第一篇:2014届高考英语 复习讲练测完形填空10
2014届高考英语复习讲练测:完形填空10
In the clinic, I asked if Michael could be retested, so the specialist tested him again.To my __36__, it was the same score.Later that evening, I _37_ told Frank what I had learned that day.After talking it over, we agree that we knew our _38_ much better than an IQ(智商)test.We _39_ that Michael’s score must have been a __40___ and we should treat him ___41___ as usual.We moved to Indiana in 1962, and Michael studied at Concordia High School in the same year.He got _42 _ grades in the school, especially _43_ biology and chemistry, which was a great comfort.Michael _44_ Indiana University in 1965 as a pre-medical student, soon afterwards, his teachers permitted him to take more courses than _45_.In 1968, he was accepted by the School of Medicine, Yale University.On graduation day in 1972, Frank and I _46_ the ceremony(典礼)at Yale.After the ceremony, we told Michael about the _47_ IQ score he got when he was six.Since that day, Michael sometimes would look at us and say _48_, “My dear mom and dad never told me that I couldn’t be a doctor, not until after I graduated from medical school!” It is his special way of thanking us for the _49_ we had in him.Interestingly, Michael then _50_ another IQ test.We went to the same clinic where he had _51_ the test eighteen years before.This time Michael scored 126, an increase of 36 points.A result like that was supposed to be _52_.Children often do as _53_ as what adults, particularly parents and teachers, _54_ of them.That is, tell a child he is “ _55_”, and he may play the role of a foolish child.36.A.joyB.surprise
B.fearfully
B.sonC.dislikeD.disappointmentD.hopefully 37.A.tearfully 38.A.student
39.A.argued
40.A.jokeC.cheerfullyC.friendC.decidedD.doctor B.realizedD.understood B.mistakeC.warningD wonder.41.A.specially 42.A.poor43.A.in
B.strictly
C.naturally
D.carefully
B.good
C.average
D.standard
D.for
D.entered
B.about B.chose
C.of
44.A.visited45.A.allowed46.A.missed47.A.high
C.passedC.required
B.described B.held
D.offered
C.delayed
D.attended
B.sameC.lowD.different
D.jokingly D.delight
D.prepared for
48.A.curiously 49.A.faith
B.eagerlyB.interest
C.calmlyC.pride
50.A.looked for B.asked for 51.A.received B.accepted52.A.imperfect
C.waited for
C.organized D.discussed
D.unsatisfactory
B.impossible
C.uncertain
53.A.honestly B.much54.A.hear55.A.wise
C.well
D.bravely
D.speak
B.learn
C.expect
B.rudeC.shyD.stupid
答案36.D37.A38.B39.C40.B41.C42.B43.A44.D45.C46.D47.C48.D49.A50.B51.A52.B53.C54.C55.D
It's fourteen years since I left the Philippines to live with my family in the USA.A month ago, while on summer vacation back in my motherland, I learned a lesson from mosquito(蚊子)bites.Right before36Kennedy Airport in New York, my grandma37me of the behavior of the native mosquitoes around the38like me.She said, “There's an old saying—the39you stay away from the motherland, the sweeter your blood40to the mosquitoes.” Not41it, I replied, “Grandmaaaa, that's just an old wives' tale!”
