上海市徐汇区2018年高三二模试卷(含解析)复习课程

2017学年第二学期徐汇区学习能力诊断卷高三英语试卷（满分140分，考试时间120分钟）2018.4I. Listening ComprehensionSection ADirections: In Section A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. Worried and frightened. B. Relaxed and happy.C. Quite embarrassed.D. Deeply ashamed.2. A. Bill has never used a calculator. B. Bill can work better without a calculator.C. Bill is working with a calculator.D. Bill needs a calculator for this work.3. A. To cut his jeans short. B. To go on a diet.C. To wear fitted clothes.D. To buy a pair of jeans.4. A. Having an interview. B. Filling out a form.C. Talking with a friend.D. Asking for information.5. A. Put her report on his desk. B. Read some papers he recommended.C. Mail her report to the publisher.D. Improve some parts of her paper.6. A. Make some coffee. B. Meet the woman at the library.C. Continue to read.D. Go out with some friends.7. A. The man should buy a different meal ticket every month.B. Buying the meal ticket won’t save the man any money.C. It is better for the man to pay for each meal separately.D. The price of a meal may vary from month to month.8. A. She’s upset that she missed the television program.B. She doesn’t think the television program was funny.C. She doesn’t like talking about television programs.D. She watched the television program at a friend’s house.9. A. He doubts the woman’s words. B. He hasn’t read t he novel yet.C. He enjoyed reading the novel a lot.D. He is not interested in the novel at all.10. A. The talks haven’t started yet. B. They have come to a general agreement.C. The talks haven’t achieved much.D. The talks broke down and went no further.Section BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of the passages and the conversation. The passages and theconversation will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. They learn singing and dancing. B. They attend outdoor music festivals.C. They work on the farm for charity.D. They volunteer to work for others.12. A. On the beach. B. In a park. C. On a farm. D. In a stadium.13. A. It is run on a profit-making basis. B. It has achieved growing success.C. Fans can have free lunch there.D. Only superstars are invited to perform.Questions 14 through 16 are based on the following passage.14. A. The number of refugees is increasing sharply.B. Most refugees cannot get necessary services.C. Many refugee children cannot receive education.D. More children cannot afford to go to university.15. A. No host nations want to change education systems.B. It is impossible to find so many extra teachers.C. Parents can’t afford to send their kids to school.D. The refugee population grows but there’s not enough money.16. A. The necessity of education.B. The prohibition of child labor.C. The victims of armed conflicts.D. The living conditions of the poor.Questions 17 through 20 are based on the following conversation.17. A. It has started a week-long promotion campaign.B. It has just launched its annual anniversary sales.C. It offers regular weekend sales all the year round.D. It speciali zes in the sale of men’s suits.18. A. Price reductions for its frequent customers.B. Gift cards for customers with any purchases.C. Free delivery of purchases for senior customers.D. Price adjustments within seven days of purchase.19. A. Mail a gift card to her. B. Allow her to buy on credit.C. Credit it to her account.D. Give her cash directly.20. A. It has already been sold out. B. It will be sent to the woman by mail.C. It is not available for the moment.D. It is one of the items on sale.II. Grammar and VocabularySection ADirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.Traveling Frog Stimulates ReflectionA free mobile game about a traveling frog has become a hit in China, (21)________ being available only in Japanese.Called “Tabikaeru: Travel Frog”,the main character of the game is a frog that goes on adventures around Japan. Players collect clovers(四叶草) that grow in the frog’s garden (22)________ ________ they can use them to buy supplies for the frog’s journey s. In turn, the frog sends players souvenirs and snapshots from its travels. Users cannot control when the frog chooses to go on its adventures.While news of the game’s appeal among mobile phone users on the mainland was first reported on by local media outlets last week, its popularity hasn’t decreased in any way since: “Travel Frog” on Monday was still ranked first on a list of the most (23)__________(download) games from Apple’s app store in China. It is being widely discussed on social media, (24)__________ users post photos of their frogs’ adventures.Behind the craze is Japanese game developer Hit-Point, which was previously best-known for creating the popular cat-collecting game “Neko Atsume”. Even though (25)__________ is difficult to pinpoint what has driven interest among mainland users in “Travel Frog”, local media outlets reported that the game’s slow natur e was part of its charm.The game was popular as it “tapped the trend among younger generations in China to search out ‘Zen-like’activities”, China Daily said, (26)_________(add) that those users were taken with its “Buddha-style gameplay”.But not everyone is thrilled about “Travel Frog”. In a post on social media platform Weibo last week, the state-run People’s Daily suggested that people (27)__________ aim to enrich themselves and “avoid being a lonely frog-raising youth”.As an indication of the popularity of the “Travel Frog”, Apple has already had to remove from its store an app that appeared to be the Chinese version of the original, the South China Morning Post reported. That version of the game, which (28)__________(create) by a developer called Song Yang, charged users 30 yuan ($4.74) to download the game. On Monday, another free-to-download app available on the app store claimed it offered strategies and guides in Chinese that players could adopt (29)___________(improve) gameplay.While Hit-Point has not responded to inquiries about (30)_________ it intends to develop versions of the game in other languages or not, the company did put out an English update for “Neko Atsume” in 2015.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.Before science became professionalized in the 19th century, __(31)__ naturalists were collecting information and helping us understand the natural world. A 2009 study found that nearly 50% of UK __(32)__ feed wild birds. The National Trust has more than 5 million members, and 60,000 active volunteers helping to protect the countryside as well as historic __(33)__. Now, with our environment arguably under greater threat than ever and species declining at a(n) __(34)__ rate, volunteers are once again at the forefront of efforts to limit the damage.Volunteers and enthusiasts can be powerful drivers for big changes. On the Isle of Man, more than 8,000 people (nearly 10% of the population) are involved in regular weekend beach cleans. At one recent event, 123 volunteers turned up and removed 183 bags of litter in just a couple of hours. Thanks to __(35)__ such as this, the island shares Unesco biosphere reserve status with the Galápagos, Yellowstone in the US, Uluru in Australia, and hundreds of other sites.Recreational divers are making a real difference underwater too. They monitor the spread of __(36)__ species, and record how native species respond. Divers also __(37)__ levels of marine litter and other human impacts. V olunteer divers have played an important role in collecting information about marine conservation zones. V olunteers have also made a vital contribution to the conservation of basking sharks. The work of a citizen science Basking Shark Project in the 1980s and 90s was __(38)__ in getting these sharks on the protected species list in the UK, while satellite tagging __(39)__ the first recorded transatlantic crossing by a basking shark.Volunteers and enthusiasts can be powerful drivers for big changes. No one can know better, or care more about, our most special places than the people who live in them and give up their free time to look after them. As a group of divers and __(40)__ residents who lived on the shores of the bay, they took their campaign on to national and international stages and continue to inspire people who might otherwise feel powerless when faced with threats to the places that matter to them.III. Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.Deliberate practice refers to a special type of practice that is purposeful and systematic. __(41)__ regular practice might include mindless repetitions, deliberate practice requires focused attention and is conducted with the specific goal of improving __(42)__.The greatest __(43)__ of deliberate practice is to remain focused. In the beginning, showing up is the most important thing. But after a while we begin to carelessly __(44)__ small errors and miss daily opportunities for improvement. This is because the natural tendency of the human brain is to __(45)__ repeated behaviors into automatic habits. __(46)__, when you first learned to tie yourshoes you had to think carefully about each step of the process. Today, after many repetitions, your brain can perform this sequence __(47)__. The more we repeat a task the more mindless it becomes.Mindless activity is the __(48)__ of deliberate practice. The danger of practicing the same thing again and again is that progress becomes __(49)__. Too often, we think we are getting better simply because we are gaining experience. In __(50)__, we are merely reinforcing(加强) our current habits — not improving them.Claiming that improvement requires attention and effort sounds logical enough. But what does deliberate practice actually look like in the real world?The first effective feedback system is __(51)__. This holds true for the number of pages we read, the number of pushups we do, the number of sales calls we make, and any other task that is important to us. It is only through measurement that we have any __(52)__ of whether we are getting better or worse.The second effective feedback system is coaching. One consistent finding across disciplines is that coaches are often essential for __(53)__ deliberate practice. In many cases, it is nearly impossible to both perform a task and measure your progress at the same time. Good coaches can track your progress, find small ways to improve, and hold you __(54)__ to delivering your best effort each day.Deliberate practice is not a comfortable activity. It requires sustained effort and concentration, but if you can manage to maintain your focus and __(55)__, then the promise of deliberate practice is quite tempt ing: to get the most out of what you’ve got.41. A. Since B. Whether C. While D. As42. A. awareness B. performance C. enjoyment D. intelligence43. A. equivalent B. ambition C. challenge D. appeal44. A. overlook B. insert C. detect D. implement45. A. transport B. translate C. transplant D. transform46. A. For example B. On the contrary C. As a result D. On the other hand47. A. carelessly B. accurately C. instantly D. automatically48. A. outcome B. enemy C. source D. substitute49. A. distracted B. imposed C. assumed D. noted50. A. reality B. despair C. contrast D. return51. A. encouragement B. compliment C. measurement D. management52. A. motivation B. proof C. trouble D. concern53. A. resisting B. eliminating C. defining D. sustaining54. A. accountable B. opposed C. addicted D. parallel55. A. existence B. commitment C. dignity D. perspectiveSection BDirections:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)Have you ever had the experience of talking to someoneand you think they are lying? Well, you are not alone. We’ve allhad that feeling. But did you know that there are several thingsyou can look for to see if you are being lied to?Sometimes you can tell if a person is lying by observingwhat they do with their body. When people are lying they tend not to move their arms, hands or legs ve ry far from their body. They don’t want to take up very much space because they don’t want to be noticed. Sometimes a person who is lying will not look you in the eyes. Other times people who lie try to look at you in a strong way because they want to convince you they are telling the truth.Liars also use deflection. For example, if you ask a liar the question “Did you steal Fatima’s bag?”, they may answer with something like “Fatima is my friend. Why would I do that?” In this situation the person is tell ing the truth, but they are also not answering the question. They are trying to deflect your attention. Liars may also give too many details. They may try to over-explain things. They do this because they want to convince you of what they are saying.Often when a person is lying, they do not want to continue talking about their lie. If you think someone is lying, quickly change the subject. If the person is lying, they will appear more comfortable because they are not talking about their lie any longer. A little later, change the subject back to what you were talking about before. If the person seems uncomfortable again, they may be lying.It’s very hard for a liar to avoid filling silence created by you. He or she wants you to believe the lies being woven; silence gives no feedback on whether or not you’ve bought the story. If you’re a good listener, you’ll already be avoiding interruptions, which in itself is a great technique to let the story unfold.Just because a person is showing these behaviors, it does not mean they are lying. They might be shy or nervous. But, if you think someone is lying, you might want to use some of these techniques. Hopefully, you won’t need to very often.56. By saying “Liars also use deflection”, the writer means that liars may __________.A. tell great storiesB. change tone of voiceC. ask a question in replyD. avoid direct answers57. According to the passage, a person could be lying if he or she ____________.A. offers more information than necessaryB. appears to be shy or nervousC. changes the subject of the conversationD. speaks very fast and vaguely58. Which of the following can be learned from the passage?A. Liars always try to avoid direct eye contact when they tell lies.B. We can make people lie by changing the subject in a conversation.C. Liars are often expansive in hand and arm movements while talking.D. We make liars uncomfortable by giving no feedback in a conversation.59. The passage mainly talks about __________.A. who deceives usB. why people tell liesC. how to detect liesD. what to do with liars(B)More On:go to gregIs omitting jobs from a resume lying?