【高考领航】(课标版)2015届高三一轮复习 辅导与测试 第2部分 第5讲 专题创新演练

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高三一轮复习辅导与测试:第2部分-第6讲

高三一轮复习辅导与测试:第2部分-第6讲
核心考点解读
专题创新演练
微课助学
第二部分 语法专题讲座
第六讲
非谓语动词
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ONTENTS
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核心考点解读 专题创新演练 微 课 助 学
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不定式
不定式由“to+动词原形”构成,否定形式是“not+to+动词原 形”,复合结构是“for+sb.+to+动词原形”。不定式后可以带宾语 或状语构成不定式短语,没有人称和数的变化,但有时态和语态的变 化。不定式可充当除谓语之外的所有句子成分。不定式作主语或宾语 时可用it作形式主语或形式宾语。
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不定式
2.不定式作状语 不定式作状语可表示目的、原因、结果等。 (1)不定式作目的状语往往是高考命题的重点。为了加以强调,有时可 把不定式放在句首,或在其前加上in order或so as。 In order to arrive before dark,we started early.为了在天黑前到达,我们 很早就动身了。(不定式表示目的)
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(2)不定式和动名词都可作主语。动名词多表示一般的、抽象的、泛指 的概念或一个已经完成了的动作,强调的是事情本身。而不定式则表 示具体的某一次行为或将来的动作,强调的是动作本身,不过有时二 者之间的区别很小。 Collecting stamps can enlarge one's knowledge. 集邮可以扩大知识面。 Smoking is not allowed here.此地禁止吸烟。 To look after these naughty boys is really difficult. 照看这些淘气的孩子真难。 To teach the three children is my job this afternoon. 今天下午教这三个孩子是我的工作。

2015年高考文数二轮复习讲练测专题05立体几何(测)(原卷版)

2015年高考文数二轮复习讲练测专题05立体几何(测)(原卷版)

总分 150分时间 120分钟班级 _______ 学号 _______ 得分_______ (一)选择题(12*5=60分)1. 【广东省阳江市阳东县阳东一中、广雅中学2015届高三第一次,文5】一个几何体的三视图如图所示,其中正视图与侧视图都是底边长为6、腰长为5的等腰三角形,则这个几何体的侧面积为().A. B. C. D.2. 【广东实验中学2015届高三上学期第一次阶段考试数学,文8】已知直线平面,直线平面,则“”是“”的()A.充要条件B.必要不充分条件C.充分不必要条件D.既不充分又不必要条件3. 【江西省抚州市临川一中2015届高三10月月考,文7】在正四面体P﹣ABC中,D,E,F 分别是AB,BC,CA的中点,下面四个结论中不成立的是()A.BC∥平面PDF B.DF⊥平面PAEC.平面PDF⊥平面ABC D.平面PAE⊥平面ABC4. 【江西省抚州市临川一中2015届高三10月月考,文9】已知一个空间几何体的三视图如图所示,其中俯视图是边长为6的正三角形,若这个空间几何体存在唯一的一个内切球(与该几何体各个面都相切),则这个几何体的全面积是()A.18 B.36 C. 45 D.545. 【内蒙古一机一中2015届高三上学期期中考试,文6】如图,三棱柱中,侧棱垂直底面,底面三角形是正三角形,是中点,则下列叙述正确的是()。

