )<0；当x ∈(a ，＋∞)时，f ′(x )>0，从而函数f (x )在x ＝a 处取得极小值，且极小值为f (a )＝a －a ln a ，无极大值．综上，当a ≤0时，函数f (x )无极值；当a >0时，函数f (x )在x ＝a 处取得极小值a －a ln a ，无极大值． 18．， 如图1－5所示，在正方形OABC 中，O 为坐标原点，点A 的坐标为(10，0)，点C 的坐标为(0，10)．分别将线段OA 和AB 十等分，分点分别记为A 1，A 2，…，A 9和B 1，B 2，…，B 9，联结OB i ，过A i 作x 轴的垂线与OB i 交于点P i (i ∈，1≤i ≤9)．(1)求证：点P i (i ∈，1≤i ≤9)都在同一条抛物线上，并求该抛物线E 的方程；(2)过点C 作直线l 与抛物线E 交于不同的两点M ，N ，若△OCM 与△OCN 的面积比为4∶1，求直线l 的方程．图1－518．解：(1)方法一：依题意，过A i (i ∈，1≤i ≤9)且与x 轴垂直的直线方程为x ＝i ，B i的坐标为(10，i )，所以直线OB i 的方程为y ＝i10x .设P i 的坐标为(x ，y )，由⎩⎪⎨⎪⎧x ＝i ，y ＝i10x ， 得y ＝110x 2，即x 2＝10y .所以点P i (i ∈，1≤i ≤9)都在同一条抛物线上，且抛物线E 的方程为x 2＝10y . 方法二：点P i (i ∈，1≤i ≤9)都在抛物线E ：x 2＝10y 上．证明如下：过A i (i ∈，1≤i ≤9)且与x 轴垂直的直线方程为x ＝i ，B i 的坐标为(10，i )，所以直线OB i 的方程为y ＝i 10x .由⎩⎪⎨⎪⎧x ＝i ，y ＝i 10x 解得P i 的坐标为⎝⎛⎭⎫i ，i 210， 因为点P i 的坐标都满足方程x 2＝10y ，所以点P i (i ∈，1≤i ≤9)都在同一条抛物线上，且抛物线E 的方程为x 2＝10y . (2)依题意，直线l 的斜率存在，设直线l 的方程为y ＝kx ＋10.由⎩⎪⎨⎪⎧y ＝kx ＋10，x 2＝10y ， 得x 2－10kx －100＝0.此时Δ＝100k 2＋400>0，直线l 与抛物线E 恒有两个不同的交点M ，N .设M (x 1，y 1)，N (x 2，y 2)，则⎩⎪⎨⎪⎧x 1＋x 2＝10k ，①x 1·x 2＝－100，②因为S △OCM ＝4S △OCN ，所以|x 1|＝4|x 2|.又x 1·x 2<0，所以x 1＝－4x 2，分别代入①和②，得⎩⎪⎨⎪⎧－3x 2＝10k ，－4x 22＝－100，解得k ＝±32. 所以直线l 的方程为y ＝±32x ＋10，即3x －2y ＋20＝0或3x ＋2y －20＝0.19．，， 如图1－6所示，在四棱柱ABCD －A 1B 1C 1D 1中，侧棱AA 1⊥底面ABCD ，AB ∥DC ，AA 1＝1，AB ＝3k ，AD ＝4k ，BC ＝5k ，DC ＝6k (k >0)．(1)求证：CD ⊥平面ADD 1A 1；(2)若直线AA 1与平面AB 1C 所成角的正弦值为67，求k 的值；(3)现将与四棱柱ABCD －A 1B 1C 1D 1形状和大小完全相同的两个四棱柱拼接成一个新的四棱柱．规定：若拼接成的新四棱柱形状和大小完全相同，则视为同一种拼接方案．问：共有几种不同的拼接方案？在这些拼接成的新四棱柱中，记其中最小的表面积为f (k )，写出f (k )的解析式．(直接写出答案，不必说明理由)图1－619．解：(1)证明：取CD 的中点E ，联结BE . ∵AB ∥DE ，AB ＝DE ＝3k ， ∴四边形ABED 为平行四边形， ∴BE ∥AD 且BE ＝AD ＝4k .在△BCE 中，∵BE ＝4k ，CE ＝3k ，BC ＝5k ， ∴BE 2＋CE 2＝BC 2， ∴∠BEC ＝90°，即BE ⊥CD ，又∵BE ∥AD ，所以CD ⊥AD .∵AA 1⊥平面ABCD ，CD ⊂平面ABCD ，∴AA 1⊥CD .又AA 1∩AD ＝A ， ∴CD ⊥平面ADD 1A 1.(2)以D 为原点，DA →，DC →，DD 1→的方向为x ，y ，z 轴的正方向建立如图所示的空间直角坐标系，则A (4k ，0，0)，C (0，6k ，0)，B 1(4k ，3k ，1)，A 1(4k ，0，1)，所以AC →＝(－4k ，6k ，0)，AB 1→＝(0，3k ，1)，AA 1→＝(0，0，1)．设平面AB 1C 的法向量＝(x ，y ，z )，则由⎩⎪⎨⎪⎧AC →·n ＝0，AB 1→·n ＝0，得⎩⎪⎨⎪⎧－4kx ＋6ky ＝0，3ky ＋z ＝0.取y ＝2，得＝(3，2，－6k )．设AA 1与平面AB 1C 所成角为θ，则sin θ＝|cos 〈AA 1→，〉|＝⎪⎪⎪⎪⎪⎪AA 1→·n |AA 1→|·|n |＝6k 36k 2＋13＝67， 解得k ＝1，故所求k 的值为1. (3)共有4种不同的拼接方案．f (k )＝⎩⎨⎧72k 2＋26k ，0<k ≤518，36k 2＋36k ，k >518.20．，， 已知函数f (x )＝sin(ωx ＋φ)(ω>0，0<φ<π)的周期为π，图像的一个对称中心为⎝⎛⎭⎫π4，0.将函数f (x )图像上所有点的横坐标伸长到原来的2倍(纵坐标不变)，再将所得到的图像向右平移π2个单位长度后得到函数g (x )的图像．(1)求函数f (x )与g (x )的解析式；(2)是否存在x 0∈⎝⎛⎭⎫π6，π4，使得f (x 0)，g (x 0)，f (x 0)g (x 0)按照某种顺序成等差数列？若存在，请确定x 0的个数；若不存在，说明理由；(3)求实数a 与正整数n ，使得F (x )＝f (x )＋ag (x )在(0，n π)内恰 (Ⅰ)选修4－2：矩阵与变换已知直线l ：ax ＋y ＝1在矩阵＝对应的变换作用下变为直线l ′：x ＋by ＝1.(1)求实数a ，b 的值；(2)若点P (x 0，y 0)在直线l 上，且⎝ ⎛⎭⎪⎫x 0y 0)＝⎝ ⎛⎭⎪⎫x 0y 0)，求点P 的坐标． (Ⅰ)解：(1)设直线l ：ax ＋y ＝1上任意点M (x ，y )在矩阵对应的变换作用下的像是M ′(x ′，y ′)．由⎝ ⎛⎭⎪⎫x ′y ′)＝又点M ′(x ′，y ′)在l ′上，所以x ′＋by ′＝1， 即x ＋(b ＋2)y ＝1.依题意得⎩⎪⎨⎪⎧a ＝1，b ＋2＝1，解得⎩⎪⎨⎪⎧a ＝1，b ＝－1. (2)由⎝ ⎛⎭⎪⎫x 0y 0)＝⎝ ⎛⎭⎪⎫x 0y 0)，得⎩⎪⎨⎪⎧x 0＝x 0＋2y 0，y 0＝y 0，解得y 0＝0. 又点P (x 0，y 0)在直线l 上，所以x 0＝1. 故点P 的坐标为(1，0)．(Ⅱ)选修4－4：坐标系与参数方程在平面直角坐标系中，以坐标原点为极点，x 轴的非负半轴为极轴建立极坐标系，已知点A 的极坐标为⎝⎛⎭⎫2，π4，直线l 的极坐标方程为ρcos ⎝⎛⎭⎫θ－π4＝a ，且点A 在直线l 上． (1)求a 的值及直线l 的直角坐标方程；(2)圆C 的参数方程为⎩⎪⎨⎪⎧x ＝1＋cos α，y ＝sin α(α为参数)，试判断直线l 与圆C 的位置关系．(Ⅱ)解：(1)由点A 2，π4在直线ρcos θ－π4＝a 上，可得a ＝ 2.所以直线l 的方程可化为ρcos θ＋ρsin θ＝2，从而直线l 的直角坐标方程为x ＋y －2＝0.(2)由已知得圆C 的直角坐标方程为(x －1)2＋y 2＝1. 所以圆C 的圆心为(1，0)，半径r ＝1， 因为圆心C 到直线l 的距离d ＝12＝22<1， 所以直线l 与圆C 相交． (Ⅲ)选修4－5：不等式选讲设不等式|x －2|<a (a ∈)的解集为A ，且32∈A ，12∉A .(1)求a 的值；(2)求函数f (x )＝|x ＋a |＋|x －2|的最小值．(Ⅲ)解：(1)因为32∈A ，且12∉A ，所以⎪⎪⎪⎪32－2<a ，且⎪⎪⎪⎪12－2≥a . 解得12<a ≤又因为a ∈，所以a ＝1.(2)因为|x ＋1|＋|x －2|≥|(x ＋1)－(x －2)|＝3，当且仅当(x ＋1)(x －2)≤0，即－1≤x ≤2时取到等号，所以f (x )的最小值为3.。

