1、专专 题题 4 4数形结合思想数形结合思想一、数形结合的概念及本质：一、数形结合的概念及本质：数形结合亦即：代数问题可以几何化（借数形结合亦即：代数问题可以几何化（借形辅数），几何问题可以代数化（以数促形）。形辅数），几何问题可以代数化（以数促形）。数形结合的本质：数量关系决定了几何图数形结合的本质：数量关系决定了几何图形的性质，几何图形的性质反映了数量关系。形的性质，几何图形的性质反映了数量关系。二、数形结合的应用：二、数形结合的应用：（1）借助于数的精确性来阐明形的某些属性；）借助于数的精确性来阐明形的某些属性；（2）借助于形的几何直观来阐明数之间的某）借助于形的几何直观来阐明数之间的某种
2、关系。种关系。;_,3)2(,)1.(122的最大值是的最大值是那么那么满足满足如果实数如果实数xyyxyx ._.11,:;2,:,0).2(条件条件那么甲是乙的那么甲是乙的且且满足满足两个实数两个实数命题乙命题乙满足满足两个实数两个实数命题甲命题甲已知已知hbhabahbabah 3必要非充分条件必要非充分条件注：注：探究集合命题间的充要性常利用数轴把探究集合命题间的充要性常利用数轴把数的问题看成点的问题数的问题看成点的问题3.2.1.0.)(1sin2).3(DCBAxx解的个数是解的个数是方程方程 C（4）一游泳池长）一游泳池长90m，甲、乙两人分别在，甲、乙两人分别在游泳池相对两边同
3、时朝另一边游泳，甲的游泳池相对两边同时朝另一边游泳，甲的速度是速度是3m/秒，乙的速度是秒，乙的速度是2m/秒，若不计秒，若不计转向时间，则从开始到转向时间，则从开始到3分钟止，他们相遇分钟止，他们相遇的次数为（的次数为（）A.2 B.3 C.4 D.5D.84444,84,.2222222的最小值的最小值求求满足满足设实数设实数 yxyxyyxyxyx2注：注：本题利用方程的曲线解题，借用方程本题利用方程的曲线解题，借用方程曲线图象，使抽象问题转化为形象问题来曲线图象，使抽象问题转化为形象问题来思考，这是突破解题困境的方法之一思考，这是突破解题困境的方法之一。.)2()2()2(844442
4、2222222 yxyxyxyxyyx.)(,1925.322的最大的圆的最大的圆包括边界上包括边界上圆内部圆内部与椭圆短轴相切且在椭与椭圆短轴相切且在椭求在椭圆的右半部分求在椭圆的右半部分已知椭圆已知椭圆 yx.052422 xyx注：注：本题用数助形，解题的关键在理解题本题用数助形，解题的关键在理解题意，意，“椭圆上的点在圆外或圆上椭圆上的点在圆外或圆上”，而不，而不等式恒成立，可转化为等式恒成立，可转化为T0。XOY.,10,0.4lg1的范围的范围求求且且设设xyxyyxx .11004 xyxy或或注：注：数和形是变量关系的两种形式，故在数和形是变量关系的两种形式，故在解决一个数学问
5、题时，往往存在着数解决一个数学问题时，往往存在着数,形之形之间的多次转换，巧妙地运用这种变形可使间的多次转换，巧妙地运用这种变形可使问题得到简捷地解答。问题得到简捷地解答。.)2(,0.5bxxaaxa 的不等式的不等式试解关于试解关于已知已知).22,(,2;2,(,22abaabxbaaxba 时时当当时时当当注：注：在解不等式在解不等式f(x)g(x)时，若时，若f(x)与与g(x)的图象较易作出，则可考虑借助图形以求的图象较易作出，则可考虑借助图形以求获得简解。获得简解。.342:).2(2)()(,lg)(.62 bbbafbfafbabaxxf求证求证且且满足满足正数正数设函数设函
6、数注：注：在代数推理中，在代数推理中，“形形”可助你思考，但不能可助你思考，但不能代替代替“数数”上的演绎证明，即形上发现的信息必上的演绎证明，即形上发现的信息必须严格证明才可运用。此外，在对抽象函数（如须严格证明才可运用。此外，在对抽象函数（如未给出解析式）进行的推理中，寻找满足条件的未给出解析式）进行的推理中，寻找满足条件的特例也是发现隐含信息的重要途径。如在对满足特例也是发现隐含信息的重要途径。如在对满足条件条件f(xy)=f(x)+f(y)(x0,y0)的函数的函数f(x)进行有关进行有关推理时，常利用对数函数的性质，去联想猜测推理时，常利用对数函数的性质，去联想猜测f(x)的有益于破
7、题的隐含信息，为推理提供方向。的有益于破题的隐含信息，为推理提供方向。Unit 9 Saving the earthBy Ivyriver 2006.9.27By Ivyriver 2006.9.27What problems is the earth facing?problems the earth is facing:problems the earth is facing:air pollutionwater pollutionnoise pollutionsoil erosionwhite pollutionoverpopulationpovertywar&violence(rubb
8、ish)aidsWhat can we do to help the earth solve the problems its facing?In order to help the earth,the United Nations held a In order to help the earth,the United Nations held a meeting to discuss the problems.meeting to discuss the problems.Question:Whats the name of the meeting?The Earth Summit.ear
9、th summit IntroductionIntroduction Body BodyConclusionConclusionSample outlineIntroduce the Earth Summit to the readers.What we can do Para.1Para.1Para.2 Para.3 Para.4 Para.5 Para.6Para.7impor-tanceGive more detailed information about the problemsPara Main idea Key words 1A 1 to 1972&2002 Earth Summ
10、its Take better care of the earth,problems facing our planet,progress made,one of the theme2 2 The big three and the results caused by them Three biggest killers,contaminated drinking water,3 ,air pollution 3The 4 Of the richer countries Poverty,war,violence,do whatever to help,Prosper,sustainable d
11、evelopment 4How to save the earth Understand,existing serious problem,5 ,changing how we live 6 Understanding of the Environment and their 6 to act are important Students,learning more,earth issues,betterUnderstanding of environment,willingness to act,what to do to help7One of the solutions to the p
12、roblems-7 Key to future,build a better society,8 nature,put an end to,death&suffering,caused by the big three Brief introductionsustainable development poor sanitationresponsibilitiestake action willingnesseducationin harmony with1.When and where was the first Earth Summit held?2.Whats the purpose o
13、f the first Earth Summit?3.Where was the 2002 Earth Summit held?4.Whats the main theme of this Earth Summit?Read Para.1:1.When and where was the first Earth Summit held?2.Whats the purpose of the first Earth Summit?In 1972 in Stockholm,Sweden.To share the ideas about ways to take better care of the
