武汉大学网络教育2006年秋季入学考试模拟卷1.doc

武汉大学网络教育2006年秋季入学考试模拟卷1高等数学（专升本）一、单项选择题（每小题2分，共20分）1. 函数在点x=x0处连续是在点x=x0处可导的 。A充要条件B充分条件C必要条件D无关条件2. x时，无穷小量与等价，则k= 。A0B1C2D33当时，与比较是A较高阶的无穷小量；B较低阶的无穷小量；C同阶的无穷小量；D等价的无穷小量。4下列等式正确的是A；B；C； D5设是的一个原函数，则ABCD6级数绝对收敛的条件是A；B；C；D7判断函数的导数有（）个实根。A1B2C3D08设，则（）A(n+1)!Bn!C(n-1)!Dn9下列广义积分收敛的是A；B；C；D10已知函数，则A；B；C；D二、填空题（每小题2分，共20分） 11函数二阶可微，且，则 12设函数在点x0可导，则 。13函数的极值点为。14设在点处连续，则=151617函数在区间上应用拉格朗日中值定理时所得的点 18.已知向量与垂直，则19.将积分化为极坐标系下的累次积分，则。20.幂级数的收敛半径。三、计算下列各题（每小题5分，共35分）21已知，求22求级数的收敛半径和收敛区间23求24.求方程满足条件的特解。25. 已知，求26.已知，求四、综合题（25分）27设二元函数可微分，则它的两个偏导数，必定存在，对不对？ 28设函数满足，证明武汉大学网络教育入学考试模拟试卷2高等数学（专升本）一、单项选择题（每小题2分，共20分）1、设 f (x) = 在x = 0连续，则等于： （A） 0； （B） 1； (C) 2； (D) 3；2、 设f（x）dx=x2e2x+c，则f（x）= A、2xe2xB、2x2e2xC、xe2xD、2xe2x（1+x）3、设（t）dt=f（x）-，且f（0）=1，则f（x）= A、exB、exC、e2xD、e2x 4、下列广义积分收敛的是： (A)； (B)； (C)； (D)；5、当时，都是无穷小量，则的： （A） 高阶无穷小； (B) 低阶无穷小； (C) 同阶无穷小； (D) 等阶无穷小；6、在（-1，1）区间上满足罗定理条件的函数是： （A） (B) ； (C) ； (D) ；7、设f(x)有连续的导数，则下列命题正确的是 A、f(2x)dx=B、f(2x)dx=f(2x)+CC、f(2x)dx=2f (2x)D、f(2x)= f(2x)8、设= A、sinx+xcosxB、sinx- xcosxC、xcosx -sinxD、-(sinx+ cosx)9、设I1= I2= I3=则I1、 I2、I3的大小关系为 。A. I1I2I3 B. I2I1I3C. I3I1I2D. I1I3I210、设y1, y2是二阶常系数线性齐次方程y+Py+qy=0的两个特解,C1、C2是两个任意常数，则下列命题正确的是 。A. C1y1+C2y2是该方程的通解B. C1y1+C2y2不是该方程的通解C. C1y1+C2y2是该方程的解D. C1y1+C2y2不是该方程的解二、填空题（每小题2分，共20分）1已知函数在点处可导，且，则2设在点处连续，且，则3已知，则45已知，则6已知，则7设，则8级数收敛，其和等于5，则9已知向量，则10微分方程的通解为三、计算下列各题（每小题5分，共35分）1求2求3求4设 由方程 确定，求 , 。5求6.求的值，使7. 设z = u2lnv，而u =，v=3x-2y，求四、综合题（25分）1 过点作抛物线的切线。求：由抛物线，上述切线及轴所围成的平面图形面积。2设，函数在a, b上连续，（a, b）内可导，试利用柯西中值定理，证明存在一点，使得武汉大学网络教育2006年秋季入学考试模拟卷1英语(专升本) I. Reading comprehension (40%)Directions:There are four reading passages in this part. Each passage is followed by some questions or unfinished statements. For each of them there are four choices marked A ), B ), C) and D). You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the centerQuestions 1 to 5 are based on the following passage:In ancient times the most important examinations were spoken, not written. In the school of ancient Greece and Rome, testing usually consisted of saying poetry aloud or giving speeches.In the European universities of the Middle Ages, students who were working for advanced degrees had to discuss questions in their field of study which people who had made a special study of the subject. This custom exists today as part of the process of testing candidates for the doctors degree.Generally, however, modern examinations are written. The written examination, where all students are tested on the same questions, was probably not known until the nineteenth century. Perhaps it came into existence with the great increase in population and the development of modern industry. A room full of candidates for a state examination, timed exactly by electric clocks and carefully watched over by managers, resembles a group of workers at an automobile factory. Certainly, during examinations teachers and students are expected to act like machines.One type of test is sometimes called an objective test. It is intended to deal with facts, not personal opinions. To make up an objective test the teacher writes a series of questions , each of which has only one correct answer. Along with each question the teacher writes the correct answer and also three statements that like answers to students who have not learned the material-properly.1. In the Middle Ages students _A. took objective tests. B. specialized in one subject. C. were timed by electric clocks.D. never wrote exams.2. The main idea of paragraph 3 is _A. workers now take examinations.B. the population has grown.C. there are only. written exams today.D. examinations are now written and timed.3. The kind of exams where students must select answers are _A. personal. B. objective. C. spoken. D. written.4. Modern industry must have developed _ A. before the Middle Ages. B. around the 19th century. C. in Greece or Rome. D. machines to take tests.5. It may