2013年全国部分省市高考英语听力原文及答案(一)2013高考英语听力:福建、广西(大纲)、江苏、江西、吉林、山西、山东、云南、河南、新疆、河北、甘肃、海南、内蒙古、贵州、海南、宁夏、黑龙江、西藏、安徽、辽宁、共用，听力原文:1.Man: I’ve got my camera with me. Am I allowed to take photos for you?Woman: I think so. It doesn’t say you can’t.2. A: I really like living here in this flat, because it’s so near to central town.B: That’s true. But it gets really noisy at night.3. A: Hi, Maggie. I’m coming, but it’s snowing and the traffic is moving slowly.B: Ok, David. Take your time. We’ll wait for you, so we can have dinner together.4. A: Celia, you see those girls over there? They need another player for a basketball game. Wouldyou like to join them?B: Seems like it’s a game for fun. Sure, I’ll be there in minute.5. A: I won’t have anything to wear to work on Monday unless I pick up my clothes at dry cleaners’.(给力英语网 )B: Then you’d better hurry. It closes at noon on Sundays.A: Oh! I should have gone there on Saturday. 6. A: Alright, Sara, we know that you are planning something big for John’s birth day. Could you tell us just what you have in your mind?B: I want to make his birthday a very special event. John has asister living in France. And I’llsend her a plane ticket, so that she can be here for his birthday.A: Boy! What an excellent plan! That’s something special. I can’t guess some secret plans and we are waiting for the right time to tell him. B: Well, I didn’t want to say anything until I was sure she could come.7. A: Hey, Peter, I’m sorry!B: Hi, Diana, what’s wrong?A: We were goi ng to Hong Kong this weekend, but I’m afraid I can’t go.B: How come?A: I have a really big geography test and I have to study for it.B: We can go next week instead.A: No, I don’t want to ruin your weekend. You go ahead and please take the book I bought to my friend Sally. Tell her I have to study all weekend, because I can’t afford to fail the test.B: Ok, then I’ll go with them. But it’s a pity you can’t come.8. A: Hello, this is Andrea.B: Hello, Andrea, this is Alex. I have some very big news for you. Miranda was very satisfied with you and said she was very much lookingforward to working with you. Isn’t that wonderful? Congratulations dear! How does it feel to be Miranda’s new assistant? How I imagine thatyou’ll just be delighted with this news. So let’s see, you can starton Monday, right?A: Umm, well, I don’t think I can start on Monday. I am visiting my father in Baltimore. And because I don’t live in New York, I’ll need a couple of days to find a flat and buy some furniture and move my things from Avon.B: Oh, well then, in that case I suppose Wednesday will be good. Ok, see you then! 9. Woman: Hello, Mr. Jan Erick Freedman. You’re afrequent traveler. And we also know that you eat out twice a day. Howcan you get so far and eating out.Man: When I my first job back in 1982 and started travelling. I hadno other choice but eat out I found that I felt different due to what I was eating, so I tried to find places that served food that made me feel good. The secret was the quality of the food and how well the food was prepared. I made an effort to find out good restaurants as well as nice dishes.Woman: How did you manage to make a list of 218 favorite restaurants?Man: I’ve lived in cities and when I moved back to Sweden from the United States, people asked me where to go and eat and went to thecities I know. I got a lot of ideas. Then I wrote about restaurants fora Swedish club magazine and some suggested I gather information aboutrestaurants together since I had all the facts about the restaurantsI’ve been to. I started to do that.Woman: How do you find restaurants?Man: The best way is to ask the people there. I may talk to thepeople at the street market or take a walk and look for place for myself.I never asked hotel clerks o r taxi drivers. I don’t go either restaurants or places with menus too difficult to understand.10. (给力英语网 )Man: At the beginning of the tour, we all started the most important place at my town which is the Plaza Leon. The Plaza Leon is more than100 ye ars old. It’s a gathering place for young people on Friday and Saturday nights, and for parents and children on Sunday afternoon. Four streets lead to the Plaza which have white sidewalks and tree lined. Hemandes Street which was named after writers born in the city contains all of the food stalls fish markets and vegetable stands. Femando Street which was named after a famous educator is where all of the government offices, shops and houses. Via del Mar Street which is the only street which has old stone surfaces. Finally we cameto the Hewish’s Street on which there are two universities, one of which is the most famousuniversity in my country. That’s why it’s my favorite street ofall.听力答案:1.A2. C3. A4. C5. B6. B7. B8. A9. B 10. A 11. B 12. A 13. C14. A 15. A 16. B 17. C 18. B 19. C 20. C (二)2013高考英语听力:北京，听力原文:短对话1W: Good evening. How can I help you? M: Do you have any rooms?W: Ye s, would yo u like a single room, a double room, or a twin room?M: Single, please.2M: I’m going t o the shops in a minute. What do we need?W: We are ok for the vegetables and meat, but we need some bread. Can you go and get some?M: No problem. I’ll go and get it.W: Ok, see you later then.3W: I’m so glad the weekend is finally here. Where are you going?M: Me? I’m thinking of going fishing in the river nearby. How about you? W: I’m going to go camping in the mountain. I want to go jogging while I am thereM: That sounds exciting.4W: Hello, is this everything for you today? M: YesW: Ok. The total is 8 dollars.M: Can you break a fifty,W : No problem. Here’s your change, 42dollars.M: Thank you5M: It’s so good to see the sun again.W: Yes, much better than the rain we’ve been having.M: It is supposed to be cloudy this afternoon. W: Oh, what a pity.6.7题A:I’d like two tickets for the movie on Friday, please B:For which movie ,madam?A:Oh, that’s right. Dark and Stormy NightB: I’m sorry, that show is sold out[来源:给力英语] A:Well, how about Saturday or Sunday?B:Yes madam, we do have tickets avail able for that movie on those days A: Are there any seats left for the middle row for Saturday?B :Yes, but they are not next to each other.A: Oh, that’s a pity. We prefer to sit together.B: In that case, we still have some seats together i n the front orat the back A: The front row sounds good. How much are the tickets?B:25 dollars in total.A: Ok, I’ll take them.8-9题M:Are you free on the 13th? I was wondering if we could have lunch together. W: No I am afraid not. I am meeting John then. How about the 14th?M: The 14th ? Let me check my schedule. Oh, I am sorry. I am in a meeting the whole day. W: I can also manage the day after. Are you free then?M: You mean the 15th ? Let me see. Yes. I think I am. Shall we have the lunch at the Mass restaurantW: Good idea. What time shall we meet?M: Is 1 o’clock ok with you?W: Great. See you then.10-12题A: The service is really slow here. I’ve been trying to get the waiter’s attention for the last ten minutes.B:I hope he takes our order soon. Otherwise I’ll be late for my class at two o’clock.A:Me,too. I have a class at 2 as well.B: I’ve noticed you have a math book. Do you like the summer school here?A: It’s pretty good. I think I’ve learned a lot.B: Yeah, I only wish the class were a little smaller, but I like my teachers a lot. They are very kind and patient.A: I see. By the way, where are you from?B: I’m from Boston. How about you?A: I’m from Washington DC. I’m only staying here for three more weeks. Then I’ll go to Columbia University in New Yo rk.’B: On, here comes the waiter. It seems we are going to get served after all. A: Good ,I’m starving13-15题Before I go on a vacation, I always plan my trip very carefully. I usually go on online to look up all the nece ssary information on the internet. Because I don’t trust the descriptions in the guide books or what the travel agency tells me. To begin with, I look up possible destinations and compare them carefully to see which one best suits my needs. Then, I check the cost of travellingto that particular place. If I am going by plane, then I have to compare the prices of the different airlines in order to get cheapest tickets. If I am travelling by train, then I have to look into train passes or special train ticket office. I seldom travel by buses，because of thehigh rate of traffic accidents on the high way. I also need to check hotels. Usually I choose to stay cheap hotels. Finally I try to plan how much I need spend on meals and sightse eing. If I plan carefully, I can usually have a good time for the lowest cost.15-20题W: Hello, Peppy’s Pizza. How can I help you?M: I’d like to order a pizza pleas eW:Is this for pickup or delivery?