07真题
2007年考研数学一真题与解析
2007年硕士研究生入学考试数学一试题及答案解析一、选择题：(本题共10小题，每小题4分，共40分. 每小题给出的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后的括号内)(1) 当0x +→(A) 1-. (B) ln. (C)1. (D) 1-.[ B ]【分析】 利用已知无穷小量的等价代换公式，尽量将四个选项先转化为其等价无穷小量，再进行比较分析找出正确答案.【详解】 当0x +→时，有1(1)~-=--1~2111~.22x -= 利用排除法知应选(B).(2) 曲线1ln(1)x y e x=++，渐近线的条数为(A) 0. (B) 1. (C) 2. (D) 3. [ D ]【分析】 先找出无定义点，确定其是否为对应垂直渐近线；再考虑水平或斜渐近线。
【详解】 因为01lim[ln(1)]x x e x→++=∞，所以0x =为垂直渐近线；又 1lim [ln(1)]0x x e x→-∞++=，所以y=0为水平渐近线；进一步，21ln(1)ln(1)lim lim[]lim x x x x x y e e x x x x →+∞→+∞→+∞++=+==lim11xx x e e →+∞=+， 1l i m [1]l i m [l n (1)]x x x y xe x x→+∞→+∞-⋅=++-=lim[ln(1)]x x e x →+∞+-=lim[ln (1)]lim ln(1)0x x x x x e e x e --→+∞→+∞+-=+=，于是有斜渐近线：y = x . 故应选(D).(3) 如图，连续函数y =f (x )在区间[−3，−2]，[2，3]上的图形分别是直径为1的上、下半圆周，在区间[−2，0]，[0，2]的图形分别是直径为2的上、下半圆周，设0()().xF x f t dt =⎰则下列结论正确的是(A) 3(3)(2)4F F =--. (B) 5(3)(2)4F F =.(C) )2(43)3(F F =-. (D))2(45)3(--=-F F .[ C ]【分析】 本题考查定积分的几何意义，应注意f (x )在不同区间段上的符号，从而搞清楚相应积分与面积的关系。
07年专八真题及答案
2007年英语专八试卷真题及答案Part2 Reading Comprehension (30min)Text AThe Welsh language has always been the ultimate marker of Welsh identity, but a generation ago it looked as if Welsh would go the way of Manx. once widely spoken on the isle of Man but now extinct. Government financing and central planning, however, have helped reverse the decline of Welsh. Road signs and official public documents are written in both Welsh and English, and schoolchildren are required to learn both languages. Welsh is now one of the most successful of Europe’s regional languages, spoken by more than a half-million of the country’s three million people.The revival of the language, particularly among young people, is part of a resurgence of national identity sweeping through this small, proud nation. Last month Wales marked the second anniversary of the opening of the National Assembly, the first parliament to be convened here since 1404. The idea behind devolution was to restore the balance within the union of nations making up the United Kingdom. With most of the people and wealth, England has always had bragging rights. The partial transfer of legislative powers from Westminster, implemented by Tony Blair, was designed to give the other members of the club- Scotland, Northern Ireland, and Wales-a bigger say and to counter centrifugal forces that seemed to threaten the very idea of the union.The Welsh showed little enthusiasm for devolution. Whereas the Scots voted overwhelmingly for a parliament, the vote for a Welsh assembly scraped through by less than one percent on a turnout of less than 25 percent. Its powers were proportionately limited. The Assembly can decide how money from Westminster or the European Union is spent. It cannot, unlike its counterpart in Edinburgh, enact laws. But now that it is here, the Welsh are growing to like their Assembly. Many people would like it to have more powers. Its importance as figurehead will grow with the opening in 2003, of a new debating chamber, one of many new buildings that are transforming Cardiff from a decaying seaport into a Baltimore-style waterfront city. Meanwhile a grant of nearly two million dollars from the European Union will tackle poverty. Wales is one of the poorest regions in Western Europe- only Spain, Portugal, and Greece have a lower standard ofliving.Newspapers and magazines are filled with stories about great Welsh men and women, boosting self-esteem. To familiar faces such as Dylan Thomas and Richard Burton have been added new icons such as Catherine Zeta-Jones, the movie star, and Bryn Terfel, the opera singer. Indigenous foods like salt marsh lamb are in vogue. And Wales now boasts a national airline. Awyr Cymru. Cymru, which means “land of compatriots,” is the Welsh name for Wales. The red dragon, the nation’s symb ol since the time of King Arthur, is everywhere- on T-shirts, rugby jerseys and even cell phone covers.“Until very recent times most Welsh people had this feeling of being second-class citizens,” said Dyfan Jones, an 18-year-old student. It was a warm summer night, and I was sitting on the grass with a group of young people in Llanelli, an industrial town in the south, outside the rock music venue of the National Eisteddfod, Wales’s annual cultural festival. The disused factory in front of us echoed to the sounds of new Welsh bands.“There was almost a genetic tendency for lack of confidence,” Dyfan continued. Equally comfortable in his Welshness as in his membership in the English-speaking, global youth culture and the new federal Europe, Dyfan, like the rest of his generation, is growing up with a sense of possibility unimaginable ten years ago. “We used to think. We can’t do anything, we’re only Welsh. Now I think that’s changing.”11. According to the passage, devolution was mainly meant toA. maintain the present status among the nations.B. reduce legislative powers of England.C. create a better state of equality among the nations. √D. grant more say to all the nations in the union.12. The word “centrifugal” in the second paragraph meansA. separat ist.√B. Conventional.C. feudal.D. political13. Wales is different from Scotland in all the following aspects EXCEPTA. people’s desire for devolution.B. locals’ turnout for the voting.C. powers of the legislative body.D. status of the national language.√14. Which of the following is NOT cited as an example of the resurgence of Welsh national identityA. Welsh has witnessed a revival as a national language.B. Poverty-relief funds have come from the European Union.√C. A Welsh national airline is currently in operation.D. The national symbol has become a familiar sight.15. According to Dyfan Jones what has changed isA. people’s mentality. √B. pop culture.C. town’s appearance.D. possibilities for the people.Text BGetting to the heart of Kuwaiti democracy seems hilariously easy. Armed only with a dog-eared NEWSWEEK ID, I ambled through the gates of the National Assembly last week. Unscanned, unsearched, my satchel could easily have held the odd grenade or an anthrax-stuffed lunchbox. The only person who stopped me was a guard who grinned and invited me to take a swig of orange juice from his plastic bottle.Were I a Kuwaiti woman wielding a ballot, I would have been a clearer and more present danger. That very day Parliament blocked a bill giving women the vote; 29 M.P.s voted in favour and 29 against, with two abstentions. Unable to decide whether the bill had passed or not, the government scheduled another vote in two weeks- too late for women to register for June’s municipal elections. The next s uch elections aren’t until 2009. Inside the elegant, marbled Parliament itself, a sea of mustachioed men in white robes sat in green seats, debating furiously. The ruling emir has pushed for women’s political rights for years. Ironically, the democraticall y elected legislature has thwarted him. Traditionalists and tribal leaders are opposed. Liberals fret, too, that Islamists will let their multiple wives vote, swelling conservative ranks. “When I came to Parliament today, people who voted yes didn’t even shake hands with me,” said one Shia clerc. “Why can’t we respect each other and work together?”Why not indeed? By Gulf standards, Kuwait is a democratic superstar. Its citizens enjoy free speech (as long as they don’t insult their emir, naturally) and boas t a Parliament that can actually pass laws. Unlike their Saudi sisters, Kuwaiti women drive, work and travel freely. They run multibillion-dollar businesses and serve as ambassadors. Their academic success is such that colleges have actually lowered the grades required for make students to get into medical andengineering courses. Even then, 70 percent of university students are females.In Kuwait, the Western obsession with the higab finds its equivalent. At a fancy party for NEWSWEEK’s Arabic edition, som e Kuwaiti women wore them. Others opted for tight, spangled, sheer little numbers in peacock blue or parrot orange. For the party’s entertainment, Nancy Ajram, the Arab world’s answer to Britney Spears, sang passionate songs of love in a white mini-dress. She couldn’t dance for us, alas, since shaking one’s body onstage is illegal in Kuwait. That didn’t stop whole tables of men from raising their camera-enabled mobile phones and clicking her picture. You’d think not being able to vote or dance in public would anger Kuwait’s younger generation of women. To find out, I headed to the malls-Kuwait’s archipelago of civic freedom. Eager to duckStrict parents and the social taboos of dating in public. young Kuwaitis have taken to cafes, beaming flirtatious infrared e-mails to one another on their cell photos. At Starbucks in the glittering Al Sharq Mall, I found only tables of men, puffing cigarettes and grumbling about the service .At Pizza Hut, I thought I’d got an answer after encountering a young woman who loo ked every inch the modern suffragette—drainpipe jeans,strappy sliver high-heeled sandals and a higab studded with purple rhinestones. But, no, Miriam Al-Enizi, 20,studying business administration at Kuwait University, doesn’t think women need the vote.” Me n are better at politics than women,”she explained, adding that women in Kuwait already have everything they need. Welcome to democracy, Kuwait style.16. According to the passage, which of the following groups of people might be viewed as being dangerous by the guards?A. Foreign tourists.B. Women protestors.√C. Foreign journalists.D. Members of the National Assembly.17. The bill giving women the vote did not manage to pass becauseA. Different interest groups held different concerns.