Well, less than a week42my arrival in Manila, I was already carpeted with a43of mosquito bites.I took many measures to keep myself from being44, but they all proved useless.Late one45in my cousin's home, I couldn't bear the46of the bites.Hoping to find some comfort, I47my cousin, who was sleeping peacefully in the bed next to mine.Unhappy for being48she said, “There is nothing you can do.Go back to sleep.”With a few turns, she slept again.Enviously(妒嫉地)49her sleep, I hoped a big mosquito would50on her face.However, the mosquitoes would just lightly dance around her forehead and fly away quickly, never biting her.Amazed(惊奇的), I ran to others'51, only to find they were all sleeping52as the same thing occurred again and again.From those bites, I came to53my grandma's silly tale.From then on, I've always tried to keep a(n)54mind about those strange old wives' tales55they do have some truth to them.36.A.leavingB.passingfinding
37.A.persuaded
B.remindedC.warnedD.informed
D.C.visitingD.38.A.studentsB.foreignersC.passengersvisitors
39.A.earlier40.A.growsremains
B.longerC.soonerD.later B.goes
C.flowsD.41.A.expectingB.understandingC.recognizingD.believing 42.A.afterB.before
C.whenD.as
D.43.A.shadeB.pileC.cloudblanket
44.A.touchedB.bittenC.defeatedD.discovered 45.A.morningB.afternoon46.A.noiseB.hiteffect
47.A.woke upB.shouted atC.looked fordropped on
48.A.blamedB.interruptedC.movedfrightened
49.A.having
C.eveningD.night C.pain
D.D.D.B.watchingC.makingD.helping
50.A.landB.fly
C.fall
D.wait
51.A.housesB.flatsC.roomsD.homes 52.A.joyfullyB.anxiouslyworriedly
53.A.tellB.knowC.remember
D.accept
C.soundlesslyD.54.A.openB.activeC.clear55.A.andB.so
C.because答案36.A37.C38.D39.B40.A41.D42.A43.D44.B45.D46.C47.A48.B49.B50.A51.C52.C53.D54.A55.C
D.honest D.until
第二篇:2014届高考英语 复习讲练测教案5
2014届高考英语复习讲练测:教案5 1.persuade vt.说服,劝服,使相信
persuade sb.to do sth.=persuade sb.into doing sth.说服某人做某事 persuade sb.not to do sth.=persuade sb.out of doing sth.说服某人不做某事 persuade sb.of sth.说服某人信服某事 persuade sb.+thatclause 使某人相信„„
He persuaded me to study hard.=He persuaded me into studying hard.他说服我努力学习。易混辨析persuade与advise persuade sb.to do sth.表示成功地说服某人去做某事;其中try to persuade sb.to do sth.表示试图说服某人做某事,含有没有成功的意思。
advise sb.to do sth.表示建议某人做某事,对方是否采纳则不一定。①Jack finally persuaded his father to give up smoking.杰克终于说服他父亲戒了烟。
②We tried to persuade her to go out with us,but she refused.我们试图说服她和我们一起出去,但被她拒绝了。
③I advised them to start early so that they could arrive there before dark.我建议他们早一点动身,以便能天黑前赶到那儿。
反馈1.1The boy was ______ to follow his friends' idea and was pleased to see it worked better than expected.A.advised
B.allowed C.forbidden D.persuaded 反馈1.2 I ______ her to kick the habit of smoking,but she wouldn't listen.A.tried to persuade B.persuaded C.suggested D.expected 反馈1.3I ______ him not to smoke,but he didn't follow my advice.A.persuaded B.suggested C.advised D.hoped 反馈1.4(2012·浙江宁波十校联考)One of us ______ us all taking shelter under the tree.Unluckily,one boy bought it and was struck by lightning as a result.A.advised B.suggested C.persuaded D.urged
①All possible means ______ been tried.②Every possible means ______ been tried.反馈2.4______ the underemployed university graduates,the highttech project is expected to create 10,000 or so jobs in the fields of computer programming and testing.A.Meaning to benefit B.Meaning benefiting C.Meant benefiting D.Meant to benefit 反馈2.5For him ______ stage is just ______ means of making a living.A.a;a B.the;a C.the;the D.a;the 3.benefit vt.有利于,使„„受益 n.利益,福利,好处
benefit sb./sth.使某人/某物获益 benefit from...从„„中获益 have/get/receive the benefit of 得益于 for the benefit of...为了„„的利益 be of benefit to sb.对某人有益 beneficial adj.有益的,有利的
be beneficial to(=be of benefit to)对„„有益
①Do you really benefit from playing computer games every day? 你真的能从每天玩电脑游戏中获益吗?