A.与是异面直线B.C.是异面直线,且D.6. 【浙江省嘉兴市第一中学2015届高三上学期期中考试,文3】已知为一条直线,为两个不同的平面,则下列说法正确的是()A.若B.若则C.若D. 若7. 【四川省成都外国语学校2015届高三11月月考,文3】某几何体正视图与侧视图相同,其正视图与俯视图如图所示,且图中的四边形都是边长为2的正方形,正视图中两条虚线互相垂直,则该几何体的体积是()A.B.6 C.4 D.8. 【河南省名校2015届高三上学期期中数学,文8】某几何体的三视图如图所示,且该几何体的体积是3,则正视图中的x的值是()A.2 B.C. D.39. 【广东省韶关市十校2015届高三10月联考,文8】已知为异面直线,平面,平面,,则直线()A. 与都相交B. 与都不相交C. 与中至少一条相交D. 至多与中的一条相交10. 【辽宁师范大学附属中学2015届高三上学期期中考试,文9】一个几何体的三视图如图所示,其中主视图和左视图是腰长为4的两个全等的等腰直角三角形,若该几何体的所有顶点在同一球面上,则该球的表面积是( ).A.12π B.24π C.32π D.48π11. 【江西省六校2015届高三上学期第一次联考,文4】某空间几何体的三视图如图所示,则此几何体的体积为()A.有最小值2 B.有最大值2C.有最大值6 D.有最大值412. 【四川省成都实验外国语高2015届高三11月月考,文7】在正方体ABCD-A1B1C1D1中,点P在线段AD1上运动,则异面直线CP与BA1所的θ角的取值范围是( )A. B. C.D.(二)填空题(4*5=20分)13.【南昌二中2014—2015学年度上学期第四次考试高三数学试卷】是正三角形ABC的斜二测画法的水平放置直观图,若的面积为,那么的面积为.14.【河南省实验中学2015届高三上学期期中考试,文15】已知在四面体中,分别是的中点,若,则与所成的角为15.【内蒙古一机一中2015届高三上学期期中考试,文16】如图,正方体的棱长为1,C,D 分别是两条棱的中点,A,B,M是顶点,那么点M到面ABCD的距离是__________________16.【四川省成都市新都一中2015届高三10月考,文11】在棱长为1的正方体ABCD﹣A1B1C1D1中,点M和N分别是矩形ABCD和BB1C1C的中心,则过点A、M、N的平面截正方体的截面面积为_________ .三、解答题题(6*12=72分)18.【四川省泸州市2015届高三上学期第一次教学质量诊断性考试,文】如图,在四棱锥P -ABCD中,AB∥ CD,AB⊥AD,CD=2AB,平面PAD⊥底面ABCD,PA⊥AD. E和F分别是CD和PC的中点.求证:(1)PA⊥底面ABCD;(2)BE∥平面PAD;(3)平面BEF⊥平面PCD.19.【湖南省衡阳市2015届高三上学期五校联考,文18】如图,在底面为菱形的四棱锥中,,为的中点,,(1)求证:平面(2)求与面所成角的正弦值20.【河南省中原名校2015届高三上学期第一次摸底考试,文19】如图,直三棱柱中,D,E 分别是AB,的中点(I)证明:;(Ⅱ)设,求三棱锥的体积22.【浙江省嘉兴市第一中学2015届高三上学期期中考试,文21】已知正方形的边长为,.将正方形沿对角线折起,使,得到三棱锥,如图所示.(1) 当时,求证:;(2) 当二面角的大小为时,求AB与平面BCD所成角的正弦值.。

【高考领航】2015届高考数学新一轮总复习 12.2 数系的扩充与复数的引入基础盘点系统化AB演练

【高考领航】2015届高考数学新一轮总复习 12.2 数系的扩充与复数的引入基础盘点系统化AB演练

【高考领航】2015届高考数学新一轮总复习 12.2 数系的扩充与复数的引入基础盘点系统化AB 演练 理A 组 基础演练1.(2013·某某)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 .第四象限解析:由条件知:z =1-2i ,其在复平面内对应的点为(1,-2),在第四象限,选D. 答案:D2.(2013·某某)已知i 是虚数单位,则(-1+i)(2-i)=( )A .-3+iB .-1+3iC .-3+3iD .-1+i解析:(-1+i)(2-i)=-1+3i ,选B. 答案:B3.(2013·某某)复数z 满足(z -3)(2-i)=5(i 为虚数单位),则z 的共轭复数z 为( )A .2+iB .2-iC .5+iD .5-i解析:由题意得z =52-i +3=52+i2-i 2+i +3=5+i ,∴z =5-i ,故选D. 答案:D4.(2013·某某)复数z =1i -1的模为( )A.12B.22C.2D .2解析:z =1i -1=i +1i +1i -1=1+i -1-1=-12-12i.|z |=⎝ ⎛⎭⎪⎫-122+⎝ ⎛⎭⎪⎫-122=22,故选B. 答案:B5.(2013·某某)若复数z 满足i z =2+4i ,则在复平面内,z 对应的点的坐标是( ) A .(2,4) B .(2,-4) C .(4,-2) D .(4,2)解析:由已知条件得z =2+4ii =4-2i ,所以z 对应的点的坐标为(4,-2),故选C.答案:C6.(2013·课标全国Ⅰ)1+2i1-i2= ( )A .-1-12iB .-1+12iC .1+12iD .1-12i解析:1+2i 1-i 2=1+2i-2i=1+2i i -2i i =-2+i 2=-1+12i ,故选B.答案:B7.(2013·某某)i 为虚数单位,设复数z 1,z 2在复平面内对应的点关于原点对称,若z 1=2-3i ,则z 2=________.解析:在复平面内,复数z =a +b i 与点(a ,b )一一对应. ∵点(a ,b )关于原点对称的点为(-a ,-b ), 则复数z 2=-2+3i. 答案:-2+3i8.(2013·某某)已知a ,b ∈R ,i 是虚数单位.若(a +i)·(1+i)=b i ,则a +b i =________.解析:∵(a +i)(1+i)=a +a i +i +i 2=(a -1)+(a +1)i.又由已知(a +i)(1+i)=b i ,得⎩⎪⎨⎪⎧a -1=0,a +1=b .解得a =1,b =2,所以a +b i =1+2i.答案:1+2i9.(2013·某某)设z =(2-i)2(i 为虚数单位),则复数z 的模为________.解析:∵z =(2-i)2=3-4i , ∴|z |=32+-42=5.答案:5B组能力突破1.(2013·)在复平面内,复数(2-i)2对应的点位于( ) A.第一象限 B.第二象限C.第三象限 D.第四象限解析:(2-i)2=4-4i+i2=3-4i,对应的点为(3,-4),位于第四象限,故选D.答案:D2.(2013·某某)设z1,z2是复数,则下列命题中的假命题是( ) A.若|z1-z2|=0,则z1=z2B.若z1=z2,则z1=z2C.若|z1|=|z2|,则z1·z1=z2·z2D.若|z1|=|z2|,则z21=z22解析:A中,|z1-z2|=0,则z1=z2,故z1=z2成立.B中,z1=z2,则z1=z2成立.C中,|z1|=|z2|,则|z1|2=|z2|2,即z1z1=z2z2,C 正确.D不一定成立,如z1=1+3i,z2=2,则|z1|=2=|z2|,但z21=-2+23i,z22=4,z21≠z22.答案:D3.(2013·某某)已知集合M={1,2,z i},i为虚数单位,N={3,4},M∩N={4},则复数z =( ) A.-2i B.2iC.-4i D.4i解析:由M∩N={4}知4∈M,所以z i=4,z=-4i,选C.答案:C4.(2013·某某)设i是虚数单位,z是复数z的共轭复数.若z·z i+2=2z,则z=( ) A.1+i B.1-iC.-1+i D.-1-i解析:设z=a+b i(a,b∈R),则z·z i+2=(a+b i)·(a-b i)·i+2=2+(a2+b2)i,故2=2a,a2+b2=2b,解得a=1,b=1.∴z=1+i. 答案:A。

