2011走向高考,贾凤山,高中总复习,英语,必修4语法8

2011走向高考-贾凤山-高中总复习-第8篇1-2DA．26 B．24C．19 D．20[答案] D4．已知定义在R上的奇函数f(x)的图象关于直线x ＝1对称，并且当x∈(0,1]时，f(x)＝x2＋1，则f(2010)的值为() A．2 B．0C．1 D．－1[答案] B[解析]∵f(x)为奇函数，∴f(－x)＝－f(x)，∵f(x)图象关于直线x＝1对称，∴f(2－x)＝f(x)，∴f(2＋x)＝f(－x)＝－f(x)，∴f(4＋x)＝f(2＋(2＋x))＝－f(2＋x)＝f(x)，∴f(x)是周期为4的周期函数，∴f(2010)＝f(2)，∵f(2＋x)＝f(－x)成立，∴f(2)＝f(0)，又f(x)是R上的奇函数，∴f(0)＝0，∴f(2010)＝0.5．n个连续自然数按规律排成下表：根据规律，从2008到2010的箭头方向依次为()A．↓→B．→↑C．↑→D．→↓[答案] A[解析] 观察图例可见，位序相同的数字都是以4为公差的等差数列，故从2008至2010，其位序应与相同，故选A.6．用反证法证明命题“三角形的内角中至少有一个不大于60°”时，反设正确的是( )A ．假设三内角都不大于60°B ．假设三内角都大于60°C ．假设三内角至多有一个大于60°D ．假设三内角至多有两个大于60°[答案] B7．某种商品计划提价，现有四种方案，方案(Ⅰ)先提价m %，再提价n %；方案(Ⅱ)先提价n %，再提价m %；方案(Ⅲ)分两次提价，每次提价(m ＋n 2)%；方案(Ⅳ)一次性提价(m ＋n )%，已知m >n >0，那么四种提价方案中，哪一种提价最多？( )A ．ⅠB ．ⅡC ．ⅢD ．Ⅳ[答案] C[解析] 设商品原价为a ，方案(Ⅰ)：a (1＋m %)(1＋n %)＝a [1＋(m ＋n )%＋m %n %]方案(Ⅱ)：a (1＋n %)(1＋m %)＝a (1＋(m ＋n )%＋m %n %)方案(Ⅲ)：a (1＋m ＋n 2%)2＝a (1＋(m ＋n )%＋(m＋n2%)2)方案(Ⅳ)：a[1＋(m＋n)%]＝a(1＋(m＋n)%)又∵(m＋n2%)2≥(mn%)2＝m%n%故选C.8．已知平面α外不共线的三点A、B、C到α的距离都相等，则正确的结论是()A．平面ABC必平行于αB．平面ABC必与α相交C．平面ABC必不垂直于αD．存在△ABC的一条中位线平行于α或在α内[答案] D[解析]由三点A、B、C可以不在平面α的同一侧，知A错；由三点A、B、C可以在平面α的同一侧，知B错；可以找到平面ABC垂直于平面α，知C错．[点评]如何证明选项D，请读者给出自己的理由．9．设a、b、c∈R＋，P＝a＋b－c，Q＝b＋c－a，R ＝c＋a－b，则“PQR>0”是“P、Q、R同时大于零”的() A．充分而不必要条件B．必要而不充分条件C．充要条件D．既不充分也不必要条件[答案] C[解析]首先若P、Q、R同时大于零，则必有PQR>0成立．其次，若PQR>0，且P、Q、R不都大于0，则必有两个为负，不妨设P<0，Q<0，即a＋b－c<0，b＋c－a<0，∴b<0与b∈R＋矛盾，故P、Q、R都大于0.10．