14、earth.3.Where was the 2002 Earth Summit held?4.Whats the main theme of this Earth Summit?In Johannesburg in South Africa.One of the main themes of the summit was“sustainable development”,or the question how we can continue developing the world without damaging the environment.Read Para.2:1.Whats the
15、“big three”?2.How many people die from the“big three”every year?3.How many people die from air pollution every year?1.Whats the“big three”?contaminated drinking waterpoor sanitationair pollutionthe three biggest killers in the world2.How many people die from the“big three”every year?3.How many peopl
16、e die from air pollution every year?More than seven million.Almost three million.Read Para.3:1.What other problems were talked about in the meeting?2.Global development is necessary.At the same time,global development has bad effect(影响影响)on us.In the text,whats the bad effect?3.What did Chinas then
17、Premier Zhu Rongji stress?And what should the developed countries do?1.What other problems were talked about in the meeting?Poverty,war and violence.2.Global development is necessary.At the same time,global development has bad effect(影响影响)on us.In the text,whats the bad effect?All too often,global d
18、evelopment means rich people get richer while the poor get poorer.the need for equality and fairness in the worldChinas then Premier Zhu Rongji stressedRich countries have a responsibility towards poor countries and mustdo whatever they can to help others.3.What did Chinas then Premier Zhu Rongji st
19、ress?And what should the developed countries do?Read Para.4:1.How can we save the earth?Only by changing the way we live can we save the earth.Read Para.5What did the visitor say in our text?“Had I known that air conditioners cause so much pollution,I would never have bought one.Not until we know mo
20、re will we be able to improve the situation.If all of us make small changes,we could make a big difference.”Read Para.4-6:Do you think the Earth Summit is meaningful and helpful?Why?the meaning of the Earth Summit:To help people understand that there exists serious problems and that there is still t
21、ime to take action.(A better understanding of the environment is necessary,as is the willingness to act.)To tell us what we can do to help.Read Para.7:1.In order to solve the problem,whats the most important thing in the future?2.Why is education so important?1.In order to solve the problem,whats th
22、e most important thing in the future?2.Why is education so important?Education is the key to the future.a.With better education,people will be able to build a better society in harmony with nature and perhaps put an end to the death and suffering caused by the big three.b.b.Much of the poverty can b
23、e wiped out.c.There is a good chance that we will see less violence and fewer wars.1.Which is TRUE about the Earth Summit?A.Its held every 3 years in Stockholm.B.So far it has been held twice:in 1972 and in 2002.C.Sustainable development is the only theme of the summit.D.At the summit people discuss
24、 how to take good care of the earth.2.Which of the following is the main cause of millions of deaths in rural areas?A.Lack of drinking water B.Poor sanitation C.Air pollution D.Freezing cold3.According to the text,air pollution alone causes about _ of all the deaths in the world every year.A.6.5%B.1
25、5%C.20%D.35%4.At the summit,Chinas then Premier Zhu Rongji probably mentioned the following EXCEPT _.A.International cooperationB.Sustainable developmentC.Ways of preventing some diseases from spreadingD.Equality and fairness in the world.5.The fourth paragraph suggests that_.A.Its not too late for