----------------------- How to handle stress at work------------------------ How can men and women work better together?------------------------ How will cancer treatment affect my son’s resume?------------------------ What to do if you drank too much at the companyholiday partyLetter 1January 28, 2018 | 3:31pm I work for an e-commerce Website. If one of our merchandisers has a question or wants to make a correction, they e-mail the entire department. In my opinion, this is rude and unnecessary. It seems to me that mass e-mail is appropriate for good or neutral news, rather than making a correction. Do you agree? Moreover, if you were the recipient of the correction, how would you respond?The only people who should be included in an e-mail are those who need to know or respond. Including everyone is rude and unprofessional as well as annoying to recipients. I t’s not like we don’t have enough in our inbox already. I don’t agree that e-mail is only for good or neutral news, however. Sometimes you need to alert people or create a record of bad news. But no one should use e-mail to blame other people. If you’ve go t a problem with someone, pick up the phone or take it outside (for a coffee, not a fist fight…geez). As for how to respond, e-mail is usually ineffective for resolving conflict. Have a conversation with the sender and explain why his or her approach isn’t the best and what you recommend.Letter 2January 14, 2018 | 9:24 pmIt’s the start of a new year and I believe it’s time for a change. What’s the best way to explain to a prospective employer that you are in need of something new without seeming flighty and without complaining about your current employer?The new year is as good a time as any to take stock, but not the only reason for making a change. At least, that’s not what you communicate to a prospective employer. Your reason for looking for a new job is less important to your new employer than why you want to work there. Needing a change might be the catalyst(催化剂), but the job search is like dating, and you wouldn’t ask someone out and explain you’re just bored in your current relationship, right? At least I hope not, otherwise you’re likely to be as lonely as Barry Manilow sounds w hen he sings “It’s Just Another New Year’s Eve”.60. What is discussed in the first letter?A. How to ask questions in a polite way.B. How to respond to a false charge.C. How to make a correction at work.D. How to handle rude mass emails at work.61. According to Greg, expressing your dissatisfaction with your present job in an interview would be the same as __________.A. talking about your family issues in publicB. complaining about your prior partner on a first dateC. demonstrating your qualifications to your new bossD. bragging about your experience to your partner62. It can be inferred that “go to greg” mainly offers advice on people’s __________.A. career choicesB. social relationshipsC. working problemsD. health problems(C)Earlier this year a series of papers in The Lancet reported that 85 percent of the $265 billion spent each year on medical research is wasted because too often absolutely nothing happens after initial results of a study are published. No follow-up investigations to replicate(复制) or expand on a discovery. No one uses the findings to build new technologies.The problem is not just what happens after publication — scientists often have trouble choosing the right questions and properly designing studies to answer them. Too many studies test too few subjects to arrive at firm conclusions. Researchers publish reports on hundreds of treatments for diseases that work in animal models but not in humans. Drug companies find themselves unable to reproduce promising drug targets published by the best academic institutions. The growing recognition that something has gone wrong in the laboratory has led to calls for, as one might guess, more research on research — attempts to find rules to ensure that peer-reviewed studies are, in fact, valid.It will take a concerted effort by scientists and other stakeholders to fix this problem. We can do so by exploring ways to make scientific investigation more reliable and efficient. These may include collaborative team science, study registration, stronger study designs and statistical tools, and better peer review, along with making scientific data widely available so that others can replicate experiments, therefore building trust in the conclusions of those studies.Reproducing other scientists’ analyses or replicating their results has too often in the past been looked down on with a kind of “me-too” derision(嘲笑) that would waste resources —but often they may help avoid false leads that would have been even more wasteful. Perhaps the biggest obstacle to replication is the inaccessibility of data and results necessary to rerun the analyses that went into the original experiments. Searching for such information can be extremely difficult. Investigators die, move and change jobs; computers crash; online links malfunction. Data are sometimes lost — even, as one researcher claimed when confronted about spurious(伪造的) results, eaten by termites(白蚁).There has definitely been some recent progress. An increasing number of journals, including Nature and Science, have adopted measures such as checklists for study design and reporting whileimproving statistical review and encouraging access to data. Several funding agencies, meanwhile, have asked that researchers outline their plans for sharing data before they can receive a government grant.But it will take much more to achieve a lasting culture change. Investigators should be rewarded for performing good science rather than just getting statistically significant (“positive”) but nonreplicable results. Revising the present incentive(激励) structure may require changes on the part of journals, funders, universities and other research institutions.63. What is the problem reported in those papers in The Lancet?A. Great achievements in medical research failed to get published.B. Money was wasted on follow-up investigations in medical research.C. Too many new research findings are not put into use after publication.D. Few scientists are devoted to building new technologies for mankind.64. Which of the following situation is most similar to the problem described in paragraph 2?A. A high school decides to cut its art programs due to the lack of fund.B. A patient gets sicker because he does not follow the doctor’s advice.C. A marketing firm tests a website with participants that are not target population.D. A drug company fails to produce the new drug due to no access to the latest data.65. Which of the following can be inferred from the passage?A. Measures are taken to ensure publication of tested results only.B. Scientific experiments must be replicable to be considered valid.C. Experiment replication is unoriginal and not worthwhile.D. Rewards should be given only to those nonreplicable findings.66. The purpose of this article is to ___________.A. argue that scientific research lacks efficiencyB. explain the result of a recent scientific studyC. introduce some recent progress in medical researchD. highlight the possible problems of research studiesSection CDirections: Read the following passage. Fill in each blank with a proper sentence given in the box. Each sentence can be used only once. Note that there are two more sentences than you need.People di scuss their problems with friends in the hope that they’ll gain some insight into how to solve them. And even if they don’t find a way to solve their problems, it feels good to let off somesteam. (67)_______________ How problems are discussed, though, can be the difference between halving a problem or doubling it.The term psychologists use for negative problem sharing is “co-rumination”. Co-rumination is the mutual encouragement to discuss problems repeatedly going over the same problems, anticipating future problems and focusing on negative feelings.(68)________________ In a study involving children aged seven to 15 years of age, researchers found that co-rumination in both boys and girls is associated with “high-quality” and close friendships. However, in girls, it was also associated with anxiety and depression (the same association was not found with the boys). And studies suggest that co-rumination isn’t just a problem for girls. Co-rumination with work colleagues can increase the risk of stress and burn out, one study suggests.(69)________________ In a group of adults, the effects of co-rumination was compared between face-to-face contact, telephone contact, texting and social media. The positive effects of co-rumination were found in face-to-face contact, telephone contact and texting, but not in social media. The negative aspects of co-rumination (anxiety) was found in face-to-face communication and telephone contact, but not texting or social media. Verbal forms of communication seem to enhance both the positive and negative aspects of co-rumination more than non-verbal communication.Discussing problems with friends doesn’t always have to lead to worsening mental health, as long as the discussion involves finding solutions and the person with the problem acts on those solutions. Then, relationships can be positive and beneficial to both parties. (70)________________IV．Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.A Workaholic EconomyAlthough the output per hour of work has more than doubled since 1945, leisure seems reserved largely for the unemployed and underemployed. Those who work full-time spend as much time on the job as they did at the end of World War Ⅱ. In fact, working hours have increased noticeably since 1970. Bookstores now abound with manuals describing how to manage time and cope with stress.There are mainly two reasons for lost leisure.Since 1970, companies have responded to improvements in the business climate by having employees work overtime rather than by hiring extra personnel. Some firms are even downsizing as their profits climb. A host of factors pushes employers to hire fewer workers for more hours and, at the same time, compels workers to spend more time on the job. Most of those incentives(诱因) involve the structure of compensation(报酬). The way salaries and benefits are organized makes it more profitable to ask 40 employees to labor an extra hour each than to hire one more worker to do the same 40-hour job. Once people are on salary, their cost to a firm is the same whether they spend 35 hours a week in the office or 70. Therefore, it is more profitable for employers to work their existing employees harder.For all that employees complain about long hours, they, too, have reasons not to trade money for leisu re. “People who work reduced hours pay a huge penalty in career terms,”Bailyn of Massachusetts Institute of Technology maintains. “It’s taken as a negative signal abou t their commitment to the firm.”He adds that many corporate managers find it difficult to measure the contribution of their employee s to a firm’s well-being, so they estimate staff productivity in terms of hours worked. Employees know this, and they adjust their behavior accordingly.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1. 这次春游为同学们提供了放松的机会。

