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鞍山市2009年高三畢業(yè)班第二次質(zhì)量調(diào)查   語(yǔ)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

    本試卷分第一卷 (選擇題)和第二卷(非選擇題)。總分150分,考試時(shí)間為120學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

分鐘。考生請(qǐng)將答案答在答題卡上,在本試卷上答題無(wú)效?荚嚱Y(jié)束后,將本試卷和答題卡一并交回。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

第一部分:聽(tīng)力(共兩節(jié),每小題1.5, 滿(mǎn)分30分)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

第一節(jié) (共5小題;每小題1.5分,滿(mǎn)分7.5分)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

 聽(tīng)下列5段對(duì)話(huà),每段對(duì)話(huà)后有一個(gè)小題,從題中所給的A,B,C三個(gè)選項(xiàng)中選出最佳選項(xiàng),并標(biāo)在試卷的相應(yīng)位置。聽(tīng)完每段對(duì)話(huà)后,你都有10秒鐘的時(shí)間來(lái)回答有關(guān)小題和閱讀下一個(gè)小題。每段對(duì)話(huà)僅讀一遍。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

1.           How much was the driver`s tip?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A.$3.5                   B.$0.5                   C.$1.5學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

2. What does the woman mean?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. She definitely wants to know about the meeting.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

B. She would like to let him know about the next meeting.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

C. She will give him a call to ask about the next meeting.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

3. Where does the conversation take place?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.At a hairdresser`s       B. At a tailor`s                     C.At a photographer`s學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

4. What does the woman mean?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.Jack has been on the paper for several days.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.Jack is working hard on the paper.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.He works only during the day.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

5. What does the woman mean?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.The paper must be handed in on time.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.His request was made too late.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.The paper can be handed in a few days late.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

第二節(jié)(共15小題每小題1.5分,滿(mǎn)分22.5分)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面5段對(duì)話(huà)或獨(dú)白。每段對(duì)話(huà)或獨(dú)白后有幾個(gè)小題,從題中所給的A、B、C三個(gè)選項(xiàng)中選出最佳選項(xiàng),并標(biāo)在試卷的相應(yīng)位置。聽(tīng)每段對(duì)話(huà)或獨(dú)白前,你將有時(shí)間閱讀各個(gè)小題,每小題5秒鐘;聽(tīng)完后,各小題將給出5秒鐘的作答時(shí)間。每段對(duì)話(huà)或獨(dú)白讀兩遍。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面一段對(duì)話(huà),回答第6至8兩個(gè)小題,F(xiàn)在,你有15秒鐘的時(shí)間閱讀這三個(gè)小題。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

6.Why is the man going to the States?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.to visit places of interest學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.to visit his friends學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

                                                                                           學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

C.to attend a conference學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

7.When will the man leave for American?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.in two weeks             B.in mid-January          C.on January 10th學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

8.What is the man?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.a scientist                  B.a writer                            C.a traveler學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面一段對(duì)話(huà),回答第9至10兩個(gè)小題,F(xiàn)在,你有15秒鐘的時(shí)間閱讀這三個(gè)小題。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

9.Which month is it most likely now?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.January                     B.March                       C.June學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

10.Which season was the best season last year?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.Spring                      B.Summer                    C.Autumn學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面一段對(duì)話(huà),回答第11至13兩個(gè)小題,F(xiàn)在,你有15秒鐘的時(shí)間閱讀這三個(gè)小題。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

11.What are the man and the woman doing?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.They are climbing the mountain.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.They are playing basketball.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.They are going down hill.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

12.What happened to the man?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.He has sprained(扭傷) his left ankle(腳踝).學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.He has sprained his right ankle.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.He has sprained his waist.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

13.What is the woman`s message?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.be relaxed                 B.stop walking and relax                     C.sit down and rest學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面一段對(duì)話(huà),回答第14至17三小題。現(xiàn)在,你有15秒鐘的時(shí)間閱讀這三個(gè)小題。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

14.Why does the woman refuse to exchange the shoes for the man?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.The man has kept the shoes for a week.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.The man had no receipt for the shoes.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.There is a sign reading no exchange after the shoes are sold.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

15.What causes the woman to turn down refunding(退還) the man?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.her manager`s order          學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

B.her unknowing the price           學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

C.her unknowing whose fault it is學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

16.Why does the man think it isn`t his fault?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.because the shoes must be made badly學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.because the shoes must have been used before he bought them.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.because he just wore the shoes for one time and then they were broken.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

17.When did the man buy that pair of shoes?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.last week                   B.last weekend                     C.yesterday學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

聽(tīng)下面一段對(duì)話(huà),回答第18至20三個(gè)小題,F(xiàn)在,你有15秒鐘的時(shí)間閱讀這三個(gè)小題。學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

18.What does the passage talk about?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.selling a house                  B.doing housework               C.losing a job學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

19.Why did the speaker sell her house?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.Her husand had got a higher position.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.Her husband had lost his job.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.She wanted to have a cleaner house.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

20.Why did the agent call on the speaker so early in the morning?學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A.His telephone went out of order.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       B.The buyers had to leave soon.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       C.He began to work at 8 a.m.學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

第二部分:英語(yǔ)知識(shí)運(yùn)用(共兩節(jié),滿(mǎn)分45分)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

第一節(jié):?jiǎn)雾?xiàng)填空(共15小題;每小題1分,滿(mǎn)分15分)學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

21.Journalism is described as __________science of searching, recording, and reporting_________ important events.   學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. a;the                          B. a; /              C. /; /            D. /;the學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

22.The teacher thought his students needed more practice and learning skills _______ much homework.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. other than                     B. rather than                C. more than          D. in place of學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

23.We are given a three-day holiday for May Day, but Harry is given ________ for his excellent work as a reward. That is, he has a six days’ holiday.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A. another three day      B. other three days     C. three more days  D. three days學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

24. The prices of many kinds of the computers ______ quickly these days.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. are raising               B. rises                       C. raise                 D. are going up學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

25.The child, who was believed ___ by a tiger, was found in a forest. 學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. to be killed        B. having killed     C. to have been killed       D. to be killing學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

26.When I was having my holiday abroad, those children kept quarrelling and _______ my fun.   學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. destroyed          B. damaged             C. injured                        D. spoiled學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

27.________ I met him, he was working as a secretary in a big company.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A.For the first time                    B. The first time學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

C. The first time when                           D. When the first time學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

28.If the person        agrees,we sometimes use small recorders to make sure that we get all our facts straight.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

 A.interviewed    B.being interviewed  C.interviewing   D.to be interviewed學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

29.―Sam, it's too late. Our daughter ________ be back.  學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

―Don't be anxious. I dare say she ________ have some extra work to do. 學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

A. can; must       B. will; might        C. should; must       D. must; may 學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

30. Mary’s gold ring _______ from her mother as a gift for her wedding. 學(xué)科網(wǎng)(Zxxk.Com)學(xué)科網(wǎng)

       A. came from        B. came into               C. came down               D. came over

31. ______ production up by 40% , the company is certain to earn a lot this year.  

    A  As            B  For            C  With             D  Though

32.― ______ was ________ they were going to San Francisco? 

―Next week.

A. What; it that     B. It; what           C. When; that        D. When; it that

33.―Well, where is my watch?  

―_______! We just have two minutes left.

 A. Take your time   B. Come on         C. Don't worry       D. Take it easy

34. The old farmer has two sons, _________has got a job in the town and refused to do farming.

     A.each of whom    B.both of who       C.all of them         D. each of them

35. _______ has been done to prevent the factories from polluting the river, it remains a serious problem.   

        A. Though that      B. What                    C. Though what           D. Despite what

 

第二節(jié):完形填空(共20小題;每小題1.5分,滿(mǎn)分30分)

A weak old man went to live with his son,daughter-in-law, and four-year-old grandson. The family ate together at the table. But, the elderly grandfather`s  36  hands and failing sight made   37   difficult. Peas rolled off his spoon and food  38  onto the floor. When he held a glass, with his shaky hands, milk  39  on the tablecloth. His son and daughter-in-law became angry about the  40  .So, they put a small  41  in the corner. There Grandfather ate  42  , while the rest of the family enjoyed dinner together.  43  Grandfather had broken a dish or two, his food was served in a  44  bowl. When the family  45  in Grandfather`s direction, sometimes the old man had tears in his eyes.  46  ,the only words the couple had for him were  47  warnings, when he  48  a fork or spilt food. The four-year-old grandson watched it all in  49  .