√B.Liberals did not reach consensus among themselves.C. Parliament was controlled by traditionalists.D.Parliament members were all conservatives.18. What is the role of the 4th and 5th paragraphs in the development of the topic?A. To show how Kuwaiti women enjoy themselves.B. To describe how women work and study in Kuwait.C. To provide a contrast to the preceding paragraphs.√D. To provide a contrast to the preceding paragraphs.19. Which of the following is NOT true about young Kuwaiti women?A. They seem to be quite contented.B. They go in for Western fashions.C. They desire more than modern necessities.√D. They favour the use of hi-tech products.Text CRichard, King of England from 1189 to 1199, with all his characteristic virtues and faults cast in a heroic mould, is one of the most fascinating medieval figures. He has been described as the creatureand embodiment of the age of chivalry, In those days the lion was much admired in heraldry, and more than one king sought to link himself with its repute. When Richard's contemporaries called him" Coeur de Lion"(The Lion heart), they paid a lasting compliment to the king of beasts. Little did the English people owe him for his services, and heavily did they pay for his adventures. He was in England only twice for a few short months in his ten years' reign; yet his memory has always English hearts, and seems to present throughout the centuries the pattern of the fighting man. In all deeds of prowess as well as in large schemes of war Richard shone. He was tall and delicately shaped strong in nerve and sinew, and most dexterous in arms. He reioiced in personal combat, and regarded his opponents without malice as necessary agents in his fame He loved war, not so much for the sake of glory or political ends, but as other men love science or poetry, for the excitement of the struggle and the glow of victory. By this his whole temperament was toned; and united with the highest qualities of the military commander, love of war called forth all the powers of his mind and body.Although a man of blood and violence, Richard was too impetuous to be either treacherous on habitually cruel. He was as ready to forgive as he was hasty to offend; he was open-handed and munificent to profusion; in war circumspect in design and skilful in execution; in political a child, lacking in subtlety and experience. His political alliances were formed upon his likes and dislikes; his political schemes had neither unity nor clearness of purpose. The advantages gained for him by military geoids were flung away through diplomatic ineptitude. When, on the jouthey to the East,Messina in Sicily was won by his arms he was easily persuaded to share with his polished, faithless ally, Philip Augustus, fruits of a victory which more wisely used might have foiled the French King's artful schemes. The rich and tenable acquisition of Cyprus was cast away even more easily than it was won. His life was one magnificent parade, which, when ended, left only an empty plain.In 1199, when the difficulties of raising revenue for the endless war were at their height, good news was brought to King Richard. It was said there had been dug up near the castle of Chaluz, on the lands of one of his French vassals, a treasure of wonderful quality; a group of golden images of an emperor, his wife, sons and daughters, seated round a table, also of gold, had been unearthed. The King claimed this treasure as lord paramount. The lord of Chaluz resisted the demand, and the King laid siege to his small, weak castle. On the third day, as he rode daringly, near the wall. confident in his hard-tried luck, a bolt from a crossbow struck him in the left shoulder by the neck. The wound, already deep, was aggravated by the necessary cutting out of the arrow-head. Gangrene set in, and Coeur de Lion knew that he must pay a soldier’s debt. He prepared for death with fortitude and calm, and in accordance with the principles he had followed. He arranged his affairs, he divided his personal belongings among his friends or bequeathed them to charity. He declared John to be his heir, and made all present swear fealty to him. He ordered the archer who had shot the fatal bolt, and who was now a prisoner, to be brought before him. He pardoned him, and made him a gift of money. For seven years he had not confessed for fear of being compelled to be reconiled to Philip, but now he received the offices of the Church with sincere and exemplary piety, and died in the forty-second year of his age on April 6, 1199, worthy, by the consent of all men, to sit with King Arthur and Roland andother heroes of martial romance at some Eternal round Table, which we trust the Creator of the Universe in His comprehension will not have forgotten to provide.The archer was flayed alive.20 “ little did the English people own him for his service” (paragraph one) means that the EnglishA. paid few taxes to him.B. gave him little respect.C. received little protection from him.D. had no real cause to feel grateful to him.√21. To say that his wife was a “ magnificent parade’( paragraph Tw o) implies that it was to some extent.A . spent chiefly at war. B. impressive and admirable.C. lived too pompouslyD. an empty show.√22. Richard’s behaviour as death approached showed.\A. bravery and self-control.B. Wisdom and correctnessC. Devotion a nd romanceD. Chivalry and charity√23. The point of the last short paragraph is that Richard wasA. cheated by his own successorsB. determined to take revenge on his enemies.C. more generous to his enemies than his seccesors.D unable to influence the be havior of his successors.√24. Which of the following phrase best describes Richard as seen by the author?A. An aggressive king, too fond of war.B. A brave king with minor faults.√C. A competent but cunning soldier.D. A kind with great political skills.25. The relationship between the first and second paragraphs is thatA. each presents one side of the picture. √B. the first generalizes the second gives examples.C. the second is the logical result of the first.D. both present Richard’s virtues and fault s.TEXT DThe miserable fate of Enron’s employees will be a landmark in business history, one of those awful events that everyone agrees must never be allowed to happen again. This urge is understandable and noble: thousands have lost virtually all their retirement savings with the demise of Enron stock. But making sure it never happens again may not be possible, because the sudden impoverishment of those Enron workers represents something even larger than it seems. It’s the latest turn in the unwinding of one of the most audacious promise of the 20th century.The promise was assured economic security-even comfort- for essentially everyone in the developed world. With the explosion of wealth, that began in the 19th century it became possible to think about a possibility no one had dared to dream before. The fear at the center of daily living since caveman days- lack of food warmth, shelter- would at last lose its power to terrify. That remarkable promise became reality in many ways. Governments created welfare systems for anyone in need and separate programmes for the elderly (Social Security in the U.S.). Labour unions promised not only better pay for workers but also pensions for retirees. Giant corporations came into being and offered the possibility- in some cases the promise- of lifetime employmentplus guaranteed pensions.? The cumulative effect was a fundamental change in how millions of people approached life itself, a reversal of attitude that most rank as one of the largest in human history. For mi llennia the average person’s stance toward providing for himself had been. Ultimately I’m on my own. Now it became, Ultimately I’ll be taken care of.The early hints that this promise might be broken on a large scale came in the 1980s. U.S. business had become uncompetitive globally and began restructuring massively, with huge Layoffs. The trend accelerated in the 1990s as the bastions of corporate welfare faced reality. IBM ended it’s no-layoff policy. AT&T fired thousands, many of whom found such a thing simply incomprehensible, and a few of whom killed themselves. The other supposed guarantors of our economic security were also in decline. Labour-union membership and power fell to their lowest levels in decades. President Clinton signed a historic bill scaling back welfare. Americans realized that Social Security won’t provide social security for any of us.A less visible but equally significant trend a affected pensions. To make costs easier to control, companies moved away from defined benefit pension plans, which obligate them to pay out specified amounts years in the future, to defined contribution plans, which specify only how much goes into the play today. The most common type of defined-contribution plan is the 401(k). the significance ofThe 401(k) is that it puts most of the responsibility for a person’s economic fate back on the employee. Within limits the employee must decide how much goes into the plan each year and how it gets invested- the two factors that will determine how much it’s worth wh en the employee retires.Which brings us back to Enron? Those billions of dollars in vaporized retirement savings went in employees’ 401(k) accounts. That is, the employees chose how much money to put into those accounts and then chose how to invest it. E nron matched a certain proportion of each employee’s 401(k) contribution with company stock, so everyone was going to end up with some Enron in his or her portfolio; but that could be regarded as a freebie, since nothing compels a company to match employee contributions