②This project is of great benefit to everyone.这项工程对每个人都大有好处。
易混辨析benefit,interest,profit与advantage benefit为普通用词,指通过正当手段从物质或精神方面得到的任何好处或利益。它的复数形式benefits表示“救济金”;
interest作“利益”讲时,多用复数形式,既可指集团、群体的利益,又可指个人的利益。interest作不可数名词时,意为“利息”;
profit着重收益,尤指从物质、钱财等方面获得的利益;
advantage指因某方面占优势或利用某机会以及对方弱点而获得利益与好处。
①The interests of the individual must be subordinated to the interests of the collective.个人利益必须服从集体利益。
②All his wealth did not profit him.他所有的财富并没有使他受益。
她建议坐地铁去公园。
⑤I wouldn't recommend you to give up halfway.我不会劝你半途而废。
⑥Our English teacher often recommends that we(should)practise speaking English in and out of class.我们的英语老师经常劝告我们无论课堂内外都要练习说英语。
⑦The doctor suggested that he(should)try his best to lose weight from now on.医生建议他从现在开始尽力减肥。
⑧The bodyguards insisted that the president(should)keep away from the crowd for the sake of safety.出于安全考虑,警卫人员坚决要求总统远离人群。
⑨We suggest that students be sent abroad and stay there for two or three years.我们建议学生被送到国外并在那儿待上两三年。
特别提醒当suggest,insist不表示建议或坚持要某人做某事,而表示“暗示、表明”或“坚持认为”时,则用陈述语气。
She insisted that she was right.她坚持认为她是对的。
反馈4.1He's very wellconnected,so there's surely somebody to ______ him for a good job when he graduates.A.refer B.advise C.recommend D.insist 反馈4.2 It is politely requested by the hotel management that radios ______ after 11 o'clock at night.A.were not played B.not be played C.not to play D.did not play 反馈4.3The doctor recommended I ______ here ______ the sunshine before I started for home.A.came;to B.come;for C.would come;with D.will come;in 反馈4.4The young man insisted that he ______ nothing wrong and ______ free.A.did;set
D.determined;went;hoping 反馈5.2 A ______ and strongwilled man is what it takes to achieve the task.A.determining B.determined C.deciding D.decided 反馈5.3She was full of ______ to achieve her goals.A.idea B.determination C.patience D.responsibility 6.appeal vi.恳求,呼吁;有吸引力;上诉 n.呼吁;恳求 appeal to sb.for sth./to do sth.呼吁/ 要求/恳求某人做某事 appeal to sb.=attract sb.吸引/引起某人的兴趣 appeal against 为„„上诉;诉诸 appeal to the law 诉诸法律
appeal to the higher court 向高级法院提出上诉 appeal n.呼吁;恳求
make/launch an appeal to sb.向某人发出紧急呼吁 appealing adj.动人心弦的,有魅力的,有感染力的
①Martin Luther King appealed to the blacks to appeal to the highest court against racial discrimination,which raised great concern all over the world.马丁·路德·金呼吁黑人向最高法院提出上诉反对种族歧视,这引起了全世界极大的关注。
②Our English teacher's sense of humor appeals to every student in our class.我们英语老师的幽默感吸引了班里的每一位学生。③He appealed against the judge's decision.他不服法官判决而上诉。
④The teacher listened to his appeal.老师倾听了他的要求。⑤She appealed to us to go with her.她恳求我们和她同行。
反馈6.1The idea of working abroad,together with your proposals,never ______to me.A.attracts B.attract C.appeal D.appeals 反馈6.2 The Republican candidate ______ to the young people to vote for him and make a difference to the country.A.called B.requested C.asked D.appealed
⑤Even though/Though/Although I felt sorry for him,I was secretly pleased that he was having difficulties.虽然我为他感到惋惜,但对他的困难却暗自高兴。
⑥We thoroughly understand each other,even if/even though we don't always agree.我们彼此非常了解,虽然有时候也有一些分歧。