  One evening, before supper, the father noticed his son playing with wood pieces on the floor. He asked the child  50  , “What are you making?” Just as sweetly, the boy responded, “Oh, I am making little  51  for you and Mama to eat your food from when I grow up.” The four-year-old son smiled and went back to work.

  The words so  52  the parents that they were speechless. Then tears started to stream down their cheeks. That evening, the husband took Grandfather`s hand and  53  led him back to the family table, and for rest of his  54  , he ate every meal with the family. And, for some reason, neither husband nor wife seemed to  55  any longer when a fork was dropped, or milk spilt.

 

36. A. shaky                B.rough            C. tough           D. large   

37. A. talking                     B.sleeping          C.eating                D.walking 

38.   A.spread                B.rained                C.lay                     D.covered 

39.   A.fell                    B.poured               C.flowed               D.spilt    

40.   A.trouble               B.mess                  C.scene                 D.action   

41.   A.chair                  B.bench                 C.bed                    D.table    

42.   A.alone                 B.slowly                C.carefully            D.little    

43.   A.Though              B.Because              C.While                D.Once  

44.   A.glass                  B.iron                   C.golden               D.wooden 

45.   A.glanced              B.turned                C.moved               D.pointed  

46.   A.Then                  B.Therefore           C.Besides              D.However     

47.   A.valuable             B.sharp                 C.useless               D.high     

48.   A.broke                 B.brought              C.dropped             D.touched  

49.   A.silence               B.joy                    C.amusement         D.disappointing 

50.   A.curiously            B.quietly               C.angrily               D.sweetly    

51.   A.boxes                 B.bowls                 C.tools                  D.toys   

52.   A.puzzled              B.moved               C.struck                D.frightened  

53.   A.gently                B.quickly                     C.actually              D.happily  

54.   A.meal                  B.days                   C.stay                   D.belongings  

55.   A.worry                B.notice                C.shout                 D.care  

 

第三部分:閱讀理解(共20小題;每小題2分,滿(mǎn)分40分)

第一節(jié) (共15小題;每小題2分,滿(mǎn)分30分)

A

  A man accused of failing to return more than 700 children’s books to five different libraries in the county was released(釋放) from prison after a book publisher agreed to post his bond(保釋金)of $1,000.The publisher said.“There’s a story here.This is a man who loves books.He just can’t let go of them.He hasn’t stolen a single book.So what’s the crime ? We think that Mr Banish has story to tell.We plan to publish his story.”  

When asked why he didn’t return the books. Mr Banish said,”Well,how could I ? They became family to me.I was afraid to return them,because I knew that kids or dogs would get hold of these books and chew them up,throw them around,tear the pages,spill soda on them,get jelly and jelly on them,and drown them in the toilet.

  He continued,“Books are people,too! They talk to you,they take care of you,and they enrich you with wisdom,humor and love.A book is a guest in my home.How could I kick it out? I repaired torn pages.I dusted them with a soft clean cloth.I turned their pages so they could breathe and get some fresh air.”

  “Every week I recognized them on their shelves so they could meet new friends,My books were HAPPY books.You could tell just by looking at them.Now they’re all back in the libraries,on the lower shelves,on the floors,at the mercy of all those runny-nosed kids I can hear them calling me.I need to rescue them.Excuse me.I have to go now.”

56.Why was the man put into prison? 

  A.Because the book publisher persuaded the police to do so.

  B.Because he stole 700 children’s books from the five different libraries.

  C.Because he refused to return the books that he had borrowed.

  D.Because he wanted to publish his story.

57.How did the man treat books?  

  A.He treated them as his family.

  B.He treated them as his own children.

  C.He treated them as his furniture.

  D.He treated them as his job .

58.What might happen after the man was set free? 

  A.He might stop borrowing books.

  B.He might start a library of his own.

  C.He might go on borrowing books from libraries.

  D.He might return all his books.

59.What is mainly talked about in this passage?  

  A.A funny thief who loves stealing books.

  B.A person who refuses to return borrowed books and wants to look after them.

  C.A person who is crazy about books so he keeps stealing them from the library.

  D.A person who may have some mental problems.

B

Special trees that grow faster, fight pollution, produce better wood, and even sense chemical attacks are being planted by scientists in the US.

    When 40 percent of Hawaii's US$14 million-a-year papaya (木瓜)industry was destroyed by a virus five years ago, work began on creating genetically engineered (轉(zhuǎn)基因的) trees.

    Researchers successfully introduced seeds that were designed to resist the virus. Since then, more and more people have been testing genetically engineered trees.

    Some researchers put special bacteria into trees to help them grow faster and produce better wood. Others are trying to create trees that can clean polluted soil.

    Meanwhile fruit farmers are looking for trees that are strong enough to resist worms, and paper companies want trees that produce more wood and therefore more paper.

     The Pentagon (五角大樓) even gave the researchers US$500,000 this year after they developed a pine tree that changes its colours if it senses a chemical attack.

     So far, the poplar, eucalyptus (楊樹(shù)與桉樹(shù)), apple and coffee trees are among those being engineered. All this can be done today because we have a better understanding of tree genomes (基因組).

     However, some people fear that the genetically engineered trees will cause dangerous results. They are worried that the new trees will breed (繁殖)with natural species and change the balance of the forest environment.

     "It could be destructive," said Jim Diamond, an environmentalist. '"Trees are what is left of our natural environment and home to many endangered species."

    But researchers insist that science could give nature a fighting chance against both natural and man-made dangers.

    They hope to answer the critics (批評(píng)家)by stopping the new trees from breeding, so their effect on the environment can be controlled.

60. Which kind of tree is not the ones that scientists are planting in the US?                               

A. Trees that worms can't hurt.

B. Trees that can sense a chemical attack.

C. Trees that can resist wind better.

D. Genetically engineered trees.

61. What caused the American scientists to work on special trees directly? 

A. They think science could give nature a fighting chance against both natural and man-made dangers.

B. Great numbers of trees have been lost due to attacks by viruses.

C. Researchers successfully introduced seeds designed to resist the virus.

D. Tree genomes are mapped out so scientists know how to improve trees.

62. Which of the following was probably the first kind of trees being engineered? 

A. Papaya.           B. Pine.          C. Apple.             D. Poplar.

63. Why did critics think engineered trees dangerous? Because _________.

A. these trees can destroy the balance of nature

B. everything except trees has been genetically engineered

C. trees are home to many endangered species

D. these trees may affect normal trees

C

People who spend more pre-bedtime(睡前)hours using the Internet or watching television are more likely to report that they don`t get enough sleep, even though they sleep almost as long as people who spend fewer pre-bedtime hours in front of a computer or televison screen, survey findings show.

“The longer media use before sleep can trigger self-perceived(自我感覺(jué)的)insufficient(不足的)sleep,” lead researcher Dr Nakamori Suganuma of Osaka University said.

He and colleagues obtained data on self-perceived sleep problems and the use of electronic media before bedtime from a total of 5875 Japanese respondents in two separate Internet-based surveys.

Nearly half of the respondents linked their lack of sleep with electronic media use before bedtime. Those reporting longer electronic media use were also more likely to report insufficient sleep.

Overall,29 percent of light users (less than 1.5 hours)listed electronic media use as a possible cause of their insufficient sleep. By comparison, 40 percent of medium (中級(jí)的)users(1.5 to 3 hours) and 54 percent of heavy users (more than 3 hours) said the same.

However, longer Internet and television use before bedtime was not linked with less actual sleep. While heavy users averaged about 3 more hours in front of computer or television screens than light users, the heavy users averaged only about 12 minutes less pre-workday sleep than light users.Suganuma said, “Internet use affected self-perceived insufficient sleep more than TV watching in both younger Internet users and middle-aged or aged users.”

Up to 38 percent of the respondents listed accessing the Internet far into the night as a possible cause for their sleep disturbance ,while about 25 percent said watching television far into the night caused their sleep problems.The findings suggest that while heavy computer and television use before bedtime has a small effect on sleep duration, it may have a more significant effect on “sleep demand and sleep quality.” Suganuma notes.