at all.At least two special features complicate the Enron case. First, some shareholders charge top management with illegally covering up the company’s problems, prompting investors to hang on when they should have sold. Second, Enron’s 401(k) accounts were locked while the company changed plan administrators in October, when the stock wasfalling, so employees could not have closed their accounts if they wanted to.But by far the largest cause of this human tragedy is that thousands of employees were heavily overweighed in Enron stock. Many had placed 100% of their 401(k) assets in the stock rather than in the 18 other investment options they were offered. Of course that wasn’t prudent, but it’s what some of them did.The Enron employees’’ re tirement disaster is part of the larger trend away from guaranteed economic security. That’s why preventing such a thing from ever happening again may be impossible. The huge attitudinal shift to I’ll-be-taken-care-of took at least a generation. The shift back may take just as long. It won’t be complete until a new generation of employees see assured economic comfort as a 20th- century quirk, and understand not just intellectually but in their bones that, like most people in most times and places, they’re o n their own26. why does the author say at the beginning “The miserable fate of Enron’s employees will be a landmark in business history…”?A. Because the company has gone bankrupt.B. Because such events would never happen again.C. Because many Enron workers lost their retirement savings.D. Because it signifies a turning point in economic security.√27. According to the passage, the combined efforts by governments, layout unions and big corporations to guarantee economic comfort have led to a significant change inA. people’s outlook on life.√B. people’s life styles.C. people’s living standardD. people’s social values.28. Changes in pension schemes were also part ofA. the corporate lay-offs.B. the government cuts in welfare spending.√C. the economic restructuring.D. the warning power of labors unions.29. Thousands of employees chose Enron as their sole investment option mainly becauseA. The 401(k) made them responsible for their own future.B. Enron offered to add company stock to their investment.√C. their employers intended to cut back on pension spending.D. Enron’s offer was similar to a defined-benefit plan.30. Which is NOT seen as a lesson drawn from the Enron disaster?A. 401(k) assets should be placed in more than one investment option.B. Employees have to take up responsibilities for themselves.C. Such events could happen again as it is not easy to change people’s mind.D. Economic security won’t be taken for granted by future young workers.√PART Ⅲ GENERAL KNOWLEDGE（10 MIN）31. The majority of the current population in the UK are decedents of all the following tribes respectively EXCEPTA. the AnglosB. the CeltsC. the Jutes √D. the Saxons32. The Head of State of Canada is represented byA. the MonarchB. the PresidentC. the Prime MinisterD. the Governor-general √33. The Declaration of Independence was written byA. Thomas Jefferson √B. George WashingtonC. Alexander HamiltonD. James Madison34. The original inhabitants of Australia wereA. the Red IndiansB. the EskimoC. the Ab origines √D. the Maoris35. Which of the following novels was written by Emily Bronte?A. Oliver TwistB. MiddlemarchC. Jane EyreD. Wuthering Heights √36. William Butler Yeats was a(n) ______ poet and playwright.A. AmericanB. CanadianC. Irish √D. Australian37. Death of a Salesman was written byA. Arthur Miller √B. Ernest HemingwayC. Ralph EllisonD. James Baldwin38. _______ refers to the study of the internal structure of words and the rules of word formation.A. PhonologyB. Morphology √C. Semant icsD. Sociolinguistics39. The distinctive features of a speech variety may be all the following EXCEPTA. LexicalB. SyntacticC. phonologicalD. psycholinguistic √40. The word tail once referred to “the tail of a horse”, but now it is used to mean “the tail of any animal.” This is an example ofA.widening of meaning √B. narrowing of meaningC. meaning shiftD. loss of meaning英译中Good bye and good luck Scientific and technological advances are enabling us to comprehend the furthest reaches of the cosmos, the most basic constituents of matter, and the miracle of life.At the same time, today, the actions, and inaction, of human beings imperil not only life on the planet, but the very life of the planet.Globalization is making the world smaller, faster and richer. Still, 9/11, avian flu, and Iran remind us that a smaller, fatster world is not necessarily a safer world.Our world is bursting with knowledge - but desperately in need of wisdom. Now, when sound bites are getting shorter, when instant messages crowd out essays, and when individual lives grow more frenzied, college graduates capable of deep reflection are what our world needs.For all these reasons I believed - and I believe even more strongly today - in the unique and irreplaceable mission of universities.科技进步正在使我们能够探索宇宙的边陲、物质最基本的成分及生命的奇迹.与此同时，今天，人类所做的及没能做到的事情，不仅危害到这个星球上的生命，也危害到该星球的寿命。
商法07司法考试真题
07年全国司法资格考试真题（商法）一、单项选择题，每题所给的选项中只有一个正确答案。
每题1分。
25．某国有企业拟改制为公司。
除5个法人股东作为发起人外，拟将企业的190名员工都作为改制后公司的股东，上述法人股东和自然人股东作为公司设立后的全部股东。
根据我国公司法的规定，该企业的公司制改革应当选择下列哪种方式？A．可将企业改制为有限责任公司，由上述法人股东和自然人股东出资并拥有股份B．可将企业改制为股份有限公司，由上述法人股东和自然人股东以发起方式设立C．企业员工不能持有公司股份，该企业如果进行公司制改革，应当通过向社会公开募集股份的方式进行D．经批准可以突破有限责任公司对股东人数的限制，公司形式仍然可为有限责任公司26．徽南公司由甲乙丙3个股东组成，其中丙以一项专利出资。
丙以专利出资后，自己仍继续使用该专利技术。
下列哪一选项是正确的？A．乙认为既然丙可以继续使用，则自己和甲也可以使用B．甲认为丙如果继续使用该专利则需向徽南公司支付费用C．丙认为自己可在原使用范围内继续使用该专利D．丙认为甲和乙使用该项专利应取得自己的书面同意27．甲乙丙丁4人组成一个运输有限合伙企业，合伙协议规定甲、乙为普通合伙人，丙、丁为有限合伙人。
某日，丁为合伙企业运送石材，路遇法院拍卖房屋，丁想替合伙企业竞买该房，于是以合伙企业的名义将石材质押给徐某，借得20万元，竞买了房子。
徐某的债权若得不到实现，应当向谁主张权利？A．应当要求丁承担清偿责任B．应当要求甲、乙、丙、丁承担连带清偿责任C．应当要求甲、乙承担连带清偿责任D．应当要求甲、乙、丁承担连带清偿责任28．千叶公司因不能清偿到期债务，被债权人百草公司申请破产，法院指定甲律师事务所为管理人。
下列哪一选项是错误的？A．甲律师事务所租赁百草公司酒店用作管理人办公室的行为不违反破产法的规定B．甲律师事务所有权处分千叶公司的财产C．甲律师事务所有权因担任管理人而获得报酬D．如甲律师事务所不能胜任职务，债权人会议有权罢免其管理人资格29．绿杨公司因严重资不抵债向法院申请破产，法院已经受理其申请。
07年专四真题及答案详解
2007年专四真题及答案PARTⅠ DICTIONListen to the following passage. Altogether the passage will be read to you four times. During the first reading, which will be done at normal speed, listen and try to understand the meaning. For the second and third readings, the passage will be read sentence by sentence, or phrase by phrase, with intervals of 15 seconds. The last reading will be done at normal speed again and during this time you should check your work. You will then be given 2 minutes to check through your work once more.Please write the whole passage on ANSWER SHEET ONE.PART II LISTENING COMPREHENSION [20 MIN]In Sections A B and C you will hear everything ONCE ONLY. Listen carefully and then answer the questions that follow. Mark the correct answer to each question on Answer Sheet Two.SECTION A CONVERSATIONSIn this section you will hear several conversations. Listen to the conversations carefully and then answer the questions that follow.Questions 1 to 3 are based on the following conversation. At the end of the conversation, you will be given 15 seconds to answer the questions. Now, listen to the conversation.1. Which of the following is NOT needed for the Lost Property Form?B.NationalityC. AddressD.Phone number2.From the conversation we know that Mark Adams comes fromA.EssexB.EdinburghC.LondonD.The US.3.What will Mark Adams do the day after tomorrow?A.To come to the office againB.To wait for the phone callC.To call the officeD.To write to the officeQuestions 4 to 7 are based on the following conversation. At the end of the conversation, you will be given 20 seconds to answer the questions. Now, listen to the conversation.4.Members of the club are required toA.register when they arrive.B.bring up to three guests.C.register their guests.D.show membership cards on arrival.5.Which of the following details about the changing rooms is NOT correct?A.There is a change for the use of the lockerB.Showers are installed in the changing rooms.C.Lockers are located in the changing roomsD.Lockers are used to store personal belongings.6.According to the club’s rules, members can playA.for 30minutes only.B.for one hour only.C.within the booked time only.D.longer than the booked time.7.Which of the following details is NOT correct?A.Players can eat in the club room.B.Players have to leave the club by ten o’clock.C.The courts are closed earlier than the club room.D.Players can use both the club room and the courts.Questions 8 to 10 are based on the following conversation. At the end of the conversation, you will be given 15 seconds to answer the questions. Now, listen to the conversation.8.At the university Mr. Robinson specialized inA.mathsB.physicsC.water managementD.geography9.Mr. Robinson worked for the Indian Government because ofA.university links.ernment agreements.pany projects.D.degree reuirements.10.After Mr. Robinson returned from India, heA.changed jobs several times.B.went to live in Manchester.C.did similar work as in India.D.became head of a research team.SECTION B PASSAGESIn this section, you will hear several passages. Listen to the passages carefully and thenanswer the questions that follow.Questions 11 to 13 are based on the following passage. ,4t the end of the passage, you will be given 15 seconds to answer the questions. Now, listen to the passage.11.According to the talk, the owner of a bike has toA.register his bike immediatelyB.put his bike on a list at onceC.have it stamped with a numberD.report to the police station12.The speaker in the talk recommendsA.two locks for all expensive bikes.B.a good lock for an expensive bike.C.cheap locks for cheap bikes.D.good locks for