[来源:给力英语] M:Delivery please.W: Can I have your name and address please?M:It’s Cyril Smith. C-y-r-i-l ,Cyril. My address is No.2 front street.W: Is that an apartment or a house.M:It’s an apartment, No.23.W: Your phone number please.M: 748293 56.W: Ok, uh, what would you like to order today?M: A large pizza with mushrooms and extra cheese.W: One large pizza with mushrooms and extra cheese. Ok. I’ve got that all down? Is thereanything else?M:No, thanks. How mu ch would that be?W: That will be 12 pounds 50. How would you like to pay, cash, check or cr edit card? M: Cash. And how long will it take?W:About 30minutes. Mr. Smith.M:Great! Thank you. By for now.W: Bye! Thanks for calling.听力答案:1-5 ACABB 6-10 BACCB 11-15 CCABA 16. Cyril/CYRIL 17. Street/St. 18. 74829356 19. large 20. cash(三)2013高考英语听力:上海，听力原文:I. Listening ComprehensionSection ADirections: In section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, readthe four possible answers on your paper, and decide which one is the best answer to the questionyou have heard.1.W: Can you describe what you do?M: I wash office building windows. I go high up in the basket to reach the windows.Q: What is the man's job?2.M: Should we go out or eat in tonight?W: I am too tired to do any cooking.Q: What does the woman imply?3.M: Hi, Grace. Tell me something about your hometown.W: It's so beautiful and peaceful. But it's really far away from everything.Q: What does the woman think of her hometown?4. W: My printer is out of paper. I will run and get some.M: I will go with you. I need some fresh air.Q: Where will the speakers probably go?5.M: I don't like the prices on the menu. They always seem too high.W: You will have a different view after eating the delicious food.Q: What does the woman mean?6.M: I had a hard time getting through the novel.W: I know how you feel. Who could remember the names of 35 different characters?Q: What does the woman imply?7.W: Why haven't we received any newspapers yet?M: Well, sometimes it takes a while for the post office to deliver it.Q: What can we learn from the conversation?8.Q: My roommate and I are going to see a film tonight. And we are leaving at7:40.Do you want to join us?W: Sure. But my class ends at 7:30. And the professor never finishes on time.Q: What can we learn about the woman?9.W: Now that you are on the business, what’s your advice for someone to become a fashion designer?M: Go to school. I mean it. Find a good school and learn as much as you can.Q: What does the man mean?10.W: Slow down. You are passing every car on the road.M: Most drivers usually ignore the speed limit unless they think the police will stop them.Q: What does the man mean?Section BDirections: In section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper, and decide which one would be the best answer to the question you have heard.[来源:给力英语网]Questions 11-13 are based on the following passage.I am Lynn. My previous job was as principal of a language school, where I received awardsfor training teachers to teach more effectively. A year ago, I started an international company. I spent months conducting programs in the US and Russia. During this time, some Russian immigrants came to stay at my house. Fortunately, these visitors helped a lot at home andmade life easier. At the same time, I wrote several books to be published by my company and coedited a book for a major publisher.I am grateful I have a photographic memory, so I can remember everything I see. Otherwise, I might not be that productive. In addition to my work, I have a family at home. Some of my children have had serious health problems from birth, but I try to handle those problems well and efficiently. With tremendous help from my parents, the kids are fed, and clothed, and educated. I am busy from the time I get up until the time I go to bed. My time has to be carefully planned. I do not like to be interrupted because I want to accomplish my goals.Questions:11. What was the speaker’s previous job?12. What helps to make the speaker productive according to the passage?13. What does the passage mainly tell us?Questions 14-16 are based on the following passage.Job interviews can generally be divided into three types. The first is what I would call the traditional interview. This is usually just a series of standard questions about qualifications, work experience and expectations. So what you have here is basically a list of quite direct questions, like ‘What duties did you have in your previous job?’Thisis still the model for a lot of interviews today. In my view it’s not the best to select staff.Then there is the case interview. Here the interviewer presents a problem and a series of questions to find out how the candidate would approach the problem. It might go something like this, ‘A company wants to hire more graduates without spending more than its current budget.What would you advise them to do?’This can be particularly challenging, for you need to analyze the problem and solve it.The third type is known as the behavioral interview. The questions are usually designed to find out about how the candidates handle tricky situations in the past. A typical question might be ‘Can you give me an example of a situation where you had to follow orders that you didn’t agree with?’ This opens up a lot of information and the interviewer gets to see more of the candidate.Questions:14. What kind of questions are usually asked in the traditional interview?15. What does the case interview focus on about the candidate?16. What does the speaker mainly talk about?Section CDirections: In section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. Write your answers on your answer sheet.1.W: Hi, Bruce, it's Naomi.M: Hi, Naomi.W: I'm calling about the conference in Shanghai on November 8th. We have to make some changes.M: OK, go ahead.W: I don't think the peace guardian will be big enough. We need a center that can seat at least 600.M: That many? Any suggestions?W: The Palace Center will be free that day, but it will mean increasing the registration fee by 50$. From800$ to 850$.M: That won't be a problem. Anything else?W: Milan University says they are sending Cara Marasco instead of Professor Bertoni. But the talk would be the same, Opportunities and Risks in the African Market.M: Fine. Make those changes and all inform everyone at my end.2.W: David, we all know you took up skateboarding at ten. But did your parents support you?M: Yeah, my parents even let me skate in the house.W: Did they?M: Yeah, they were pretty cool.W: How about your school work?M: That was fine. I was able to get my school work done with good grades. My only problem was that I had so much physical energy that Icould not sit still in class. Then some teachers started taking my skateboard away.W: That couldn't stop you from staking?M: No way. The cool thing was that my parents managed to find me a different school. The headmaster there was wonderful. He let us plan our own P.E. classes. So guess what class I created.W: Skateboarding.M: You got it. That was my P.E. class. By that time I was turning professional and starting to show off some techniques at competitions.W: Is that when your new style became famous?M: Yeah. Other skaters had this smooth flowing style, but I was kind of like a robot always coming up with new tricks.听力答案:1-5BCBCD 6-10 BADCA 11-16ADCBDA 17. History 18. HD3309 19. Photography 20. Tuesday 21. religions 22. good friends/ more thanfriends/like a family 23. their daughter 24. a simple smile(四)2013高考英语听力:湖南，听力原文:Conversation OneM: What flights do you have from New York to London at around nine tomorrow morning,W: One moment, please. Okay we've got a nonstop flight leaving Kennedy at 9:25. M: Well, when should I get to the airport then?W: Try to be there by 8:15.M: Alright. One single ticket. First class please.Conversation TwoW: Hello!M: Hi! Jacy. Where are you? Are you at home?W: No, I’m in a taxi. I just went shopping with my mom. I’ll be there in about 10 minutes.M: Okay. I’ll wait for you. I’ll read the menu first.W: Alright. See you.Conversation ThreeW: Where is the pan? I need to start preparing dinner. M: I put itin the usual spot. What are we having tonight? W: I am not sure. Something healthy like tomatoes or carrots. M: I’d like some French fries, or fried chicken, dear.W: We’ll do that tomorrow but for today let’s make some noodles, okay?M: Well, in that case I'll have whatever you're having. Conversation FourM: Hi, Carol. Are you ready to start our project about keeping pets? W: Yes, John. What kind of pets should we focus on? M: Tom and I are thinking of a cat or a dog. Which do you prefer? W: Well, I don't know much about either of them. What about fish? M: That's a good idea. I’ll ask Tom to help. You do the survey.W: Sure. What else should we discuss, John?M: I think we should make some cards so we don't forget what we're saying during thepresentation.W: Sounds great, but I hate speaking in public so I prefer not to do the introduction.M: I don't mind at all. I’ll do that.W: I'm sure Mary can handle the summarizing.M: That’s settled.Conversation FiveM: Have you decided to go on vacation?W: Yeah. I'm going to spend two weeks in South Africa. M: Wow,that's great. Two weeks on the beach.W: Actually, I'm not going to the beaches. They’re too crowded this time of year. So I'm goingcamping in the jungle instead.M: That sounds different. Er, what do you need to bring? W: Just some clothes. The tour company provides everything like maps, hats and tents.M: What about food?W: I think the guide will prepare our meals.M: Sounds like it'll be a great vacation.W: Yeah, I'm really looking forward to it.Conversation SixM: Hi, Jane!W: How are you, Mr. Martin?M: Fine. It’s nice to see you. So, are you enjoying the party?W: Yeah, it’s great. The music, the food, everything.M: How time flies! I can't believe all you kids are graduating and this might be the last time I see some of you for a long time.W: Yeah, and I'll never forget your interesting lectures and your sense of humour. M: Thanks. Er… Do you have any plans for the summer before you go to college?W: I’ve applied for a job in a s upermarket as a salesgirl. Do you happen to know anyone else withplans for the vocation?M: Lisa is applying for a part-time job in a restaurant and Tim is going to be a volunteer in a museum.W: Oh, excuse me. Tim seems to be leaving. I've got to talk to him.M: Goodbye.Mini talkGood morning. Today I'd like to talk about how to become a confident speaker. Confidence, as we all know, is a very important element in learning to speak English. How can you sound more confident when you speak English?First, speak often. The more often you speak, the easier it becomes. Try to think of people you can talk to in English or places where English is spoken a lot. You need to put yourself in a position where you need to speak. Second, relax and think about th e message. It’s easy to get nervous ifyou only focus on the grammar rules when you're speaking. The key to relaxing when you are speaking is to talk about something that you find interesting. Third, practice what you want to say. If you are nervous, try to practice what you want to say to yourself a few times. It can make you more confident.Okay, that's all for today. Goodbye.Now you have 2 min. to write your answer on your answer sheet.This is the end of listening comprehension.听力答案:1—5 BAACA 6—10 BBCCC 11—15 CBCAA 16. Confidently 17. easier18. think about 19. you find interesting 20. yourself(五)2013高考英语听力:江西，听力原文:1.Man: I’ve got my camera with me. Am I allowed to take photos for you?Woman: I think so. It doesn’t say you can’t.2. A: I really like living here in this flat, because it’s so near to central town.B: That’s true. But it gets really noisy at night.3. A: Hi, Maggie. I’m coming, but it’s snowing and the traffic is moving slowly.B: Ok, David. Take your time. We’ll wait for you, so we can have dinner together.4. A: Celia, you see those girls over there? They need another player for a basketball game. Would you like to join them?B: Seems like it’s a game for fun. Sure, I’ll be there in minute.5. A: I won’t have anything to wear to work on Monday unless I pick up my clothes at drycleaners’.(给力英语网 )B: Then you’d better hurry. It closes at noon on Sundays.A: Oh! I should have gone there on Saturday.6. A: Alright, Sara, we know that you are planning something big for J ohn’s birthday. Could you tell us just what you have in your mind?B: I want to make his birthday a very special event. John has a sister living in France. And I’ll send her a plane ticket, so that she can be here for his birthday.A: Boy! What an excell ent plan! That’s something special. I can’t guess some secret plans and weare waiting for the right time to tell him.B: Well, I didn’t want to say anything until I was sure she could come.7. A: Hey, Peter, I’m sorry!B: Hi, Diana, what’s wrong?A: We were going to Hong Kong this weekend, but I’m afraid I can’t go.B: How come?A: I have a really big geography test and I have to study for it.B: We can go next week instead.A: No, I don’t want to ruin your weekend. You go ahead and please take the book I bought to my friend Sally. Tell her I have to study all weekend, because I can’t afford to fail the test.B: Ok, then I’ll go with them. But it’s a pity you can’t come.8. A: Hello, this is Andrea.B: Hello, Andrea, this is Alex. I have some very big news for you. Miranda was very satisfied with you and said she was very much looking forward to working with you. Isn’t that wonderful? Congratulations dear! How does it feel to be Miranda’s new assistant? How I imagine thatyou’ll just be delighted with this news. So let’s see, you can starton Monday, right?A: Umm, well, I don’t think I can start on Monday. I am visiting my father in Baltimore. And because I don’t live in New York, I’ll need a couple of days to find a flat and buy some furniture and move my things from Avon.B: Oh, well then, in that case I suppose Wednesday will be good. Ok, see you then! 9. Woman: Hello, Mr. Jan Erick Freedman. You’re afrequent traveler. And we also know that you eat out twice a day. Howcan you get so far and eating out.Man: When I my first job back in 1982 and started travelling. I hadno other choice but eat out I found that I felt different due to what I was eating, so I tried to find places that served food that made me feel good. The secret was the quality of the food and how well the food wasprepared. I made an effort to find out good restaurants as well as nice dishes.Woman: How did you manage to make a list of 218 favorite restaurants?Man: I’ve lived in cities and when I moved back to Sweden from the United States, people asked me where to go and eat and went to thecities I know. I got a lot of ideas. Then I wrote about restaurants fora Swedish club magazine and some suggested I gather information about restaurants together since I had all the facts about the restaurantsI’ve been to. I started to do that.Woman: How do you find restaurants?Man: The best way is to ask the people there. I may talk to thepeople at the street market or take a walk and look for place for myself.I never asked hot el clerks or taxi drivers. I don’t go eitherrestaurants or places with menus too difficult to understand.10. (给力英语网 )Man: At the beginning of the tour, we all started the most important place at my town which is the Plaza Leon. The Plaza Leon is more than100 years old. It’s a gathering place for young peopleon Friday and Saturday nights, and for parents and children onSunday afternoon. Four streets lead to the Plaza which have white sidewalks and tree lined. Hemandes Street which was named after writers born in the city contains all of the food stalls fish markets and vegetable stands. Femando Street which was named after a famous educatoris where all of the government offices, shops and houses. Via del MarStreet which is the only street which has old stone surfaces. Finally we came to the Hewish’s Street on which there are two universities, one of which is the most famous university in my country. That’s why it’s my favorite street of all.听力答案:1.A2. C3. A4. C5. B6. B7. B8. A9. B 10. A 11. B 12. A13. C 14. A 15. A 16. B 17. C 18. B 19. C 20. C(六)2013高考英语听力:辽宁，听力原文:1.Man: I’ve got my camera with me. Am I allowed to take photos for you?Woman: I think so. It doesn’t say you can’t.2. A: I really like living here in this flat, becau se it’s so near to central town.B: That’s true. But it gets really noisy at night.3. A: Hi, Maggie. I’m coming, but it’s snowing and the traffic is moving slowly.B: Ok, David. Take your time. We’ll wait for you, so we can have dinner together.4. A: Celia, you see those girls over there? They need anotherplayer for a basketball game. Would you like to join them?B: Seems like it’s a game for fun. Sure, I’ll be there in minute.5. A: I won’t have anything to wear to work on Monday unless I pick up my clothes at dry cleaners’.(给力英语网 )B: Then you’d better hurry. It closes at noon on Sundays.A: Oh! I should have gone there on Saturday.6. A: Alright, Sara, we know that you are planning something big for John’s birthday. Could you tell us just what you have in your mind?B: I want to make his birthday a very special event. John has a sister living in France. And I’ll send her a plane ticket, so that she can be here for his birthday.A: Boy! What an excellent plan! That’s something special. I can’t guess some secret plans and weare waiting for the right time to tell him.B: Well, I didn’t want to say anything until I was sure she could come.7. A: Hey, Peter, I’m sorry!B: Hi, Diana, what’s wrong?A: We were going to Hong Kong this weekend, bu t I’m afraid I can’t go.B: How come?A: I have a really big geography test and I have to study for it.B: We can go next week instead.A: No, I don’t want to ruin your weekend. You go ahead and please take the book I bought to my friend Sally. Tell her I have to study all weekend, because I can’t afford to fail the test.B: Ok, then I’ll go with them. But it’s a pity you can’t come.8. A: Hello, this is Andrea.。