be concluded that testing _ A. should test only opinions. B. should always be written. C. has changed since the Middle Ages. D. is given only in factories.Questions 6 to 10 are based on the following passage :Mans first real invention, and one of the most important inventions in history, was the wheel. All transportation (运输) and every machine in the world depend on it.The wheel is the simplest yet perhaps the most remarkable (值得注意的) of all inventions, because there are no wheels in nature- no living thing was ever created with wheels. How, then, d id man come to invent the wheel?Perhaps some early hunters found that they could roll the dead body of a heavy animal through the forest on logs more easily than they could carry it. However, the logs themselves weighed a lot.It must have taken a great prehistoric (史前的) thinker a long time to imagine two thin slices (薄片)of log connected at their centers by a strong stick. This would roll along just as the log did, yet be much lighter and easier to handle. Thus the wheel and axle (轴) came into being, and with them the first carts.6. The wheel is important because _. A. it was mans first real invention. B. all transportation depends on it C. every machine depends on it D. both A and C7. It was remarkable of man to invent the wheel because _.A. it led to many other inventions B. man had no use for it then C. there were no wheels, in nature D. all of the above8. The wheel was probably invented by _. A. a group of early hunters B. the first man on earth C. a great prehistoric thinker D. the man who made the first cart9. This selection says that the first wheel may have been a_.A. round piece of stone B. heavy log C. piece of metal D. slice of log10. The idea for it may have come from _. A. hunting an animalB. rolling a dead body of an animal on logs C. watching a rolling stone D. watching running animalsQuestions 11 to 15 are based on the following passage:If you are like most people, your intelligence varies from season to season. You are probably a lot sharper in the spring than you are at any other time of year. A noted scientist, Ellsworth Huntington (1876 - 1947), concluded from other mens work and his own among peoples in different climates that climate and temperature have a definite effect on our mental abilities.He found that cool weather is much more favorable for creative thinking than is summer heat. This does not mean, however, that the mental abilities of large numbers of people tend to be lowest in summer.Spring appears to be the best period of the year for thinking. One reason may be that in the spring mans mental abilities are affected by the same factors that bring about great changes in all nature.Fall is the next-best season, then winter. As for summer, it seems to be a good time to take a long vacation from thinking.11.According to the passage, mans intelligence _ A. stays the same throughout the yearC. changes from year to yearB. varies from day to dayD. changes with the seasons12. Ellsworth Huntington decided that climate and temperature have _A.some effect on most peoples intelligenceB.a great effect on everyone intelligenceC.some effect on a few peoples intelligenceD.no effect on most peoples intelligence13. Ellsworth Huntingtons conclusion was based on _A.variations of his own mental abilities from season to seasonB.the results of research done by him and other scientists among peoples in different climatesC.detailed records of temperature changes in different placesD. detailed records of different ways of thinking among peoples in different climates14. Why does the author say summer is a good time to take a long vacation from thinking?A.Because a long vacation in summer helps to improve peoples mental power.B.Because people tend to be less creative during summer.C.Because summer is a good time for outdoor activities.D. Because mental exertion in the summer heat taxes too much of peoples energy.15. The