64. The underlined word “trigger” in Paragraph 2 means “________”.   

       A.remove                            B.cause                 C.increase                     D.decrease

65. From the passage, we learn________.  

A.     what kind of people have less actual sleep

B.      self-perceived insufficient sleep is linked to electronic media use

C.      Why the use of electronic media before bedtime affects sleep

D.     Using electronic media before bedtime makes people sleepless

66. Which of the following is NOT a result of the survey?  

A.     People who use electronic media longer before bedtime are more likely to report 

insufficient sleep.

B.      About 38 percent of the respondents think accessing the Internet far into the night is a cause for sleep disturbances.

C.      Internet use affects self-perceived insufficient sleep more than watching TV.

D.     Most self-perceived insufficient sleep is connected with electronic media use before bedtime.

D

Experts say the American state of Hawaii has been affected by a small frog called the coqui(科基蛙) .There may be millions of the small frogs in Hawaii.However, they do not belong there. They are normally found in the Caribbean island of Puerto Rico and in the southeastern United States.These coqui frogs are harming Hawaii`s environment, and the extremely loud noise they make is causing problems for Hawaiian citizens and visitors. The coquis arrived in Hawaii about ten years ago. They are believed to have been brought in accidentally in shipments of plants from Puerto Rico or Florida. Their numbers have sharply increased. They have quickly spread around the Hawaiian Islands and all hidden in plants.

  The coqui is a brown frog about five centimeters long. During the day, the frogs hide in wet protected areas, such as under plant leaves. At night , the frogs move onto trees to feed, call to females and mate(交配).

  In their native Puerto Rico, local people celebrate coqui frogs. But in Hawaii, the foreign frog is thought as a harmful animal.The coqui frogs are a major threat to Hawaii`s environmental system. The frogs eat thousands of insects every night .These insects are important to plants ,and are also important food for Hawaii`s native.

  The frogs are also affecting the tourism industry in Hawaii. Increasing numbers of hotels, visitors and local people are disturbed by the loud calls made by male coqui frogs to female frogs.At night ,the noise often makes it difficult for people to sleep. The mating call of the male coqui sounds like: “ Ko-Kee! Ko-Kee!” That is how they got their name.

  The frogs do not have any natural enemies in Hawaii to reduce their population size. The warm weather permits them to lay eggs all year long.

  Many efforts have been made in Hawaii to stop the spread of the coqui. The Hawaiian Department of Agriculture is trying to find an effective chemical that can be safely used to kill the frogs. Until then, the only way to catch the frogs is by hand.

67.Coqui frogs get their name from________.  

A.     the sound of their loud calls

B.      their shape and colour

C.      their coming from other parts of the USA

D.     people who dislike them

68.Which of the following is NOT a reason why people in Hawaii dislike coquis?  

A.     They are harming Hawaii`s environment.

B.      They have a bad effect on tourism.

C.      They eat insects which are important for plants.

D.     They hide in wet places and make loud sounds during the day.

69.Which of the following contributes to the increasing number of coquis in Hawaii?  

A.     There aren`t any animals in the world which eat coquis.

B.      They are easy to catch.

C.      They are easy to breed (繁殖)there.

D.     They eat a lot of insects in one night.

70.What would be the best title for the passage?  

A.     Coquis―Good or Harmful Animals?

B.      Coquis―A Big Threat to Hawaii

C.      Coquis Make Sleep Difficult

D.     Coquis―the Number Sharply Increased

第二節(jié)(共5小題;每小題2分,滿(mǎn)分10分)

根據(jù)短文內(nèi)容,從短文后的選項(xiàng)中選出能填入空白處的最佳選項(xiàng)。備選答案中有兩項(xiàng)為多余選項(xiàng)。

Why do some people have many friends while others do not?  71 However, it is not so. Let’s look at two psychological experiments which will give you the key to happy interpersonal relations.

1,3,5

73   After Martin Luther King, Jr was killed in the 1960s, a teacher, Jane Elliott, living in an all ? white town decided to help her class of young children understand why the Civil Rights Movement had been necessary in America.

She divided the class into two groups: one with blue eyes and the other with brown eyes. Other eye colours such as hazel or green were excluded from his exercise. Then she told the class that brown ? eyed people were cleverer than blue ? eyed ones because of an agent (化學(xué)作用) for brown colour found in their blood. Blue ? eyed people were stupid, lazy and not to be trusted. Jane Elliott did not need to say any more. The brown ? eyed students quickly got used to their new role as the leaders of the class. The blue ? eyed students became quiet and withdrawn. Then she discovered something very interesting. Four poor brown ? eyed readers began to read fluently in a way they had never done before.   74  .So if you want to be successful and happy, take an interest in others whether they are your classmates or workmates. Congratulate them on their successes and sympathise(同情) with them in their troubles.   75  .

A. Before the experiment the management talked to both groups of workers and explained that they wanted to find the best working environment for them.

B. Remember that the way you treat others will decide their attitude and behaviour to you.

C. The second experiment shows what happens to personal relations if you are rude to or ignore(忽略) others.

D. The ones who have more friends usually are those who care about others.

E. Jane Elliott had shown that the way people are treated affects not only their behaviour but also their confidence and their performance.

F.You may even imagine that this ability was something they were born with because it seems so effortless to them.

G. The second experiment tells us what teachers said has a great effect on the students.

第四部分:寫(xiě)(共兩節(jié),滿(mǎn)分35分)

第一節(jié):短文改錯(cuò)(共10小題;每小題1分,滿(mǎn)分10分)

文中共有10處語(yǔ)言錯(cuò)誤,每句中最多兩處。錯(cuò)誤涉及一個(gè)單詞的增加、刪除或修改。

增加:在此處加一個(gè)漏字符號(hào)(∧),并在其下面寫(xiě)出修改的詞。

刪除:把多余的詞用斜線(xiàn)(\)劃掉。

修改:在錯(cuò)的詞下劃一橫線(xiàn),并在其下面寫(xiě)出修改后的詞。

注意:1.每處錯(cuò)誤及其修改均僅限一詞;

2.只允許修改10處,多者(從十一處起)不計(jì)分。

This is a story told by my father : When I was boy , the most exciting

thing was when to celebrate the Spring Festival . My grandma was the

best cooker in the world but could make the most delicious dishes . Once ,

I just couldn’t wait for the Spring Festival dinner . As I was about take a

piece from a cooked duck , I saw Grandma in the kitchen looking me .

Shake her head , she said , “It isn’t a good time to do that , dear .” I apologize

and controlled me at the best till the dinner started . You know , that was

a dinner we had waited for several month .       

 

第二節(jié):書(shū)面表達(dá)(滿(mǎn)分25分)

肥胖(fatness)已經(jīng)成為危害人們健康的嚴(yán)重問(wèn)題,中小學(xué)生的肥胖趨勢(shì)更為明顯。你們班對(duì)此展開(kāi)討論。根據(jù)不同的觀點(diǎn),寫(xiě)一篇100詞左右的短文。

    1.肥胖危害健康,應(yīng)該節(jié)食,鍛煉,預(yù)防肥胖。已經(jīng)超重的,應(yīng)該采取措施減肥。

2.中學(xué)生正是長(zhǎng)身體的時(shí)候,減肥不僅會(huì)影響身體發(fā)育,而且也會(huì)影響學(xué)習(xí),因此應(yīng)該順其自然。

 

 

 

鞍山市2009年第二次高三質(zhì)量調(diào)查考試

英語(yǔ)試題答案

 

1― 5  BAABA   6―10 CBACC   11―15 CBACC  16―20 CAABB

21―25 BBCDC   26―30 DBBCC  31―35 CDBAD  36―40 ACBDB

41―45 DABDA   46―50 DBCAD  51―55 BCABD  56―60 CACBC

61―65 BADBB   66―70 DADCB  71―75 FACEB

短文改錯(cuò):

This is a story told by my father : When I was∧ boy , the most exciting

                                       a

學(xué)科網(wǎng)(Zxxk.Com)thing was when to celebrate the Spring  Festival . My grandma was the

 

best cooker in the world but could make the most delicious dishes . Once ,

    cook            and

I just couldn’t wait for the Spring Festival dinner . As I was about ∧take a

                                                      to

piece from a cooked duck , I saw Grandma in the kitchen looking ∧ me .

                                                     at

Shake her head , she said , “It isn’t a good time to do that , dear .”I apologize

Shaking                                               apologized

and controlled me at the best till the dinner started . You know , that was

            myself

a dinner we had waited for several month .        

                            months

 

作文:

Fatness is one of the serious problems which have a bad effect on our health. And at present the situation in the teenagers is even worse. As to this, a discussion was carried out in our class.