2013·福建卷(文科数学)1． 复数z ＝－1－2i(i 为虚数单位)在复平面内对应的点位于( ) A ．第一象限 B ．第二象限 C ．第三象限 D ．第四象限1．C [解析] z ＝－1－2i 对应的点为P (－1，－2)，故选C.2． 设点P (x ，y )，则“x ＝2且y ＝－1”是“点P 在直线l ：x ＋y －1＝0上”的( ) A ．充分而不必要条件 B ．必要而不充分条件 C ．充分必要条件 D ．既不充分也不必要条件2．A [解析] 当x ＝2，y ＝－1时，x ＋y －1＝0；但x ＋y －1＝0不能推出x ＝2，y ＝－1，故选A.3． 若集合A ＝{1，2，3}，B ＝{1，3，4}，则A ∩B 的子集个数为( ) A ．2 B ．3 C ．4 D ．163．C [解析] A ∩B ＝{1，3}，子集共有22＝4个，故选C. 4． 双曲线x 2－y 2＝1的顶点到其渐近线的距离等于( )A.12B.22 C ．1 D. 24．B [解析] 取一顶点(1，0)，一条渐近线x －y ＝0，d ＝12＝22，故选B. 5． 函数f (x )＝ln(x 2＋1)的图像大致是( )图1－15．A [解析] f (x )是定义域为的偶函数，图像关于y 轴对称，又过点(0，0)，故选A. 6． 若变量x ，y 满足约束条件⎩⎪⎨⎪⎧x ＋y ≤2，x ≥1，y ≥0，则z ＝2x ＋y 的最大值和最小值分别为( )A ．4和3B ．4和2C ．3和2D ．2和06．B [解析] 可行域如图所示，直线z ＝2x ＋y 过点A (1，0)时，z min ＝2，过点B (2，0)时，z max ＝4，故选B.7． 若2x ＋2y ＝1，则x ＋y 的取值范围是( ) A ．[0，2] B ．[－2，0]C ．[－2，＋∞)D ．(－∞，－2]7．D [解析] 1＝2x ＋2y ≥2 2x ＋y ⇒2x ＋y ≤2－2⇒x ＋y ≤－2，当且仅当x ＝y ＝－1时，等号成立，故选D.8． 阅读如图1－2所示的程序框图，运行相应的程序．如果输入某个正整数n 后，输出的S ∈(10，20)，那么n 的值为( )图1－2A ．3B ．4C ．5D ．68．B [解析] S ＝0，k ＝1→S ＝1，k ＝2→S ＝3，k ＝3→S ＝7，k ＝4→S ＝15，k ＝5>4，故选B.9． 将函数f (x )＝sin(2x ＋θ)⎝⎛⎭⎫－π2<θ<π2的图像向右平移φ(φ>0)个单位长度后得到函数g (x )的图像．若f (x )，g (x )的图像都经过点P ⎝⎛⎭⎫0，32，则φ的值可以是( ) A.5π3 B.5π6 C.π2 D.π69．B [解析] g (x )＝f (x －φ)＝sin[2(x －φ)＋θ]，由sin θ＝32，－π2<θ<π2，得θ＝π3，又sin(θ－2φ)＝32，结合选项，知φ的一个值为5π6，故选B. 10． 在四边形ABCD 中，AC →＝(1，2)，BD →＝(－4，2)，则该四边形的面积为( ) A. 5 B ．2 5 C ．5 D ．1010．C [解析] ∵AC →·BD →＝1×(－4)＋2×2＝0，∴AC →⊥BD →，面积S ＝12|AC →|·|BD →|＝12×12＋22×（－4）2＋22＝5，故选C.11． 已知x 与y 之间的几组数据如下表：x 1 2 3 4 5 6 y21334假设根据上表数据所得线性回归直线方程为y ︿＝b ︿x ＋a ︿.若某同学根据上表中的前两组数据(1，0)和(2，2)求得的直线方程为y ＝b ′x ＋a ′，则以下结论正确的是( )A.b ︿>b ′，a ︿>a ′B.b ︿>b ′，a ︿<a ′C.b ︿<b ′，a ︿>a ′D.b ︿<b ′，a ︿<a ′11．C [解析] 画出散点图即可，选C. 12． 设函数f (x )的定义域为，x 0(x 0≠0)是f (x )的极大值点，以下结论一定正确的是( ) A ．∀x ∈，f (x )≤f (x 0)B ．－x 0是f (－x )的极小值点C ．－x 0是－f (x )的极小值点D ．－x 0是－f (－x )的极小值点 12．D [解析] 根据极值点是函数局部的性质可排除A 选项，根据函数f (x )的图像与f (－x )、－f (x )、－f (－x )的图像分别关于y 轴、x 轴、原点对称，可排除B 、C 选项，故选D.13． 已知函数f (x )＝⎩⎪⎨⎪⎧2x 3，x <0，－tan x ，0≤x <π2，则f ⎝⎛⎭⎫f ⎝⎛⎭⎫π4＝________． 13．－2 [解析] f π4＝－tan π4＝－1，f (－1)＝－2.14． 利用计算机产生0～1之间的均匀随机数a ，则事件“3a －1<0”发生的概率为________．14.13 [解析] 0<a <13，概率P ＝131＝13. 15．， 椭圆Γ：x 2a2＋y 2b 2＝1(a >b >0)的左、右焦点分别为F 1，F 2，焦距为2c .若直线y ＝3(x ＋c )与椭圆Γ的一个交点M 满足∠MF 1F 2＝2∠MF 2F 1，则该椭圆的离心率等于________．15.3－1 [解析] 如图，△MF 1F 2中，∠MF 1F 2＝60°，所以∠MF 2F 1＝30°，∠F 1MF 2＝90°.又|F 1F 2|＝2c ，所以|MF 1|＝c ，|MF 2|＝3c .根据椭圆定义得2a ＝|MF 1|＋|MF 2|＝c ＋3c ，得e ＝c a ＝23＋1＝3－1.16．， 设S ，T 是的两个非空子集，如果存在一个从S 到T 的函数y ＝f (x )满足：(i)T ＝{f (x )|x ∈S }；(ii)对任意x 1，x 2∈S ，当x 1<x 2时，恒有f (x 1)<f (x 2)，那么称这两个集合“保序同构”．现给出以下3对集合：①A ＝，B ＝；②A ＝{x |－1≤x ≤3}，B ＝{x |－8≤x ≤10}； ③A ＝{x |0<x <1}，B ＝其中，“保序同构”的集合对的序号是________．