高三一轮复习辅导与测试:第2部分-第11讲

高三一轮复习辅导与测试:第2部分-第11讲
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社会交往
二、道歉、遗憾和应答(Apologies,regrets,sympathies&responses) 1.道歉场合很多,用语也很多。有时候,在一些特殊情况下,我们也 得考虑要求别人为某人或某事道歉。比如我们有时觉得朋友受到不公 正待遇时,可以理直气壮地向对方说:“I'm sorry,but I have to say that you owe my friend an apology./Apologize to him for your rudeness.”
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(2)I'm sorry,you can't./I'm sorry,but... -Can I come and have a look at your new house? -Yes,by all means! ——我能来看一下你的新房子吗? ——行,无论何时都行!
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态度和情感
一、态度 1.同意和不同意(Agreement and disagreement) 熟悉中、英两种文化差异,掌握两个不同民族的交际习惯方式对做题 很有帮助。 (1)表示同意的常用表达 Certainly(Sure/Of course)./No problem. By all means./That's a good idea.

高三一轮复习辅导与测试:第2部分-第3讲

高三一轮复习辅导与测试:第2部分-第3讲

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形容词和副词的基本用法
(2)副词的作用 副词在句中作状语、表语、定语和宾语补足语。 I worked in Beijing almost for three years.(状语) Time is up.(表语) The building there looks very grand.(定语) Let the dog out.(宾语补足语)
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形容词和副词的基本用法
3.副词的基本用法 (1)副词的分类 副词一般分为时间、地点、方式、程度、疑问、关系、连接副词等。 ①时间副词。如:now,usually,often,always 等。 ②地点副词。如:here,there,out,everywhere 等。 ③方式副词。如:hard,well,fast,slowly 等。 ④程度副词。如:very,much,still,almost 等。 ⑤疑问副词。如:how,when,why,where 等。 ⑥关系副词。如:when,where,why 等。 ⑦连接副词。如:whether,why,when,how 等。
点津 有些副词置于句首可修饰全句,作评注性状语。
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跟踪训练
用所给词的适当形式填空 1.(2013· 课标Ⅰ卷改编)Tony can hardly boil an egg , still________cook dinner.(little)

高三一轮复习辅导与测试:第2部分-第9讲

高三一轮复习辅导与测试:第2部分-第9讲

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并列句
2.表示选择关系:常用的并列连词有or,either...or...,otherwise等。 Either you are right,or I am. 要么你对,要么我对。 Don't drive so fast or/otherwise you'll have an accident. 不要开那么快,否则你会出事的。
3.表示转折关系:常用的并列连词有but,yet,whereas,while等。 Jane said she was ill,yet I saw her in the street just now. 简说她病了,但刚才我在街上看到了她。 Some men are rich,while/whereas others are poor. 一些人很富有但其他人很贫穷。
解析: or。句意:在你关闭所有的
程序之前不要关掉电脑,否 则可能会出现问题。此处or
表示“否则”。
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时间状语从句
一、when,while与as引导的时间状语从句 1.when,while与as引导时间状语从句的区别
连词 when
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4.说明因果关系:常用的并列连词有so,for。 It must have rained last night for it is wet all over. 昨晚一定下雨了,到处都这么湿。 The shops were closed so I didn't get any milk. 商店都关门了,所以我没买到牛奶。 5.when还可用作并列连词,其意义为“那时,这时”,相当于and at

