《高等数学、大学英语》综合模拟题.doc

高等数学部分：一、选择题：在每小题给出的四个选项中，只有一项是符合题目要求的.1. 极限（ B ）A. B. 1 C. 2 D. e 2. 若，则（ C ） A. 1 B. e C. 2 D. 3. 设函数，则等于（ B ）A0 B C1 D3 4.设，则等于（ C ）A.B.C.D.5设则（ B ）A BC D6.若事件A发生必然导致事件B发生，则事件A和B的关系一定是（ A ）A. B. C. 对立事件D.互不相容事件 7. 极限( A )A等于1 B等于0 C为无穷大 D不存在8.设=( C )A BC D二、填空题：把答案填在题中的横线上.9.设函数则f f(1)= .10.已知，则k= .11.曲线y=3x5-5x4+4x-1的拐点是 .12.函数在闭区间-1,1上的最大值是 .13.设函数，则 .14. .15.若则 .16.已知，则 .9.1 10.-9 11. (1,1) 12.13. ; 14. ;15. 16.1.三、解答题：解题应写出推理、演算步骤.17.计算.18.设的一个原函数为，求.19.设函数，求.20.设函数z=xy+f(u)，u=y2-x2，其中f是可微函数. 证明：.21.求，其中为自然数.22.甲、乙两袋装有大小相同的红球和白球，甲袋装有2个红球，2个白球；乙袋装有2个红球，n个白球.由甲，乙两袋中各任取2个球.（）若n=3，求取到的4个球全是红球的概率；（）若取到的4个球中至少有2个红球的概率为，求n.23.求由曲线及围成的平面图形的面积S以及此平面图形绕x轴旋转一周所得旋转体的体积.参考答案：17. 解： 18. 解：因为，所以19. 解：因为 所以 20. 解：证明：， 21. 解：令22. 解：（I）记“取到的4个球全是红球”为事件.（II）记“取到的4个球至多有1个红球”为事件，“取到的4个球只有1个红球”为事件，“取到的4个球全是白球”为事件.由题意，得所以, ，化简，得解得，或（舍去），故 .23.求由曲线及围成的平面图形的面积S以及此平面图形绕x轴旋转一周所得旋转体的体积.解:由已知曲线画出平面图形如图所示的阴影区域.由，得交点坐标为（1，1）,则1(1,1)-112Ox大学英语部分：. PhoneticsDirections: In each of the following groups of words, there are four underlined letters or letter combinations marked A, B, C and D. Compare the underlined parts and identify the one that is different from the others in pronunciation. Mark your answer by blackening the corresponding letter on the Answer Sheet. l. A .background B .although C .blouse D .amount B2. A .civil B .curriculum C .crystal D .country A3. A. ground B. country C. thousand D. found B4. A. pour B. hour C. course D. four B. Vocabulary and Structure Directions: There are 10incomplete sentences in this section. For each sentence there are four choices marked A, B, C and D. Choose one answer that best completes the sentence and blacken the corresponding letter on the Answer Sheet. 5. Human beings should find a new _ of energy. B A. orient B. source C. origin D. souse6. The couch is comfortable to _. DA. sit B. be sat C. sitted D. sit on7. So loudly _ that all the people in the room got a fright. CA. he shouted B. shout he C. did he shout D. he did shout8. The mountain is 1,000 feet _ the sea level. CA. over B. higher C. above D. high 9. It was a _ room, with beautiful wall paper, waxed floor and nice furniture. BA. pleased B. pleasant C. pleasing D. preasant10. He regretted _the decision too hastily. CA. make B. to make C. making D. have maked11. The professor insisted that we _ our homework before next month. CA. handed in B. will hand in C. hand in D. must hand in12. When I was a child I used_ swimming in the lake. CA. to going B. going C. to go D. go 13. Sauls brother left the matter entirely up to_ and_. DA. I, he B. him, I C. me, he D. him, me 14. The 19th winter Games, held in Salt Lake City, _ an Olympic tradition which goes back almost 3 , 000 years . DA. is the part of B. are the part of C. is part of D. are part of. Cloze Directions: For each blank in the following passage , there are four choices marked A , B , C and D . Choose the one that is most suitable and mark your answer by blackening the corresponding letter on the Answer Sheet . The most extraordinary dream I ever had was one in which I fancied that, as I was going into a theater, the cloak-room attendant_15_Me in the lobby and insisted on my _16_my legs behind. I was not surprised; but I was considerably annoyed. I said I had _17_heard of such a rule at any respectable theater _18_, and that I considered it a most absurd regulation. The man replied that he was very_19_, but that those were his instructions. People complained that they could not get to and from their _20_ comfortably, because other peoples legs were always in the_21_; and it had, therefore, been decided that _22_should leave their leg outside. It seemed to me that the management, in making this order, had gone_23_their legal right; and, under ordinary circumstances, I should have disputed it. However, I didnt want to_24_a disturbance; and _25_I sat down and meekly prepared to comply with the demand. I had never before_26_that the human leg could be unscrewed. I had always _27_ it was more securely fixed. But the man showed me bow to undo them, and I found that they came off_28_easily.The discovery did not surprise_29_any more than the original