Some students think fatness does harm to our health, so it is necessary to be on a diet and take suitable exercise to prevent it. Those who are overweight should take measures to lose weight to be healthy.

But others have a different opinion. They say losing weight will be bad for the teenagers during their growth course, as well as their studies. So there is no doubt to leave it as it is.  

 

 

 

 

 

試題詳情

第9講 不等式(組)與方程(組)的應(yīng)用

 

【例題經(jīng)典】

例1 (2006年內(nèi)江市)內(nèi)江市對(duì)城區(qū)沿江兩岸的部分路段進(jìn)行亮化工程建設(shè),整個(gè)工程擬由甲、乙兩個(gè)安裝公司共同完成.從兩個(gè)公司的業(yè)務(wù)資料看到:若兩個(gè)公司合做,則恰好用12天完成;若甲、乙合做9天后,由甲再單獨(dú)做5天也恰好完成.如果每天需要支付甲、乙兩公司的工程費(fèi)用分別為1.2萬(wàn)元和0.7萬(wàn)元.

 (1)甲、乙兩公司單獨(dú)完成這項(xiàng)工程各需多少天?

 (2)要使整個(gè)工程費(fèi)用不超過(guò)22.5萬(wàn)元,則乙公司最少應(yīng)施工多少天?

 【點(diǎn)評(píng)】(1)利用方程組解決;(2)利用不等式解決,結(jié)合實(shí)際取值.

 

 

 

 

 

 

 

 

 

 

 

 

例2  (2005年濰坊市)為了加強(qiáng)學(xué)生的交通安全意識(shí),某中學(xué)和交警大隊(duì)聯(lián)合舉行了“我當(dāng)一日小交警”活動(dòng),星期天選派部分學(xué)生到交通路口值勤,協(xié)助交通警察維持交通秩序.若每一個(gè)路口安排4人,那么還剩下78人;若每個(gè)路口安排8人,那么最后一個(gè)路口不足8人,但不少于4人.求這個(gè)中學(xué)共選派值勤學(xué)生多少人?共在多少個(gè)交通路口安排值勤?

    【分析】本題與學(xué)生生活實(shí)際聯(lián)系緊密,是一道很好的列不等式組應(yīng)用題,解決本題應(yīng)注意路口人數(shù)與總?cè)藬?shù)之間的關(guān)系.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

例3  華溪學(xué)?萍枷牧顮I(yíng)的學(xué)生在3名老師的帶領(lǐng)下,準(zhǔn)備赴北京大學(xué)參觀,體驗(yàn)大學(xué)生活.現(xiàn)有兩個(gè)旅行社前來(lái)承包,報(bào)價(jià)均為每人2000元,他們都表示優(yōu)惠;希望社表示帶隊(duì)老師免費(fèi),學(xué)生按8折收費(fèi);青春社表示師生一律按7折收費(fèi).經(jīng)核算,參加兩家旅行社費(fèi)用正好相等.

    (1)該校參加科技夏令營(yíng)的學(xué)生共有多少人?

    (2)如果又增加了部分學(xué)生,學(xué)校應(yīng)選擇哪家旅行社?

 【點(diǎn)評(píng)】方程與不等式的綜合應(yīng)用,注意取值與實(shí)際生活要相符

 

 

 

 

 

 

 

 

 

 

 

【基礎(chǔ)訓(xùn)練】

1.(2006年深圳市)九年級(jí)的幾位同學(xué)拍了一張合影作留念,已知沖一張底片需要0.80元,洗一張相片需要0.35元.在每位同學(xué)得到一張相片、共用一張底片的前提下,平均每人分?jǐn)偟腻X(qián)不足0.5元,那么參加合影的同學(xué)人數(shù)(  )

    A.至多6人     B.至少6人    C.至多5人     D.至少5人

2.現(xiàn)用甲、乙兩種運(yùn)輸車(chē)將46噸抗旱物資運(yùn)往災(zāi)區(qū),甲種運(yùn)輸車(chē)載重5噸,乙種運(yùn)輸車(chē)載重4噸,安排車(chē)輛不超過(guò)10輛,則甲種運(yùn)輸車(chē)至少應(yīng)安排(  )

    A.4輛     B.5輛     C.6輛     D.7輛

3.(2005年內(nèi)江市)在一次“人與自然”知識(shí)競(jìng)賽中,競(jìng)賽題共25道,每道題都給4個(gè)答案,其中只有一個(gè)答案正確,選對(duì)得4分,不選或選錯(cuò)倒扣2分,得分不低于60分得獎(jiǎng),那么得獎(jiǎng)至少應(yīng)選對(duì)題(  )

    A.18道     B.19道     C.20道     D.21道

4.一種滅蟲(chóng)藥粉30千克,含藥率15%,現(xiàn)要用含藥率較高的同種滅蟲(chóng)藥粉50千克和它混合,使混合后的含藥率大于20%而小于35%,則所用藥粉的含藥率x的范圍是( )

    A.15%<x<23%    B.15%<x<35%     C.23%<x<47%    D.23%<x<50%

5.(2005年吉林省)某林場(chǎng)原計(jì)劃在一定期限內(nèi)固沙造林240公頃,實(shí)際每天固沙造林的面積比原計(jì)劃多4公頃,結(jié)果提前5天完成任務(wù),設(shè)原計(jì)劃每天固沙造林x公頃,根據(jù)題意下列方程正確的是(  )

   

6.(2006年內(nèi)江市)某學(xué)校要印刷一批完全材料,甲印務(wù)公司提出制版費(fèi)900元,另外每份材料收印刷費(fèi)0.5元;乙印務(wù)公司提出不收制版費(fèi),每份材料收印刷費(fèi)0.8元.

    (1)分別寫(xiě)出兩家印務(wù)公司的收費(fèi)y(元)與印刷材料的份數(shù)x(份)之間的函數(shù)關(guān)系式.

    (2)若學(xué)校預(yù)計(jì)要印刷5000份以?xún)?nèi)的宣傳材料,請(qǐng)問(wèn)學(xué)校應(yīng)選擇哪一家印務(wù)公司更合算?

 

 

 

 

 

 

 

 

7.水是人類(lèi)最寶貴的資源之一,我國(guó)水資源人均占有量遠(yuǎn)遠(yuǎn)低于世界平均水平,為了節(jié)約用水,保護(hù)環(huán)境,學(xué)校于本學(xué)期初制定了詳細(xì)的用水計(jì)劃.如果實(shí)際每天比計(jì)劃多用一噸水,那么本學(xué)期的用水總量將會(huì)超過(guò)2300噸;如果實(shí)際每天計(jì)劃節(jié)約一噸水,那么本學(xué)期用水量將會(huì)不足2100噸.如果本學(xué)期的在校時(shí)間按110天(22周)計(jì)算,那么學(xué)校計(jì)劃每天用水量是在什么范圍?(結(jié)果保留四個(gè)有效數(shù)字)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 8.某商場(chǎng)購(gòu)進(jìn)甲、乙兩種服裝后,都加價(jià)40%標(biāo)價(jià)出售.“春節(jié)”期間商場(chǎng)搞優(yōu)惠促銷(xiāo),決定將甲、乙兩種服裝分別按標(biāo)價(jià)的八折和九折出售.某顧客購(gòu)買(mǎi)甲、乙兩種服裝共付款182元,兩種服裝標(biāo)價(jià)之和為210元,問(wèn)這兩種服裝的進(jìn)價(jià)和標(biāo)價(jià)各是多少元?

 

 

 

 

 

 

 

 

 

 

 

 

 

【能力提升】

9.(2006年江陰市)某公司開(kāi)發(fā)的960件新產(chǎn)品,需加工后才能投放市場(chǎng),現(xiàn)有甲、乙兩個(gè)工廠都想加工這批產(chǎn)品,已知甲工廠單獨(dú)加工完成這批產(chǎn)品比乙工廠單獨(dú)加工完成這批產(chǎn)品多用20天,而乙工廠每天比甲工廠多加工8件產(chǎn)品.在加工過(guò)程中,公司需每天支付50元?jiǎng)趧?wù)費(fèi)請(qǐng)工程師到廠進(jìn)行技術(shù)指導(dǎo).

    (1)甲、乙兩個(gè)工廠每天各能加工多少件新產(chǎn)品?