【高考领航】(课标版)2015届高三英语一轮复习辅导与测试 第1部分 Unit 4 Astronom

【高考领航】(课标版)2015届高三英语一轮复习辅导与测试 第1部分 Unit 4 Astronom

Astronomythe science of the stars Ⅰ.阅读理解A(2014·湖南十校联考)Fernando and I were arguing about why I never took any real vacations.When he suggested we go off somewhere for three entire weeks,“You decide.〞 I said.He chose a little fishing village off the coast and he planned out a schedule.Our trip was full of wonder and fun,but when we got there,the shabby hotel failed to satisfy us,so we left a day early for the beach.As we drove,we passed two orphanages(孤儿院).Christmas was only a few days away,and I felt that I should stop to do something for the children.Then Fernando came up with a plan to help the poor children we saw.We made a list of names,and then we went into town to buy new clothes,toys,and school supplies.For the rest of the day,we filled backpacks.We were excited about the celebration we had planned for the next day,December 26,when we'd invite the families to the beach in front of the hotel and hand out the presents.Fernando and I were still in bed at around 9∶00 the next morning when we heard a cracking sound.“What is that?〞 I asked.As if in response,water started pouring into our room.The children's backpacks we had arranged so neatly on the floor began floating around.The next thing I knew was that the roof was torn off,and Fernando and I were swept out.I thought I was going to die.Under the water,I forced myself to calm down and then I popped out.Suddenly I saw Fernando only four feet away.“What just happened?〞 I asked Fernando.“Tsunami(海啸)!〞he shouted to me.“Just be strong.Whatever it was,〞 he told me,“it's all over now.〞 But a few seconds later,another wave buried us.I triedto grab him as he reached out to me,but he fell back under the water,and I never saw him again.1.What can we learn about the trip?A.Fernando often argued with the author about their trips.B.The author chose a little fishing village off the coast.C.They would stay in the orphanages for Christmas Day.D.Their trip was satisfying at the beginning.2.The author and Fernando left for the beach early because________.A.they were afraid of being lateB.the hotel disappointed themC.they wanted to be there ahead of othersD.they wanted to do something for the children3.When did the author go for the vacation?A.A few days before Christmas.B.Three weeks after Christmas.C.On Christmas Day.D.At 9∶00 on December 26.4.What do you think the author would continue to write about?A.How his trip was ruined.B.When Fernando came back to him.C.How he survived.D.Why the disaster happened.B(2014·陕西五校二模)The world is filled with smart,educated and gifted people.We meet them every day.A few days ago,my car was not running well.I pulled it into a garage and the young mechanic fixed it in just a few minutes.He knew what was wrong by simply listening to the engine sound.I was amazed.The sad truth is that great talent is not enough.I am constantly shocked at how little talented people earn.I heard the other day that less than 5 percent of Americans earn more than $ 100,000 a year.A business consultant who specializes in the medical trade told me how many doctors and dentists struggle financially.It was this business consultant who gave me the phrase,“They are one skill away from great wealth.〞There is an old saying that goes,“JOB means ‘Just Over Broke’〞.Andunfortunately,I would say that the saying applies to millions of people.Because schools do not think financial intelligence is intelligence,most workers “live_within_their_means〞.They work and they pay the bills.Instead I recommend that young people seek work for what they will learn,more than what they will earn.When I ask the classes I teach,“How many of you can cook a better hamburger than McDonald's?〞 almost all the students raise their hands.I then ask,“So if most of you can cook a better hamburger,how come McDonald's makes more money than you?〞 The answer is obvious:McDonald's is excellent at business systems.The world is filled with talented poor people.They focus on perfecting their skills at building a better hamburger rather than the skills of selling and delivering the hamburger.5.The author mentions the mechanic in the first paragraph to show that________.A.he is just one of the talented peopleB.he is ready to help othersC.he has a sharp sense of hearingD.he knows little about car repairing6.The underlined part in the third paragraph can be best replaced by“________〞.A.spend more than they can affordB.do in their own wayC.live in their own circleD.live within what they earn7.Why do talented people earn so little according to the author?A.They don't work hard enough.B.They lack financial intelligence.C.They don't make full use of their talents.D.They have no specialized skills.8.The main purpose of the author is to tell us________.A.how young people can find a satisfactory jobB.what schools should teach about financeC.why so many talented people are poorD.how McDonald's makes much moneyⅡ.七选五补缺题Raising Confident KidsSelfesteem(自尊)is a collection of beliefs or feelings we have aboutourselves.Having a healthy selfesteem can protect us through difficult times and help us remain focused on what is important to us.Research shows that children with high selfesteem grow up to be more confident adults.Selfesteem building should start young.__1__Praise actionsYoung children need feedback.It's how they measure their actions and it plays a role in learning from experience.Provide specific praise about actual actions performed and efforts made in the process.__2__Identify strengthsPreschoolers are always watching each other.On the bright side,they learn new things from each other.On the other side,they can become selfcritical when they see a peer accomplishing something they still struggle to do.__3__Tell your child to focus on his strengths when he starts to draw comparisons.Foster(培养)a sense of belongingYoung children may not understand how peer pressure(同龄人的压力)works,but they feel it when they're being excluded(排除).Show your children that they are important by listening to and responding to their needs and ideas.As much as possible,save grownup conversations for later so that you can have family conversations.__4__ __5__As much as they need us,they also need to work on taking small steps towards independence.When they know they can do things,they feel more confident.Teach problem solving skills.Step back and let them work on challenges before jumping in to help.Help by asking,“How can we do this in a different way?Let's come up with some ideas together.〞 Getting kids involved in problem solving teaches them how to deal with challenges in the future.Building and maintaining healthy selfesteem can be a lifelong process,but the sooner you start,the more confident your children will become.A.Encourage IndependenceB.Spend quality time with childrenC.Try to address their concerns as they arise,no matter how minor.D.If praise is only attached to success,kids will foc us on “winning〞.E.Be sure to point out your child's strengths regularly and be specific.F.Below are some tips to help you promote your children's selfesteem.G.Each parent has the responsibility to help children to become confident.Ⅲ.短文改错A man in Hamburg,Germany,kept getting phone,but when he picked up a receiver there was no one on the other end of the phone.To begin with,he paid the phone company block the number.Therefore,it was expensive just as to stop one call,so he phoned the police.The police soon tracked the calls to a barber shop.Which happened was that every time someone paid for the haircut by credit card,the credit card machine dialed the wrong number in mistake.It was quite beyond the police why somebody at the barber's or the credit card company noticed the problem.Fortunately,there had a happy outcome and the barber's credit card phone was reprogrammed.详解答案课时训练(十四)Ⅰ.阅读理解A【语篇解读】本文为一篇记叙文。