反馈8.1Many of them turned a deaf ear to his advice,______ they knew it to be valuable.A.as if B.now that C.even though D.so that 反馈8.2 ______ when everybody else objects to his suggestion,he won't feel upset.A.Even if B.Although C.As if D.Even 反馈8.3______ you disagree with her,her idea is still worth considering.A.If only B.Even if C.Instead of D.Despite of 9.figure out 计算出,想出,理解,弄清楚
①Even the repairman couldn't figure out what had gone wrong with the washer.连修理工也弄不明白这洗衣机出了什么毛病。
②I can't figure why they ridicule this constructive suggestion.我弄不懂他们为什么嘲笑这一建设性建议。
③Let's figure the expense first.我们先来算算费用吧。
反馈9The present situation is very complex,so I think it will take me some time to ______ its reality.A.make up B.figure out C.look through D.put off 10.get...across 讲清楚;渡过 用法拓展含有get的短语
get ahead of...领先
get along 进展,过活,相处 get away 逃掉 get away from...避免,摆脱,离开 get back 回来 get...back 收回,找回 get behind 落后 get down 记下来 get down to 认真做
get to know/love 逐渐地了解/爱上 get in 进来
反馈10.5 In China,nobody is to ______ with killing someone.A.get across B.get through C.get away D.get over
考点归纳拓展 【思路点拨】
1.1 D 根据was pleased to see it worked better可知这个男孩被劝服听朋友的话,故答案为D项。
1.2 A 句意:我试图说服她戒掉抽烟的习惯,但是她不听。try to persuade sb.to do sth.表示试图说服某人做某事,含有未能成功的意思,符合语境。
1.3 C 句意:我建议他不要抽烟,但是他没有听从我的建议。A项表示说服了他不抽烟,与后半句矛盾;advise sb.to do sth.建议某人做某事,符合语境,故C项正确。
1.4 B suggest sb.doing是唯一正确的搭配,意为“建议某人做某事”。
2.1 D 句意:如果你认为对女人好就意味着凡事都向她请示,那你恐怕就错了。mean to do sth.意为“打算做某事”;mean doing sth.意为“意味着做某事”,故选D项。
2.2 A 句意:她本意是想帮他,却反而让情况变糟了。mean to do意为“意欲做某事”。2.3 ①have ②has means意为“方式;方法”,单复数同形。当means由every修饰时,显然是单数,谓语用单数形式。如果means由all修饰则为复数,谓语用复数形式。
2.4 D 句意:旨在让那些低端就业的大学生获益,这个高科技项目有望创造1万个左右计算机编程和测试领域的就业岗位。the project和mean是被动关系,故应为meant;be meant to do是固定用法,为目的含义,故答案为D项。
2.5 B 句意:对于他来说,从艺是一种谋生手段。根据句意,stage 表示从艺,是一个抽象概念,其前不可以加不定冠词;means为单复数同形的名词,此处表示“一种方式”,用 a means of 表达。
3.1 A 句意:新的《劳动法》将使更多的人受益,特别是工人将从中受益。benefit sb.“使某人受益”;benefit from“从„„中受益”,故A项正确。
3.2 D 句意:跟上亚洲形势的发展会有帮助。beneficial “有益的”,符合题意。fortunate “幸运的”;dangerous “危险的”;safe“安全的”。
3.3 ①benefit ②advantage
3.4(1)for the benefit of(2)is beneficial to 4.1 C 句意:他很有关系,所以到毕业时肯定有人推荐他做一份好工作。recommend sb.for sth.为固定用法,意为“推荐某人某事物”,符合题意。
4.2 B 全句意思是:旅馆管理部门恳请客人晚上11点后不要打开收音机。句中的谓语动词request(请求)所引导的从句应当用虚拟语气,即动词原形或“should+动词原形”。本句的主语从句中,谓语应当用被动语态。所以,答案应为not be played。在上述这类句子中不能用动词过去时形式表示虚拟语气,所以A项不正确。not to play是动词带to的不定式,不能在句中作谓语。did not play也是动词play的过去时形式,同样不能在本句中作为
法还是值得考虑的。B make up“组成;化妆;编造”;figure out“理解;弄清楚”;look through“浏览”;put off“推迟”。句意:目前的形势非常复杂,因此我认为要花费我一些时间来弄清楚它的真实性。
10.1 A 此题考查以get为中心词的短语用法。get down to表示“开始认真对待”“开始认真考虑”。由题意可知应为“我们该认真对待我们的学习了”,故答案为A项。
10.2 A 句意:那座火山剧烈的喷发而山脚下的那个村庄竟然安然渡过危险。此处用come through表示“(安然渡过)危机,疾病等”。
10.3 A 考查动词短语的用法。get along“(勉强)生活;进展”;come on “开始”或用于祈使句表鼓励、催促等;watch out“当心,注意”;set off “动身;出发”。根据句意可知A项正确。
10.4 B A项意为“偶遇”;B项意为“克服(困难等)”;C项意为“来访”;D项意为“下车”。句意:如果我们能克服目前的困难,那么一切都会好起来的。
10.5 C 句意:在中国,没有人在杀了人的情况下能逃脱惩罚。get away with(doing)sth.意为“在犯了某罪的情况下逃脱惩罚”。
第三篇:2014高考英语完形填空黄金练44
2014高考英语完形填空黄金练44