如果四棱锥的四条侧棱都相等，就称它为“等腰四棱锥”，四条侧棱称为它的腰，以下4个命题中，假命题．．．是() A．等腰四棱锥的腰与底面所成的角都相等B．等腰四棱锥的侧面与底面所成的二面角都相等或互补C．等腰四棱锥的底面四边形必存在外接圆D．等腰四棱锥的各顶点必在同一球面上[答案] B[解析]如右图，由“等腰四棱锥”的定义知，PA＝PB＝PC＝PD.设P点在底面ABCD内的射影为O，则OA＝OB＝OC＝OD，从而∠PAO＝∠PBO＝∠PCO＝∠PDO，且四边形存在以O为圆心的外接圆，故A，C都对；在△PAO所在平面内作线段PA的中垂线交PO于M.则MP＝MA，从而MP＝MA＝MB＝MC＝MD.故四棱锥的顶点都在以M为球心的球面上．故D正确；显然当四棱锥为正四棱锥时，各侧面与底面成的角相等．当底面上四点任意排布在⊙O的圆周上时，B错．考查命题的判断与信息捕捉分析能力．二、填空题11．已知点A n(n，a n)为函数y＝x2＋1的图象上的点，B n(n，b n)为函数y＝x图象上的点，其中n∈N*，设c n＝a n－b n，则c n与c n＋1的大小关系为________．[答案]c n>c n＋1[解析]∵a n＝n2＋1，b n＝n，c n＝n2＋1－n＝1n2＋1＋n，随n的增大而减小，∴c n＋1<c n.12．(文)设f(x)定义如表，数列{x n}满足x1＝5，x n＋1＝f(x n)，则x2011x 12345 6f(x)45126 3[答案] 4[解析]由条件知x1＝5，x2＝f(x1)＝f(5)＝6，x3＝f(x2)＝f(6)＝3，x4＝f(x3)＝f(3)＝1，x5＝f(x4)＝f(1)＝4，x6＝f(x5)＝f(4)＝2，x7＝f(x6)＝f(2)＝5＝x1，可知{x n}是周期为6的周期数列，∴x2011＝x1＝4.据此可知，{x n}周期为4，∴x2011＝x3＝1.(理)(09·福建)五位同学围成一圈依序循环报数，规定：①第一位同学首次报出的数为1，第二位同学首次报出的数也为1，之后每位同学所报出的数都是前两位同学所报出的数之和；②若报出的数为3的倍数，则报该数的同学需拍手一次．已知甲同学第一个报数，当五位同学依序循环报到第100个数时，甲同学拍手的总次数为________．[答案] 5[解析] 根据规则可知报数为1,1,2,3,5,8,13,21，…，被3除的余数规律为1,1,2,0,2,2,1,0,1,1,2,0，…，而是3的倍数的数出现在4的倍数位置．又甲在第1,6,11,16，…等次数上，则同时满足的有16,36,56,76,96共5个数．13．(文)(09·江苏)在平面上，若两个正三角形的边长的比为12，则它们的面积比为1 4.类似地，在空间，若两个正四面体的棱长比为12，则它们的体积比为________． [答案] 18(理)E 、F 是△ABC 的边AB 、AC 上的点，△ABC被线段EF 分成两部分的面积之比，S △AEF S △ABC ＝AE ·AF AB ·AC ，类比此结论，则对于三棱锥P －ABC ，若E 、F 、G 分别为三条棱PA 、PB 、PC 上的点，则有________．