26、us to do something to save the earth.B.We neednt be so worried about the environment of the earth.C.There are problems facing the earth,but not serious enough.D.We will change our way of life sooner or later.6.One visitors words are quoted in the text in order to show _.A.that the Earth Summit is ve
27、ry popular among ordinary peopleB.that we can help save the earth by changing our way of lifeC.how we can develop the world without damaging the environmentD.how people can stop the death and suffering caused by the“big three”7.“A better understanding of the environment is necessary,as is the willin
28、gness to act.”The underlined word can be replaced by _.A.which B.so C.and D.but8.The key to solving the major problems facing the earth is _.A.to educate the people of the world B.to improve the living conditions of the peopleC.to treat people equally and fairly D.to hold conferences like the Earth
29、Summit frequently 9.Which of the following best expresses the main idea of the passage?A.Different countries have different opinions about development B.Equality and fairness are badly needed in the todays world C.The Earth Summit is a way to save the earth D.Sustainable development,the future for t
30、he world 10.How many people on earth do not have access to clean water?20%A.get close to B.have chances to use C.be free to use D.get means to approachTask 1:debate:As we know the Earth Summit is a place to find solutions for the future.Some people say that money can solve all problems,but some say
31、education.Which one do you agree?Money or Education?Task 2:if you have the chance to attend the Earth Summit,what will you do?Water is the source of life,but it is not inexhaustible.If we did not take action now,the last drop of water in the world would be mans tear!水是生命之源，但它却不是取之不尽，用之不竭的。如果我们现在不采取行
32、动，世界上的最后一滴水将是人类的眼泪！1.whats _ here is the whole future of the industry.A.at question B.in question C.at issue D.at problemat issue=in question=being discussed/debatedHave you seen the latest of the magazine?issue=important topic for discussion;point in questionEg.debate/avoid/confuse/raise an issueis
33、sue=one of a regular series of publications（出版物的）期号issue stamps/shares/the magazineV.=publish2._（概括的说），the subject is so important.In summarysummarize/summarise V.=sum upHe summarised/summed up his speech in a few words.make/write/give a summary of写摘要3.The Greens _ to live a simple life.A.are conten
34、t B.is content C.are contented D.is contentedcontent n.predict its contentcontent adj.be content to do sthHe is content to remain where he is now.他安于现状=be willing to do be content with sth=be satisfied withDont be content with small success.content sb./oneself with sth V.n一块冰淇淋足以让小孩子满足了一块冰淇淋足以让小孩子满足
35、了。An icecream is enough to content the child.4.A.be representative (of sb./sth.)adj=be typical of sb/sth我是代表其他成员提出要求的我是代表其他成员提出要求的.My demand is representative of that（=the demand）of the other membersB.a representative of sb/sth n.=typical example of a class or group典型，有典型的人或事物展览会是现代中国艺术的代表展览会是现代中国艺术
36、的代表The exhibition is a representative of the modern Chinese art.a legal representative 法定代理人法定代理人 5.Swittzerland has _ the sea _the River Rhine.A.an access to;by B.access to;via C.an access to;through D.access to;acrossgain/get/have access toA.access to sth=approach to sthn什么是成功之道什么是成功之道？What is the
37、 access to success?B.access to sb/sth=means of approaching or entering(a place);way in（接近或进入某地方的方法；通路=opportunity or right to use sth or approach sbIts difficult to gain access to him.接近他很难6.on earth/on the earthWhat _ do you mean？你究竟是什么意思？你究竟是什么意思？when,what,who,where,how,whyon earth/in the worlduse
38、d for emphasislook/be/feel like nothing on earth=very bad;unwell;peculiar他穿着奇装怪服难看级了He looks like nothing on earth in those strange clothes.on earth7.I have never been to this _ island _before.A.alone;lonely B.alone;alone C.lonely;lonely D.lonely;alone1.,alone:A.with out any companionsI dont like go