【创新设计】2015届高考数学一轮复习(基础+提升)第8篇 第5讲 椭 圆精品课时训练 北师大版

【创新设计】2015届高考数学一轮复习(基础+提升)第8篇 第5讲 椭 圆精品课时训练 北师大版

第5讲 椭 圆基础巩固题组 (建议用时:40分钟)一、选择题1.已知△ABC 的顶点B ,C 在椭圆x 23+y 2=1上,顶点A 是椭圆的一个焦点,且椭圆的另外一个焦点在BC 边上,则△ABC 的周长是( ). A .2 3 B .6 C .4 3D .12解析 由椭圆的定义知:|BA |+|BF |=|CA |+|CF |=2a (F 是椭圆的另外一个焦点),∴周长为4a =4 3. 答案 C2.(2014·某某模拟)椭圆x 29+y 24+k =1的离心率为45,则k 的值为( ).A .-21B .21C .-1925或21D.1925或21 解析 若a 2=9,b 2=4+k ,则c =5-k ,由c a =45,即5-k 3=45,解得k =-1925; 若a 2=4+k ,b 2=9,则c =k -5,由c a =45,即k -54+k =45,解得k =21. 答案 C3.(2014·某某模拟)已知椭圆x 210-m +y 2m -2=1,长轴在y 轴上.若焦距为4,则m 等于( ).A .4B .5C .7D .8解析 将椭圆的方程转化为标准形式为y 2m -22+x 210-m2=1,显然m -2>10-m ,即m >6,且(m -2)2-(10-m )2=22,解得m =8. 答案 D4.(2014·西工大附中模拟)一个椭圆中心在原点,焦点F 1,F 2在x 轴上,P (2,3)是椭圆上一点,且|PF 1|,|F 1F 2|,|PF 2|成等差数列,则椭圆方程为( ). A.x 28+y 26=1 B.x 216+y 26=1 C.x 28+y 24=1 D.x 216+y 24=1 解析 设椭圆的标准方程为x 2a 2+y 2b 2=1(a >b >0).由点(2,3)在椭圆上知4a 2+3b2=1.又|PF 1|,|F 1F 2|,|PF 2|成等差数列, 则|PF 1|+|PF 2|=2|F 1F 2|,即2a =2·2c ,c a =12,又c 2=a 2-b 2,联立解得a 2=8,b 2=6. 答案 A5.(2013·某某卷)已知椭圆C :x 2a 2+y 2b2=1(a >b >0)的左焦点为F ,C 与过原点的直线相交于A ,B 两点,连接AF ,BF .若|AB |=10,|BF |=8,cos ∠ABF =45,则C 的离心率为( ).A.35B.57C.45D.67解析 如图,设|AF |=x ,则cos ∠ABF =82+102-x 22×8×10=45.解得x =6,∴∠AFB =90°,由椭圆及直线关于原点对称可知|AF 1|=8,∠FAF 1=∠FAB +∠FBA =90°,△FAF 1是直角三角形,所以|F 1F |=10,故2a =8+6=14,2c =10,∴c a=57. 答案 B 二、填空题6.(2014·某某模拟)设椭圆x 2m 2+y 2n2=1(m >0,n >0)的右焦点与抛物线y 2=8x 的焦点相同,离心率为12,则此椭圆的方程为________.解析 抛物线y 2=8x 的焦点为(2,0),∴m 2-n 2=4①,e =12=2m ,∴m =4,代入①得,n2=12,∴椭圆方程为x 216+y 212=1.答案x 216+y 212=1 7.已知F 1,F 2是椭圆C :x 2a 2+y 2b2=1(a >b >0)的两个焦点,P 为椭圆C 上的一点,且PF 1→⊥PF 2→.若△PF 1F 2的面积为9,则b =________. 解析 由题意知|PF 1|+|PF 2|=2a ,PF 1→⊥PF 2→, ∴|PF 1|2+|PF 2|2=|F 1F 2|2=4c 2, ∴(|PF 1|+|PF 2|)2-2|PF 1|·|PF 2|=4c 2, ∴2|PF 1|·|PF 2|=4a 2-4c 2=4b 2. ∴|PF 1|·|PF 2|=2b 2,∴S △PF 1F 2=12|PF 1|·|PF 2|=12×2b 2=b 2=9.∴b =3. 答案 38.(2013·某某卷)椭圆Γ:x 2a 2+y 2b2=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F 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________.解析 因为直线y =3(x +c )过椭圆左焦点,且斜率为3,所以∠MF 1F 2=60°,∠MF 2F 1=30°,∠F 1MF 2=90°, 故|MF 1|=c ,|MF 2|=3c 由点M 在椭圆上知,c +3c =2a . 故离心率e =c a=23+1=3-1.答案3-1三、解答题9.已知椭圆的两焦点为F 1(-1,0),F 2(1,0),P 为椭圆上一点,且2|F 1F 2|=|PF 1|+|PF 2|.(1)求此椭圆的方程;(2)若点P 在第二象限,∠F 2F 1P =120°,求△PF 1F 2的面积.解 (1)依题意得|F 1F 2|=2, 又2|F 1F 2|=|PF 1|+|PF 2|,∴|PF 1|+|PF 2|=4=2a .∴a =2,c =1,b 2=3. ∴所求椭圆的方程为x 24+y 23=1.(2)设P 点坐标为(x ,y ), ∵∠F 2F 1P =120°,∴PF 1所在直线的方程为y =(x +1)·tan 120°, 即y =-3(x +1).