request that I should take them off. Nothing does surprise one in a dream.15. A. called B. helped C. stopped D. met C16. A. leave B. leaves C. leaving D. left C17. A. ever B. never C. once D. always B18. A. before B. after C. during D. behind A19. A. angry B. sorry C. friendly D. helpful B20. A. homes B. jobs C. arms D. seats D21. A. road B. lobby C. theater D. way D22. A. somebody B. everybody C. anybody D. nobody B23. A. beyond B. from C. to D. around A24. A. understand B. make C. have D. learn B25 . A. as B. because C. while D. so D26. A. know B. known C. knowing D. knows B27. A. believe B. considered C. thought D. distrusted C28. A. quite B. much C. do D. greatly A29. A. him B. them C. me D. us CIV . Reading Comprehension Directions: There are five reading passages in this part. Each passage is followed by four questions. For each question there are four suggested answers marked A, B, C and D. Choose one best answer and blacken the corresponding letter on the Answer Sheet. Passage One Are you aware that you actually possess six senses? The sixth is a muscular sense responsible for directing your muscles intelligently to the exact extent necessary for each action you perform. For example, when you reach for an object, the sensory nerves linking the muscles to the brain stop your hand at the correct spot. This automat is perception of the position of your muscles in relation to the object is your muscular sense in action.Muscles are strongly bundles of fibers varying from one five-thousandth of an inch to about three inches. They have three unique characteristics, they can become shorter and thicker; they can stretch; and they can retract to their original positions. Under a high-powered microscope, muscle tissue is seen as long, slender cells with a grainy texture like wood.More than half of a persons body is composed of muscle fibers, most of which are involuntaryin other words, work without conscious direction. The voluntary muscles, those that we move consciously to perform particular actions, number more than five hundred. Women have only 60 to 70 percent as much muscle as men for their body mass. That is why an average woman cant lift as much, throw as far, or hit as hard as an average man.30. According to the selection, the muscular sense is responsible for _.CA. the efficiency of our muscles B. the normal breathing functionC. directing our muscles intelligently D. the work of only our involuntary muscles 31. Intelligent use of the muscles means that _.CA. one always knows what his muscles are doingB. one performs simple actions without workingC. ones muscles are used only to the extent necessary for each action they performD. one improves muscular action consciously32. Muscles are unique fibers because, they can _.DA. contract B. stretch C. retract D. do all of the above33. Under a microscope, muscle cells appear to be _.AA. textured like wood B. colored like woodC. smooth and red D. short and thickPassage Two “Fingers were made before forks” when a person gives up good manners, puts aside knife and fork, and dives into his food, someone is likely to repeat that saying.The fork was an ancient agricultural tool, but for centuries no one thought of eating with it. Not until the eleventh century, when a young lady from Constantinople brought her fork to Italy, did the custom reach Europe.By the fifteenth century the use of the fork was widespread in Italy. The English explanation was that Italians were averse to eating food touched with fingers, “Seeing all mens fingers are not alike clean.” English travelers kept their friends in stitches while describing this ridiculous Italian custom.Anyone who used a fork to eat with was laughed at in England for the next hundred years. Men who used forks were thought to be sissies, and women who used them were called show-offs and overnice. Not until the late 1600s did using a fork become a common custom.34. The custom of eating with a fork w as _.CA. brought to Europe from America B. begun when forks were inventedC. brought to Europe from Asia D. invented by Italians35. By the fifteenth century forks were used _.AA. all over Italy B. only