cheap bikes.13.What is the main idea of the talk?A.How to have the bike stamped.B.How to protect your bike.C.How to buy good locks.D.How to report your lost bike to the police.Questions 14 to 17 are based on the following passage. At the end of the passage, you will be given 20 seconds to answer the questions. Now, listen to the passage.14.Which course(s) runs or run for one hour each time?A.Conversation class.B.Writing Skills class.C.Examination Skills class.D.All of the three courses.15.Which course(s) does or do NOT require enrolment beforehand?A.Conversation class.B.Writing Skills class.C.Examination Skills class.D.All of the three courses.16.Which course(s) is(are) designed especially for students of economics and social sciences?A.Conversation class.B.Writing Skills class.C.Examination Skills class.D.All if the three courses.17.Which course(s) is(are) the shortest?A.Conversation class.B.Writing skills classC.Examination Skills class.D.All language courses.Questions 18 to 20 are based on the following passage. At the end of the passage, you will be given 15 seconds to answer the questions. Now, listen to the passage.18.How old was Leonardo da Vinci when he moved to Milan?A.25.B.30.C.35.D.40.19.Throughout his life, Leonardo da Vinci worked as all the following EXCEPTA.a painterB.an engineerC.an architectD.a builder20.Where did Leonardo da Vinci die?A.In FranceB.In MilanC.In FlorenceD.In TuscanySECTION C NEWS BROADCASTIn this section, you will hear several news items. Listen to them carefully and then answer the questions that follow.Questions 21 to 22are based on the following news. At the end of the news item, you will be given 15 seconds to answer the questions. Now. listen to the news.21.Who had to leave the Gaza Strip and the West Bank?A.The Israeli army.B.The Jewish settlers.C.The Palestinians.D.The Israeli Prime Minister.22.How many settlements would have to be removed altogrther in the Gaza Strip and the West Bank?A.2B.4C.21D.25Questions 23 to 24 are based on the following news. At the end of the news item, you will be given 15 seconds to answer the questions. Now. listen to the news.23. Which of the following in NOT mentioned in the news?A.The agreement has to be approved by Romania.B.The agreement has to be approved by Bulgaria.C.The agreement has to be approved by some EU states.D.The agreement has to be approved by all the EU states.24.Romania and Bulgaria can not join the EU in 2007 unless they carry out reforms in the following areas EXCEPTA.manufacturing.B.border control.C.adminstration.D.justice.Questions 25 to 26are based on the following news. At the end of the news item, you will be given 15 seconds to answer the questions. Now. listen to the news.25.What is the theme of the forum?A.Business leadership.B.Global business community.C.Economic prospects in China.D.Business and government in China.26.According to the news, the first forum was heldA.10 years ago.B.3 years ago.C.in 1999.D.in 2001.Questions 27to 28 are based on the following news. At the end of the news item, you will be given 15 seconds to answer the questions. Now. listen to the news.27.About ______of the 15000 visitors on the opening day of HongKong Disneyland camefrom the mainland.A.4000B.5000C.6000D. 700028.According to the news, residents in ______showed least interest in visiting the theme park.A.BeijingB.GuangzhouC.ShanghaiD.HongKongQuestions 29 to 30 are based on the following news. At the end of the news item, you will be given 15 seconds to answer the questions. Now. listen to the news.29.What is the news mainly about?A.Religious violence.B.Refugee issues.C.A ferry disaster.D.A rescue operation30.The ferry boat was designed to carry______passengers.A.198B.200C.290D.500PART III CLOSE [15 MIN]Decide which of the choices given below would best complete the passage if inserted in the corresponding blanks.Mark the best choice for each blank on your answer sheet.Until I took Dr Offutt’s class in DeMatha High school , I was an underachieving student,but I left that class (31)_______never to underachieve again.He not only Taught me to think,he convinced me,(32)________by example as words that it was my moral (33)_______to do so and to serve others.(34)_____of us could know how our relationship would(35)_______over the years .When I came back to DeMatha to teach English, I worked for Dr Offutt,the department chair.My discussions with him were like graduate seminars in adolescent(36)______,classroom management and school leadership.After several years,I was (37) _______department chair,and our relationship (38)________ again. I thought that it might be (39)______chairing the department ,since all of my (40)______English teachers were(41)_______there,but Dr. Offutt supported me(42)_______.He knew when to give me advice(43)_______curriculum,texts personnel ,and when to let me (44)______my own course.In 1997,I needed his (45)______about leaving DeMatha to become principal at another school.(46)_______he had asked me to stay at DeMatha,I might have .(47)_______,he encouraged me to seize the opportunity.Five years ago ,I became the principal of DeMatha.(48)________,Dr Offutt was there for me,letting me know that I could (49)_______him. I have learned from him that great teachers have an inexhaustible(50)________of lessons to teach.31. A.concerned B.worried C.determined D.decided32. A. as much B. much as C. as such D. such as33.A. work B. job C. duty D.obligation34.A. Both B. Neither C. Either D. Each35. A. evolve B. stay C. remain D. turn36.A.process B.procedure C.development D.movement37.A.called d C.asked D.invited38.A. moved B. altered C. went D. shifted39.A.awkward B.uneasy C.unnatural D.insensitive40.A. older B.experienced C.former D. /41. A. / B.still C.even D.already42. A.through B.throughout C.at the beginning D.all the way43. A.for B.at C.over D.about44. A.chart B.head C.describe D.manage45.A.opinion B.request C.permission D.order46.A.Even if B.Although C.If D.When47.A.Naturally B.Instead C.Consequently D.Still48.A.Once again B.Repeatedly C.Unusally D.Unexpectedly49.A.count in B.count down C.count out D.count on50.A.stock B.bank C.wealth D.storePART IV GRAMMER &VOCABULARY [15MIN]There are thirty sentences in this section. Beneath each sentence there are four words or phrases marked A,B,C and D. Choose one word or phrase that best completes the sentences.51. There are as good fish in the sea _____ever came out of it .A.thanB.likeC.asD.so52.All the President’s Men ______one of the important books for historians who study the Watergate Scandal.A.remainB.remainsC.remainedD.is remaining53.“You ______ borrow my notes provided you take care of them,” I told my friend.A.couldB.shouldC.mustD.can54.If only the patient ______a different treatment instead of using the antibiotics, he might still be alive now.A.had receivedB.receivedC.should receiveD.were receiving55.Linda was _____the experiment a month ago,but she changed her mind at the last minute.A. to startB.to have startedC.to be startingD.to have been starting56.She _____fifty or so when I first met her at the conference.A. must beB.had beenC.could beD.must have been57.It is not ______much the language as the background that makes the book difficult to understand.A.thatB.asC.soD.very58.The comminttee has anticipated the problems that ________in the road construction project.A.ariseB.will ariseC.aroseD.have arisen59.The student said there were a few points in the essay he _______impossible to comprehend.A.had foundB.findsC.has foundD.would find60.He would have finished his college education,but he _______to quit and find a job to support his family.A.had hadB.hasC.hadD.would have61.The research requires more money than ________.A.have been put inB.has been put inC.being put inD.to be put in62.Overpopulation poses a terrible threat to the human race.Yet it is probably ________a threat to the human race than enviromental destruction.A.no moreB.not moreC.even moreD.much more63.It is not uncommon for there _______problems of communication between the old and the young.A.beingB.would beC.beD.to be64.________at in his way,the situation does not seem so desperate.A.LookingB.lookedC.Being lookedD.to look65.It is absolutely essential that William________his study in spite of some learning difficulties.A.will continueB.continuedC.continueD.continues66.The painting he bought at the street market the other day was a_______forgery.A.man-madeB.naturalC.crudeD.real67.She’s always been kind to me –I can’t just turn ______on her now that she needs my help.A.my backB.my headC.my eyeD.shoulder68.The bar in the club is for the ______use of its members.A.extensiveB.exclusiveC.inclusiveprehensive69.The tutition fees are ______to students coming from low-income families.A.approachableB.payableC.reachableD.affordable70.The medical experts warned the authorities of the danger of diseases in the _______of the earthquake.A.consequenceB.aftermathC.resultsD.effect71.This sort of rude behaviour in public hardly ______a person in your position.A.becomesB.fitsC. supportsD.improves72.I must leave now._______,if you want that book I’ll bring it next time.A.AccidentallyB.IncidentallyC.EventuallyD.Naturally73.After a long delay,she ______replying to my e-mail.A.got away withB.got back atC.got byD.got round to74.Personal computers are no longer something beyond the ordinary people;they are________available these days.A.promptlyB.instantlyC.readilyD.quickly75.In my first year at the university I learnt the _______of journalism.A.basicsB.basicC.elementaryD.elements76.According to the new tax law,any money earned over that level is taxed at the ______of 59 percentA.ratioB.percentageC.proportionD.rate77.Thousands