central idea of this passage is _A.mans intelligence varies from place to placeB.mans mental abilities change from season to seasonC.man should take a long vacation in summerD.if you want to do creative thinking, go to a cool placeQuestions 16 to 20 are based on the following passage:The incident happened one morning outside Albert Schweitzers hospital in the African Jungle(密林). A patient had gone fishing in another mans boat. The owner of the boat thought he should be given all the fish that were caught. Dr. Schweitzer said to the boat owner:You are right because the other man ought to have asked permission to use your boat. But you are wrong because you are careless and lazy. You simply twisted (缠绕) the chain of your canoe round a tree instead of fastening (栓牢)it with a lock. Of laziness you are guilty (有罪的) because you were asleep in your shed instead of making use of the good chance for fishing. He turned to the patient: But you were in the wrong when you took the boat without asking the owners permission. You were in the right because you were not so lazy as he was and you did not want to let the night go by without making some use of it. Dr. Schweitzer divided the catch among the fisherman, the boat owner, and the hospital.16. Dr. Schweitzer settled the argument because _ A. he was the judge (法官) there. B. it took place at his hospital.C. he wanted some of the fish. D. he wanted to help the patient.17. Schweitzer told the man that _A. each was partly right and partly wrong.B. both men were completely right.C. both men were completely wrong.D. one man was more guilty than the other.18. The owner of the canoe was wrong because _ A. the canoe did not really belong to him. B. he should have locked his boat to a tree. C. he wasted a good fishing night. D. both B and C.19. Schweitzers patient was right because _ A. the canoe really belonged to the hospital. B. he had used the night well. C. he had asked for permission to use the boat.D. both A and C. 20. Implied (暗示) but not stated:A. Both men were patientsB. The natives trusted Dr. Schweitzer.C. Dr. Schweitzers hospital was in the jungle.D. The canoe was fastened with a rope.ll. Vocabulary & Structure (45%)Directions:There are 45 incomplete sentences in this part. For each sentence there are four choices marked A), B), C) and D ). Choose the One that best completes the sentence. Then blacken the corresponding letter on the Answer Sheet with a single line through the center21.His achievements _ him to greater efforts.A. qualified B. Accelerated C. obligedD. stimulated22.In our time of information, the Internet will open _ of the people. A. eyesight B. View C. Horizon D. vision23.His knowledge and experience _ to the progress of the work.A.promoted B. Advanced C. respondedD. contributed24.If you want to know the times of buses, please _ at the office.A.inquire B. Require C. requestD. acquire25.Alex, a student of Chinese literature from Australia, is very _ on Beijing opera.A.interestedB. fond C. favoriteD. keen26.They sat around a table and had a pleasant chat _ a cup of coffee.A.withB. of C. overD. to27.The judge would give reconsideration to his decision when new evidence came to _A.the light B. Lights C. lightD. lighting28.Jack came to the party with a young woman, whom I _to be his girlfriend.A.pretended B. Persuaded C. assumedD. granted29.The government _to pressure from the trade union and decided to better the working conditions.A.responded B. Impressed C. commentedD. considered30.Good work _ good pay.A.requests B. Deserves C. attainsD. awards31.Important people dont always have much free time as their work _ all their time.A.takes away B. takes in C. takes overD. takes up32.His humor attracted a large audience who _ with laughter at his jokes.A.exploded B. Groaned C. roaredD. cracked33.Ive got a bad memory these days. Please _ me to mail this letter.A.remember B. Remind C. recallD. memorize34.It