2017-2018学年第二学期徐汇区学习能力诊断卷高三数学 2018.4一、填空题（本大题共有12题，满分54分，第1-6题每题4分，第7-12题每题5分） 考生应在答题纸的相应位置直接填写结果．1．已知全集R U =，集合{}0322>--=x x x A ，则=A C U .2．在61x x ⎛⎫+ ⎪⎝⎭的二项展开式中，常数项是 .3．函数()lg(32)x xf x =-的定义域为_____________． 4．已知抛物线2x ay =的准线方程是14y =-，则a = . 5．若一个球的体积为323π，则该球的表面积为_________． 6．已知实数x y ，满足001x y x y ≥⎧⎪≥⎨⎪+≤⎩，，． 则目标函数z x y =-的最小值为___________．7．函数()2sin cos 1()11x x f x +-=的最小正周期是___________．8．若一圆锥的底面半径为3，体积是12π，则该圆锥的侧面积等于 .9．将两颗质地均匀的骰子抛掷一次，记第一颗骰子出现的点数是m ，记第二颗骰子出现的点数是n ，向量()2,2a m n =--，向量()1,1b =，则向量a b ⊥的概率．．是 . 10．已知直线12:0,:20l mx y l x my m -=+--=.当m 在实数范围内变化时，1l 与2l 的交点P 恒在一个定圆上，则定圆方程是 .11．若函数222(1)sin ()1x xf x x ++=+的最大值和最小值分别为M 、m ，则函数()()()sin 1g x M m x M m x =+++-⎡⎤⎣⎦图像的一个对称中心是 ．12．已知向量,a b 的夹角为锐角，且满足8||15a =、4||15b =，若对任意的{}(,)(,)||1,0x y x y xa yb xy ∈+=>，都有||1x y +≤成立，则a b ⋅的最小值为 .二、选择题（本大题共有4题，满分20分，每题５分）每题有且只有一个正确选项。