I truly feel that my mother led me here,to Morzaine,and to my future as happy wife and bussinesswoman.When Mum21in October 2007,I was cook..In December that year.while Iwas working for a wedding,apearl neeklace Mum had left me22.I was distraught(忧心如焚的).Some days later,I was23that a guy who was working with us that day。“could prnhably have made a fortune24the neeklace he found.”25.he returnde it.Hearing he I’d26Mum for six months before her death,he said,”Christmas is going to be27—why not go out to the Alps for a couple of I come to M? ,a small ,friendly village in the Alps and___28_ fell in love with it.What was __29__to be a stopgap(权宜之计)trip turned into a new life.I kept travelling between London and here and felt _30__than I had in months.In December 2008 , I was __31_as a hotel manager and moved here full time.A month later, I met Paul, who was traveling here.We fell in love.In the beginning , I didn’t want to discuss___32__, because the sadness of losing Mum__33__felt great.Paul understood that and sever___34__me.But, by summer, we got married.A year later, we used his saving, and the money from the sale of Mom’s house, to build our own ___35__.We want to give our guests a ___36__ feel, so each room is themed(以„„为题)around memories from our lives.There are also style to remind me of Mom----a tiny chair which ___37___ be in her bedroom is set in one room.We are having a wonderful life Mum ___38___ naturally part of it, _39___ there’s no way we would be here.If it wasn’t for the __40__ she gave me.I know she’s here in spirit, keeping an eye on us.21.A.diedB.cameC.returnedD.visited
22.A.burnedB.disappearedC.brokeD.dropped
23.A.shownB.comfortedC.persuadedD.told
24.A.B.stealingC.sellingD.wearing 25.A.LucklyB.NaturallyC.SurelyD.Hopefully
26.A.nursedB.curedC.missedD.guarded
27.A.longB.hardC.merryD.free 28.A.suddenlyB.finallyC.nearlyD.immediately
29.A.saidB.provedC.supposedD.judged
30.A.smarterB.higherC.firuerD.lighter 31.A.phonnuredB.hiredC.regardedD.trained
32.A.travelB.businessC.childrenD.marriner
33.A.recentlyB.onceC.stillD.first
34.A.leftB.pushedC.surprisedD.interrupted
35.A.hotelB.restaurantC.homeD.shop
36.A.homelyB.livelyC.motherlyD.friendly
37.A.ought toB.used toC.mightD.could
38.A.takesB.keepsC.looksD.feels
39.A.unlessB.whileC.becauseD.though
40.A.B.chairC.houseD.neeklace
【答案】21-25ABDCA26-30ABDCD31-35BDCBA36-40ABDCD
I used to hate being called upon in class mainly because I didn’t like attention drawn to myself.And36otherwise assigned(指定)a seat by the teacher, I always37to sit at the back of the classroom.All this38after I joined a sports team.It began when a teacher suggested I try out for the basketball team.At first I thought it was a crazy39because I didn’t have a good sense of balance, nor did I have the40to keep pace with the others on the team and they would tease me.But for the teacher who kept insisting on my “41forit”, I wouldn’t have decided to give a try.Getting up the courage to go to the tryouts was only the42of it!When I first started43the practice sessions, I didn’t even know the rules of the game, much44what I was doing.Sometimes I’d get45and take a shot at the wrong direction—which made me feel really stupid.46, I wasn’t the only one “new” at the game, so I decided to47on learning the game, do my best at each practice session, and not be too hard on myself for the things I didn’t48
“just yet”.I practiced and practiced.Soon I knew the49and the “moves”.Being part of a team was fun and motivating.Very soon the competitive50in me was winning over my lack of confidence.With time, I learned how to play and made friends in the51— friends who respected my efforts to work hard and be a team player.I never had so much fun!