was here that the scattered forces of the revolution _ in the autumn of 1928.A.collected B. Assembled C. huddledD. concentrated35.The doctor took his temperature, and it was two degrees above _A.average B. Regular C. ordinaryD. normal36.Of the many plans submitted, the committee selected the one that seemed most _A.possible B. Feasible C. probableD. permissible37.The sailing ship was waiting for a _ of wind in order to travel to the east.A. variety B. Difference C. shiftD. adjustment38.The wounded policeman did not _ and open his eyes until three days later.A. come up B. come to C. come onD. come down39.There are many small islands _ all over the China South Sea.A. existed B. Scattered C. isolatedD. diffused40.These mails must be _ to the headquarters by noon. They are very urgent.A. sent away B. sent for C. sent outD. sent off41. John is very good _ football. A. in. B. for C. at D. with42. We were not prepared_ the tragic news and it came as a shock.A. to B. at C. from D. for43. It is quite important _ to master a foreign language.A. we B. that we C. for us D. for we 44. She seemed pleased when she met her cousin _ the first time. A. at B. in C. for D. by 45. Zhang Hong arrives _ Monday.A. in B. at C. for D. on 46. London is _ the Thames.A. to B. in C. on D. at 47. What time is it _ your watch?A. by B. on C. in D. at 48. During the night I was waken up_ the barking of a dog.A. with B. to C. by D. from49. China is rich _ natural resources. A. of B. in C. with D. for50. English isnt easy, _I like it.A. but B. or C. since D. because51. His behavior is _. No one knows what has happened to him.A. authoritative B. extraordinary C. characteristic D. professional52. We must _ the people to the dangers facing our country.A. awaken B. avoid C. adapt D. adopt53. Even the doctors were surprised at the _ improvement in his condition.A. rational B. diverse C. derivative D. dramatic54. I wish I _ longer this morning, but I had to get up and come to class. A. could have slept B. slept C. might have slept D. have slept55. We didnt know his telephone number, otherwise we _ him. A. would have telephonedB. must have telephoned C. would telephone D. had telephoned56. The Social Security Retirement Program is made up of two trust funds, _ could go penniless by next year. A. the larger one B. the larger of which C. the largest one D. the largest of which57. He moved away from his parents, and missed them _enjoy the exciting life in New York. A. too much to B. enough to C. very much to D. much so as to58. What _would happen if the director knew you felt that way? A. do you suppose B. you suppose C. will you suppose D. you would suppose59. We grow all our own fruit and vegetables, _ saves money, of course. A. what B. which C. as D. that60. _ is generally accepted, economical growth is determined by the smooth development of production. A. What B. That C. It D. As61. Look at the terrible situation I am in! If only I _ your advice.A. follow B. had followed C. would follow D. have followed62. It is recommended that the project _ until all the preparations have been made.A. is not started B. will no be started C. not be started D. is not to be started63. Having no money but _ to know, he simply said he would go without dinner. A. not to want anyone B. not wanting anyone C. wanted no one D. to want no one64. I remember _ to help us if we ever got into trouble. A. once offering B. him once offering C. him to offer D. to offer him65. As the fire was nearly out and it was getting late, they prepared to_ for the night.A. sit up B. retire C. stay up D. returnIII .Cloze (20%)Directions: There are 20 blanks in the following passage. For each blank there are four choices marked A), B), C) and D) on the right side of the paper. You should choose the ONE that best fits into the passage. Then mark the corresponding letter on the Answer Sheet with a single line through the center.Since the earliest t