(写出所有“保序同构”的集合对的序号)16．①②③ [解析] 函数f (x )为定义域S 上的增函数，值域为T .构造函数f (x )＝x ＋1，x ∈， 则f (x )值域为*，且为增函数，①正确．构造过两点(－1，－8)，(3，10)的线段对应的函数f (x )＝92x －72，－1≤x ≤3，满足题设条件，②正确．构造函数f (x )＝tan x －12π，0<x <1，满足题设条件，③正确． 17．， 已知等差数列{a n }的公差d ＝1，前n 项和为S n . (1)若1，a 1，a 3成等比数列，求a 1； (2)若S 5>a 1a 9，求a 1的取值范围．17．解：(1)因为数列{a n }的公差d ＝1， 且1，a 1，a 3成等比数列，所以a 21＝1×(a 1＋2)， 即a 21－a 1－2＝0，解得a 1＝－1或a 1＝2. (2)因为数列{a n }的公差d ＝1，且S 5>a 1a 9， 所以5a 1＋10>a 21＋8a 1， 即a 21＋3a 1－10<0，解得－5<a 1<2. 18．， 如图1－3，在四棱锥P －ABCD 中，PD ⊥平面ABCD ，AB ∥DC ，AB ⊥AD ，BC ＝5，DC ＝3，AD ＝4，∠P AD ＝60°.(1)当正视方向与向量AD →的方向相同时，画出四棱锥P －ABCD 的正视图(要求标出尺寸，并写出演算过程)；(2)若M 为P A 的中点，求证：DM ∥平面PBC ； (3)求三棱锥D －PBC 的体积．图1－318．解：(1)在梯形ABCD 中，过点C 作CE ⊥AB ，垂足为E . 由已知得，四边形ADCE 为矩形，AE ＝CD ＝3，在Rt △BEC 中，由BC ＝5，CE ＝4，依勾股定理得BE ＝3，从而AB ＝6. 又由PD ⊥平面ABCD 得，PD ⊥AD .从而在Rt △PDA 中，由AD ＝4，∠P AD ＝60°，得PD ＝4 3. 正视图如图所示．(2)方法一：取PB 中点N ，联结MN ，CN .在△P AB 中，∵M 是P A 中点，∴MN ∥AB ，MN ＝12AB ＝3.又CD ∥AB ，CD ＝3，∴MN ∥CD ，MN ＝CD ， ∴四边形MNCD 为平行四边形，∴DM ∥CN . 又DM ⊄平面PBC ，CN ⊂平面PBC ， ∴DM ∥平面PBC .方法二：取AB 的中点E ，联结ME ，DE . 在梯形ABCD 中，BE ∥CD ，且BE ＝CD ， ∴四边形BCDE 为平行四边形，∴DE ∥BC .又DE ⊄平面PBC ，BC ⊂平面PBC ， ∴DE ∥平面PBC .又在△P AB 中，ME ∥PB ，ME ⊄平面PBC ，PB ⊂平面PBC ，∴ME ∥平面PBC . 又DE ∩ME ＝E ，∴平面DME ∥平面PBC . 又DM ⊂平面DME ，∴DM ∥平面PBC .(3)V D －PBC ＝V P －DBC ＝13S △DBC ·PD ，又S △DBC ＝6，PD ＝4 3，所以V D －PBC ＝8 3. 19．， 某工厂有25周岁以上(含25周岁)工人300名，25周岁以下工人200名．为研究工人的日平均生产量是否与年龄有关，现采用分层抽样的方法，从中抽取了100名工人，先统计了他们某月的日平均生产件数，然后按工人年龄在“25周岁以上(含25周岁)”和“25周岁以下”分为两组，再将两组工人的日平均生产件数分成5组：[50，60)，[60，70)，[70，80)，[80，90)，[90，100]分别加以统计，得到如图1－4所示的频率分布直方图．图1－4(1)从样本中日平均生产件数不足60件的工人中随机抽取2人，求至少抽到一名“25周岁以下组”工人的概率；(2)规定日平均生产件数不少于80件者为“生产能手”，请你根据已知条件完成2×2列联表，并判断是否有90%的把握认为“生产能手与工人所在的年龄组有关”？附：χ2＝n （n 11n 22－n 12n 21）2n 1＋·n 2＋·n ＋1·n ＋2P (χ2≥k )0.100 0.050 0.010 0.001 k2.7063.8416.63510.828⎝⎛⎭⎪⎫注：此公式也可以写成K 2＝n （ad －bc ）2（a ＋b ）（c ＋d ）（a ＋c ）（b ＋d ）19．解：(1)由已知得，样本中有“25周岁以上组”工人60名，“25周岁以下组”工人40名．所以，样本中日平均生产件数不足60件的工人中，“25周岁以上组”工人有60×0.05＝3(人)，记为A 1，A 2，A 3；“25周岁以下组”工人有40×0.05＝2(人)，记为B 1，B 2.从中随机抽取2名工人，所有的可能结果共有10种，它们是：(A 1，A 2)，(A 1，A 3)，(A 2，A 3)，(A 1，B 1)，(A 1，B 2)，(A 2，B 1)，(A 2，B 2)，(A 3，B 1)，(A 3，B 2)，(B 1，B 2)．其中，至少有1名“25周岁以下组”工人的可能结果共有7种，它们是：(A 1，B 1)，(A 1，B 2)，(A 2，B 1)，(A 2，B 2)，(A 3，B 1)，(A 3，B 2)，(B 1，B 2)．故所求的概率P ＝710.(2)由频率分布直方图可知，在抽取的100名工人中，“25周岁以上组”中的生产能手有60×0.25＝15(人)，“25周岁以下组”中的生产能手有40×0.375＝15(人)，据此可得2×2列联表如下：生产能手 非生产能手合计 25周岁以上组 15 45 60 25周岁以下组15 25 40 合计3070100所以得K 2＝n （ad －bc ）2（a ＋b ）（c ＋d ）（a ＋c ）（b ＋d ）＝100×（15×25－15×45）260×40×30×70＝2514≈1.79.因为1.79<2.706.所以没有90%的把握认为“生产能手与工人所在的年龄组有关”． 20．， 如图1－5，抛物线E ：y 2＝4x 的焦点为F ，准线l 与x 轴的交点为A .