of _______at the stadium came to their feet to pay tribute to an outstanding performance.A.audienceB.participantsC.spectatorsD.observers78.We stood still ,gazing out over the limitless ______of the dessert.A.spaceB.expanseC.stretchnd79.Doctor often ______uneasiness in the people they deal with.A.smellB.hearC.senseD.tough80.Mary sat at the table, looked at the plate and ______her lips.A.smackedB.openedC.partedD.seperated PART V READING COMPREHENSION [25MIN]In this section there are four passages followed by questions or unfinished statements,each with four suggested answers marked A,B,C and D. Choose the one that you think is the best answer.TEXT AIf you like the idea of staying with with a family,living in house might be the answer.Good landladies---those who are superb cooks and launderers,are figures as popular in fiction as the bad ones who terrorize their guests and overcharge them at the slightest opportunity.The truth is probably somewhere between the two extremes.If you are lucky,the food will be adequate, some of your laundry may be done for you and you will have a reasonable amount of comfort and companionship .For the less fortunate ,house rules may restrict the freedom to invite friends to vistit,and shared cooking and bathroom facilities can be frustrating and row-provoking if tidy and untidy guests are living under the same roof.The same disadvantages can apply to flat sharing,with the added difficulties that arise from deciding who pays for what,and in what proportion.One person may spend hours on the phone,while another rarely makes calls. If you want privacy with a guest , how do you persuade the others to go out; how do you persuade them to leave you in peace,especially if you are student and want to study?Conversely,flat sharing can be cheap,there will always be someone to talk to and go out with,and the chores,in theory,can be shared.81.According to the passage ,landladies are ________ually strict.B.always mean.C.adequately competent.D.very popular with their guests.82.What is the additional disadvantage of flat sharing ?A.Problems of sharing and paying.B.Differences in living habits.C.Shared cooking and bathroom facilities.D.Restriction to invite friends to visit.83.What is NOT mentioned as a benefit of flat sharing?A.Rent is affordableB.There is companionship.C.Housework can be shared.D.There is peace and quiet.TEXT B(1) Travelling through the country a couple of weeks ago on business,I waslistening to the talk of the late UK writer Douglas Adams’ masterwork “The Hitchhiker’s Guide to the Galaxy” on the radio and thought-I know,I’ll pick up the next hitchhikers I see and ask them what the state of real hitching is today in Britain.(2)I drove and drove on main roads and side roads for the next few days and never saw a single one.(3)When I was in my teens and 20s ,hitchhiking was a main form of long-distance transport.The kindness or curiosity of strangers took me all over Europe,North America,Asia and southern Africa,Some of the lift-givers became friends ,many provided hospitality on the road.(4)Not only did you find out much more about a country than when traveling by train or plane ,but there was that element of excitement about where you would finish up that night.Hitchhiking featured importantly in Western culture.It has books and songs about it .So what has happened to it?(5)A few years ago ,I asked the same question about hitching in a column ofa newspaper.Hundreds of people from all over the world responded with their view on the state of hitchhiking .(6)Rural Ireland was recommended as a friendly place for hitching,as was Quebec,Canada-“if you don’t mind being criticized for not speaking French”.(7)But while hitchhiking was clearly still alive and well in some places ,the general feeling was that throughtout much of the west it was doomed.(8)With so much news about crime in the media,people assumed that anyone on the open road without the money for even a bus ticket must present a danger.But do we need to be so wary both to hitch and to give a lift?(9)In Poland in the 1960s,according to a Polish woman who e-mail me ,＂the authorities introduced the Hitchhiker’s Booklet.The booklet contained coupons for drivers,so each time a driver picked somebody ,he or she received a coupon.At the end of the season,drivers who had picked up the most hikers were rewarded with various prizes.Everyone was hitchhiking then”.(10)Surely this is a good idea for society.Hitchhiking would increase respect by breaking down barriers between strangers.It would help fight global warming by cutting down on fuel consumption as hitchhikers would be using existing fuels.It would also improve educational standards by delivering instant lessons in geography ,history,politics and sociology.(11)A century before Douglas Adams wrote his “Hitchhiker’s Guide”,another adventure story writer,Robert Louis Stevenson, gave us that what should be the hitchhiker’s motto:＂To travel hopefully is a better thing than to arrive.” What better time than putting a holiday weekend into practice. Either put it to the test yourself, or help out someone who is trying to travel hopefully with thumb outstretched.84. In which paragraph(s) does the writer comment on his experience of hitchhiking?A. (3)B. (4)C. (3) and (4)D. (4) and (5)85. What is the current situation of hitchhiking?A. It is popular in some parts of the world.B. It is popular throughout the west.C. It is popular only in the North Amercia.D.It’s still popular in Poland.86. What is the writer’s attitude towards the practice in Poland?A. Critical.B. Unclear.C. Somewhat favourable.D. Strongly favourable.87. The writer has mentioned all the following benefits of hitchhiking EXCEPTA. promoting mutual respect between strangers.B. increasing one’s confidence in strangers.C. protecting enviroment.D. enriching one’s knowledge.88.＂Either put it to the test yourself…”in Paragraph (11) meansA. to experience the hopefulness.B. to read Adams’ book.C. to offer someone a lift.D.to be a hitchhiker.TEXT CI am afraid to sleep. I have been afraid to sleep for the last few weeks. I am so tired that, finally, I do sleep, but only for a few minutes. It is not a bad dream that wakes me ; it is the realiry I took with me into sleep . I try to think of something else.Immediately the woman in the marketplace comes into my mind.I was on my way to dinner last night when I saw her . She was selling skirts. She moved with the same ease and loveliness I often saw in the women of Laos. Her long black hair was as shiny as the black silk of the skirts she was selling . In her hair, she wore three silk ribbons, blue ,green, and white. They reminded me of my childhood and how my girlfriends and I used to spend hours braiding ribbons into our hair.I don’t know the word for “ribbons”, so I put my hand to my own hair and , with three fingers against my head , I looked at her ribbons and said “Beautiful.”She lowered her eyes and said nothing. I wasn’t sure if she understood me (I don’t speak Laotian very well).I looked back down at the skirts. They had designs in them: squares and triangles and circles of pink and green silk. They were very pretty. I decided to buy one of those skirts, and I began to bargain with her over the price. It is the custom to bargain in Asia. In Laos bargaining is done in soft voices and easy moves with the sort of quiet peacefulness.She smiled, more with her eyes than with her lips. She was pleased by the fewwords I was able to say in her language, although they were mostly numbers, and she saw that I understood something about the soft playfulness of bargaining. We shook our heads in disagreement over the price; then, immediately, we made another offer and then another shake of the head. She was so pleased that unexpectedly, she accepted the last offer I made. But it was too soon. The price was too low. She was being too generous and wouldn’t make enough money. I moved quickly and picked up two more skirts and paid for all three at the price set; that way I was able to pay her three times as much before she had a chance to lower the price for the larger purchase. She smiled openly then, and, for the first time in months, my spirit lifted. I almost felt happy.The feeling stayed with me while she wrapped the skirts in a newspaper and handed them to me. When I left, though, the feeling left, too. It was as though it stayed behind in the marketplace. I left tears in my throat. I wanted to cry. I didn’t , of course.I have learned to defend myself against what is hard; without knowing it, I have also learned to defend myself against what is soft and what should be easy.I get up, light a candle and want to look at the skirts. They are still in the newspaper that the woman wrapped them in. I remove the paper, and raise the skirts up to look at them again before I pack them. Something falls to floor. I reach down and feel something cool in my hand. I move close to the candlelight to see what I have. There are five long silk ribbons in my hand, all different colours. The woman in the maketplace! She has given these ribbons to me!There is no defense against a generous spirit, and this time I cry, and very hard, as if I could make up for all the months that I didn’t cry.89.According to the writer, the woman in the marketplaceA refused to speak to her.B was pleasant and attractive.C was selling skirts ribbons.D recognized her immediately.90. Which of the following in NOT corret?A. The writer was not used to bargaining.B. People in Asia always bargain when buying things.C. Bargaining in Laos was quiet and peaceful.D.The writer was ready to bargain with