[答案] V P －EFG V P －ABC ＝PE ·PF ·PG PA ·PB ·PC 14．(文)若a 、b 、c 为Rt △ABC 的三边，其中c 为斜边，那么a n ＋b n 与c n (其中n ∈N *且n >2)的大小关系是________．[答案] a n ＋b n <c n[解析] ∵△ABC 为Rt △，且c 为斜边，∴c 2＝a 2＋b 2，∴c >a >0，c >b >0，∴0<a c <1,0<b c <1，当n >2时，⎝ ⎛⎭⎪⎪⎫a c n ＋⎝ ⎛⎭⎪⎪⎫b c n <⎝ ⎛⎭⎪⎪⎫a c 2＋⎝ ⎛⎭⎪⎪⎫b c 2＝a 2＋b 2c 2＝1， 即a n ＋b n <c n .(理)设x>0，y>0，a＝x＋y，b＝x cos2θ·y sin2θ(θ∈R)，则a与b的大小关系为________．[答案]a>b[解析]∵x>0，y>0，∴x＋y>x，x＋y>y，∴(x＋y)cos2θ>x cos2θ，(x＋y)sin2θ>y sin2θ，∴b＝x cos2θ·y sin2θ<(x＋y)cos2θ·(x＋y)sin2θ＝(x＋y)sin2θ＋cos2θ＝x＋y＝a.三、解答题15．(文)先解答(1)，再根据结构类比解答(2)：(1)已知a，b为实数，且|a|<1，|b|<1，求证：ab＋1>a＋b.(2)已知a，b，c均为实数，且|a|<1，|b|<1，|c|<1，求证：abc＋2>a＋b＋c.[解析](1)ab＋1－(a＋b)＝(a－1)(b－1)>0.(2)∵|a|<1，|b|<1，|c|<1，据(1)得(ab)·c＋1>ab＋c，∴abc＋2＝[(ab)·c＋1]＋1>(ab＋c)＋1＝(ab＋1)＋c>a＋b＋c.你能再用归纳推理方法猜想出更一般地结论吗？即x i∈R，|x i|<1(i＝1,2，…，n)时，有________．(理)在Rt△ABC中，CA⊥CB，斜边上的高为h，则1h2＝1AC2＋1BC2，先证明此性质，再类比此性质，给出在四面体P－ABC中，若PA、PB、PC两两垂直，底面ABC上的高为h，写出得到的正确结论并证明之．[解析] (1)1h 2＝1PA 2＋1PB 2＋1PC2 (2)Rt △ABC 中，AC 2＝AD ·AB ，BC 2＝BD ·AB ，∴1AC 2＋1BC 2＝1AD ·AB ＋1BD ·AB ＝1AB ⎝ ⎛⎭⎪⎪⎫1AD ＋1BD ＝1AB ·AD ＋BD AD ·BD ＝1AD ·BD ＝1h 2. 四面体P －ABC 中，PA 、PB 、PC 两两垂直，设PD 、PE 、PF 分别垂直于BC 、AB 、AC ，PO ⊥平面ABC ，即PO ＝h .∴△APD 为直角三角形．∴1PA 2＋1PD 2＝1h2. 同理，1PB 2＋1PF 2＝1h2， 1PC 2＋1PE 2＝1h2， ∴⎝ ⎛⎭⎪⎪⎫1PA 2＋1PB 2＋1PC 2＋⎝ ⎛⎭⎪⎪⎫1PD 2＋1PE 2＋1PF 2＝3h 2(*) 又△APB 为直角三角形，∴1PA 2＋1PB 2＝1PE2.