in ConstantinopleC. widely in Europe D. In England36. To English travelers in Italy, the use of forks seemed _.DA. clever B. necessary C. good manner D. ridiculous37. The English thought that Italians used forks in order to _.BA. imitate the people of the East B. keep their food cleanC. impress visitors with their good manners D. amuse the EnglishPassage Three Whats the best way to protect a tender, green seedling from the hungry stomach of deer? Give the seedling bad breath!The same chemical that gives people bad breath after they have eaten garlic can save small trees from being eaten by animals.A kind of chemical selenium(硒), which is also found in garlic, is planted in the soil near a young tree. The trees roots absorb the selenium which is then carried to the leaves.From there the selenium is used to form a chemical called dimethyl selenide (乙烷硒化物)the same chemical made in the human mouth after eating garlic. As deer wander around looking for food, they smell the seedlings leaves and leave the plants alone.The selenium is important. Why? Because each year deer eat millions of dollars worth of trees farm seedlings.So far, selenium has been tested only on Douglas fir (枞树) seedlings, but researchers think they could protect fruit trees and garden plants, too.38. When people eat garlic, _.AA. they send out a horrible smell B. they are out of breathC. they will feel sick D. it is hard for them to breathe39 According to this passage the bad smell given off from those leaves is that of _.BA. the young trees absorb garlicB. the roots of the young trees smell like garlicC. the young trees arent fit for the deer to eatD. the leaves of the young trees smell like garlic40. Up till the time the news was announced, this kind of chemical was used _.DA. all over the world B. all over the United StatesC. on fruit trees and garden trees D. on Douglas fir young trees41. The best title of this passage is _.CA. Hungry Deer and Young Trees B. Why Dont Deer Eat Young Fruit TreesC. Plants Saved by “Bad Breath” D. How to Protect Young Trees Passage Four I was only eight years old when the Second World War ended, but I can still remember something about the victory celebrations in the small town where I lived on the day when the war in Europe ended. We had not suffered much from the war there. But both at home and at school I had become accustomed to the phrases before the war and when the wars over. Before the war , apparently , things had been better , though I was too young to understand why , except that there had been no bombs then , and people had eaten things like ice-cream and bananas, which I had only heard of . When the war was over we would go back to London, but this meant little to me. I did not remember what London was like. What I remember now about VE (Victory in Europe) Day was the May evening. After dinner I said I wanted to see the bonfire（大火堆）, so when it got dark my father took me to the end of the street. The bonfire was very high, and somehow people had collected some old clothes to dress the unmistakable figure with the moustache（胡子）they had to put on top of it. Just as we arrived, they set light to it. The flames rose and soon swallowed the guy. Everyone was cheering and shouting, and an old woman came out of her house with two chairs and threw them on the fire to keep it going. I stood beside my father until the fire started to go down, not knowing what to say. He said nothing, either. He had fought in the First World War and may have been remembering the end of that. At last he said, Well, thats it, son. Lets hope that this time it really will be the last one. 42. Where did the author live before the Second World War? AA. In London. B. In a small town. C. In Europe. D. In the countryside. 43. The unmistakable figure with the moustache most probably represents_. DA. those who died in the war B. those who had won C. an imaginary figure D. the most hated person in the war-Hitler 44. Which of the following statements is true? BA. The authors father built a bonfire on VE Day. B. The authors father had fought in the First World War. C. The authors father had fought in the Second World War. D