2017 学年第二学期徐汇区学习能力诊断卷高三语文试卷（满分 150 分，考试时间 150 分钟） 2018.4一、积累应用 10 分1. 按要求填空。

⑴云无心以出岫，__________________。

”（陶渊明《______________》）⑵是日也，天朗气清，__________________。

（王羲之《兰亭集序》）⑶无论是《老子》中的“千里之行，始于足下”，还是《荀子·劝学》中的“________，_________”，都是以“行路”来形象地阐释积累的重要性。

【答案】 (1). 鸟倦飞而知还 (2). 归去来兮辞 (3). 惠风和畅 (4). 不积跬步 (5). 无以致千里2. 按要求选择。

假设你为学校“读书节”设计一张宣传海报，下列诗文中最适合选用的是（）A. 纸上得来终觉浅，绝知此事要躬行。

B. 世事洞明皆学问，人情练达即文章。

C. 察己则可以知人，察今则可以知古。

D. 问渠那得清如许，为有源头活水来。

【答案】D【解析】试题分析：本题考查用语要得体。

本题主题是:为学校“读书节”设计一张宣传海报，主要是宣传多读书，D选自（南宋）朱熹的《观书有感》，这首诗告诉我们，正像源源不断的活水使池塘变得如此清澈，人需要不断读书，不断汲取新的知识，心智才能更加开豁，更加敏锐。

符合读书节的主题。

A“纸上得来终觉浅,绝知此事要躬行”出自陆游的《冬夜读书示子聿》一诗，意思是说,从书本上得到的知识毕竟比较肤浅,要透彻地认识事物还必须亲自实践。

与读书节主题相反。

B“世事洞明皆学问，人情练达即文章。

”出自《红楼梦》第五回中的一副对联。

其大意是：明白世事，掌握其规律，这些都是学问；恰当地处理事情，懂得道理，总结出来的经验就是文章。

与读书无关。

C出自《吕氏春秋》。

意思应该是:通过了解自己可以了解别人,也就是说每个人都有共性,差别不是很大,而后一句意思也相同;通过了解当今而了解古时。

与读书无关。

3. 下面是某高三学生参加高校自主招生的自荐信，画线部分可能存在不得体的表达。

2017-2018 学年第二学期徐汇区学习能力诊断卷高三语文试卷（满分150 分，考试时间150 分钟）2018.4一、积累应用10 分1. 按要求填空。

（5 分）⑴云无心以出岫，。

”（陶渊明《》）⑵是日也，天朗气清，。

（王羲之《兰亭集序》）⑶无论是《老子》中的“千里之行，始于足下”，还是《荀子·劝学》中的“，”，都是以“行路”来形象地阐释积累的重要性。

2. 按要求选择。

（5 分）⑴假设你为学校“读书节”设计一张宣传海报，下列诗文中最适合选用的是（）。

（2 分）A. 纸上得来终觉浅，绝知此事要躬行。

B. 世事洞明皆学问，人情练达即文章。

C. 察己则可以知人，察今则可以知古。

D. 问渠那得清如许，为有源头活水来。

⑵下面是某高三学生参加高校自主招生的自荐信，画线部分可能存在不得体的表达。

尊敬的学校领导：您好!①感谢您在百忙之中阅读我的自荐信。

我是XX，来自XX 市XX中学，学习成绩优秀，曾担任校学生会文艺部部长，爱好写作。

我获得过第十九届“语文报杯”全国中学生作文竞赛高中组一等奖；也曾代表学校参加市中学生辩论大赛，②以敏捷的反应和出众的口才令对手自惭形秽，③获得“最佳辩手”称号。

贵校历史悠久，底蕴深厚，④能进入贵校中文系学习是我的理想。

⑤贵校的自主招生条件也非常符合我的标准。

⑥请您一定不要拒绝我，⑦圆我的大学中文系之梦。

此致敬礼！自荐人：XXXXX 年 X 月 X 日有几处画线部分存在不得体的表达？（）（3 分）A. 1 处B. 2 处C. 3 处D. 4 处二、阅读（70 分）（一）阅读下文，完成第3—7 题。

（16 分）①美国波士顿一所公立学校日前选用了一种全新标准的世界地图，令学生们看后困惑不已：美国、加拿大、欧洲的版图不再如印象中那般阔大，南美洲和大洋洲也不像原先看起来那样狭小。

最令人惊讶的是非洲——和美国比起来，非洲才是真正的巨人，连俄罗斯都无法与之相提并论。

②世界地图也有多种版本吗？哪个版本才是正确的呢？要解答这些问题，首先要对地图投影有所了解。

2018学年第二学期上海市徐汇区学习能力诊断卷高三语文试卷2019.04一积累应用10分1.按要求填空。

（5分）（1）虽无丝竹管弦之盛，______________，亦足以畅叙幽情。

（__________《兰亭集序》）（2）王国维在《___________》中借用了柳永的词句“__________，___________”来类比成就大事业、大学问必经的第二境界。