同理，1PB 2＋1PC 2＝1PD 2，1PA 2＋1PC 2＝1PF 2. ∴(*)式变为1PA 2＋1PB 2＋1PC 2＋21PA 2＋1PB 2＋1PC 2＝3h 2.∴1PA 2＋1PB 2＋1PC 2＝1h 2. 16．观察①sin 210°＋cos 240°＋sin10°cos40°＝34； ②sin 26°＋cos 236°＋sin6°cos36°＝34. 由上面两题的结构规律，你能否提出一个猜想？并证明你的猜想．[解析] 观察40°－10°＝30°，36°－30°＝6°，由此猜想：sin 2α＋cos 2(30°＋α)＋sin α·cos(30°＋α)＝34. 证明：sin 2α＋cos 2(30°＋α)＋sin α·cos(30°＋α) ＝1－cos2α2＋1＋cos(60°＋2α)2＋12[sin(30°＋2α)－sin30°]＝1＋12[cos(60°＋2α)－cos2α]＋12sin(30°＋2α)－12＝1＋12[－2sin(30°＋2α)sin30°]＋12⎣⎢⎢⎡⎦⎥⎥⎤sin(30°＋2α)－12 ＝34－12sin(30°＋2α)＋12(sin30°＋2α)＝34. 17．(文)已知△ABC 中，AB ＝AC ＝2，BC 边上有2011个不同的点P 1、P 2、…、P 2011，记M i ＝AP 2i ＋BP i ·CP i (i ＝1、2、…、2011)，求M 1＋M 2＋…＋M 2011的值．[解析] 可取特殊点试验M i 的值，例如，取BC 的中点P ，则∵AB ＝AC ，∴AP ⊥BC ，∴M ＝AP 2＋BP ·PC ＝AP 2＋BP 2＝AB 2＝4，再猜想所有M i 的值可能均为4.验证：取BC 中点P ，又P i 为BC 上任一点，∴M i＝AP 2i ＋BP i ·P i C ＝AP 2i ＋(BP －PP i )(CP ＋PP i )＝AP 2i ＋(BP －PP i )(BP ＋PP i )＝AP 2i ＋BP 2－P i P 2＝(AP 2i －P i P 2)＋BP 2＝AP 2＋BP 2＝AB 2＝4，从而猜想正确，∴M 1＋M 2＋…＋M 2011＝4×2011＝8044.(理)设数列{a n }的首项a 1＝a ≠14，且a n ＋1＝⎩⎪⎨⎪⎧12a n ，n 为偶数a n ＋14，n 为奇数.记b n ＝a 2n －1－14，n ＝1,2,3，…. (1)求a 2，a 3；(2)判断{b n }是否为等比数列，并证明你的结论．[解析] (1)a 2＝a 1＋14＝a ＋14， a 3＝12a 2＝12a ＋18. (2)∵a 4＝a 3＋14＝12a ＋38. ∴a 5＝12a 4＝14a ＋316. ∴b 1＝a 1－14＝a －14≠0， b 2＝a 3－14＝12⎝ ⎛⎭⎪⎪⎫a －14， b 3＝a 5－14＝14⎝ ⎛⎭⎪⎪⎫a －14.猜想{b n }是公比为12的等比数列． 证明如下：∵b n ＋1＝a 2n ＋1－14＝12a 2n －14＝12⎝ ⎛⎭⎪⎪⎫a 2n －1＋14－14 ＝12⎝ ⎛⎭⎪⎪⎫a 2n －1－14＝12b n (n ∈N *)． ∴{b n }是首项为a －14，公比为12的等比数列。