点C 在抛物线E 上，以C 为圆心，|CO |为半径作圆，设圆C 与准线l 交于不同的两点M ，N .(1)若点C 的纵坐标为2，求|MN |； (2)若|AF |2＝|AM |·|AN |，求圆C 的半径．图1－520．解：(1)抛物线y 2＝4x 的准线l 的方程为x ＝－1. 由点C 的纵坐标为2，得点C 的坐标为(1，2)， 所以点C 到准线l 的距离d ＝2，又|CO |＝5，所以|MN |＝2 |CO |2－d 2＝2 5－4＝2.(2)设C ⎝⎛⎭⎫y 204，y 0，则圆C 的方程为⎝⎛⎭⎫x －y 2042＋(y －y 0)2＝y 4016＋y 20，即x 2－y 202x ＋y 2－2y 0y ＝0.由x ＝－1，得y 2－2y 0y ＋1＋y 202＝0.设M (－1，y 1)，N (－1，y 2)，则⎩⎨⎧Δ＝4y 20－4⎝⎛⎭⎫1＋y 202＝2y 20－4>0，y 1y 2＝y22＋1.由|AF |2＝|AM |·|AN |，得|y 1y 2|＝4， 所以y 202＋1＝4，解得y 0＝±6，此时Δ>0.所以圆心C 的坐标为⎝⎛⎭⎫32，6或⎝⎛⎭⎫32，－6， 从而|CO |2＝334，|CO |＝332，即圆C 的半径为332. 21．， 如图1－6，在等腰直角△OPQ 中，∠POQ ＝90°，OP ＝2 2，点M 在线段PQ上．(1)若OM ＝5，求PM 的长；(2)若点N 在线段MQ 上，且∠MON ＝30°，问：当∠POM 取何值时，△OMN 的面积最小？并求出面积的最小值．图1－621．解：(1)在△OMP 中，∠OPM ＝45°，OM ＝5，OP ＝2 2， 由余弦定理得，OM 2＝OP 2＋MP 2－2OP ·MP ·cos 45°，得MP 2－4MP ＋3＝0， 解得MP ＝1或MP ＝3. (2)设∠POM ＝α，0°≤α≤60°， 在△OMP 中，由正弦定理，得OM sin ∠OPM ＝OP sin ∠OMP ，所以OM ＝OP sin 45°sin （45°＋α），同理ON ＝OP sin 45°sin （75°＋α）.故S △OMN ＝12OM ·ON ·sin ∠MON＝14×OP 2sin 2 45°sin （45°＋α）sin （75°＋α） ＝1sin （45°＋α）sin （45°＋α＋30°）＝1sin （45°＋α）⎣⎡⎦⎤32sin （45°＋α）＋12cos （45°＋α）＝132sin 2（45°＋α）＋12sin （45°＋α）cos （45°＋α）＝134[1－cos （90°＋2α）]＋14sin （90°＋2α） ＝134＋34sin 2α＋14cos 2α ＝1 34＋12sin （2α＋30°）. 因为0°≤α≤60°，30°≤2α＋30°≤150°，所以当α＝30°时，sin(2α＋30°)的最大值为1，此时△OMN 的面积取到最小值．即∠POM ＝30°时，△OMN 的面积的最小值为8－4 3.22．， 已知函数f (x )＝x －1＋a ex (a ∈，e 为自然对数的底数)．(1)若曲线y ＝f (x )在点(1，f (1))处的切线平行于x 轴，求a 的值； (2)求函数f (x )的极值；(3)当a ＝1时，若直线l ：y ＝kx －1与曲线y ＝f (x )没有公共点，求k 的最大值． 22．解：(1)由f (x )＝x －1＋a e x ，得f ′(x )＝1－aex .又曲线y ＝f (x )在点(1，f (1))处的切线平行于x 轴，得f ′(1)＝0，即1－ae ＝0，解得a ＝e.(2)f ′(x )＝1－aex ，①当a ≤0时，f ′(x )>0，f (x )为(－∞，＋∞)上的增函数，所以函数f (x )无极值． ②当a >0时，令f ′(x )＝0，得e x ＝a ，x ＝ln a . 当x ∈(－∞，ln a )时，f ′(x )<0； 当x ∈(ln a ，＋∞)时，f ′(x )>0，所以f (x )在(－∞，ln a )上单调递减，在(ln a ，＋∞)上单调递增，故f (x )在x ＝ln a 处取得极小值，且极小值为f (ln a )＝ln a ，无极大值．综上，当a ≤0时，函数f (x )无极值；当a >0时，f (x )在x ＝ln a 处取得极小值ln a ，无极大值．(3)方法一：当a ＝1时，f (x )＝x －1＋1e x .令g (x )＝f (x )－(kx －1)＝(1－k )x ＋1ex ，则直线l ：y ＝kx －1与曲线y ＝f (x )没有公共点， 等价于方程g (x )＝0在上没有实数解．假设k >1，此时g (0)＝1>0，g ⎝⎛⎭⎫1k －1＝－1＋1e 1k －1<0，又函数g (x )的图像连续不断，由零点存在定理，可知g (x )＝0在上至少有一解，与“方程g (x )＝0在上没有实数解”矛盾，故k ≤1.又k ＝1时，g (x )＝1e x >0，知方程g (x )＝0在上没有实数解．所以k 的最大值为1.方法二：当a ＝1时，f (x )＝x －1＋1e x .直线l ：y ＝kx －1与曲线y ＝f (x )没有公共点，等价于关于x 的方程kx －1＝x －1＋1e x 在上没有实数解，即关于x 的方程：(k －1)x ＝1ex (*)在上没有实数解．①当k ＝1时，方程(*)可化为1e x ＝0，在上没有实数解．②当k ≠1时，方程(*)化为1k －1＝x e x . 令g (x )＝x e x ，则有g ′(x )＝(1＋x )e x . 令g ′(x )＝0，得x ＝－1，当x 变化时，g ′(x )，g (x )的变化情况如下表： x (－∞，－1)－1 (－1，＋∞)g ′(x )－＋g (x )－1e当x ＝－1时，g (x )min ＝－1e ，同时当x 趋于＋∞时，g (x )趋于＋∞，从而g (x )的取值范围为－1e，＋∞.所以当1k －1∈⎝⎛⎭⎫－∞，－1e 时，方程(*)无实数解． 解得k 的取值范围是(1－e ，1)．综上①②，得k 的最大值为1.。