2.阅读下面文字，按要求选择。

（5分）2016年，由地球物理学家黄大年领衔的“中国深部探测技术”项目研究成果达到国际一流水平。

黄大年对他的团队成员说：在“巡天探地潜海”领域，我们一直在跟跑；经过5年的努力，我们进入了并跑阶段。

要达到领跑水平，我们更要戮力同心，沉下心来做研究。

常常有队员拿实验报告来向我__，或发来论文让我__，不时能看到你们的__，我很欣慰，也很骄傲。

目前我们取得了骄人的成绩，但从并跑到领跑的路还很长，“___，___”我们任重道远。

（1）按顺序填入空格处的词语，用语贴切的一项是（）。

（3分）A.请示指正不经之谈B.垂询斧正不根之论C.请教斧正不易之论D.咨询指正不刊之论（2）填入画线处的句子，合适的一项是（）。

（2分）A.千淘万漉虽辛苦，吹尽狂沙始到金。

B.路漫漫其修远兮，吾将上下而求索。

C.雄关漫道真如铁，而今迈步从头越。

D.宝剑锋从磨砺出，梅花香自苦寒来。

二阅读70分（一）阅读下文，完成第3—7题。

（15分）科幻作品的价值①近几年，随着刘慈欣的《三体》获雨果奖，以及《黑客帝国》《阿凡达》等科幻电影迸发出炽烈的“科幻热”，科幻作品拥有了数量庞大的受众，但这依然未能改变科幻作品的尴尬地位：它既不是科学领域的主流，也不是文学领域的主流，而是被大部分国人习惯看作“科普读物”沉沦在边缘状态。

如何定位科幻作品，我们似乎应该厘清一个基本问题：科幻作品的价值到底是什么?②1866年，人们在海上发现了一只被称为“独角鲸”的大怪物，生物学家阿龙纳斯应邀参加了捕捉这只“怪物”的行动。

Lvhui2017-2018 学年第二学期徐汇区学习能力诊断卷高三语文试卷（满分150 分，考试时间150 分钟）2018.4一、积累应用10 分1. 按要求填空。

（5 分）⑴云无心以出岫，。

”（陶渊明《》）⑵是日也，天朗气清，。

（王羲之《兰亭集序》）⑶无论是《老子》中的“千里之行，始于足下”，还是《荀子·劝学》中的“，”，都是以“行路”来形象地阐释积累的重要性。

2. 按要求选择。

（5 分）⑴假设你为学校“读书节”设计一张宣传海报，下列诗文中最适合选用的是（）。

（2 分）A. 纸上得来终觉浅，绝知此事要躬行。

B. 世事洞明皆学问，人情练达即文章。

C. 察己则可以知人，察今则可以知古。

D. 问渠那得清如许，为有源头活水来。

⑵下面是某高三学生参加高校自主招生的自荐信，画线部分可能存在不得体的表达。

尊敬的学校领导：您好!①感谢您在百忙之中阅读我的自荐信。

我是XX，来自XX 市XX中学，学习成绩优秀，曾担任校学生会文艺部部长，爱好写作。

我获得过第十九届“语文报杯”全国中学生作文竞赛高中组一等奖；也曾代表学校参加市中学生辩论大赛，②以敏捷的反应和出众的口才令对手自惭形秽，③获得“最佳辩手”称号。

贵校历史悠久，底蕴深厚，④能进入贵校中文系学习是我的理想。

⑤贵校的自主招生条件也非常符合我的标准。

⑥请您一定不要拒绝我，⑦圆我的大学中文系之梦。

此致敬礼！自荐人：XXXXX 年 X 月 X 日有几处画线部分存在不得体的表达？（）（3 分）A. 1 处B. 2 处C. 3 处D. 4 处二、阅读（70 分）（一）阅读下文，完成第3—7 题。

（16 分）①美国波士顿一所公立学校日前选用了一种全新标准的世界地图，令学生们看后困惑不已：美国、加拿大、欧洲的版图不再如印象中那般阔大，南美洲和大洋洲也不像原先看起来那样狭小。