选修八Module 4～6综合技能测试本卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

满分150分，考试时间120分钟。

第Ⅰ卷(选择题共115分)第一部分：听力(共两节，满分30分)略第二部分：基础知识运用(共两节，满分45分)第一节：单项填空(共15小题；每小题1分，满分15分)从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。

21．—Guess what! I have got an A for my term paper.—Great! You ________ read widely and put a lot of work into it.A．must B．shouldC．must have D．should have答案：C由“have got an A”可知是对过去发生事情的推测。

故选C项must have, 表示对过去发生事情的语气十分肯定的推测。

22．I think your sister is old enough to know ________ to spend all her money on beautiful dresses.A．other than B．rather thanC．better than D．more than答案：C know better than that/to do sth.意为“明白事理而不至于……”。

23．A diet with no exercise is bad for the health, because it will ________ a loss of both fat and muscle tissue.A．result from B．make upC．result in D．end up答案：C result in意为“导致”；result from意为“由……引起”；make up意为“形成；构成；弥补”；end up意为“结束”，根据句意选C项。

选修八题型专攻1ATemperature is part of my married romance coming to New Y ork from Baltimore—where there is just one small snowstorm each year. I was__1__by a fireplace in my new home, with fires__2__all day, just as what ancient people did at a wedding.My husband, Peter, comes from northern Ontario, where winter__3__from September to May and cold wind is__4__.“When Canadians have 30 below, they__5__it，” he says.“Cold wind is for crybabies.”So to marry this man I had to learn to__6__for serious cold. To get me from Baltimore's Inner Harbor to Albany's frozen Hudson, Peter piled me__7__jackets and sweaters, scarves and gloves even a hat with ear flaps. The gift of Sorel boots—comfortably warm at Canada's 30 below, was a__8__we were getting serious.That first winter together, living in upstate New Y ork, I thought I'd__9__. My boots were good below freezing, but my fingers could__10__tie them. Physical adaptation is real, but it came slowly. And there is also emotional__11__to cold. Some days I tell myself that I have enough beach memories to stick to on__12__days and other days I am reminded that living cold does indeed build__13__.__14__，having a warm house is important. After my first marriage ended, for years I__15__went on a second date with a man whose response to my“I'm cold”was“Put on a sweater”. Now I'm married to a man who__16__that cold hands do not mean a warm heart. And that a big oil bill is better than roses. But surprisingly, I've grown, too. I am__17__，in this new life and climate, to go to look for that cost-saving sweater.The word comfortable did not__18__refer to being contented. Its Latin root, comfortare, means to strengthen. The Holy Spirit is Comforter; not to make us comfortable, but to make us__19__. We__20__not be warm but we are indeed comforted.文章大意：本文讲述了作者因嫁给了加拿大人Peter，从温暖的Baltimore来到New Y ork。

选修八Module 4～6综合技能测试本卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

满分150分，考试时间120分钟。

第Ⅰ卷(选择题共95分)第一部分英语知识运用(共三节，满分50分)第一节：语音知识(共5小题；每小题1分，满分5分)从A、B、C、D四个选项中，找出其划线部分与所给单词的划线部分读音相同的选项，并在答题卡上将该项涂黑。

1．medicineA．except B．record C．increase D．physics2．considerA．comfort B．condition C．concert D．continent3．headA．bread B．seaside C．heat D．mean4．extremeA．experience B．excellent C．exist D．explanation5．suggestionA．impression B．information C．invitation D．question答案：1—5ABAAD第二节：语法和词汇知识(共15小题；每小题1分，满分15分)从A、B、C、D四个选项中，选出可以填入空白处的最佳选项，并在答题卡将该项涂黑。

6．—Guess what! I have got an A for my term paper.—Great! You ________ read widely and put a lot of work into it.A．must B．shouldC．must have D．should have答案：C由“have got an A”可知是对过去发生事情的推测。

故选C项must have, 表示对过去发生事情的语气十分肯定的推测。

7．I think your sister is old enough to know ________ to spend all her money on beautiful dresses.A．other than B．rather than C．better than D．more than答案：C know better than that/to do sth.意为“明白事理而不至于……”。