the woman.91. The writer assumed that the woman accepted the last offer mainly because the womanA. thought that the last offer was reasonable.B.thought she could still make much money.C.was glad that the writer knew their way of bargaining.D. was tired of bargaining with the writer any more.92. Why did the writer finally decide to buy three skirts?A.The skirts were cheap and pretty.B.She liked the patterns on the skirts.C.She wanted to do something as compensation.D.She was fed up with further bargainning with the woman.93.When the writer left the marketplace, she wanted to cry, but did not becauseA. she had learned to stay cool and unfeeling.B. she was afraid of crying in public.C.she had learned to face difficulties bravely.D. she had to show in public that she was strong.94. Why did the writer cry eventually when she looked at the skirts again?A.she suddently felt very sad.B.she liked the ribbons so much.C.she was overcome by emotion.D.she felt sorry for the woman.TEXT DThe kids are hanging out. I pass small bands of students, on my way to work these mornings.They have become a familiar part of the summer landscape.These kids are not old enough for jobs. Nor are they rich enough for camp. They are school children without school. The calendar called the school year ran out on them a few weeks ago. Once supervised by teachers and principals, they now appear to be “self care”.Passing them is like passing through a time zone. For much of our history, after all, Americans arranged the school year around the needs of work and family. In 19th century cities, schools were open seven or eight hours a day, 11 months a year.In rural America, the year was arranged around the growing season. Now, only 3 percent of families follow the agricultural model, but nearly all schools are scheduled as if our children went home early to milk the cows and took months off to work the crops. Now, three-quarters of the mothers of school-age children work, but the calendar is written as if they were home waiting for the school bus.The six-hour day, the 180-day school year is regarded as something holy. But when parents work an eight-hour day and a 240-day year, it means something different. It means that many kids go home to empty houses. It means that, in the summer, they hang out.“We have a huge mismatch between the school calendar and the realisties of family life,”says Dr. Ernest Boyer ,head of the Carnegie Foundation for the Advancement of Teaching.Dr. Boyer is one of many who believe that a radical revision of the school calendar is inevitable.＂School, whether we like it or not, is educational. It always has been.”His is not popular idea. Schools are routinely burdened with the job of solving all our social problems. Can they be asked to meet the needs of our work and family lives?It may be easier to promote a longer school year on its educational merits and, indeed, the educational case is compelling. Despite the complaints and studies about our kids’ lack of learning, the United State still has a shorter school year than any industrial nation. In most of Europe, the school year is 220 days. In Japan, it is 240 days long. While classroom time alone doesn’t produce a well-educated。
高考数学真题07 导数中的问题(教师版)
专题07 导数中的问题【高考真题】1．(2022·新高考Ⅱ) 曲线y ＝ln|x|过坐标原点的两条切线的方程为____________，____________．1．答案 y ＝1e x y ＝－1e x 解析 因为y ＝ln|x|，当x ＞0时y ＝ln x ，设切点为(x 0，ln x 0)，由y ′＝1x，所以y ′|x ＝x 0＝1x 0，所以切线方程为y －ln x 0＝1x 0(x －x 0)，又切线过坐标原点，所以－ln x 0＝1x 0(－x 0)，解得x 0＝e ，所以切线方程为y －1＝1e (x －e)，即y ＝－1e x ；当x ＜0时y ＝ln(－x )，设切点为(x 1，ln(－x 1))，由y ′＝1x，所以y ′|x ＝x 1＝1x 1，所以切线方程为y －ln(－x 1)＝1x 1 (x －x 1)，又切线过坐标原点，所以－ln(－x 1)＝1x 1(－x 1)，解得x 0＝－e ，所以切线方程为y －1＝－1e (x ＋e)，即y ＝－1e x ；故答案为y ＝1e x ；y ＝－1ex ． 2．(2022·新高考Ⅱ)若曲线y ＝(x ＋a )e x 有两条过坐标原点的切线，则a 的取值范围是________．2．答案 (－∞，－4)∪(0，＋∞) 解析 ∵y ＝(x ＋a )e x ，∴y ′＝(x ＋1＋a )e x ，设切点为(x 0，y 0),则y 0＝(x 0 ＋a )e x 0,切线斜率k ＝(x 0＋1＋a )e x 0，切线方程为y －(x 0＋a )e x 0＝(x 0＋1＋a )e x 0(x －x 0)．∵切线过原点，∴－(x 0＋a )e x 0＝(x 0＋1＋a )e x 0(－x 0)，整理得，x 02＋a x 0－a ＝0．∵切线有两条，∴△＝a 2＋4a >0,解得a <－4或a >0，∴a 的取值范围是(－∞，－4)∪(0，＋∞)，故答案为(－∞，－4)∪(0，＋∞)．3．(2022·全国乙文)函数f (x )＝cos x ＋(x ＋1)sin x ＋1在区间[0，2π]的最小值、最大值分别为( )A ．－π2，π2B ．－3π2，π2C ．－π2，π2＋2D ．－3π2，π2＋2 3．答案 D 解析 f ′(x )＝－sin x ＋sin x ＋(x ＋1)cos x ＝(x ＋1)cos x ，所以f (x )在区间(0，π2)和(3π2，2π)上f ′(x )>0， 即f (x )单调递增；在区间(π2，3π2)上f ′(x )＜0，即f (x )单调递减，又f (0)＝f (2π)＝2，f (π2)＝π2＋2，f (3π2)＝－(3π2＋1)＋1＝－3π2，所以f (x )在区间[0，2π]上的最小值为－3π2，最大值为π2＋2．故选D ． 4．(2022·新高考Ⅱ)已知函数f (x )＝x 3－x ＋1，则( )A ．f (x )有两个极值点B ．f (x )有三个零点C ．点(0，1)是曲线y ＝f (x )的对称中心D ．直线y ＝2x 是曲线y ＝f (x )的切线4．答案 AC 解析 由题，f ′(x )＝3x 2－1，令f ′(x )>0得x ＞33或x ＜－33，令f ′(x )＜0得－33＜x ＜33， 所以f (x )在(－33，33)上单调递减，在(－∞，－33)，(33，＋∞)上单调递增，所以x ＝±33是极值点，故A 正确；因f (－33)＝1＋239>0，f (33)＝1－239>0，f (－2)＝－5＜0，所以，函数f (x )在(－∞，－33)上有一个零点，当x ≥33时，f (x )≥f (33)>0，即函数f (x )在(33，＋∞)上无零点，综上所述，函数f (x )有一个零点，故B 错误；令h (x )＝x 3－x ，该函数的定义域为R ，h (－x )＝(－x )3－(－x )＝－x 3＋x ＝－h (x )，则h (x )是奇函数，(0，0)是h (x )的对称中心，将h (x )的图象向上移动一个单位得到f (x )的图象，所以点(0，1)是曲线y ＝f (x )的对称中心，故C 正确；令f ′(x )＝3x 2－1＝2，可得x ＝±1，又f (1)＝f (－1)＝1，当切点为(1，1)时，切线方程为y ＝2x －1，当切点为(－1，1)时，切线方程为y ＝2x ＋3，故D 错误．故选AC ．5．(2022·新高考Ⅱ) 已知函数f (x )＝sin(2x ＋φ)(0<φ<π)的图像关于点(2π3，0)中心对称，则( ) A ．f (x )在区间(0，5π12)单调递减 B ．f (x )在区间⎝⎛⎭⎫－π12，11π12有两个极值点 C ．直线x ＝7π6是曲线y ＝f (x )的对称轴 D ．直线y ＝32－x 是曲线y ＝f (x )的切线 5．答案 AD 解析 由题意得，f (2π3)＝sin(4π3＋φ)＝0，所以4π3＋φ＝k π，k ∈Z ，即φ＝－4π3＋k π，k ∈Z ， 又0<φ<π，所以k ＝2时，φ＝2π3，故f (x )＝sin(2x ＋2π3)．对A ，当x ∈(0，5π12)时，2x ＋2π3∈(2π3，3π2)，由正弦函数y ＝sin u 图象知y ＝f (x )在(0，5π12)上是单调递减；对B ，当x ∈⎝⎛⎭⎫－π12，11π12时，2x ＋2π3∈(π2，5π2)，由正弦函数y ＝sin u 图象知y ＝f (x )只有1个极值点，由2x ＋2π3＝3π2，解得，即x ＝5π12为函数的唯一极值点；对C ，当x ＝7π6时，2x ＋2π3＝3π，f (7π6)＝0，直线x ＝7π6不是对称轴；对D ，由y ′＝2cos(2x ＋2π3)＝－1，得cos(2x ＋2π3)＝－12，解得2x ＋2π3＝2π3＋2k π(k ∈Z )或2x ＋2π3＝4π3＋2k π(k ∈Z )，从而得，x ＝k π(k ∈Z )或x ＝π3＋k π(k ∈Z )，所以函数y ＝f (x )在点(0，32)处的切线斜率为k ＝y ′|x ＝0＝2cos 2π3＝－1，切线方程为y ＝32－x ．故选AD ． 6．(2022·全国乙理)已知x ＝x 1和x ＝x 2分别是函数f (x )＝2a x －ex 2(a >0且a ≠1)的极小值点和极大值点．若 x 1＜x 2，则a 的取值范围是____________．6．答案 (1e，1) 解析 f ′(x )＝2ln a a x －2ex ，因为x 1，x 2分别是函数f (x )＝2a x －ex 2的极小值点和极大值 点，所以函数f (x )在(－∞，x 1)和(x 2，＋∞)上递减，在(x 1，x 2)上递增，所以当x ∈(－∞，x 1)和(x 2，＋∞)时，f ′(x )＜0，当x ∈(x 1，x 2)时，f ′(x )>0，若a >1时，当x ＜0时，2ln a a x >0，2ex ＜0，则此时，f ′(x )>0，与前面矛盾，故a >1不符合题意，若0<a <1时，则方程2ln a a x －2ex ＝0的两个根为x 1，x 2，即方程ln a a x ＝ex 的两个根为x 1，x 2，即函数y ＝ln a a x 与函数y ＝e x 的图象有两个不同的交点，∵0<a <1，∴函数y ＝a x 的图象是单调递减的指数函数，又∵ln a <0，∴y ＝ln a a x 的图象由指数函数y ＝a x 向下关于x 轴作对称变换，然后将图象上的每个点的横坐标保持不变，纵坐标伸长或缩短为原来的|ln a |倍得到，如图所示：设过原点且与函数y ＝g (x )的图象相切的直线的切点为(x 0，ln a a x 0)，则切线的斜率为g ′(x )＝ln 2a a x 0，故切线方程为y －ln a a x 0＝ln 2a a x 0(x －x 0)，则有－ln a a x 0＝－x 0 ln 2a a x 0，解得x 0＝1 ln a ，则切线的斜率为122ln ln eln a a a a ⋅=，因为函数y ＝ln a a x 与函数y ＝e x 的图象有两个不同的交点，所以e ln 2a <e ，解得1e<a <e ，又0<a <1，所以1e <a <1，综上所述，a 的范围为(1e，1)． 7．(2022·新高考Ⅱ) 已知正四棱锥的侧棱长为l ，其各顶点都在同一球面上．若该球的体积为36π，且3≤l ≤33，则该正四棱锥体积的取值范围是( )A ．[18，814]B ．[274，814]C ．[274，643] D ．[18，27] 7．答案 C 解析 ∵ 球的体积为36π，所以球的半径R ＝3，设正四棱锥的底面边长为2a ，高为h ，则l 2＝2a 2＋h 2，32＝2a 2＋(3－h )2．所以6h ＝l 2，2a 2＝l 2－h 2，所以正四棱锥的体积V ＝13Sh ＝13×4a 2×h ＝23×(l 2－l 436)×l 26＝19(l 4－l 636)，所以V ′＝19(4l 3－l 56)＝19l 3 (24－l 26)，当3≤l ≤26时，V ′＞0，当26≤l ≤33时，V ′＜0，所以当l ＝26时，正四棱锥的体积V 取最大值，最大值为643，又l ＝3时，V ＝274，l ＝33时， V ＝814．所以正四棱锥的体积V 的最小值为274，所以该正四棱锥体积的取值范围是[274，643]．故选C ． 【知识总结】1．导数的几何意义(1)f ′(x 0)的几何意义：曲线y ＝f (x )在点(x 0，f (x 0))处的切线的斜率，该切线的方程为y －f (x 0)＝f ′(x 0)·(x －x 0)．(2)切点的两大特征：①在曲线y ＝f (x )上；②在切线上．2．利用导数研究函数的单调性(1)求可导函数单调区间的一般步骤①求函数f (x )的定义域；②求导函数f ′(x )；③由f ′(x )>0的解集确定函数f (x )的单调递增区间，由f ′(x )<0的解集确定函数f (x )的单调递减区间．(2)由函数的单调性求参数的取值范围①若可导函数f (x )在区间M 上单调递增，则f ′(x )≥0(x ∈M )恒成立；若可导函数f (x )在区间M 上单调递减，则f ′(x )≤0(x ∈M )恒成立；②若可导函数在某区间上存在单调递增(减)区间，f ′(x )>0(或f ′(x )<0)在该区间上存在解集；③若已知f (x )在区间I 上的单调性，区间I 中含有参数时，可先求出f (x )的单调区间，则I 是其单调区间的子集．3．利用导数研究函数的极值与最值(1)求函数的极值的一般步骤①确定函数的定义域；②解方程f ′(x )＝0；③判断f ′(x )在方程f ′(x )＝0的根x 0附近两侧的符号变化：若左正右负，则x 0为极大值点；若左负右正，则x 0为极小值点；若不变号，则x 0不是极值点．(2)求函数f (x )在区间[a ，b ]上的最值的一般步骤①求函数y ＝f (x )在区间(a ，b )内的极值；②比较函数y ＝f (x )的各极值与端点处的函数值f (a )，f (b )的大小，最大的一个是最大值，最小的一个是最小值．【同类问题】题型一 曲线的切线方程1．(2021·全国甲)曲线y ＝2x －1x ＋2在点(－1，－3)处的切线方程为________． 1．答案 5x －y ＋2＝0 解析 y ′＝⎝ ⎛⎭⎪⎫2x －1x ＋2′＝2(x ＋2)－(2x －1)(x ＋2)2＝5(x ＋2)2，所以y ′|x ＝－1＝5(－1＋2)2＝5，所 以切线方程为y ＋3＝5(x ＋1)，即5x －y ＋2＝0．2．(2020·全国Ⅱ)函数f (x )＝x 4－2x 3的图象在点(1，f (1))处的切线方程为( )A ．y ＝－2x －1B ．y ＝－2x ＋1C ．y ＝2x －3D ．y ＝2x ＋12．答案 B 解析 f (1)＝1－2＝－1，切点坐标为(1，－1)，f ′(x )＝4x 3－6x 2，所以切线的斜率为k ＝f ′(1) ＝4×13－6×12＝－2，切线方程为y ＋1＝－2(x －1)，即y ＝－2x ＋1．3．(2018·全国Ⅰ)设函数f (x )＝x 3＋(a －1)x 2＋ax ．若f (x )为奇函数，则曲线y ＝f (x )在点(0，0)处的切线方程 为( )A ．y ＝－2xB ．y ＝－xC ．y ＝2xD ．y ＝x3．答案 D 解析 法一 因为函数f (x )＝x 3＋(a －1)x 2＋ax 为奇函数，所以f (－x )＝－f (x )，所以(－x )3＋(a －1)(－x )2＋a (－x )＝－[x 3＋(a －1)x 2＋ax ]，所以2(a －1)x 2＝0．因为x ∈R ，所以a ＝1，所以f (x )＝x 3＋x ，所以f ′(x )＝3x 2＋1，所以f ′(0)＝1，所以曲线y ＝f (x )在点(0，0)处的切线方程为y ＝x ．故选D ． 法二 因为函数f (x )＝x 3＋(a －1)x 2＋ax 为奇函数，所以f (－1)＋f (1)＝0，所以－1＋a －1－a ＋(1＋a －1＋a )＝0，解得a ＝1，此时f (x )＝x 3＋x (经检验，f (x )为奇函数)，所以f ′(x )＝3x 2＋1，所以f ′(0)＝1，所以曲线y ＝f (x )在点(0，0)处的切线方程为y ＝x ．故选D ．法三 易知f (x )＝x 3＋(a －1)x 2＋ax ＝x [x 2＋(a －1)x ＋a ]，因为f (x )为奇函数，所以函数g (x )＝x 2＋(a －1)x ＋a 为偶函数，所以a －1＝0，解得a ＝1，所以f (x )＝x 3＋x ，所以f ′(x )＝3x 2＋1，所以f ′(0)＝1，所以曲线y ＝f (x )在点(0，0)处的切线方程为y ＝x ．故选D ．4．(2020·全国Ⅰ)曲线y ＝ln x ＋x ＋1的一条切线的斜率为2，则该切线的方程为________．4．答案 2x －y ＝0 解析 设切点坐标为(x 0，y 0)，因为y ＝ln x ＋x ＋1，所以y ′＝1x＋1，所以切线的斜率 为1x 0＋1＝2，解得x 0＝1．所以y 0＝ln 1＋1＋1＝2，即切点坐标为(1，2)，所以切线方程为y －2＝2(x －1)，即2x －y ＝0．5．(2019·全国Ⅱ)曲线y ＝2sin x ＋cos x 在点(π，－1)处的切线方程为( )A ．x －y －π－1＝0B ．2x －y －2π－1＝0C ．2x ＋y －2π＋1＝0D ．x ＋y －π＋1＝05．答案 C 解析 设y ＝f (x )＝2sin x ＋cos x ，则f ′(x )＝2cos x －sin x ，∴f ′(π)＝－2，∴曲线在点(π，－1) 处的切线方程为y －(－1)＝－2(x －π)，即2x ＋y －2π＋1＝0．故选C ．6．(2021·新高考Ⅱ)若过点(a ，b )可以作曲线y ＝e x 的两条切线，则( )A ．e b <aB ．e a <bC ．0<a <e bD ．0<b <e a6．答案 D 解析 根据y ＝e x 图象特征，y ＝e x 是下凸函数，又过点(a ，b )可以作曲线y ＝e x 的两条切线， 则点(a ，b )在曲线y ＝e x 的下方且在x 轴的上方，得0<b <e a ．