    (2)該公司要選擇省時(shí)又省錢(qián)的工廠加工,乙工廠預(yù)計(jì)甲工廠將向公司報(bào)加工費(fèi)用為每天800元,請(qǐng)問(wèn):乙工廠向公司報(bào)加工費(fèi)用每天最多為多少元時(shí),才可滿(mǎn)足公司要求,有望加工這批產(chǎn)品.

 

 

 

 

 

 

 

 

 

 

 

10.(2006年揚(yáng)州市)“中國(guó)荷藕之鄉(xiāng)”揚(yáng)州市寶應(yīng)縣有著豐富的荷藕資源.某荷藕加工企業(yè)已收購(gòu)荷藕60噸,根據(jù)市場(chǎng)信息,如果對(duì)荷藕進(jìn)行粗加工,每天可加工8噸,每噸可獲利1000元;如果進(jìn)行精加工,每天可加工0.5噸,每噸可獲利5000元.由于受設(shè)備條件的限制,兩種加工方式不能同時(shí)進(jìn)行.

    (1)設(shè)精加工的噸數(shù)為x噸,則粗加工的噸數(shù)為_(kāi)_____噸,加工這批荷藕需要____天,可獲利______元(用含x的代數(shù)式表示)

    (2)為了保鮮需要,該企業(yè)必須在一個(gè)月(30天)內(nèi)將這批荷藕全部加工完畢,精加工的噸數(shù)x在什么范圍內(nèi)時(shí),該企業(yè)加工這批荷藕的獲利不低于80000元?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

11.(2005年河南省)某公司為了擴(kuò)大經(jīng)營(yíng),決定購(gòu)進(jìn)6臺(tái)機(jī)器用于生產(chǎn)某種活塞.現(xiàn)有甲、乙兩種機(jī)器供選擇,其中每種機(jī)器的價(jià)格和每臺(tái)機(jī)器日生產(chǎn)活塞的數(shù)量如下表所示.經(jīng)過(guò)預(yù)算,本次購(gòu)買(mǎi)機(jī)器所耗資金不能超過(guò)34萬(wàn)元.

 

價(jià)格(萬(wàn)元/臺(tái))

 7

5

每臺(tái)日產(chǎn)量(個(gè))

100

60

    (1)按該公司要求可以有幾種購(gòu)買(mǎi)方案?

    (2)若該公司購(gòu)進(jìn)的6臺(tái)機(jī)器的日生產(chǎn)能力不能低于380個(gè),那么為了節(jié)約資金應(yīng)選擇哪種購(gòu)買(mǎi)方案?

 

 

 

 

 

 

 

 

 

 

 

 

 

12.(2005年貴州省)為迎接“2005.中國(guó)貴州黃果樹(shù)瀑布節(jié)”,園林部門(mén)決定利用現(xiàn)有的3600盆甲種花卉和2900盆乙種花奔搭配A、B兩種園藝造型共50個(gè),擺放在迎賓大道兩側(cè),搭配每個(gè)造型所需要花奔情況如下表所示:

造型

 A

90盆

30盆

 B

40盆

100盆

    (1)符合題意的搭配方案有哪幾種?

    (2)若搭配一個(gè)A種造型的成本為1000元,搭配一個(gè)B種造型的成本為1200元,試說(shuō)明選用(1)中哪種方案成本最低?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

【應(yīng)用與探究】

13.(2006年長(zhǎng)沙市)我市某鄉(xiāng)A、B兩村盛產(chǎn)柑桔,A村有柑桔200噸,B村有柑桔300噸.現(xiàn)將這些柑桔運(yùn)到C、D兩個(gè)冷藏室,已知C倉(cāng)庫(kù)可儲(chǔ)存240噸,D倉(cāng)庫(kù)可儲(chǔ)存260噸;從A村運(yùn)往C、D兩處的費(fèi)用分別為每噸20元和25元,從B村運(yùn)往C、D兩處的費(fèi)用分別為每噸15元和18元.設(shè)從A村運(yùn)往C倉(cāng)庫(kù)的柑桔重量為x噸,A、B兩村運(yùn)往兩倉(cāng)庫(kù)的柑桔運(yùn)輸費(fèi)用分別為yA元和yB元.

    (1)請(qǐng)?zhí)顚?xiě)下表,并求出yA、yB與x之間的函數(shù)關(guān)系式:

 

  C

  D

 總計(jì)

 A

x噸

 

200噸

 B

 

 

300噸

總計(jì)

240噸

260噸

500噸

    (2)試討論A、B兩村中,哪個(gè)村的運(yùn)費(fèi)較少;

    (3)考慮到B村的經(jīng)濟(jì)承受能力,B村的柑桔運(yùn)費(fèi)不得超過(guò)4830元.在這種情況下,請(qǐng)問(wèn)怎樣調(diào)運(yùn),才能使兩村運(yùn)費(fèi)之和最小?求出這個(gè)最小值.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

答案:

例題經(jīng)典 

例1:(1)甲獨(dú)做20天,乙獨(dú)做30天 

(2)設(shè)甲做了x天,乙做了y天完成作業(yè),

解y≥15,即乙公司最少應(yīng)施工15天.

例2:學(xué)校派出158名,共有20個(gè)交通路口安排值勤

例3:(1)學(xué)生共有21人  (2)應(yīng)選青春社

考點(diǎn)精練 

1.B  2.C  3.B  4.C  5.B 

6.(1) 

(2)y<y­,∴900+0.5x<0.8x,解得x>3000,

∴選甲公司 

7.應(yīng)控制在:19.91到20.09噸之間 

8.甲進(jìn)價(jià)為50元,標(biāo)價(jià)70元,乙進(jìn)價(jià)為100元,標(biāo)價(jià)140元 

9.解:(1)設(shè)甲工廠每天加工x件,則乙公司每天加工(x+8)件 

由題意得:,解之得:x1=-24,x2=16.

經(jīng)檢驗(yàn),x1、x2均為所列方程的根,但x1=-24不合題意,舍去.

此時(shí)x+8=24.

答:甲工廠每天加工16件,乙工廠每天加工24件.

(2)由(1)可知加工960件產(chǎn)品,甲工廠要60天,乙工廠要40天.

所以甲工廠的加工總費(fèi)用為60×(800+50)=51000(元).

設(shè)乙工廠報(bào)價(jià)為每天m元,則乙工廠的加工總費(fèi)用為40×(m+50)元.

由題意得:40×(m+50)≤51000,解得m≤1225.

答:乙工廠所報(bào)加工費(fèi)每天最多為1225元,可滿(mǎn)足公司要求,有望加工這批產(chǎn)品. 

10.(1)(60-x)噸,()天,[5000x+(60-x)×1000]元 

(2)5(噸)≤x≤12(噸) 

11.(1)有3種方案:①甲0臺(tái),乙6臺(tái),②甲1臺(tái),乙5臺(tái),③甲2臺(tái),乙4臺(tái) 

(2)應(yīng)選方案② 

12.(1) 

A

30

31

32

B

20

19

18

(2)設(shè)費(fèi)用為y=1000x+1200(50-x)=-200x+60000,∴A32天,B18個(gè)費(fèi)用最低. 

13. (1)

 

  C

  D

 總計(jì)

 A

x噸

(200-x)噸

200噸

 B

(240-x)噸

(60+x)噸

300噸

總計(jì)

240噸

260噸

500噸

yA=-5x+5000(0≤x≤2000),yB=3x+4680(0≤x≤200).

 (2)當(dāng)yA=yB時(shí),-5x+5000=3x+4680,x=40;

當(dāng)yA>yB時(shí),-5x+5000>3x+4680,x<40;

當(dāng)yA<yB時(shí),-5x+5000<3x+4689,x>40,

∴當(dāng)x=40時(shí),yA=yB即兩村運(yùn)費(fèi)相等;

當(dāng)0≤x<40時(shí),yA>yB即B村運(yùn)費(fèi)較少;

當(dāng)40<x≤200時(shí),yA<yB即A村費(fèi)用較。

(3)由yB≤4830,3x+4680≤4830,∴x≤50,

設(shè)兩村運(yùn)費(fèi)之和為y,∴y=yA+yB,即:y=-2x+9680.

又∵0≤x≤50時(shí),y隨x增大而減。

∴當(dāng)x=50時(shí),y有最小值,y最小值=9580(元).