选修八题型专攻2Ⅰ.阅读理解AYou don't expect your child to grow up to be a heroin addict. From the moment of her birth, you have hopes and dreams about the future, but they never include heroin addiction. That couldn't happen to your child, because addiction is the result of a bad environment, bad parenting. There is most definitely someone or something to blame.That's what I used to believe. But after failed rehab and long periods of separation from my heroin-addicted daughter, after years of holding my breath, waiting for another relapse, I now believe there is no blame.After Katie admitted her addiction, I struggled to understand how this could have happened to my daughter—a bright, beautiful, talented and most importantly, loved young woman. When the initial shock wore off, I analyzed and inventoried all the whys and hows of Katie's addiction. I searched for someone or something to blame. I blamed her friends. I blamed her dad. I blamed our divorce. But mostly, I blamed myself. My desperate heart convinced me that I should have prevented Katie's addiction, and that given another chance, I could correct my mistakes.When Katie came home from rehab, I approached each day with the zeal of a drill sergeant. I championed the 12-step program and monitored her improvement daily as though curing heroin addiction was as simple as nursing a cold. I drove her to therapy sessions and AA meetings. I_controlled_everything_and_left_nothing_to_chance. But in spite of my efforts, Katie didn't get better. She left my home, lost again to the powerful grip of addiction.In the long days, weeks and months that followed, I gathered bits and pieces of old beliefs and tried to assemble them into something whole. Sometimes I gave up, and sometimes I simply let go. Gradually, my search for blame changed to a longing for hope. I comforted myself with the only thing that still connected me to my daughter：love.I thought about Katie every day, and I missed her. I cried, and worried about her safety and whereabouts. I wrote letters I knew she'd never see. Sometimes I woke up panicked in the middle of the night, certain that mother's intuition(直觉)was preparing me for something bad. But through it all, I loved her.I don't know why or how my daughter became addicted to heroin; I do know that it doesn't really matter. Life goes on, and Katie is still my daughter.Katie and I meet for breakfast on Friday mornings now. We drink coffee and talk. I don't try to heal her. I just love her. Sometimes there is pain and sorrow, but there is no blame. I believe there is only love.文章大意：本文是记叙文。

选修八Module 1Ⅰ.单词拼写1．The film was a huge ________ (商业的) success.2．That was a/an ________ (极其) cold winter morning.3．As a new teacher, Susan tried to ________ (促进) good feelings between students and her.4．She had the time and the ________ (灵感) to develop her talent.5．It is important to assess the ________ (可靠性) of the data.6．A small child has to learn to keep its b________ before it can walk far.7．Quick! Call an ambulance! This is an e________！8．The club members have the p________ of using the lending service of the library.9．Plant the seeds at a d________ of about 2 cm.10．Her a________ from the party made her good friends very angry.答案：mercial 2.extremely 3.promote 4.inspiration 5.reliability 6.balance 7.emergency8.privilege9.depth10．absenceⅡ.根据句意，用所给单词或短语的适当形式填空1．They still haven't ________ a name for their baby.2．The facts are clearly ________ in the report.3．In that area, they started an ________ movement to protect wild animals.4．We are being ________ on Grammar tomorrow.5．A camel ________ in the desert.6．They held completely different views, and ________，he had to stay in hospital for a whole month.7．Those in authority were in a ________ position.8．He saved my life ________ of losing his own.9．Nobody has ever ________ the lonely island.10．________ all the fish died did the villagers realize how serious the pollution was.答案：e up with 2.stated 3.ecology 4.tested 5.came into sight 6.as a result 7.privileged8.taking a risk9．set foot on10.Not untilⅢ.完成句子1．我们应尽量保持工作与休闲的平衡。

选修八Module 4～6综合技能测试本卷分第Ⅰ卷(选择题)和第Ⅱ卷(非选择题)两部分。

满分150分，考试时间120分钟。

第Ⅰ卷(选择题共115分)第一部分：听力(共两节，满分30分)略第二部分：基础知识运用(共两节，满分45分)第一节：单项填空(共15小题；每小题1分，满分15分)从A、B、C、D四个选项中，选出可以填入空白处的最佳选项。

21．—Guess what! I have got an A for my term paper.—Great! You ________ read widely and put a lot of work into it.A．must B．shouldC．must have D．should have答案：C由“have got an A”可知是对过去发生事情的推测。

故选C项must have, 表示对过去发生事情的语气十分肯定的推测。

22．I think your sister is old enough to know ________ to spend all her money on beautiful dresses.A．other than B．rather thanC．better than D．more than答案：C know better than that/to do sth.意为“明白事理而不至于……”。

23．A diet with no exercise is bad for the health, because it will ________ a loss of both fat and muscle tissue.A．result from B．make upC．result in D．end up答案：C result in意为“导致”；result from意为“由……引起”；make up意为“形成；构成；弥补”；end up意为“结束”，根据句意选C项。