最令人惊讶的是非洲——和美国比起来，非洲才是真正的巨人，连俄罗斯都无法与之相提并论。

②世界地图也有多种版本吗？哪个版本才是正确的呢？要解答这些问题，首先要对地图投影有所了解。

绝密★启用前上海市徐汇区2018届高三下学期学习能力诊断（二模）数学试题第I 卷（选择题）一、单选题1．在四边形ABCD 中， AB DC = ，且AC ·BD＝0，则四边形ABCD 是--------（ ）A. 菱形B. 矩形C. 直角梯形D. 等腰梯形2．若无穷等比数列{}n a 的前n 项和为n S ，首项为1，公比为12，且lim n n S a →∞=，(*n N ∈)，则复数1z a i=+（i 为虚数单位）在复平面上对应的点位于----------（ ）A. 第一象限．B. 第二象限．C. 第三象限．D. 第四象限．3．在ABC ∆中，“cos sin cos sin A A B B +=+”是“090C ∠=”的（ ） A. 充分非必要条件 B. 必要非充分条件 C. 充要条件 D. 既不充分也不必要条件4．如图，圆C 分别与x 轴正半轴，y 轴正半轴相切于点,A B ，过劣弧AB 上一点T 作圆C 的切线，分别交x 轴正半轴， y 轴正半轴于点,M N ，若点()2,1Q 是切线上一点，则MON ∆周长的最小值为------------------------------------------------------------------( )A. 10B. 8C. 第II 卷（非选择题）二、填空题5．已知全集U R =，集合{}2230A x x x =-->，则U C A =_______.6．在的二项展开式中，常数项是_______7．函数()()lg 32x xf x =-的定义域为_____________．8．已知抛物线2x ay =的准线方程是14y =-，则a =_______ . 9．若一个球的体积为323π，则该球的表面积为_________． 10．已知实数x y ，满足0{0 1x y x y ≥≥+≤，，．则目标函数z x y =-的最小值为___________．11．函数()()2sin cos 111x x f x +-=的最小正周期是___________． 12．已知圆锥的底面半径为3，体积是12π，则圆锥侧面积等于___________. 13．将两颗质地均匀的骰子抛掷一次，记第一颗骰子出现的点数是m ，记第二颗骰子出现的点数是n ，向量()2,2a m n =-- ，向量()1,1b = ，则向量a b ⊥的概率是_______.14．已知直线12:0,:20l mx y l x my m -=+--=.当m 在实数范围内变化时， 1l 与2l 的交点P 恒在一个定圆上，则定圆方程是 ______ .15．若函数()()2221sin 1x xf x x ++=+的最大值和最小值分别为M 、m ，则函数()()()sin 1g x M m x M m x ⎡⎤=+++-⎣⎦图像的一个对称中心是_______．16．已知向量,a b的夹角为锐角，且满足a =、b = ，若对任意的()(){},,||1,0 x y x y xa yb xy ∈+= ，都有1x y +≤成立，则a b ⋅的最小值为_______.三、解答题17．如图在长方体1111ABCD A BC D -中， 2AB =， 4AD =， 1AC =，点M 为AB 的中点，点N 为BC 的中点． （1）求长方体1111ABCD A BC D -的体积；（2）求异面直线1A M 与1B N 所成角的大小（用反三角函数表示）．18．如图：某快递小哥从A 地出发，沿小路AB BC →以平均时速20公里/小时，送快件到C 处，已知10BD =（公里），045,30DCB CDB ∠=∠=， ABD ∆是等腰三角形， 0120ABD ∠=．（1） 试问，快递小哥能否在50分钟内将快件送到C 处？（2）快递小哥出发15分钟后，快递公司发现快件有重大问题，由于通讯不畅，公司只能派车沿大路AD DC →追赶，若汽车平均时速60公里/小时，问，汽车能否先到达C 处？19．已知函数()231f x x tx =-+，其定义域为][0,312,15⎡⎤⋃⎣⎦，(1) 当2t =时，求函数()y f x =的反函数；(2) 如果函数()y f x =在其定义域内有反函数，求实数t 的取值范围．20．如图， ,A B 是椭圆22:12x C y +=长轴的两个端点， ,M N 是椭圆上与,A B 均不重合的相异两点，设直线,,AM BN AN 的斜率分别是123,,k k k . (1)求23k k ⋅的值；(2)若直线MN 过点,02⎛⎫ ⎪ ⎪⎝⎭，求证： 1316k k ⋅=-； (3)设直线MN 与x 轴的交点为(),0t (t 为常数且0t ≠)，试探究直线AM 与直线BN 的交点Q 是否落在某条定直线上？若是，请求出该定直线的方程；若不是，请说明理由．21．已知数列{}n a 的前n 项和n A 满足()*1112n n A A n N n n +-=∈+，且11a =，数列{}n b 满足()*2120n n n b b b n N ++-+=∈， 32b =，其前9项和为36．(1)求数列{}n a 和{}n b 的通项公式；(2)当n 为奇数时，将n a 放在n b 的前面一项的位置上；当n 为偶数时，将n b 放在n a 前面一项的位置上，可以得到一个新的数列： 1122334455,,,,,,,,,,a b b a a b b a a b ⋅⋅⋅，求该数列的前n 项和n S ； (3)设1n n nc a b =+，对于任意给定的正整数()2k k ≥，是否存在正整数,()l m k l m <<，使得,,k l m c c c 成等差数列？若存在，求出,l m (用k 表示)；若不存在，请说明理由．1．A【解析】由题意，根据两个向量相等的定义，由AB DC =，可知AB 与DC 平行且相等，所以四边形ABCD 为平行四边形，又0AC BD ⋅=，即AC BD ⊥，亦是平行四边形ABCD 的对角线互相垂直，因此可判断平行四边形ABCD 为菱形.3．B【解析】试题分析：由cos sin cos sin A A B B +=+两边平方，得1+sin2=1sin2,2222A B A B A B A B π+=+=因为、为三角形的内角，所以或,所以2A B A B π=+=或，即2A B C π==或；若2C π=，则A+B=2π，所以cos +sin =cos -sin sin +cos 22A A B B B B ππ⎛⎫⎛⎫+-= ⎪ ⎪⎝⎭⎝⎭.因此选B.考点：充分、必要、充要条件的判断；二倍角公式；诱导公式. 点评：熟练掌握三角形内的隐含条件：sin()sin ,sin()sin ,sin(B )sin A B C A C B C A +=+=+=； cos()-cos ,cos()-cos ,cos(B )-cos A B C A C B C A +=+=+=.4．A【解析】由题意，可设切线的斜率为k （k 必存在），圆C 的半径为r ，则切线的方程为()1200kx y k x r -+-=≤≤r =， ()12y k x -=-，则点,M N 的坐标分别为21,0k k -⎛⎫⎪⎝⎭， ()012k -，，且210{ 120k kk ->->，，即0k <，所以MON C ∆= 10.5．[]1,3-【解析】由已知得， {}()()2230,13,A x x x =--=-∞-⋃+∞，又全集为R ，根据补集的定义可得[]13U A =-，ð.所以正确答案为[]13-，.7．()0,+∞【解析】由题意，根据对数函数的概念及其定义域可得， 320x x ->，即32x x >，由指数函数13x y =与22x y =的图象可知，如图所示，当0x >时， 32x x >恒成立，所以正确答案为()0+∞，.8．1【解析】由题意，可知该抛物线的开口方向为y 轴的正半轴，其标准方程为()220x py p =>，又其准线方程为14y =-，所以124p =，则12p =，所以21a p ==.9．16π【解析】由题意，根据球的体积公式343V R π=，则343233R ππ=，解得2R =，又根据球的表面积公式24S R π=，所以该球的表面积为24216S ππ=⋅=.10．1-点睛：此题主要考查简单线性规划问题中的最优解，以及数形结合法在解决实际问题中的应用等有关方面的知识与基本技能，属于中低档题型，也是常考题.此类问题一般流程是：首先根据约束条件画出可行域区域图；第二步是将目标函数进行转化，常转化为直线的斜截式；第三步，通过平移该直线（在区域范围内），找到直线在y 轴上截距的最值.从而得到问题的最优解. 11．π【解析】由题意得， ()()2sin cos 1sin22f x x x x =++=+，结合正弦函数()sin y A x ωϕ=+的最小正周期的计算公式2T πω=，得函数()f x 的最小正周期为22T ππ==. 12．15π【解析】试题分析：求圆锥侧面积必须先求圆锥母线，既然已知体积，那么可先求出圆锥的高，再利用圆锥的性质(圆锥的高，底面半径，母线组成直角三角形)可得母线，221131233V r h h πππ==⋅⋅=， 4h =，5l ==， 15S rl ππ==侧．