With my52self-confidence comes more praise from teachers and classmates.I have gone from“53”in the back of the classroom and not wanting to call attention to myself,54raising my hand— even when I sometimes wasn’t and not 100 percent55I had the right answer.Now I have more self-confidence in myself.36.A.asB.untilC.unlessD.though
37.A.hopedB.agreedC.meantD.chose
38.A.continuedB.changedC.settledD.started
39.A.ideaB.planC.beliefD.saying
40.A.rightB.chanceC.abilityD.patience
41.A.goingB.lookingC.cheeringD.applying
42.A.pointB.halfC.restD.basis
43.A.enjoyingB.preparingC.attendingD.watching
44.A.lessB.laterC.worseD.further 45.A.committedB.motivatedC.embarrassedD.confused
46.A.InterestinglyB.FortunatelyC.ObviouslyD.hopefully
47.A.focusB.actC.relyD.try
48.A.wantB.doC.supportD.know
49.A.stepsB.ordersC.rulesD.games
50.A.rolesB.partC.mindD.value
51.A.processB.operationC.movementD.situation
52.A.expressedB.improvedC.preservedD.recognized
53.A.dreamingB.playingC.relaxingD.hiding
54.A.byB.forC.withD.to
55.A.luckyB.happyC.sureD.satisfied
【答案】CDBACABCADBADCBABDDC
第四篇:高考英语完形填空复习教案
高考英语完形填空复习教学设计
教学设计
学习内容:高三完形填空复习学习目标:
一、语言技能目标: 能进一步强化基于信息词完形填空的能力 二、语言知识目标:能进一步强化信息词的了解。
三、学习策略、文化意识、情感态度价值观目标:能进一步强化基于信息词进行完形填空的策略。教学过程: step1:revison revise the skills when doing cloze: 解题思路:
一.跳读全文,辨体裁,抓大意。
1.把握开头,注意主题句,把握5w和1h,抓故事情节。力求首段把握文章主题。
2.根据每段信息词,概括每段大意。
3.注意尾段信息词所强调的中心,往往形成前后呼应。二.试填,找暗示,先易后难。
三.复核,通读全文,检查思路是否顺畅,有无逻辑错误,同时填补遗漏的难题。高考常考命题点: 1.复现:同词、同义、结构复现
2.关联关系:因果、并列(同类)、类属、相对(转折)关系 3.常识运用(背景知识、生活常识)4.固定搭配
step2:finding the informative words and understanding the main idea.1.style:narrative(记叙文)
2.ask a student to report the main idea of the passage.3.class work: discuss the main factors of this passage.who: an old man and i what: he was doing a language research by asking a saleswoman for a way many times.when: before my first year of university where: in a department store the result: the man became my university professor.group work: discuss the mistakes the students made.and:(1)which answer is correct?
(2)why?