解方程组⎩⎪⎨⎪⎧y =-3x +1,x 24+y 23=1,并注意到x <0,y >0,可得⎩⎪⎨⎪⎧x =-85,y =335.∴S △PF 1F 2=12|F 1F 2|·335=335.10.(2014·某某模拟)如图,椭圆x 2a 2+y 2b2=1(a >b >0)的左、右焦点分别为F 1(-c,0),F 2(c,0).已知点M ⎝⎛⎭⎪⎫3,22在椭圆上,且点M 到两焦点距离之和为4. (1)求椭圆的方程;(2)设与MO (O 为坐标原点)垂直的直线交椭圆于A ,B (A ,B 不重合),求OA →·OB →的取值X 围.解 (1)∵2a =4,∴a =2, 又M ⎝ ⎛⎭⎪⎫3,22在椭圆上, ∴34+12b2=1,解得b 2=2, ∴所求椭圆方程x 24+y 22=1.(2)由题意知k MO =66,∴k AB =- 6. 设直线AB 的方程为y =-6x +m ,联立方程组⎩⎪⎨⎪⎧x 24+y 22=1,y =-6x +m ,消去y ,得13x 2-46mx +2m 2-4=0,Δ=(46m )2-4×13×(2m 2-4)=8(12m 2-13m 2+26)>0,∴m 2<26,设A (x 1,y 1),B (x 2,y 2),由根与系数的关系得x 1+x 2=46m 13,x 1x 2=2m 2-413,则OA →·OB →=x 1x 2+y 1y 2=7x 1x 2-6m (x 1+x 2)+m 2=3m 2-2813∈⎣⎢⎡⎭⎪⎫-2813,5013.∴OA →·OB →的取值X 围是⎣⎢⎡⎭⎪⎫-2813,5013.能力提升题组 (建议用时:25分钟)一、选择题1.(2014·某某模拟)已知椭圆:x 24+y 2b2=1(0<b <2),左、右焦点分别为F 1,F 2,过F 1的直线l 交椭圆于A ,B 两点,若|BF 2|+|AF 2|的最大值为5,则b 的值是( ). A .1 B. 2 C.32D. 3解析 由题意知a =2,所以|BF 2|+|AF 2|+|AB |=4a =8,因为|BF 2|+|AF 2|的最大值为5,所以|AB |的最小值为3,当且仅当AB ⊥x 轴时,取得最小值,此时A ⎝ ⎛⎭⎪⎫-c ,32,B ⎝⎛⎭⎪⎫-c ,-32,代入椭圆方程得c 24+94b 2=1,又c 2=a 2-b 2=4-b 2,所以4-b 24+94b 2=1,即1-b 24+94b 2=1,所以b 24=94b 2,解得b 2=3,所以b = 3.答案 D2.设F 1,F 2是椭圆E :x 2a 2+y 2b 2=1(a >b >0)的左、右焦点,P 为直线x =3a2上一点,△F 2PF 1是底角为30°的等腰三角形,则E 的离心率为( ). A.12 B.23 C .34 D.45解析令c =a 2-b 2.如图,据题意,|F 2P |=|F 1F 2|,∠F 1PF 2=30°,∴∠F 1F 2P =120°, ∴∠PF 2x =60°,∴|F 2P |=2⎝ ⎛⎭⎪⎫3a 2-c =3a -2c . ∵|F 1F 2|=2c ,∴3a -2c =2c ,∴3a =4c ,∴c a =34,即椭圆的离心率为34.答案 C 二、填空题3.(2014·某某五校联考)椭圆x 2a 2+y 25=1(a 为定值,且a >5)的左焦点为F ,直线x =m 与椭圆相交于点A ,B .若△FAB 的周长的最大值是12,则该椭圆的离心率是________. 解析设椭圆的右焦点为F ′,如图,由椭圆定义知,|AF |+|AF ′|=|BF |+|BF ′|=2a . 又△FAB 的周长为|AF |+|BF |+|AB |≤|AF |+|BF |+|AF ′|+|BF ′|=4a , 当且仅当AB 过右焦点F ′时等号成立. 此时4a =12,则a =3.故椭圆方程为x 29+y 25=1,所以c =2,所以e =c a =23.答案 23三、解答题4.(2014·某某省三市调研)已知圆G :x 2+y 2-2x -2y =0经过椭圆x 2a 2+y 2b2=1(a >b >0)的右焦点F 及上顶点B .过椭圆外一点M (m,0)(m >a )作倾斜角为56π的直线l 交椭圆于C ,D 两点.(1)求椭圆的方程;(2)若右焦点F 在以线段CD 为直径的圆E 的内部,求m 的取值X 围. 解 (1)∵圆G :x 2+y 2-2x -2y =0经过点F ,B , ∴F (2,0),B (0,2), ∴c =2,b =2,∴a 2=b 2+c 2=6,椭圆的方程为x 26+y 22=1.(2)由题意知直线l 的方程为y =-33(x -m ),m >6, 由⎩⎪⎨⎪⎧x 26+y 22=1,y =-33x -m ,消去y ,得2x 2-2mx +(m 2-6)=0. 由Δ=4m 2-8(m 2-6)>0, 解得-23<m <2 3. ∵m >6,∴6<m <2 3. 设C (x 1,y 1),D (x 2,y 2), 则x 1+x 2=m ,x 1x 2=m 2-62,∴y 1y 2=⎣⎢⎡⎦⎥⎤-33x 1-m ·⎣⎢⎡⎦⎥⎤-33x 2-m =13x 1x 2-m 3(x 1+x 2)+m 23.∵FC →=(x 1-2,y 1).FD →=(x 2-2,y 2),∴FC →·FD →=(x 1-2)(x 2-2)+y 1y 2=43x 1x 2-m +63(x 1+x 2)+m 23+4=2m m -33.∵点F 在圆E 内部, ∴FC →·FD →<0, 即2mm -33<0,解得0<m <3.又6<m<23,∴6<m<3.故m的取值X围是(6,3).。