答:當(dāng)A村調(diào)往C倉(cāng)庫(kù)的柑桔重量為50噸,調(diào)往D倉(cāng)庫(kù)為150噸,B村調(diào)往C倉(cāng)庫(kù)為190噸,調(diào)往D倉(cāng)庫(kù)110噸的時(shí)候,兩村的運(yùn)費(fèi)之和最小,最小費(fèi)用為9580元.

 

試題詳情

初三數(shù)學(xué)復(fù)習(xí)教學(xué)案

第8講 一元一次不等式(組)及應(yīng)用

 

【回顧與思考】

【例題經(jīng)典】

 

不等式的性質(zhì)及運(yùn)用

例1 下列四個(gè)命題中,正確的有(  )

    ①若a>b,則a+1>b+1;②若a>b,則a-1>b-1;

    ③若a>b,則-2a<-2b;④若a>b,則2a<2b.

    A.1個(gè)    B.2個(gè)    C.3個(gè)    D.4個(gè)

  【分析】注意觀察前后兩個(gè)式子的變化,想一想與不等式的性質(zhì)是否相符.

 

會(huì)解一次不等式,并理解解集用數(shù)軸表示的意義

例2 (2006年嘉興市)解不等式x>x-2,并將其解集表示在數(shù)軸上.

  【點(diǎn)評(píng)】步驟類(lèi)似于解一元一次方程,但要注意不等號(hào)方向的變化.

 

借助數(shù)軸,解一元一次不等式組

例3  (2006年淄博市)解不等式組,并在數(shù)軸上表示解集.

     

  【點(diǎn)評(píng)】先求每個(gè)不等式的解集,再借助數(shù)軸求不等式組的解集.

 

會(huì)列不等式(組)解應(yīng)用題

例4 (2006年廣東。⿲⒁幌涮O(píng)果分給若干個(gè)小朋友,若每位小朋友分5個(gè)蘋(píng)果,則還剩12個(gè)蘋(píng)果;若每位小朋友分8個(gè)蘋(píng)果,則有一個(gè)小朋友分不到8個(gè)蘋(píng)果.求這一箱蘋(píng)果的個(gè)數(shù)與小朋友的人數(shù).

 【點(diǎn)評(píng)】從題意尋求兩個(gè)不等關(guān)系,列出不等式組,求出解集,并取正整數(shù)解.

 

【基礎(chǔ)訓(xùn)練】

1.(2006年蕪湖市)已知a>b>0,則下列不等式不一定成立的是(  )

    A.a(chǎn)b>b2     B.a(chǎn)+c>b+c    C.<     D.a(chǎn)c>bc

2.(2006年紹興市)不等式2-x>1的解集是(  )

    A.x>1     B.x<1     C.x>-1     D.x<-1

3.如圖,數(shù)軸上所表示的不等式組的解集是(  )

A.x>-1     B.-1<x≤2    C.-1≤x≤2    D.x≤2

4.(2006年深圳市)下列不等式組的解集,在數(shù)軸上表示為如圖所示的是(  )

5.不等式組的解集在數(shù)軸上表示正確的是(  )

6.(2006年包頭市)不等式組的解集是(  )

    A.0<x≤4     B.3<x<4     C.1<x≤4    D.2<x≤8

7.關(guān)于x的不等式組只有4個(gè)整數(shù)解,則a的取值范圍是(  )

   A.-5≤a≤-     B.-5≤a≤-    C.-5<a≤-      D.-5<a<-

8.(2006年隨州市)不等式組的整數(shù)解是_______.

9.(2006年包頭市)一堆玩具分給若干個(gè)小朋友,若每人分3件,則剩余3件;若前面每人分5件,則最后一人得到的玩具不足3件.則小朋友的人數(shù)為_(kāi)_____人.

10.一次普法知識(shí)競(jìng)賽共有30道題,規(guī)定答對(duì)一道題得4分,答錯(cuò)或不答一道題得-1分,在這次競(jìng)賽中,小明獲得優(yōu)秀(90分或90分以上),則小明至少答對(duì)了______道題.

 

 

 

【能力提升】

11.(2006年懷化市)求不等式+2y≤-+8所有正整數(shù)解的和.

 

 

 

12.解下列不等式組

(1)              (2)(2006年綿陽(yáng)市)

 

 

 

 

 

 

 

 

 

 

 

 

13.解不等式組,并把其解集在數(shù)軸上表示出來(lái).

 

 

 

 

 

 

 

 

 

14.(2006年滬州市)九年級(jí)(3)班學(xué)生到學(xué)校閱覽室上課外閱讀課,班長(zhǎng)問(wèn)老師要分成幾個(gè)小組,老師風(fēng)趣地說(shuō):假如我把43本書(shū)分給各小組,若每組8本,還有剩余;若每組分9本,卻不夠,你知道該分幾個(gè)組嗎?(請(qǐng)你幫助班長(zhǎng)分組,注意寫(xiě)出解題過(guò)程,不能僅有分組的結(jié)果喲!)

 

 

 

 

15.

    根據(jù)對(duì)話(huà)的內(nèi)容,試求出餅干和牛奶的標(biāo)價(jià)各是多少元?

 

 

 

 

 

 

 

 

【應(yīng)用與探究】

16.(2005年重慶市)由于電力緊張,某地決定對(duì)工廠實(shí)行錯(cuò)峰用電.規(guī)定:在每天的7:00到24:00為用電高峰期,電價(jià)為a元/kW?h;每天0:00到7:00為用電平穩(wěn)期,電價(jià)為b元/kW?h;下表為某廠4月和5月兩個(gè)月的用電量和電費(fèi)的情況統(tǒng)計(jì)表:

月份

用電量(萬(wàn)kW?h)

電費(fèi)(萬(wàn)元)

 4

        12

    6.4

 5

        16

    8.8

    (1)若4月份在平穩(wěn)期的用電量占當(dāng)月用電量的,5月份在平穩(wěn)期的用電量占當(dāng)月用電量的,求a,b的值.

    (2)若6月份該廠預(yù)計(jì)用電20萬(wàn)kW?h,為將電費(fèi)探究在10萬(wàn)元至10.6萬(wàn)元之間(不含10萬(wàn)元和10.6萬(wàn)元),那么6月份在平穩(wěn)期的用電量占當(dāng)月用電量的比例應(yīng)控制在什么范圍?

 

 

 

 

 

 

 

 

 

答案:

例題經(jīng)典

 例1:B 

例2:x>-3 

例3:x≥13  例4:設(shè)有x個(gè)小朋友,則蘋(píng)果為(5x+12)個(gè),

所以0<8x-(5x+12)<8,解之得4<x<,

所以x取5或6,當(dāng)x=5時(shí),5x+12=37,當(dāng)x=6時(shí)5x+12=42.

考點(diǎn)精練 

1.D  2.B  3.B  4.D  5.B  6.A  7.C 

8.有±1和0  9.3人  10.24道 

11.和為6  12.(1)-1≤x<3  (2)x≤- 

13.-2<x≤3  數(shù)略表示略 

14.設(shè)分x個(gè)組  則取整數(shù)x=5 

15.解:設(shè)餅干的標(biāo)價(jià)每盒x元,牛奶的標(biāo)價(jià)為每袋y元,

            由②得y=9.2-0.9x.④.

            把④代入①得,x+9.2-0.9x>10,

            ∴x>8.由③得8<x<10.

            ∵x是整數(shù),∴x=9.

            將x=9代入④,得y=9.2-0.9×9=1.1,

            答:餅干一盒標(biāo)價(jià)9元,一袋牛奶標(biāo)價(jià)1.1元 

            16.解:(1)根據(jù)題意得 

            (2)設(shè)6月份在平穩(wěn)期的用電量占當(dāng)月用電量的x,

            根據(jù)題意得10<20?(1-x)?0.6+20?x?0.4<10.6,解得0.35<x<0.5,

            故6月份在平穩(wěn)期的用電量應(yīng)占當(dāng)月用電量的0.35至0.5.

             

             

            試題詳情

            初三數(shù)學(xué)復(fù)習(xí)教學(xué)案

            第7講 分式方程及應(yīng)用

             

            【回顧與思考】

             

            【例題經(jīng)典】

             

            理解分式方程的有關(guān)概念

            例1  指出下列方程中,分式方程有(  )

                ①=5  ②=5  ③x2-5x=0  ④+3=0

                A.1個(gè)     B.2個(gè)     C.3個(gè)     D.4個(gè)

              【點(diǎn)評(píng)】根據(jù)分式方程的概念,看方程中分母是否含有未知數(shù).