故选D ．7．已知曲线f (x )＝x 3－x ＋3在点P 处的切线与直线x ＋2y －1＝0垂直，则P 点的坐标为( )A ．(1，3)B ．(－1，3)C ．(1，3)或(－1，3)D ．(1，－3)7．答案 C 解析 设切点P (x 0，y 0)，f ′(x )＝3x 2－1，又直线x ＋2y －1＝0的斜率为－12，∴f ′(x 0)＝3x 20－1 ＝2，∴x 20＝1，∴x 0＝±1，又切点P (x 0，y 0)在y ＝f (x )上，∴y 0＝x 30－x 0＋3，∴当x 0＝1时，y 0＝3；当x 0＝－1时，y 0＝3．∴切点P 为(1，3)或(－1，3)．8．(2019·江苏)在平面直角坐标系xOy 中，点A 在曲线y ＝ln x 上，且该曲线在点A 处的切线经过点(－e ， －1)(e 为自然对数的底数)，则点A 的坐标是________．8．答案 (e ，1) 解析 设A (m ，n )，则曲线y ＝ln x 在点A 处的切线方程为y －n ＝1m(x －m )．又切线过点 (－e ，－1)，所以有n ＋1＝1m(m ＋e)．再由n ＝ln m ，解得m ＝e ，n ＝1．故点A 的坐标为(e ，1)． 9．设函数f (x )＝x 3＋(a －1)·x 2＋ax ，若f (x )为奇函数，且函数y ＝f (x )在点P (x 0，f (x 0))处的切线与直线x ＋y＝0垂直，则切点P (x 0，f (x 0))的坐标为 ．9．答案 (0，0) 解析 ∵f (x )＝x 3＋(a －1)x 2＋ax ，∴f ′(x )＝3x 2＋2(a －1)x ＋a ．又f (x )为奇函数，∴f (－x )＝－f (x )恒成立，即－x 3＋(a －1)x 2－ax ＝－x 3－(a －1)x 2－ax 恒成立，∴a ＝1，f ′(x )＝3x 2＋1，3x 20＋1＝1，x 0＝0，f (x 0)＝0，∴切点P (x 0，f (x 0))的坐标为(0，0)．10．过定点P (1，e)作曲线y ＝a e x (a >0)的切线，恰有2条，则实数a 的取值范围是________．10．答案 (1，＋∞) 解析 由y ′＝a e x ，若切点为(x 0，0e x a )，则切线方程的斜率k ＝0'|x x y =＝0e x a >0， ∴切线方程为y ＝0e x a (x －x 0＋1)，又P (1，e)在切线上，∴0e x a (2－x 0)＝e ，即e a＝0e x (2－x 0)有两个不同的解，令φ(x )＝e x (2－x )，∴φ′(x )＝(1－x )e x ，当x ∈(－∞，1)时，φ′(x )>0；当x ∈(1，＋∞)时，φ′(x )<0，∴φ(x )在(－∞，1)上单调递增，在(1，＋∞)上单调递减，∴φ(x )max ＝φ(1)＝e ，又x →－∞时，φ(x )→0；x →＋∞时，φ(x )→－∞，∴0<e a<e ，解得a >1，即实数a 的取值范围是(1，＋∞)． 题型二 曲线的公切线方程11．(2020·全国Ⅲ)若直线l 与曲线y ＝x 和圆x 2＋y 2＝15都相切，则l 的方程为( ) A ．y ＝2x ＋1 B ．y ＝2x ＋12 C ．y ＝12x ＋1 D ．y ＝12x ＋1211．答案 D 解析 易知直线l 的斜率存在，设直线l 的方程y ＝kx ＋b ，则|b |k 2＋1＝55①．设直线l 与曲线y ＝x 的切点坐标为(x 0，x 0)(x 0>0)，则y ′|x ＝x 0＝12x 0－12＝k ②，x 0＝kx 0＋b ③，由②③可得b ＝12x 0，将b ＝12x 0，k ＝12x 0－12代入①得x 0＝1或x 0＝－15(舍去)，所以k ＝b ＝12，故直线l 的方程y ＝12x ＋12． 12．已知f (x )＝e x (e 为自然对数的底数)，g (x )＝ln x ＋2，直线l 是f (x )与g (x )的公切线，则直线l 的方程为 ．12．答案 y ＝e x 或y ＝x ＋1 解析 设l 与f (x )＝e x 的切点为(x 1，y 1)，则y 1＝1e x ，f ′(x )＝e x ，∴f ′(x 1)＝1e x ，∴切点为(x 1，1e x )，切线斜率k ＝1e x ，∴切线方程为y －1e x ＝1e x (x －x 1)，即y ＝1e x ·x －11e x x ＋1e x，①，同理设l 与g (x )＝ln x ＋2的切点为(x 2，y 2)，∴y 2＝ln x 2＋2，g ′(x )＝1x ，∴g ′(x 2)＝1x 2，切点为(x 2，ln x 2＋2)，切线斜率k ＝1x 2，∴切线方程为y －(ln x 2＋2)＝1x 2(x －x 2)，即y ＝1x 2·x ＋ln x 2＋1，②，由题意知，①与②相同，∴111122121e e , e e ln 1,x x x x x x x x -⎧=⇒=⎪⎨⎪-+=+⎩③④把③代入④有－11e x x ＋1e x ＝－x 1＋1，即(1－x 1)(1e x －1)＝0，解得x 1＝1或x 1＝0，当x 1＝1时，切线方程为y ＝e x ；当x 1＝0时，切线方程为y ＝x ＋1，综上，直线l 的方程为y ＝e x 或y ＝x ＋1．13．若直线l 与曲线y ＝e x 及y ＝－14x 2都相切，则直线l 的方程为________．13．答案 y ＝x ＋1 解析 设直线l 与曲线y ＝e x 的切点为(x 0，0x e )，直线l 与曲线y ＝－14x 2的切点为 ⎝⎛⎭⎫x 1，－x 214，因为y ＝e x 在点(x 0，0x e )处的切线的斜率为y ′|x ＝x 0＝0x e ，y ＝－x 24在点⎝⎛⎭⎫x 1，－x 214处的切线的斜率为y ′|x ＝x 1＝⎝⎛⎭⎫－x 2|x ＝x 1＝－x 12，则直线l 的方程可表示为y ＝0x e x －x 0e 0x e ＋0x e 或y ＝－12x 1x ＋14x 21，所以⎩⎨⎧ 0x e ＝－x 12，－x 00x e ＋0x e ＝x 214，所以0x e ＝1－x 0，解得x 0＝0，所以直线l 的方程为y ＝x ＋1．14．曲线C 1：y ＝ln x ＋x 与曲线C 2：y ＝x 2有________条公切线．14．答案 1 解析 由y ＝ln x ＋x 得y ′＝1x＋1，设点(x 1，ln x 1＋x 1)是曲线C 1上任一点，∴曲线C 1在点(x 1， ln x 1＋x 1)处的切线方程为y －(ln x 1＋x 1)＝⎝⎛⎭⎫1x 1＋1(x －x 1)，即y ＝⎝⎛⎭⎫1x 1＋1x ＋ln x 1－1．同理可得曲线C 2在点(x 2，x 22)处的切线方程为y －x 22＝2x 2(x －x 2)，即y ＝2x 2x －x 22．依题意知两切线重合，∴⎩⎪⎨⎪⎧ 1x 1＋1＝2x 2，ln x 1－1＝－x 22，消去x 2得1x 21＋2x 1＋4ln x 1－3＝0，①，令f (x )＝1x 2＋2x ＋4ln x －3(x >0)，则f ′(x )＝－2x 3－2x 2＋4x ＝4x 2－2x －2x 3＝2(2x ＋1)(x －1)x 3，当x ∈(0,1)时，f ′(x )<0；当x ∈(1，＋∞)时，f ′(x )>0，∴f (x )在(0，1)上单调递减，在(1，＋∞)上单调递增，∴f (x )min ＝f (1)＝0，∴f (x )只有一个零点．即方程①只有一个解，故曲线C 1与C 2只有1条公切线．15．已知曲线y ＝x ＋ln x 在点(1，1)处的切线与曲线y ＝ax 2＋(a ＋2)x ＋1相切，则a ＝ ．15．答案 8 解析 方法一 因为y ＝x ＋ln x ，所以y ′＝1＋1x，y ′|x ＝1＝2．所以曲线y ＝x ＋ln x 在点(1，1) 处的切线方程为y －1＝2(x －1)，即y ＝2x －1．因为y ＝2x －1与曲线y ＝ax 2＋(a ＋2)x ＋1相切，所以a ≠0(当a ＝0时曲线变为y ＝2x ＋1与已知直线平行)．由⎩⎪⎨⎪⎧y ＝2x －1，y ＝ax 2＋(a ＋2)x ＋1，消去y ，得ax 2＋ax ＋2＝0．由Δ＝a 2－8a ＝0，解得a ＝8．方法二 同方法一得切线方程为y ＝2x －1．设y ＝2x －1与曲线y ＝ax 2＋(a ＋2)x ＋1相切于点(x 0，ax 20＋(a ＋2)x 0＋1)．因为y ′＝2ax ＋(a ＋2)，所以0|x x y '＝＝2ax 0＋(a ＋2)．由⎩⎪⎨⎪⎧ 2ax 0＋(a ＋2)＝2，ax 20＋(a ＋2)x 0＋1＝2x 0－1，解得⎩⎪⎨⎪⎧x 0＝－12，a ＝8. 16．(2016·课标全国Ⅱ)若直线y ＝kx ＋b 是曲线y ＝ln x ＋2的切线，也是曲线y ＝e x 的切线，则b ＝________．16．答案 0或1 解析 设直线y ＝kx ＋b 与曲线y ＝ln x ＋2的切点为(x 1，y 1)，与曲线y ＝e x 的切点为(x 2，y 2)，y ＝ln x ＋2的导数为y ′＝1x ，y ＝e x 的导数为y ′＝e x ，可得k ＝e x 2＝1x 1．又由k ＝y 2－y 1x 2－x 1＝e x 2－ln x 1－2x 2－x 1，消去x 2，可得(1＋ln x 1)·(x 1－1)＝0，则x 1＝1e 或x 1＝1，则直线y ＝kx ＋b 与曲线y ＝ln x ＋2的切点为⎝⎛⎭⎫1e ，1或(1,2)，与曲线y ＝e x 的切点为(1，e)或(0，1)，所以k ＝e －11－1e＝e 或k ＝1－20－1＝1，则切线方程为y ＝e x 或y ＝x ＋1，可得b ＝0或1．17．若直线y ＝kx ＋b 是曲线y ＝ln x ＋2的切线，也是曲线y ＝ln(x ＋1)的切线，则b ＝________．17．答案 1－ln 2 解析 y ＝ln x ＋2的切线为y ＝1x 1·x ＋ln x 1＋1(设切点横坐标为x 1)．y ＝ln(x ＋1)的切线为 y ＝1x 2＋1x ＋ln(x 2＋1)－x 2x 2＋1(设切点横坐标为x 2)．∴⎩⎨⎧1x 1＝1x 2＋1，ln x 1＋1＝ln(x 2＋1)－x 2x 2＋1，解得x 1＝12，x 2＝－12，∴b ＝ln x 1＋1＝1－ln2． 18．已知函数f (x )＝x ln x ，g (x )＝x 2＋ax (a ∈R )，直线l 与f (x )的图象相切于点A (1，0)，若直线l 与g (x )的图象也相切，则a 等于( )A ．0B ．－1C ．3D ．－1或318．答案 D 解析 由f (x )＝x ln x 求导得f ′(x )＝1＋ln x ，则f ′(1)＝1＋ln 1＝1，于是得函数f (x )在点A (1，0)处的切线l 的方程为y ＝x －1，因为直线l 与g (x )的图象也相切，则方程组⎩⎪⎨⎪⎧y ＝x －1，g x ＝x 2＋ax ，有唯一解，即关于x 的一元二次方程x 2＋(a －1)x ＋1＝0有两个相等的实数根，因此Δ＝(a －1)2－4＝0，解得a ＝－1或a ＝3，所以a ＝－1或a ＝3．19．若曲线C 1：y ＝ax 2(a >0)与曲线C 2：y ＝e x 存在公共切线，则a 的取值范围为________．19．答案 ⎣⎡⎭⎫e 24，＋∞ 解析 由y ＝ax 2(a >0)，得y ′＝2ax ，由y ＝e x ，得y ′＝e x ，曲线C 1：y ＝ax 2(a >0)与曲线C 2：y ＝e x 存在公共切线，设公切线与曲线C 1切于点(x 1，ax 21)，与曲线C 2切于点(x 2，2e x )，则2ax 1＝222121e e ,x x ax x x -=-可得2x 2＝x 1＋2，∴a ＝1121e 2x x +，记f (x )＝12e 2x x +，则f ′(x )＝122e (2)4x x x +-，当x ∈(0，2)时，f ′(x )<0，f (x )单调递减；当x ∈(2，＋∞)时，f ′(x )>0，f (x )单调递增．∴当x ＝2时，f (x )min ＝e 24．∴a 的取值范围是⎣⎡⎭⎫e 24，＋∞． 20．已知曲线f (x )＝ln x ＋1与g (x )＝x 2－x ＋a 有公共切线，则实数a 的取值范围为 ．20．答案 8 解析 设切线与f (x )＝ln x ＋1相切于点P (x 0，ln x 0＋1)，f ′(x 0)＝1x 0，∴切线方程为y －(ln x 0＋ 1)＝1x 0(x －x 0)，即y ＝1x 0x ＋ln x 0，联立⎩⎪⎨⎪⎧ y ＝1x 0x ＋ln x 0，y ＝x 2－x ＋a ，得x 2－⎝⎛⎭⎫1＋1x 0x ＋a －ln x 0＝0，∴Δ＝⎝⎛⎭⎫1＋1x 02－4(a －ln x 0)＝0，即1x 20＋2x 0＋1－4a ＋4ln x 0＝0，即4a ＝1x 20＋2x 0＋1＋4ln x 0有解，令φ(x )＝1x 2＋2x＋1＋4ln x (x >0)，φ′(x )＝－2x 3－2x 2＋4x ＝4x 2－2x －2x 3＝2(2x ＋1)(x －1)x 3，当x ∈(0，1)时，φ′(x )<0，当x ∈(1，＋∞)时，φ′(x )>0，∴φ(x )在(0，1)上单调递减，在(1，＋∞)上单调递增，∴φ(x )min ＝φ(1)＝4，又x →＋∞时，φ(x )→＋∞，故φ(x )的值域为[4，＋∞)，所以4a ≥4，即a ≥1，故实数a 的取值范围是[1，＋∞)． 题型三 函数的性质21．设函数f (x )＝2(x 2－x )ln x －x 2＋2x ，则函数f (x )的单调递减区间为( )A ．⎝⎛⎭⎫0，12B ．⎝⎛⎭⎫12，1 C ．(1，＋∞) D ．(0，＋∞) 21．答案 B 解析 由题意可得f (x )的定义域为(0，＋∞)，f ′(x )＝2(2x －1)ln x ＋2(x 2－x )·1x－2x ＋2＝(4x － 2)ln x ．由f ′(x )＜0可得(4x －2)ln x ＜0，所以⎩⎪⎨⎪⎧4x －2＞0，ln x ＜0或⎩⎪⎨⎪⎧4x －2＜0，ln x ＞0，解得12＜x ＜1，故函数f (x )的单调递减区间为⎝⎛⎭⎫12，1，选B ．22．已知定义在区间(0，π)上的函数f (x )＝x ＋2cos x ，则f (x )的单调递增区间为 ．22．答案 ⎝⎛⎭⎫0，π6，⎝⎛⎭⎫5π6，π 解析 f ′(x )＝1－2sin x ，x ∈(0，π)．令f ′(x )＝0，得x ＝π6或x ＝5π6，当0<x <π6时，f ′(x )>0，当π6<x <5π6时，f ′(x )<0，当5π6<x <π时，f ′(x )>0，∴f (x )在⎝⎛⎭⎫0，π6和⎝⎛⎭⎫5π6，π上单调递增，在⎝⎛⎭⎫π6，5π6上单调递减．23．函数f (x )＝2|sin x |＋cos2x 在[－π2，π2]上的单调递增区间为( ) A ．[－π2，－π6]和[0，π6] B ．[－π6，0]和[π6，π2] C ．[－π2，－π6]和[π6，π2] D ．[－π6，π6] 23．答案 A 解析 由题意，因为f (－x )＝2|sin(－x )|＋cos(－2x )＝2|sin x |＋cos2x ＝f (x )，所以f (x )为偶函数，当0≤x ≤π2时，f (x )＝2sin x ＋cos2x ，则f ′(x )＝2cos x －2sin2x ，令f ′(x )≥0，得sin x ≤12，所以0≤x ≤π6，由f (x )为偶函数，可得当－π6≤x ≤0时，f (x )单调递减，则在[－π2，－π6]上单调递增，故选A ． 24．设函数f (x )＝2x＋ln x ，则( ) A ．x ＝12为f (x )的极大值点 B ．x ＝12为f (x )的极小值点 C ．x ＝2为f (x )的极大值点 D ．x ＝2为f (x )的极小值点24．答案 D 解析 f ′(x )＝－2x 2＋1x ＝x －2x 2(x ＞0)，当0＜x ＜2时，f ′(x )＜0，当x ＞2时，f ′(x )＞0，所以x ＝2为f (x )的极小值点．25．已知函数f (x )＝2e f ′(e)ln x －x e，则f (x )的极大值点为( )A ．1eB ．1C ．eD ．2e 25．答案 D 解析 f ′(x )＝2e f ′(e)x －1e ，故f ′(e)＝1e ，故f (x )＝2ln x －x e ，令f ′(x )＝2x －1e>0，解得0<x <2e ，令 f ′(x )<0，解得x >2e ，故f (x )在(0，2e)上递增，在(2e ，＋∞)上递减，∴x ＝2e 时，f (x )取得极大值2ln 2，则f (x )的极大值点为2e ．26．若x ＝－2是函数f (x )＝(x 2＋ax －1)e x －1的极值点，则f (x )的极小值为( ) A ．－1 B ．－2e －3 C ．5e －3 D ．126．答案 A 解析 f ′(x )＝(2x ＋a )e x －1＋(x 2＋ax －1)e x －1＝[x 2＋(a ＋2)x ＋a －1]e x －1．∵x ＝－2是f (x )的极值点，∴f ′(－2)＝0，即(4－2a －4＋a －1)e －3＝0，得a ＝－1．∴f (x )＝(x 2－x －1)e x －1，f ′(x )＝(x 2＋x －2)e x －1．由f ′(x )＞0，得x ＜－2或x ＞1；由f ′(x )＜0，得－2＜x ＜1．∴f (x )在(－∞，－2)上单调递增，在(－2，1)上单调递减，在(1，＋∞)上单调递增，∴f (x )的极小值点为1，∴f (x )的极小值为f (1)＝－1．27．设f ′(x )为函数f (x )的导函数，已知x 2f ′(x )＋xf (x )＝ln x ，f (1)＝12，则下列结论不正确的是( ) A ．xf (x )在(0，＋∞)上单调递增 B ．xf (x )在(0，＋∞)上单调递减C ．xf (x )在(0，＋∞)上有极大值12D ．xf (x )在(0，＋∞)上有极小值1227．答案 ABC 解析 由x 2f ′(x )＋xf (x )＝ln x 得x ＞0，则xf ′(x )＋f (x )＝ln x x ，即[xf (x )]′＝ln x x ，设g (x )＝xf (x )， 即g ′(x )＝ln x x，由g ′(x )＞0得x ＞1，由g ′(x )＜0得0＜x ＜1，即xf (x )在(1，＋∞)上单调递增，在(0，1)上单调递减，即当x ＝1时，函数g (x )＝xf (x )取得极小值g (1)＝f (1)＝12．故选ABC ． 28．(多选)已知函数f (x )＝x 2＋x －1e x，则下列结论正确的是( ) A ．函数f (x )存在两个不同的零点B ．函数f (x )既存在极大值又存在极小值C ．当－e<k ≤0时，方程f (x )＝k 有且只有两个实根D ．若x ∈[t ，＋∞)时，f (x )max ＝5e 2，则t 的最小值为2 28．答案 ABC 解析 由f (x )＝0，得x 2＋x －1＝0，∴x ＝－1±52，故A 正确．f ′(x )＝－x 2－x －2e x ＝ －(x ＋1)(x －2)e x，当x ∈(－∞，－1)∪(2，＋∞)时，f ′(x )<0，当x ∈(－1，2)时，f ′(x )>0，∴f (x )在(－∞，－1)，(2，＋∞)上单调递减，在(－1，2)上单调递增，∴f (－1)是函数的极小值，f (2)是函数的极大值，故B 正确．又f (－1)＝－e ，f (2)＝5e2，且当x →－∞时，f (x )→＋∞，x →＋∞时，f (x )→0，∴f (x )的图象如图所示，由图知C 正确，D 不正确．29．已知函数f (x )＝2sin x ＋sin2x ，则f (x )的最小值是________．29．答案 －332解析 ∵f (x )的最小正周期T ＝2π，∴求f (x )的最小值相当于求f (x )在[0，2π]上的最小 值．f ′(x )＝2cos x ＋2cos2x ＝2cos x ＋2(2cos 2x －1)＝4cos 2x ＋2cos x －2＝2(2cos x －1)(cos x ＋1)．令f ′(x )＝0，解得cos x ＝12或cos x ＝－1，x ∈[0，2π]．∴由cos x ＝－1，得x ＝π；由cos x ＝12，得x ＝53π或x ＝π3．∵函数的最值只能在导数值为0的点或区间端点处取到，f (π)＝2sinπ＋sin2π＝0，f ⎝⎛⎭⎫π3＝2sin π3＋sin 2π3＝332，f ⎝⎛⎭⎫53π＝－332，f (0)＝0，f (2π)＝0，∴f (x )的最小值为－332． 30．(多选)设函数f (x )＝x ＋e |x |e|x |，则下列选项正确的是( ) A ．f (x )为奇函数 B ．f (x )的图象关于点(0，1)对称C ．f (x )的最大值为1e ＋1D ．f (x )的最小值为－1e＋1 30．答案 BCD 解析 f (x )＝x e |x |＋1，不满足f (－x )＝－f (x )，故A 项错误；令g (x )＝x e |x |，则g (－x )＝－x e|－x |＝ －x e |x |＝－g (x )，所以g (x )为奇函数，则f (x )关于点(0，1)对称，B 项正确；设f (x )＝x e|x |＋1的最大值为M ，则g (x )的最大值为M －1，设f (x )＝x e|x |＋1的最小值为N ，则g (x )的最小值为N －1，当x ＞0时，g (x )＝x e x ，所以g ′(x )＝1－x ex ，当0＜x ＜1时，g ′(x )＞0，当x ＞1时，g ′(x )＜0，所以当0＜x ＜1时，g (x )单调递增，当x ＞1时，g (x )单调递减，所以g (x )在x ＝1处取得最大值，最大值为g (1)＝1e，由于g (x )为奇函数，所以g (x )在x ＝－1处取得最小值，最小值为g (－1)＝－1e ，所以f (x )的最大值为M ＝1e＋1，最小值为N ＝－1e＋1，故C 、D 项正确．故选B 、C 、D ．。
07专升本计算机真题
安徽省2007年普通高等学校专升本招生考试计算机基础一、单项选择题（共70小题，每题1分，共70分。
在给出的选项中，只有一项是最准确的，请将你选择的答案写在答题纸上相应位置处）1．当前的微型计算机，其主要元器件由______构成。
A.电子管B.晶体管C.中小规模集成电路D.大规模和超大规模集成电路2．微型计算机硬件系统中，核心的部件是______。
A.硬盘B.存储器C.中央处理器D.输入输出设施3．对显示性能影响最大的是______。
A.显示器外观B.显示器大小C.显示器重量D.显示卡4．ASCII码是_____编码。