考点：圆锥的体积与面积公式，圆锥的性质．13．16【解析】由题意知， {},1,2,3,4,5,6m n ∈，则(),m n 共有36种，由a b ⊥，得()()220m n -+-=，即m n =，共有6种，根据古典概型的计算公式可得，所求概率为16p =. 点睛：此题主要考了向量的位置关系在求概率问题中的应用，以及古典概型概率的计算等有关方面的知识与技能，属于中低档题型，也是常考题.此题中，抛掷两颗骰子的试验中所有可能的情况为36种，结合题中条件，从中找出满足条件所求事件的个数，再根据古典概型概率的计算公式进行求解，从而问题可得解. 14．2220x y x y +--= 【解析】由题意，联立两直线方程0{20xm y x my m -=+--=，利用代入消元法，消去m 得20y yx y x x+⋅--=，整理后可得，所求定圆方程是2220x y x y +--=. 15．114⎛⎫ ⎪⎝⎭，点睛：此题主要考查函数的奇偶性、最值、对称中心，以及三角函数值的运算等方面的知识与技能，属于中档题型，也是常考题.此题中需要对函数的解析式进行化简整理，观察其解析式是由常函数与奇函数加减而成，从而通过计算其中奇函数的最值，由其性质易知，奇函数的最大值与最小值互为相反函数，从而问题可得解. 16．815【解析】17．（1）8（2）arccos10【解析】试题分析：（1）由题意，长方体的体对角线长为1AC =,从而可求得该长方体的高1AA ，再由长方体体积的计算公式即可求其体积； （2）根据题意，可采用坐标法进行求解，分别以1,,DA DC DD 为,,x y z 轴建立空间直角坐标系，根据向量数量积公式求出向量1A M 与1B N的夹角，从而可求出异面直线1A M 与1B N 所成的角. （2）解法一：如图建立空间直角坐标系则()14,0,1A 、()4,1,0M 、()14,2,1B 、()2,2,0N ，所以()10,1,1A M =-、()12,0,1B N =--，10分则向量1A M 与1B N所成角θ满足1111cos A M B N A M B Nθ⋅==⋅∴异面直线1A M 与1B N所成的角等于arccos10． 解法二：取AD 的中点E ，连1A E 、EM ． 11////EN AB A B ， ∴四边形11A B NE 为平行四边形， 11//A E B N ∴， ∴ 1EA M ∠等于异面直线1A M 与1B N 所成的角或其补角． 1AM =， 2AE =， 11AA =，得1A M =1A E =，EM =∴1cos EA M ∠==1EA M ∠=． ∴异面直线1A M 与1B N所成的角等于． 18．（1）不能（2）能试题解析：（1）10AB =（公里），BCD ∆中，由00sin45sin30BD BC=，得BC =于是，由106051.215020+≈>知， 快递小哥不能在50分钟内将快件送到C 处．（2）在ABD ∆中，由22211010210103002AD ⎛⎫=+-⋅⋅⋅-= ⎪⎝⎭，得AD =，在BCD ∆中， 0105CBD ∠=，由00sin105sin30CD =，得(51CD =（公里），-由(5160152045.9851.2160⨯+=+≈<（分钟）知，汽车能先到达C 处．点睛：此题主要考查了解三角形中正弦定理、余弦定理在实际生活中的应用，以及关于路程问题的求解运算等方面的知识与技能，属于中低档题型，也是常考题型.在此类问题中，总是正弦定理、余弦定理，以及相关联的三角函数的知识，所以根据题目条件、图形进行挖掘，找到与问题衔接处，从而寻找到问题的解决方案. 19．（1）[][]38,1{373,136x y x ∈-=+∈（2）][()][(),02,46,810,t ∈-∞⋃⋃⋃+∞试题解析：(1) [][]38,1{373,136x y x ∈-=∈；(2) 01 若302t≤，即0t ≤，则()y f x =在定义域上单调递增，所以具有反函数；---8分02 若3152t≥，即10t ≥，则()y f x =在定义域上单调递减，所以具有反函数；--10分03 当33122t ≤≤，即28t ≤≤时，由于区间[]0,3关于对称轴32t的对称区间是 []33,3t t -，于是当312{ 332t t <≥或3315{ 3122t t ->≤，即[)2,4t ∈或(]6,8t ∈时，函数()y f x =在定义域上满足1-1对应关系，具有反函数． 综上， ][()][(),02,46,810,t ∈-∞⋃⋃⋃+∞．点睛：此题主要考查了函数的单调性、对称性、反函数，以及分段函数的定义域、值域等有关方面的知识与技能，属于中档题型，也是常考题型.若要求一函数的反函数，首先要求出此函数的单调区间，最好求出对应的值域，然后在各个单调区间进行运算求解，并将,x y 进行互换，定义域与值域互换，从而得到反函数. 20．（1）2312k k ⋅=-（2）见解析（3）落在定直线2x t=上 （3）同（2）法，由点,M N 的纵坐标，求出直线,AM BN 的方程，联立两直线方程，求出其交点Q 的横坐标2x t=与点,M N 的坐标无关，从而可判断交点Q 落在定直线2x t=上，从而问题可得解.试题解析：(1)设()00,N x y，由于()),A B，所以2023202y k k x ⋅==-， 因为()00,N x y 在椭圆C 上，于是220012x y +=，即220022x y -=-， 所以202320122y k k x ⋅==--.(2)设直线:2MN x my =+， ()()1122,,,M x y N x y，由22{ 222x my x y =++=得()223202m y ++-=，于是()12122322y y y y m +=⋅=-+，13k k ⋅==()()2222332212396322222m m m m m --+===---+++．两式相除，可知1222211my y t y y y y y +===((()22212212122222222t mt m t y m t t m ym m t m t y m -⎛⎫⋅++-- ⎪-+-+++⎝⎭==-⋅++()212m t m y --+==，于是2xt =，所以2x t =，即直线AM 与直线BN 的交点Q 落在定直线2x t=上． 21．（1）()*n a n n N =∈， ()1*n b n n N =-∈（2）2221,243{,4 3 41,414n n n k n S n k n n k =+==--=-（3）当2k ≥时，存在正整数221,452l k m k k =-=-+，满足k l m <<，且使得,,k l mc c c 成等差数列．试题解析： (1)因为()*1112n n A A n N n n +-=∈+，于是数列n A n ⎧⎫⎨⎬⎩⎭是首项为1，公差为12的等差数列， 所以1122n A n n =+，即()()*12n n n A n N +=∈， 当2n ≥时， 1n n n a A A n -=-=，又因为11a =，所以()*n a n n N =∈.- 又因为()*2120n n n b b b n N ++-+=∈，于是数列{}n b 是等差数列，设{}n b 的前n 项和为n B ，由于95936B b ==，则54b =，由于32b =， 所以()1*n b n n N =-∈． (2)数列{}n a 的前n 项和()12n n n A +=，数列{}n b 的前n 项和()12nn n B -=． 当()2*n k k N =∈时， ()()221122n k k k k k k k S S A B k +-==+=+=；当()43*n k k N =-∈时，()()()243212221231463n k k k S S A B k k k k k k ---==+=-+--=-+；-当()41*n k k N =-∈时，()()241212212142n k k k S S A B k k k k k k --==+=-+-=-；-所以2221,243{,4 3 41,414n n n k n S n k n n k =+==--=-，其中*k N ∈．--()2211421k k k l -=-+--，即()2211421k m k k l -=+---，--则对任意的()*2,k k k N ≥∈， 421k l --能整除()221k -，且4210k l -->.由于当2k ≥时， 21k -中存在多个质数， 所以421k l --只能取1或21k -或()221k ---若4211k l --=，则21l k =-， 2452m k k =-+，于是()()24734310m l k k k k -=-+=-->，符合k l m <<；-若42121k l k --=-，则k l =，矛盾，舍去；-若()242121k l k --=-，则2m k +=，于是0m ≤，矛盾．综上，当2k ≥时，存在正整数221,452l k m k k =-=-+，满足k l m <<，且使得,,k l m c c c 成等差数列．。