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【高考领航】(课标版)2015届高三一轮复习辅导与测试第2部分第5讲专题创新演练Ⅰ.用所给词的适当形式填空1.—Is your mother still teaching at No.3 Middle School?—Yes,she’ll retire in three years.And she________at the school for thirty years.(teach)解析:has been teaching。

考查现在完成进行时。

句意:——你母亲还在第三中学教学吗?——是的,她还要三年才退休。

她已经在这个学校教了30年了。

此处表示从过去某一时间开始一直延续到现在的动作,并且有可能持续下去,故用现在完成进行时。

2.This year,many parts of our country________by the heat.(affect)解析:are affected。

考查被动语态。

句意:今年我们国家的大部分地区都受到了高温的影响。

many parts of our country与affect之间是动宾关系,同时从时间状语This yea r 可知此处应用一般现在时的被动语态。

3.—Did Jack join you in riding bikes yesterday?—No,he________.(invite)解析:wasn’t invited。

考查时态与语态。

句意:——Jack昨天参加你们骑自行车的活动了吗?——没有,他没被邀请。

由时间状语yesterday可知,此处表示过去,且he与invite 之间为动宾关系,故用一般过去时的被动语态。

4.A huge playground,which they hope to complete next year,________here.(build) 解析:is being built。

考查现在进行时。

句意:这里正在建一个大操场,他们期望明年竣工。

根据句意可知,此处表示操场正在被建,故用现在进行时的被动语态。

5.Some timely help and information ________ since an earthquake happened to Zhang County,Gansu Province.(offer)解析:have been offered。

考查时态与语态。

句意:自从甘肃漳县发生地震以来,及时的援助和信息已被提供。

since所在的句子用一般过去时,主句则用现在完成时。

同时由于some timely help and information与offer之间是动宾关系,故用现在完成时的被动语态。

6.Both the US and Europe________experiments of this kind well before the Second World War.(conduct)解析:had conducted。

考查过去完成时。

句意:在二战之前美国和欧洲就已经把这种实验做得很好了。

the Second World War是一个过去时间,在二战之前表示过去的过去,要用过去完成时。

7.Nowadays with the development of science and technology,more a nd more new techniques ________ to the fields of IT.(introduce)解析:are being introduced。