A.英文字符B.汉字C.图像D.显示卡5．计算机断电后，其RAM中的信息将_____。
A.全部丢失B.不会丢失C.部分丢失D.被保存6．下列存储器中，访问速度最快的是_____。
A.硬盘B.Cache（高速缓存）C.外存D.内存7．CAI的含义是_____。
A.计算机辅助制造B.计算机辅助设计C.计算机辅助数学D.计算机辅助测试8．某U盘可用空间为1GB，理论上可存储大小为4MB的音乐_____首。
A.25B.256C.510D.10009．微机的内存容量通常是指其_____的总字节数。
A.ROMB.RAMC.CacheD.CMOS10．计算机软件系统由_____构成。
A.系统软件和应用软件B.操作系统和数据库管理系统C.操作系统和应用软件D.数据库管理系统和应用软件11．GB-18030标准收录汉字约_____个。
A.6700B.12000C.27000D.42000 12．计算机能够直接识别和执行的语言是_____。
A.机器语言B.汇编语言C.高级语言D.智能语言13．高级语言编译程序属于_____。
A.系统软件B.文字处理软件C.操作系统软件D.应用软件14．在计算机中存储汉字使用的编码是_____。
A.外码B.交换码C.字形码D.内码15．在计算机内部，处理和传递的信息是以_____形式出现。
2024年07版小学六年级下册第1次英语第5单元真题
2024年07版小学六年级下册英语第5单元真题考试时间：90分钟（总分:110）A卷考试人：_________题号一二三四五总分得分一、综合题(共计100题)1、填空题：It is fun to _______ on the playground.2、听力题：A ____ has a long body and can slither across the ground.3、What is the name of the famous American national park known for its geysers and hot springs?A. YellowstoneB. YosemiteC. Grand CanyonD. Zion答案:A4、听力题：A _______ is a tool that can help to visualize electrical circuits.5、Which animal is known for its ability to change colors?A. ChameleonB. FrogC. LizardD. Snake6、选择题：What do we call a snowman made of snow?A. SculptureB. FigurineC. Winter DecorationD. Snow Figure7、填空题：The ________ (文化价值观) shape societies.8、填空题：I love going to ______ (夏令营) during the summer. It’s a chance to make new friends and try new activities.9、填空题：The garden is full of ______ (昆虫) in summer.10、听力题：The Sahara Desert is one of the hottest _______ on Earth.11、What do we call the study of the earth's landforms?A. GeographyB. GeologyC. CartographyD. Topography答案: B. Geology12、小狮子) plays with its cubs. 填空题：The ___13、填空题：The _____ (蒲公英) spreads seeds in the wind.14、填空题：My favorite sport is ________ (篮球). I practice every day with my ________ (朋友).15、填空题：A _____ (果实) can contain many seeds.16、填空题：The __________ is a large lake located in North America. (大湖区)17、填空题：My teacher is _______ and helpful.18、选择题：What do we call the measurement of how hot or cold something is?A. TemperatureB. PressureC. VolumeD. Density19、What is the name of the tallest building in the world?A. Burj KhalifaB. Taipei 101C. Empire State BuildingD. One World Trade Center答案：A20、填空题：The __________ (历史的回顾) informs contemporary issues.21、填空题：My ________ (玩具) is a magical part of my life.22、What is the capital of the Democratic Republic of the Congo?a. Kinshasab. Lubumbashic. Matadid. Kisangani答案:a23、听力题：In a circuit, electricity needs a complete _______.24、读短文，将颜色词的标号填入相应的括号中，将物品词的标号填在相应的圈中。
07年考研数学一真题及答案
2007年考研数学一真题一、选择题（本题共10小题，每小题4分，满分40分，在每小题给的四个选项中，只有一项符合题目要求，把所选项前的字母填在题后括号内） （1） 当0x +→( )A. 1-B.C. 1D.1-(2) 曲线y=1ln(1x e x++), 渐近线的条数为 ( ) A.0 B.1 C.2 D.3(3)如图，连续函数y=f(x)在区间[-3，-2]，[2，3]上的图形分别是直径为1的上、下半圆周，在区间[-2，0]，[0，2]的图形分别是直径为2的上、下半圆周，设F(x)=0()xf t dt ⎰.则下列结论正确的是 ( ) A. F(3)=3(2)4F -- B. F(3)=5(2)4F C. F(3)=3(2)4F + D. F(3)= 5(2)4F -- (4)设函数f （x ）在x=0处连续，下列命题错误的是 ( )A. 若0()limx f x x →存在，则f （0）=0 B. 若0()()lim x f x f x x→+- 存在，则f （0）=0C. 若0()lim x f x x → 存在，则'(0)f =0D. 若0()()lim x f x f x x→-- 存在，则'(0)f =0(5)设函数f （x ）在（0, +∞）上具有二阶导数，且"()f x o >, 令n u =f(n)=1,2,…..n, 则下列结论正确的是 ( )A.若12u u >，则{n u }必收敛B. 若12u u >，则{n u }必发散C. 若12u u <，则{n u }必收敛D. 若12u u <，则{n u }必发散(6)设曲线L ：f(x, y) = 1 (f(x, y)具有一阶连续偏导数），过第Ⅱ象限内的点M 和第Ⅳ象限内的点N,T 为L 上从点M 到N 的一段弧，则下列小于零的是 ( ) A.(,)rx y dx ⎰ B. (,)rf x y dy ⎰C.(,)rf x y ds ⎰D.'(,)'(,)x y rf x y dx f x y dy +⎰（7）设向量组1α，2α，3α线形无关，则下列向量组线形相关的是： ( ) （A ）,,122331αααααα--- （B ） ,,122331αααααα+++（C ） 1223312,2,2αααααα--- （D ）1223312,2,2αααααα+++（8）设矩阵A=211121112--⎛⎫ ⎪-- ⎪ ⎪--⎝⎭，B=100010000⎛⎫ ⎪⎪ ⎪⎝⎭，则A 于B ( )(A) 合同，且相似(B) 合同，但不相似 (C) 不合同，但相似(D)既不合同，也不相似（9）某人向同一目标独立重复射击，每次射击命中目标的概率为p ()01p <<，则此人第4次射击恰好第2次命中目标的概率为： ( ) （A ）23(1)p p - (B)26(1)p p - (C) 223(1)p p -(D) 226(1)p p -(10) 设随即变量（X ，Y ）服从二维正态分布，且X 与Y 不相关，()X f x ，()Y f y 分别表示X ，Y 的概率密度，则在Y ＝y 的条件下，X 的条件概率密度|(|)X Yf x y 为 ( )（A ）()X f x(B) ()Y f y(C) ()X f x ()Y f y(D)()()X Y f x f y 二．填空题：11－16小题，每小题4分，共24分，请将答案写在答题纸指定位置上 （11）31211x e dx x⎰＝_______. （12）设(,)f u v 为二元可微函数，(,)y xz f x y =，则zx∂∂＝______. (13)二阶常系数非齐次线性方程2''4'32x y y y e -+=的通解为y ＝____________. (14)设曲面∑：||||||1x y z ++=，则(||)x y ds ∑+⎰⎰＝_____________.(15)设矩阵A ＝0100001000010000⎛⎫ ⎪⎪ ⎪ ⎪⎝⎭，则3A 的秩为________. （16）在区间（0，1）中随机地取两个数，则这两个数之差的绝对值小于12的概率为________. 三．解答题：17~24小题，共86分.请将解答写在答题纸指定的位置上.解答应写出文字说明、证明过程或演算步骤.222222(,)2{(,)4,0}f x y x y x y D x y x y y =+-=+≤≥(17)（本题满分11分）求函数在区域上的最大值和最小值。
07生物化学真题
中国科学院研究生院2007年招收攻读硕士学位研究生入学统一考试试题科目名称：生物化学(乙)考生须知：1．本试卷满分为150分，全部考试时间总计180分钟。
2．所有答案必须写在答题纸上，写在试题纸上或草稿纸上一律无效。
一、选择题（共30分，1.5分/题）1. 蛋白质组分中，哪一种在280nm有最大的光吸收?A．苯丙氨酸的苯环B．酪氨酸的酚环C．胱氨酸的二硫键D．色氨酸的吲哚环2. 生物体内甲基的直接供体是A．Ｓ－腺苷蛋氨酸B．半胱氨酸Ｃ．蛋氨酸Ｄ．牛磺酸3. 下列氨基酸不能引起偏振光旋转的是A．Ala B．Gly Ｃ．Met Ｄ．Ser4. 在一个肽平面中含有的原子数为A．3 B．4 Ｃ．5 Ｄ．65. 下列途径中不产生化学能的是A．淀粉消化B．好氧糖酵解 Ｃ．柠檬酸循环Ｄ．电子传递链6. 下列辅酶不含腺嘌呤的是A．FAD B．NAD Ｃ．CoA Ｄ．FMN7. 根据Watson-Crick模型，求得1μm DNA双螺旋含核苷酸对的平均数为：A．25400 B．2540 Ｃ．29411 Ｄ．2941科目名称：生物化学(乙) 第1页共4页8. 艾滋病病毒HIV是一种什么病毒？A．双链DNA病毒B．单链DNA病毒Ｃ．双链RNA病毒Ｄ．单链RNA病毒9. 下列哪种性质可用于分离DNA与RNA？A．在NaCl溶液中的溶解度不同B．颜色不同Ｃ．T m值不同Ｄ．旋光性不同10. 长期食用精米和精面的人容易得癞皮病，这是因为缺乏：A．烟酸和烟酰胺B．泛酸Ｃ．磷酸吡哆醛Ｄ．硫辛酸11. 生物分子中大多数重要功能基团A．都含有氧和/或氮，并且是酸性的B．都含有氧，是一种碱Ｃ．都含有氧和/或氮，并且是极性的 Ｄ．都含有氮和一个磷酸基12. 下列物质中不能扩散通过脂双分子层的物质是A．水B．氧Ｃ．H+Ｄ．无机离子13. 辅酶Q作为中间体的作用是A．传递电子B．传递氢Ｃ．传递氧Ｄ．传递CO2 14. 下列哪种方式保证了免疫球蛋白的多样性？A．转化B．转染Ｃ．转位Ｄ．转导15. 合成尿素的器官是：A．肝脏B．肾脏Ｃ．肌肉Ｄ．心脏16. 下列哪种氨基酸能直接氧化脱氨基？A．谷氨酸B．丙氨酸Ｃ．天冬氨酸Ｄ．亮氨酸17. 紫外光对DNA的损伤主要是A．导致碱基置换B．造成碱基缺失Ｃ．引起DNA链的断裂Ｄ．形成嘧啶二聚体18. 真核基因表达受下列哪个成分调控？A．操纵基因B．非组蛋白Ｃ．组蛋白Ｄ．阻遏蛋白科目名称：生物化学(乙) 第2页 共4页19. 下列哪一种物质不是在肝脏合成？A．尿素B．脂肪酸Ｃ．糖原Ｄ．免疫球蛋白20. 苯巴比妥治疗婴儿先天性黄疸的机理主要是A．诱导葡萄糖醛酸转移酶的生成B．使肝重量增加，体积增大Ｃ．肝血流量增多Ｄ．肝细胞摄取胆红素能力加强二．请用“对”或“错”判断下列说法(共10分，1分/题）1．人类有些氨基酸必须由食物供给才能正常生存，其原因是人体不能合成这些氨基酸。
07东南大学考研真题
东南大学2007年招收硕士学位研究生入学考试试卷请考生注意：试题解答务请考生做在专用“答题纸”上！做在其他答题纸上或试卷上的解答将被视为无效答题，不予评分。
科目代码：942 科目名称：材料科学基础一、选择题（单项选择，每题2分，共40分）1、在三元相图的水平截面的两相区中，连接线之间（a）必定相交；（b）必定平行；（c）可以相交或平行；（d）不能相交也不能平行。
2、非均匀形核的形核功（非）和接触角（）和（晶核和杂质之间的界面能）之间的关系为：（a）越小，越大，非越大；（b）越大，越大，非越小；（c）越小，越小，非越大；（d）越小，越小，非越小。
3、引入极射赤面投影的目的是（a）表示晶体结构的周期性；（b）晶体结构的对称性；（c）表示晶面之间或晶向之间的取向关系；（d）表征晶体中阵点或原子的投影位置。
4、单相固溶体凝固时，若k0<1，则：（a）k e=1时，偏析最严重；（b）k e=k0时，偏析最严重；（c）k<k e<1时，偏析最严重；（d）偏析与k e及k0均无关。
5、二元材料形成伪共晶的必要条件之一是：（a）两种组元必须都是金属元素；（b）溶液在凝固时必须以足够慢的速度冷却；（c）溶液在冷却时必须有适当的过冷度；（d）某一组元的含量必须高于相图中共晶点所示的值。
6、纳米材料的特征之一是：（a）具有与单晶体相近的性能特征；（b）具有超塑性；（c）具有超高强度效应；（d）具有表面效应。
7、空间点阵是用来描述晶体结构的周期性，因此（a）自然界存在的晶体结构和空间点阵的数量相同；（b）任何一个晶体的晶体结构和空间点阵完全等同；（c）表征晶体结构周期性的空间点阵的数量少于自然界晶体结构的种类；（d）表征晶体结构周期性的空间点阵的数量多于自然界晶体结构的种类。
8、离子晶体和正常价化合物都符合化合价规律，但它们分属不同的晶体类型，原因是：（a）离子晶体的密度高于正常价化合物；（b）离子晶体的致密度与正常价化合物不同；（c）离子晶体的电子浓度与正常价化合物不同；（d）离子晶体具有陶瓷的性能特征，正常价化合物属金属间化合物。
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10. 下列有关再生障碍性贫血发病机制的检查结果，错误的是C
A. 血清IL-2水平增高
B. 血清TNF水平增高
C. CD4+T细胞增高
D. CD8+T细胞增高
E. CD25+T细胞增高
12. 下列不属于骨髓增生异常综合征骨髓常见病态造血表现的是E
A. 红系核将发育不平衡
B. 粒系核分叶过多
C. 粒系核颗粒过多
D. 粒系核颗粒过少
E.见到幼稚型巨核细胞
31. 下列属于扩张型心肌病特征的是
A. 主要表现为舒张功能障碍
B. 为伴有特异性系统疾病的心肌病
C. 心脏扩大，室壁运动普遍减弱
D. 心室充盈受限和舒张期容量下降
E. 右室心肌被纤维脂肪组织所替代
47. 有关全身性感染致病菌的描述正确的是E
A. 革兰阳性球菌感染多出现低温、低白细胞、低血压
B. 厌氧菌感染多为一般细菌感染后的二重感染
C. 革兰阳性球菌感染多为克雷伯菌
D. 革半阴性杆菌感染多数抗生素可杀菌和消除内毒素
E. 革兰阳性球菌感染倾向于血液播散，形成转移性脓肿
76. 直肠息肉中癌变倾向最大的是
A. 管状腺瘤
B. 绒毛状腺瘤
C. 增生性息肉
D. 炎性息肉
E. 幼年性息肉
123～124题共用备选答案
A. β受体阻滞剂
B. 利尿剂
C. α受体阻滞剂
D. 血管紧张素II受体阻滞剂
E. 钙通道阻滞剂
123. 冠心病稳定型心绞痛合并高血压首选E
124. 糖尿病肾病合并高血压首选D
男性，30岁。
头痛，时有呕吐，逐渐加重1个月，近期嗜睡，反应迟钝，时有头晕、猝倒，无头部外伤及急性炎症病史，血压正常。
检查见视神经乳头水肿，血常规、血沉正常。
143. 初步的临床诊断应考虑为
A. 颅脑损伤
B. 颅内肿瘤
C. 颅内感染
D. 急性脑疝
E. 椎动脉型颈椎病
144. 根据以上的初步诊断，其首选的辅助检查应是
A. 头颈X线摄片
B. 腰椎穿刺
C. 脑血管造影
D. 脑CT
E. 脑MRI
145. 根据以上的检查结果，最重要的治疗是
A. 降低颅内压
B. 药物镇静治疗
C. 手术治疗
D. 抗炎治疗
E. 吸氧治疗
10．2岁男孩，因智能低下查染色体核型为46，XY，-14，+t(14q21q)，查其母为平衡易位染色体携带者，核型应为
A．45，XX，-14，-21，＋t(14g21q)
B．45，XX，-15，-21，＋t(15g22q)
C．46，XX
D．46，XX，-14，＋t（14q21q)
E．46，XX，-21，＋t（14q21q)
答案：A
男婴，8个月。
腹泻3天，大便10余次／日，蛋花汤样伴少量粘液，呕吐，4～5次／日。
嗜睡，口干，尿量少。
体检：精神萎靡，皮肤干燥、弹性较差，眼窝及前囟明显凹陷，哭时泪少。
血钠132mmol/L，血钾4mmol/L
13．该患儿诊断为婴儿腹泻合并
A．轻度等渗脱水
B．中度等渗脱水
C．重度等渗脱水
D．中度高渗脱水
E．重度等渗脱水
答案：B
试题点评：有脱水表现而无周围循环衰竭表现，故为中度脱水；血钠正常，故为等渗性脱水。
14．该患儿第一天选择的液体种类是
A．1:4含钠液
B．2:3:1含钠液
C．ORS含钠液
D．1.4%碳酸氢钠
E．2:6:1含钠液
答案：B
试题点评：等渗性脱水给予1/2张含钠液体。
15．第2天如需静脉补充生理需要量，液体应选择
A．10%葡萄糖
B．0．9%氯化钠
C．ORS含钠液
D．1:4含钠液
E．1:1含钠液
答案：D
试题点评：补充生理需要量给予1/5张液体。
岁男孩，浮肿，尿色红2天入院，查体：颜面眼睑浮肿，心肺听诊无异常，尿常规有红细胞（＋＋＋），蛋白（＋），患儿半月前患过扁桃体炎。
15．为明确诊断，最有意义的检查是
A．ASO与ESR
B．ASO与血浆蛋白电泳
C．ESR与补体C3
D．ESR与血BUN
E．血BUN与Cr
答案：C
试题点评：患扁桃体炎2周后出现血尿、蛋白尿、水肿，考虑为急性肾炎；起病2周后补体C3降低对诊断有意义。
6．化脓性脑膜炎合并硬膜下积液，常见的病原菌是
A．金黄色葡萄球菌
B．大肠杆菌
C．B族溶血性链球菌
D．流感嗜血杆菌
E．绿脓杆菌
答案：D
4．细菌性肝脓肿的主要治疗是
A．抗生素治疗
B．穿刺抽脓，脓腔注入抗生素
C．切开引流
D．理疗
E．内引流术
答案：C
9．在孕妇腹壁上听诊，与母体心率相一致的音响是A．胎心音
B．子宫杂音
C．脐带杂音
D．胎动音
E．肠蠕动音
答案：B
22．有关盆腔脓肿的治疗错误的是
A．盆腔脓肿未形成时，应以药物为主，辅以物理疗法
B．小脓肿可采用非手术治疗
C．脓肿较大时，须手术治疗
D．可采用经腹腔排脓
E．已婚妇女可采用后穹隆途径排脓
答案：D
115.上消化道出血表现为呕血或黑便，主要取决于 2000
A.出血的速度和量
B.出血部位的高低
C.病变的性质
D.凝血机制
E.胃肠蠕动情况
您所选的答案：
本题正确答案：B
16.胃大部切除术后数月或数年多发生的合并症为
A.腹泻
B.碱性反流性胃炎
C.出血
D.呕吐
E.吻合口溃疡
答案：B
167.与痛经无关的疾病是 2003
A.无排卵性功血
B.子宫粘膜下肌瘤
C.慢性盆腔炎
D.子宫内膜异位症
E.子宫腺肌病
您所选的答案：
本题正确答案：A
初产妇，胎头吸引器加会阴侧切助产分娩足月活婴，胎盘胎膜完整。
产后4
小时阴道流血约500ml.查：BP90／60mmHg，脉搏100次／分，宫底脐上3横指，轮廓清，阴道口少量活动性流血，可凝固。
（183~184共用题干）
183.导致出血最可能的原因是
A.子宫收缩乏力
B.软产道损伤
C.胎盘残留
D.凝血功能障碍
E.尿潴留
您所选的答案：
本题正确答案：A
184.首选处理措施是
A.按摩子宫
B.导尿
C.注射止血剂
D.检查软产道
E.刮宫
您所选的答案：
本题正确答案：A
27岁初产妇，妊娠39周，规律宫缩6小时，枕左前位，估计胎儿体重2700g，胎心142次／分。
阴道检查：宫口开大3cm，未破膜，S=+1，骨盆外测量未见异常。
2003
（186~188共用题干）
186.此时恰当处理应是
A.抑制宫缩，使其维持至妊娠40周
B.等待自然分娩
C.人工破膜加速产程进展
D.静脉滴注缩宫素
E.行剖宫产术
您所选的答案：
本题正确答案：B
187.出现上述临床表现的原因是
A.子宫收缩节律性异常
B.子宫收缩对称性异常
C.子宫收缩极性异常
D.子宫收缩缩复作用异常
E.腹肌和膈肌收缩力异常
您所选的答案：
本题正确答案：A
188.若此后宫缩逐渐减弱，产程已18小时，胎膜已破，宫口开大8cm，此时恰当处理应是
A.静注地西泮加速产程进展
B.静脉滴注缩宫素
C.肌内注射缩宫素
D.静脉注射麦角新碱
E.立即行剖宫产术
您所选的答案：
本题正确答案：B
A
66、一定与系统性红斑狼疮的疾病活动性有关的免疫学检测指标是
A、抗核抗体
B、抗双链DNA抗体
C、抗Sm抗体
D、抗SSA抗体
E、抗中性粒细胞胞浆抗体
6、ChilD肝功能分级依据，不包括：食管静脉曲张程度(确定，
5版外科P601)(我错)
41。
重度先兆子娴孕妇血液生化改变不包括我选的是二氧化碳结合力升高(重度先兆子娴应该有酸中毒：尿酸增高) 。
42妊娠心脏听到什么杂音是器质性病变：我选舒张杂音应该对的哈
53。
子宫内膜异位到卵巢：手术后不该用什么药
22。
引起血清钙离子浓度降低的因素是：甲状旁腺功能亢进28、4-6月增体重：500-600(确定)
32、VD手抽阴性：Trousseau征(确定)。