2013年普通高等学校招生全国统一考试(福建卷)文科综合（地理部分）第 I 卷（选择题共 48分）本卷共12小题，每小题 4 分，共 48分。

在每小题给出的四个选项中，只有一项是最符合题目要求的。

循环农业是美丽乡村建设的途径之一。

图1示意采循环农业模式，读图回答1～2题。

图11.最适宜该模式的是A. 河套平原B. 黄淮平原C. 辽东丘陵D. 闽浙丘陵【答案】D【解析】根据图中的甘蔗（我国产区：珠江三角洲、湛江与海南、广西、闽东南、云南、四川盆地及台湾省），判定选D。

2. 循环农业对建设美丽乡村的主要作用是①提高经济效益②加快城镇发展③提供清洁能源④促进民居集中A. ①②B. ①③C. ②③D. ②④【答案】B【解析】图中循环农业，农业产业构成多元化，各农业产业间形成了良性农业生态系统，且可利用沼气池，提供可再生的清洁能源。

图2示意我国某家电企业组织的空间分布，读图回答3～5题。

图23.影响该企业研发中心布局的主导因素是A. 科技与市场B. 市场与交通C. 交通与资金D. 科技与劳动力【答案】A【解析】从图中可知企业研发中心主要分布在发达国家和地区，其有科技优势和市场优势。

4. 该跨国企业的空间布局特点是A. 组织空间分布具有集聚性B. 信息中心分布具有分散性C. 研发中心分布在发达国家D. 生产基地分布在发展中国家【答案】B【解析】该企业组织遍布各大洲较分散，研发中心大部分在发达国家（中韩例外），生产基地在发达国家和发展中国家均有分布。

5. 地理信息系统能够辅助A. 企业空间布局决策B. 总部调控生产C. 总部监控产品质量D. 研发中心创意【答案】A【解析】地理信息系统是在计算机硬、软件系统支持下，对整个或部分地球表层（包括大气层）空间中的有关地理分布数据进行采集、储存、管理、运算、分析、显示和描述的技术系统。

可辅助于企业空间布局决策。

图3示意某省气候舒适度分布。

以平均气温 24℃、相对湿度70 %、平均风速2m/s作为人体最舒适气候条件，据此划分出最舒适区、舒适区、一般区、不舒适区与最不舒适区。