             

            掌握分式方程的解法步驟

            例2  解方程:

            (1)(2006年成都市);

             

                (2)(2006年紹興市)。

            【點(diǎn)評(píng)】注意分式方程最后要驗(yàn)根。

             

             

            分式方程的應(yīng)用

            例3  (2006年長(zhǎng)春市)某服裝廠裝備加工300套演出服,在加工60套后,采用了新技術(shù),使每天的工作效率是原來(lái)的2倍,結(jié)果共用9天完成任務(wù),求該廠原來(lái)每天加工多少套演出服.

             【點(diǎn)評(píng)】要用到關(guān)系式:工作效率=。

             

             

             

            【基礎(chǔ)訓(xùn)練】

            1.如果分式的值相等,則x的值是(  )

            A.9      B.7       C.5     D.3

             

            2.(2005年宿遷市)若關(guān)于x的方程=0有增根,則m的值是(  )

            A.3      B.2       C.1        D.-1

             

            3.(2006年嘉興市)有兩塊面積相同的小麥試驗(yàn)田,分別收獲小麥9000kg和15000kg.已知第一塊試驗(yàn)田每公頃的產(chǎn)量比第二塊少3000kg,若設(shè)第一塊試驗(yàn)田每公頃的產(chǎn)量為xkg,根據(jù)題意,可得方程(  )

             

            4.已知方程有增根,則這個(gè)增根一定是(  )

            A.2       B.3         C.4        D.5

             

            5.方程的解是(  )

            A.1       B.-1       C.±1       D.0

             

            6.張老師和李老師同時(shí)從學(xué)校出發(fā),步行15千米去縣城購(gòu)買(mǎi)書(shū)籍,張老師比李老師每小時(shí)多走1千米,結(jié)果比李老師早到半小時(shí),兩位老師每小時(shí)各走多少千米?設(shè)李老師每小時(shí)走x千米,依題,得到的方程是(  )

             

            7.(2006年懷化市)方程的解是_______.

             

            8.若關(guān)于x的方程-1=0無(wú)實(shí)根,則a的值為_(kāi)______.

             

            9.若x+=2,則x+=_______.

             

            【能力提升】

            10.解下列方程:

              (1)=1;          (2)(2006年河南省)=3。

             

             

             

             

             

             

             

            11.(2006年長(zhǎng)沙市)在社會(huì)主義新農(nóng)村建設(shè)中,某鄉(xiāng)鎮(zhèn)決定對(duì)一段公路進(jìn)行改造.已知這項(xiàng)工程由甲工程隊(duì)單獨(dú)做需要40天完成;如果由乙工程隊(duì)先單獨(dú)做10天,那么剩下的工程還需要兩隊(duì)合做20天才能完成.

              (1)求乙工程隊(duì)單獨(dú)完成這項(xiàng)工程所需的天數(shù);

              (2)求兩隊(duì)合做完成這項(xiàng)工程所需的天數(shù).

             

             

             

             

             

             

             

            12.(2006年懷化市)懷化市某鄉(xiāng)積極響應(yīng)黨中央提出的“建設(shè)社會(huì)主義新農(nóng)村”的號(hào)召,在本鄉(xiāng)建起了農(nóng)民文化活動(dòng)室,現(xiàn)要將其裝修.若甲、乙兩個(gè)裝修公司合做需8天完成,需工錢(qián)8000元;若甲公司單獨(dú)做6天后,剩下的由乙公司來(lái)做,還需12天完成,共需工錢(qián)7500元.若只選一個(gè)公司單獨(dú)完成.從節(jié)約開(kāi)始角度考慮,該鄉(xiāng)是選甲公司還是選乙公司?請(qǐng)你說(shuō)明理由.

             

             

             

             

             

             

             

             

            13.請(qǐng)根據(jù)所給方程=1,聯(lián)系生活實(shí)際,編寫(xiě)一道應(yīng)用題(要求題目完整題意清楚,不要求解方程)

             

             

             

             

             

             

            14.先閱讀下列一段文字,然后解答問(wèn)題.

                已知:

                方程x-=1的解是x1=2,x2=-;

                方程x-=2的解是x1=3,x2=-;

                方程x-=3的解是x1=4,x2=-;

                方程x-=4的解是x1=5,x2=-

                問(wèn)題:觀察上述方程及其解,再猜想出方程x-=10的解,并寫(xiě)出檢驗(yàn).

             

             

             

             

             

             

            【應(yīng)用與探究】

            15.閱讀理解題:

                閱讀下列材料,關(guān)于x的方程:

                x+=c+的解是x1=c,x2=;

                x-=c-的妥是x1=c,x2=-

                x+=c+的解是x1=c,x2=

                x+=c+的解是x1=c,x2=……

                (1)請(qǐng)觀察上述方程與解的特征,比較關(guān)于x的方程x+(m≠0)與它們的關(guān)系,猜想它的解是什么,并利用“方程的解”的概念進(jìn)行驗(yàn)證.

                (2)由上述的觀察、比較、猜想、驗(yàn)證,可以得出結(jié)論:如果方程的左邊是未知數(shù)與其倒數(shù)的倍數(shù),方程右邊的形式與左邊完全相同,只把其中未知數(shù)換成了某個(gè)常數(shù),那么這樣的方程可以直接得解,請(qǐng)用這個(gè)結(jié)論解關(guān)于x的方程:x+.

             

             

             

             

             

             

            答案:

            例題經(jīng)典 

            例1:B 

            例2:(1)x=-  (2)x=4 

            例3:設(shè)服裝廠原來(lái)每天加工x套,則=9,解之得x=20,

            經(jīng)檢驗(yàn)x=20是原方程的根,答:略

            考點(diǎn)精練 

            1.A  2.B  3.C  4.B  5.D  6.B 

            7.x=0  8.a(chǎn)=1  9.x2+=2 

            10.(1)x=2  (2)x=- 

            11.(1)解:設(shè)乙工程隊(duì)單獨(dú)完成這項(xiàng)工程需要x天,

            根據(jù)題意得:×20=1,

            解之得:x=60,經(jīng)檢驗(yàn):x=60是原方程的解.

            答:乙工程隊(duì)單獨(dú)完成這項(xiàng)工程所需的天數(shù)為60天.

            (2)解:設(shè)兩隊(duì)合做完成這項(xiàng)工程需的天數(shù)為y天,

            根據(jù)題意得:()y=1,解得:y=24.

            答:兩隊(duì)合做完成這項(xiàng)工程所需的天數(shù)為24天 

            12.解:設(shè)甲獨(dú)做x天完成,乙獨(dú)做y天完成

            設(shè)甲每天工資a元,乙每天工資b元.

            ∴甲獨(dú)做12×750=9000,乙獨(dú)做24×250=6000,

            ∴節(jié)約開(kāi)支應(yīng)選乙公司. 

            13.略 

            14.x1=11,x2=-  檢驗(yàn)略 

            15.(1)x1=c,x2=.

             

             

            試題詳情

            初三數(shù)學(xué)復(fù)習(xí)教學(xué)案

            第6講 一元二次方程及應(yīng)用

            【回顧與思考】

            【例題經(jīng)典】

            掌握一元二次方程的解法

            例1  解方程:

                (1)3x2+8x-3=0;(2)9x2+6x+1=0;(3)x-2=x(x-2);(4)x2-2x+2=0

            會(huì)判斷一元二次方程根的情況

            例2  不解方程判別方程2x2+3x-4=0的根的情況是(  )

                A.有兩個(gè)相等實(shí)數(shù)根;    B.有兩個(gè)不相等的實(shí)數(shù)根;

                C.只有一個(gè)實(shí)數(shù)根;      D.沒(méi)有實(shí)數(shù)根

              【點(diǎn)評(píng)】根據(jù)b2-4ac與0的大小關(guān)系來(lái)判斷

            一元二次方程的應(yīng)用

            例3  (2006年包頭市)某印刷廠1月份印刷了書(shū)籍60萬(wàn)冊(cè),第一季度共印刷了200萬(wàn)冊(cè),問(wèn)2、3月份平均每月的增長(zhǎng)率是多少?