39、ing out alone after dark.B.without the help of other people or thingsI prefer to work on it alone.2.leave/let sb/sth alonenot try to influence or change sb/sth;not touch sb/sth不想左右或改变某人；不触摸我早告诉过你不要动我的东西Ive told you before-leave my things alone.3.let aloneI havent decided on the menu yet,let alne bou
40、ght the food.我还没决定吃什么菜呢，更不必说买好了=without considering 不必考虑8.He came here_to see you,_after he heard that you returned from abroad.A.specially;mainly B.especially;specially C.specially;especially D.especially;especially9.If we _ to develop the world successfully,we must make that everyone is able to ta
41、ke part in the new world we create.A.ought B.are going C.are D.ready be to do sthA.expressing duty;necessityYou are to report to the police.B.expressing arrangement;purpose;intentionThey are to be married.C.expressing posibilityThe book was not to be(could not be)found.D.expressing destinyHe was nev
42、er to see his wife again.10.The end of the holiday came _ soon.A.all too B.too much C.too only D.none tooall+too/adjs/advs=more than desirable过于all too often/soon/quickly他过于兴奋 He was all too excited.11.Among the speakers was Chinas then Premier Zhu Rongji,who stressed the need for quality and fairne
43、ss in the world.A.then attrib.The then Prime Minister took her husband with her on all her travels.当时的首相每次外出都与夫偕行B.stress=put stress or emphasis on sth在会议上，他强调了教育的重要性在会议上，他强调了教育的重要性。He stressed the importance of education at the meeting.lay/put place stress on sth 重视重视/强调强调一些学生不重视英语学习。一些学生不重视英语学习。nS
44、ome Students lay/put little stress on English study.under great stress在很大的压力下nHe is under great stress because of his new work.12.have/take/bear(a)responsibility for 承担。的责任Its ones responsibility to do sthIts my responsibility to lock the doors.我负责锁门。be resposible for13.If you dont go to the party,_
45、.A.So do I B.nor do I C.so will I D.nor will Ias is the willingness to act=so is the willingness to act14.The key _the problem is to meet the demand _ by the customers.A.to solving;making B.to solving,made C.to solve;making D.to solve;made the key to sth/doing sth=thing that provides access,control
46、or understanding关键；要诀the key to the questions15.He soon found himself _ his new co-workers.A.in harmony with B.along well with C.get along well with D.at harmony within harmony（with sb/sth）=agreeing/matching协调一致，相配n大海与天空的和谐构成一幅美妙图画。大海与天空的和谐构成一幅美妙图画。harmony =agreement/pleasing combination of related
47、things一致，匀称，协调The harmony of sea and sky makes a beautiful picture.My cat and my dog live in perfect harmony.n我的猫和狗生活的非常和谐。我的猫和狗生活的非常和谐。16.put an end to sth=stop sth from happening abolish sth终止，废止终止，废止n我们结束争吵吧。我们结束争吵吧。Lets put an end to this e to an end The meeting came to an end early.bringto an e
48、ndHe brought his lecture to an end around 10 oclock.17.wipe outA.clean the inside of搽拭。内部The vase wasnt wipedout properly before it was put away.这个花瓶没檫干净就收起来了。2.removeor cancel sth 除去或取消某事物wipe out还清债物 wipe out ones debtsC.destroy sth completelyDoctors are trying to wipe out such a disease.医生正在尽力消除这
49、种疾病18.There is a chance that.chance=possibility/likelihoodchance of(doing)sth/to do sth/that有可能得到今晚演出的票吗？Is there any chance of getting tickets for tonight?She has a goog chance/no chance/not much chance/only a slim chance of winning.take measures/steps take action(on)be content to do sthbe content
50、with stha contented smilehave/gain/get access to n/vingwith violencelay/put/place stress onunder the stress of take/bear/have responsibility forin harmony without of harmony withput an end to sth;bring sth to end采取措施采取措施采取行动采取行动乐于做某事乐于做某事对对满意满意一个满意的微笑一个满意的微笑通往通往,有有权利权利/机会机会猛烈地猛烈地,用力地用力地强调强调,重视重视在压力下