(3)which point does it match with? 1.复现:同词、同义、结构复现 2.词义辨析
3.关联关系:因果、并列(同类)、类属、相对(转折)关系 4.常识运用(背景知识、生活常识)5.固定搭配
4.check the answers one by one.ask some groups to report,discussing with other groups or individual students or the whole class if necessary.5.in the meantime,show the passage on the screen and point out where we can get the information.step 3: conclusion t: what mistakes do you mainly make?
1、关联关系;
2、词义辨析;,step4: homework let’s do more exercise to consolidate.reflection and summary:
1、高考完型填空题型专题复习备考时,学生要随时跳出应试者的角色,改变角色,变应试者为故事剧中人的角色,联系语境,设身处地换位思考理解剧中人的思想情感去选出答案,或进一步变为出题人的角色,站在更高的角度,熟悉高考常考命题点,去把握本题型答题技巧,备考策略,可能会有意想不到的收获。
2、完形填空的短文通常没有标题且文章的首句和尾句,一般不设空,要特别注重对首、尾句的理解,因为它们往往提示或点明文章的主题,对理解全文有较大帮助。
3、第一遍通读带有空缺单词的短文时可能一时把握不住短文内容,弄 不清头绪,这是很正常的。此时要注意克服畏难情绪和急躁心理,应稳定情绪,再将短文读一、二遍,直到明确大意为止。
4、做题时切勿一看到一个空格就急着选出一个答案,这样往往只见树木不见树林。由于缺乏全局观念,极易导致连续选错。因为完形填空不同于单个句子的选词填空,其空白处是位于一篇文章之中,因此必须纵观全文、通篇考虑。
总之,做完形填空题,了其大意,先易后难,瞻前顾后,通过直接暗示、间接暗示,前、后暗示,层次、段落暗示,逻辑、推断暗示做题是非常关键的。当然,更重要的是扩大阅读面,增加阅读量,积累语言经验,培养语感能力。望大家反复认真阅读,对提高解答完形填空的能力大有裨益。
第五篇:高考数学专题复习讲练测——专题五 数列、数学归纳法 专题方法总结
专题方法总结
本专题由数列和数学归纳法两部分主要内容组成,它融代数、三角、几何于一体,性质多、技巧性强、方法灵活、应用广泛、综合能力要求高.等差、等比数列的运算和性质是本专题复习的重点,以等差、等比数列为载体的代数推理问题,数列的实际应用问题及数学归纳法的应用是难点,它们都是高考命题的热点;方程观点、等价转换、消元法、待定系数法是贯穿于本专题的重要数学思想和方法;运算能力、逻辑思维能力、分析问题和解决问题的能力是复习好本专题的基本要求.
1.关于等差、等比数列
(1)等差、等比数列的判定:①利用定义判定;②an+an+2=2an+1
anan+2=an+1(an≠0)
22{an}是等差数列,{an}{an}是等差数{an}是等比数列;③an=an+b(a,b为常数)是等差数列,Sn=an+bn(a,b为常数,Sn是数列{an}的前n项和)
列.
(2)等差、等比数列性质的应用:注意脚码、奇偶项的特点等.
(3)数列是定义域为自然数集(或自然数集的子集)的函数,即an=f(n)(n∈N).因此我们可运用函数的思想方法去研究处理数列问题.如等差数列当公差d≠0时的通项公式为n的一次函数,前n项和为n的二次函数,有关前n项和的最大、最小问题可运用二次函数的性质来解决.
2.关于一般数列
(1)已知数列的前n项和,求通项公式,这类问题常利用
S1(n=1),an= Sn-Sn-1(n≥2)求解.
(2)用递推公式给出来的数列,常利用“归纳—猜想—证明”的方法求解.
3.关于数列的求和
(1)公式法:①等差、等比数列的前n项和公式;②自然数的方幂和公式.
(2)错位相减法.
(3)倒序相加法.
(4)裂(拆)项法.
4.关于数学归纳法
(1)数学归纳法的原理.
(2)数学归纳法的应用:①证明与自然数有关的恒等式;②用数学归纳法证明不等式;③用数学归纳法证明整除性问题.
(3)归纳—猜想—证明.