考查时态与语态。

句意:现在,随着科技的发展,越来越多的新技术正在被引入到IT领域。

more and more new techniques与introduce之间是动宾关系;同时题目讲的是目前正在发生的一种状况,故用一般现在时的被动语态。

8.You are great!More practice and you________your oral English.(improve)解析:will improve。

考查一般将来时。

句意:你很棒!只要多训练,你的口语一定会提高。

此处是“祈使句+and+陈述句”句型,陈述句中应用一般将来时。

9.—May I meet your headmaster at fou r o’clock this afternoon?—I’m sorry.He________to a conference long before then.(go)解析:will have gone。

考查将来完成时。

句意:——今天下午四点我可以见见你们校长吗?——对不起。

在那之前,他已经去开会了。

根据long before then可知,此处应用将来完成时,表示在将来某个时间之前已经完成的动作。

10.The popular TV series The Legend of Lu Zhen________a story of the only female minister in our Chinese history.(tell)解析:tells。

考查一般现在时。

句意:受欢迎的电视连续剧《陆贞传奇》讲述的是中国历史上唯一的女相的故事。

故事的叙述,小说、戏剧、电影的情节介绍,书籍的内容及图片的说明等常用一般现在时。

11.—Do you know our Tao Ran Ting Hotel?—Sorry.This is the first time I________in Beijing.(be)解析:have been。

考查现在完成时。

句意:——你知道我们的陶然亭宾馆吗?——对不起。

我是第一次来北京。

在“This is the+序数词+time+that从句”句型中,从句谓语动词常用现在完成时,that可省略。

12.—What happened to you the other day?—I ________to Shanghai,but I missed my flight.(fly)解析:was going to fly。

考查过去将来时。

句意:——前几天你怎么了?——我打算坐飞机去上海,但是我错过了航班。

此处was going to do sth.表示“过去打算做某事”。

13.—The old house might fall down soon unless we ________ some quick repair work.(do)—I’m afraid so.解析:do。

考查一般现在时。

句意:——除非我们做一些快速修复工作,不然这座老房子可能很快会倒塌的。

might意为“或许,可能”,表示对将来不太肯定的推测,因此unless 引导的条件状语从句中谓语动词应用一般现在时。

14.At least 20 children died and dozens ________ to hospital with food poisoningaf ter eating a meal provided for free at their school in the Indian state of Bihar.(take)解析:were taken。

考查时态和语态。

句意:印度Bihar一所学校的学生在吃完免费午餐后发生食物中毒,至少20名学生死亡,数十名学生被送往医院。

dozens表示dozens of students,与take之间是动宾关系;且由died可知此处叙述的是过去的情况,故用一般过去时的被动语态。

15.I________of going to Korea this summer,but the air crash made me change my mind.(think)解析:had thought。

考查过去完成时。

句意:我本想这个暑假去韩国,但是飞机失事的事故使我改变了主意。

根据句意可知,think的动作发生在made之前,即表示过去的过去。

Ⅱ.单句改错1.—Catherine,everyone w as at the two­hour concert except you.—Sorry,but I am helping my mother cleaning up the whole apartmen t.____________________________________________________________________2.Tom flew home,but his father has already died.____________________________________________________________________3.Tom,hurry up.You are wanting on the phone.____________________________________________________________________4.He is afraid that he will soon abandoned by his company and his fans.____________________________________________________________________5.He knew that he would be punishing for his parking offence.____________________________________________________________________6.Our fur is being using to make sweaters for people like you.____________________________________________________________________7.The road is being repaired,so we had to take another one.____________________________________________________________________8.I hope all of our view ers have inspired by the hero’s deeds.____________________________________________________________________9.There is no doubt that his new novel is sold well in this bookstore.____________________________________________________________________10.It is estimated that the to tal cost of the trip will be cost over one thousand dollars.____________________________________________________________________答案:1.am改为was 2.has改为had 3.wanting改为wanted 4.soon后加be5.punishing改为punisheding改为used7.is改为was8.have后加been9.sold 改为selling 10.删去第二个costⅢ.短文填空在下面短文中的空白处填上适当的动词形式,使短文意思通顺Famous sports hero survives Hua Fei, the flying robot,nearly stayed in space. Yesterday I 1.________(visit) the Olympic medalist,Hua Fei.who nearly died when he 2.________(fall) from 30,000 feet. He 3.________(lie) in his hospital bed with two broken legs and a cut on his head.He 4.________(begin) his flying for the 79th Olympic flying gymnastics competition when his parachute 5.________(fail) to open .He fell turning over and over till he 6.________(hit) the side of a mountain.Everybody was afraid that he 7.________(be) too broken to be ter when he 8.________(come) to himself,he said, “I’ve been saved from a serious injury.I hope I 9.________(be) able to compete for China again after I10.________(recover)”.答案:1.visited 2.fell 3.waslying 4.was beginning 5.failed 6.hit 7.would be 8.came 9.will be 10.am recovered。

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