              【點(diǎn)評(píng)】設(shè)2、3月份平均每月的增長(zhǎng)率為x,即60+60(1+x)+60(1+x)2=200

            【基礎(chǔ)訓(xùn)練】

            1.(2006年溫州市)方程x2-9=0的解是(  )

                A.x1=x2=3           B.x1=x2=9       C.x1=3,x2=-3       D.x1=9,x2=-9

            2.下列方程中肯定是一元二次方程的是(  )

                A.-ax2+bx+c=0       B.3x2-2x+1=mx2     C.x+=1         D.(a2+1)x2-2x-3=0

            3.(2006年廣州市)一元二次方程x2-2x-3=0的兩個(gè)根分別為(  )

                A.x1=1,x2=-3       B.x1=1,x2=3

            C.x1=-1,x2=3       D.x1=-1,x2=-3

            4.在一幅長(zhǎng)80cm,寬50cm的矩形風(fēng)景畫(huà)的四周鑲一條金色紙邊,制成一幅矩形圖.如果要使整個(gè)掛圖的面積是5400cm2,設(shè)金色紙邊的寬為xcm,那么x滿(mǎn)足的方程是( )

                A.x2+130x-1400=0     B.x2+65x-350=0

            C.x2-130x-1400=0     D.x2-65x-350=0

            5.兩圓的半徑分別是方程x2-3x+2=0的兩根.且圓心距d=1,則兩圓的位置關(guān)系是(  )

            A.外切       B.內(nèi)切       C.外離         D.相交

            6.(2006年常德市)已知一元二次方程有一個(gè)根是2,那么這個(gè)方程可以是_______(填上你認(rèn)為正確的一個(gè)方程即可).

            7.方程(x-2)(x-3)=6的解為_(kāi)_____.

             

            8.(2006年成都市)已知某工廠計(jì)劃經(jīng)過(guò)兩年的時(shí)間,把某種產(chǎn)品從現(xiàn)在的年產(chǎn)量100萬(wàn)臺(tái)提高到121萬(wàn)臺(tái),那么每年平均增長(zhǎng)的百分?jǐn)?shù)約是________.按此年平均增長(zhǎng)率,預(yù)計(jì)第4年該工廠的年產(chǎn)量應(yīng)為_(kāi)____萬(wàn)臺(tái).

             

            9.若一個(gè)等腰三角形三邊長(zhǎng)均滿(mǎn)足方程x2-6x+8=0,則此三角形的周長(zhǎng)為_(kāi)____.

             

             

             

             

             

             

             

             

            【能力提升】

            10.方程(m+1)|m|+1+(m-3)x-1=0.

                (1)m取何值時(shí),方程是一元二次方程,并求出此方程的解;

            (2)m取何值時(shí),方程是一元一次方程.

             

             

             

             

             

             

             

            11.解下列方程:

            (1)x2-12x-4=0;                 (2)(2006年浙江。﹛2+2x=2;

             

             

            (3)(2006年蕪湖市)x2-4x-12=0;  (4)(x+1)2-4=0

             

             

             

             

             

             

             

             

            12.(2006年黃岡市)市政府為了解決市民看病難的問(wèn)題,決定下調(diào)藥品的價(jià)格.某種藥品經(jīng)過(guò)連續(xù)兩次降價(jià)后,由每盒200元下調(diào)至128元,求這種藥品平均每次降價(jià)的百分率是多少?

             

             

             

             

             

             

             

            13.某商場(chǎng)將進(jìn)貨價(jià)為30元的臺(tái)燈以40元售出,平均每月能售出600個(gè).調(diào)查表明:這種臺(tái)燈的售價(jià)每上漲1元,其銷(xiāo)售量就將減少10個(gè).為了實(shí)現(xiàn)平均每月10000元的銷(xiāo)售利潤(rùn),這種臺(tái)燈的售價(jià)應(yīng)定為多少?這時(shí)應(yīng)進(jìn)臺(tái)燈多少個(gè)?

            請(qǐng)你利用方程解決這一問(wèn)題.

             

             

             

             

             

             

             

             

             

            14.(2006年重慶市)機(jī)械加工需要用油進(jìn)行潤(rùn)滑以減少摩擦,某企業(yè)加工一臺(tái)大型機(jī)械設(shè)備潤(rùn)滑用油量為90千克,用油的重復(fù)利用率為60%,按此計(jì)算,加工一臺(tái)大型機(jī)械設(shè)備的實(shí)際耗油量為36千克.為了建設(shè)節(jié)約型社會(huì),減少油耗,該企業(yè)的甲、乙兩個(gè)車(chē)間都組織了人員為減少實(shí)際耗油量進(jìn)行攻關(guān).

                (1)甲車(chē)間通過(guò)技術(shù)革新后,加工一臺(tái)大型機(jī)械設(shè)備潤(rùn)滑油用油量下降到70千克,用油的重復(fù)利用率仍然為60%.問(wèn)甲車(chē)間技術(shù)革新后,加工一臺(tái)大型機(jī)械設(shè)備的實(shí)際耗油量是多少千克?

                (2)乙車(chē)間通過(guò)技術(shù)革新后,不僅降低了潤(rùn)滑用油量,同時(shí)也提高了用油的重復(fù)利用率,并且發(fā)現(xiàn)在技術(shù)革新的基礎(chǔ)上,潤(rùn)滑用油量每減少1千克,用油量的重復(fù)利用率將增加1.6%.這樣乙車(chē)間加工一臺(tái)大型機(jī)械設(shè)備的實(shí)際耗油量下降到12千克.問(wèn)乙車(chē)間技術(shù)革新后,加工一臺(tái)大型機(jī)械設(shè)備潤(rùn)滑用油量是多少千克?用油的重復(fù)利用率是多少?

            【應(yīng)用與探究】

            15.填空:

              (1)方程x2+2x+1=0的根為x1=____,x2=_____,則x1+x1=______,x1?x2=_____;

              (2)方程x2-3x-1=0的根為x1=____,x2=_____,則x1+x2=______,x1?x2=_____;

              (3)方程3x2+4x-7=0的根為x1=_____,x2=_____,則x1+x2=______,x1?x2=_____.

                由(1)(2)(3)你能得到什么猜想?并證明你的猜想.請(qǐng)用你的猜想解答下題

            已知2+是方程x2-4x+C=0的一個(gè)根求方程的另一個(gè)根及C的值.

             

             

             

             

             

             

             

             

             

             

             

             

            答案:

            例題經(jīng)典 

            例1:(1)x1=-3,x2=  (2)x1=x2=-  (3)x1=1,x2=2  (4)x1=+,x2=- 例2:B  例3:設(shè)增長(zhǎng)率為x列方程60+60(1+x)+60(1+x)2=200

            考點(diǎn)精練 

            1.C  2.D  3.C  4.B  5.B 

            6.略  7.x1=0,x2=5  8.10%,146  9.6或10或12 

            10.(1)m=1,x1=  (2)m=0或m=-1 

            11.(1)x1=6+2,x2=6-2 

            (2)x1=-1+,x2=-1-  (3)x1=6,x2=-2,(4)x1=-3,x2=1 

            12.設(shè)百分率為x,則200(1-x)2=128,

            解之得x1=1.8(舍去),x2=0.2,即百分率為20% 

            13.設(shè)售價(jià)為x元,則(x-30)[600-(x-40)×10]=10000,

            解得x=50,x=80,即售價(jià)為50元時(shí)進(jìn)500個(gè).售價(jià)為80元時(shí)進(jìn)200個(gè). 

            14.解:(1)由題意,得70×(1-60%)=70×40%=28(千克).

            (2)設(shè)乙車(chē)間加工一臺(tái)大型機(jī)械設(shè)備潤(rùn)滑用油量為x千克.

            由題意,得:x×[1-(90-x)×1.6%-60%]=12,

            整理得x-65x-750=0,解得:x1=75,x2=-10(舍去),(90-75)×1.6%+60%=84%.

            答:(1)技術(shù)革新后,甲車(chē)間加工一臺(tái)大型機(jī)械設(shè)備的實(shí)際耗油量是28千克.(2)技術(shù)革新后,乙車(chē)間加工一臺(tái)大型機(jī)械設(shè)備潤(rùn)滑用油量是75千克,用油的重復(fù)利用率是84%. 

            15.(1)x1=-1,x2=-1,x1+x2=-2,x1?x2=1 

            (2)x1=,x1+x2=3,x2=-1

             (3)x1=1,x2=-,x1+x2=-,x1?x2=- 

            猜想:ax2+bx+c=0的兩根為x1與x2,則x1+x2=-,x1?x2=,

            應(yīng)用:另一根為2-,C=1

             

             

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