上海市徐汇区2018届高三下学期学习能力诊断（二模）数学试题一、填空题1．已知全集R U =，集合{}0322>--=x x x A ，则=A C U .2．在61x x ⎛⎫+ ⎪⎝⎭的二项展开式中，常数项是.3．函数()lg(32)x x f x =-的定义域为_____________． 4．已知抛物线2x ay =的准线方程是14y =-，则a =. 5．若一个球的体积为32π3，则该球的表面积为_________． 6．已知实数x y ，满足001x y x y ≥⎧⎪≥⎨⎪+≤⎩，，． 则目标函数z x y =-的最小值为___________．7．函数()2sin cos 1()11x x f x +-=的最小正周期是___________．8．若一圆锥的底面半径为3，体积是12π，则该圆锥的侧面积等于.9．将两颗质地均匀的骰子抛掷一次，记第一颗骰子出现的点数是m ，记第二颗骰子出现的点数是n ，向量()2,2a m n =-- ，向量()1,1b =，则向量a b ⊥ 的概率．．是. 10．已知直线12:0,:20l mx y l x my m -=+--=.当m 在实数范围内变化时，1l 与2l 的交 点P 恒在一个定圆上，则定圆方程是.11．若函数222(1)sin ()1x xf x x ++=+的最大值和最小值分别为M 、m ，则函数()()()sin 1g x M m x M m x =+++-⎡⎤⎣⎦图像的一个对称中心是．12．已知向量,a b 的夹角为锐角，且满足||a =、||b = ，若对任意的{}(,)(,)||1,0x y x y xa yb xy ∈+=> ，都有||1x y +≤成立，则a b ⋅的最小值为.二、选择题13．在四边形ABCD 中，AB DC = ，且AC ·BD＝0，则四边形ABCD 是（ ） A.菱形 B.矩形 C.直角梯形 D.等腰梯形14. 若无穷等比数列{}n a 的前n 项和为n S ，首项为1，公比为12，且a S n n =∞→lim ，(n ∈*N )，则复数ia z +=1（i 为虚数单位）在复平面上对应的点位于（ ） A.第一象限 B.第二象限 C.第三象限 D.第四象限15．在ABC ∆中，“cos sin cos sin A A B B +=+”是“090C ∠=”的（ ） A .充分非必要条件 B.必要非充分条件C.充要条件D.既不充分也不必要条件16．如图，圆C 分别与x 轴正半轴，y 轴正半轴相切于点,A B ，过劣弧AB 上一点T 作圆C 的切线，分别交x 轴正半轴，y 轴正半轴于点,M N ，若点(2,1)Q 是切线上一点，则MON ∆周长的最小值为( ) A.10 B.8C.三、解答题17． 如图在长方体1111D C B A ABCD -中，2AB =，4AD =，1AC =，点M 为AB 的中点，点N 为BC 的中点．（1）求长方体1111D C B A ABCD -的体积；（2）求异面直线M A 1与N B 1所成角的大小（用反三角函数表示）．NMD 1C 1B 1A 1DCBA18．如图：某快递小哥从A 地出发，沿小路AB BC →以平均时速20公里/小时，送快件到C 处，已知10BD =（公里），0045,30DCB CDB ∠=∠=，ABD ∆是等腰三角形，0120ABD ∠=．（1）试问，快递小哥能否在50分钟内将快件送到C 处？（2）快递小哥出发15分钟后，快递公司发现快件有重大问题，由于通讯不畅，公司只能派车沿大路AD DC →追赶，若汽车平均时速60公里/小时，问，汽车能否先到达C 处？19．已知函数2()31f x x tx =-+，其定义域为[0,3][12,15] ， (1) 当2t =时，求函数()y f x =的反函数；(2) 如果函数()y f x =在其定义域内有反函数，求实数t 的取值范围．20．如图，,A B 是椭圆22:12x C y +=长轴的两个端点，,M N 是椭圆上与,A B 均不重合的相异两点，设直线,,AM BN AN 的斜率分别是123,,k k k .(1)求23k k ⋅的值；(2)若直线MN 过点⎫⎪⎪⎝⎭，求证：1316k k ⋅=-； (3)设直线MN 与x 轴的交点为(,0)t (t 为常数且0t ≠)，试探究直线AM 与直线BN 的交点Q 是否落在某条定直线上？若是，请求出该定直线的方程；若不是，请说明理由．21．已知数列{}n a 的前n 项和n A 满足*11()12n n A A n n n +-=∈+N ，且11a =，数列{}n b 满足*2120()n n n b b b n ++-+=∈N ，32b =，其前9项和为36．(1)求数列{}n a 和{}n b 的通项公式；(2)当n 为奇数时，将n a 放在n b 的前面一项的位置上；当n 为偶数时，将n b 放在n a 前面一项的位置上，可以得到一个新的数列：1122334455,,,,,,,,,,a b b a a b b a a b ⋅⋅⋅，求该数列的前n 项和n S ； (3)设1n n nc a b =+，对于任意给定的正整数()2k k ≥，是否存在正整数,()l m k l m <<，使得,,k l m c c c 成等差数列？若存在，求出,l m (用k 表示)；若不存在，请说明理由．【参考答案】一． 填空题１．]3,1[- 2．20 3．(0,)+∞ 4．1 5．16π 6．1- 7．π 8．15π9．16 10． 2220x y x y +--= 11．114⎛⎫ ⎪⎝⎭， 12．815 二．选择题13．A 14．D 15．B 16．A 三. 解答题17．解：（1） 连AC 、1AC ． ABC ∆是直角三角形，∴AC =1111D C B A ABCD -是长方体，∴BC C C ⊥1，CD C C ⊥1，又C BC DC =⋂， ∴⊥C C 1平面ABCD ，∴AC C C ⊥1．又在1ACC Rt ∆中，1AC =，AC =∴11CC =，∴11118ABCD A B C D V -=． （2）解法一：如图建立空间直角坐标系.则()14,0,1A 、()4,1,0M 、()14,2,1B 、()2,2,0N ，所以()10,1,1A M =- 、()12,0,1B N =--， 则向量1AM 与1B N 所成角θ满足1111cos 10A M B N A M B Nθ⋅==⋅． ∴异面直线M A 1与N B 1所成的角等于．14分解法二：取AD 的中点E ，连E A 1、EM ．11////B A AB EN ，∴四边形NE B A 11为平行四边形，N B E A 11//∴，∴M EA 1∠等于异面直线M A 1与N B 1所成的角或其补角．1AM =，2AE =，11=AA，得1AM =1AE =，5=EM ，∴1cos EA M ∠==110EA M ∠=． ∴异面直线M A 1与N B 1所成的角等于． 18．解：（1）10AB =（公里），BCD ∆中，由00sin 45sin 30BD BC=，得BC =，于是，由106051.215020+≈>知， 快递小哥不能在50分钟内将快件送到C 处．（2）在ABD ∆中，由22211010210103002AD ⎛⎫=+-⋅⋅⋅-= ⎪⎝⎭，得AD =， 在BCD ∆中，0105CBD ∠=，由00sin105sin30CD =，得(51CD =+（公里），由(5160152045.9851.2160⨯+=+≈<（分钟）知，汽车能先到达C 处．END 1C 1B 1A 1D CBA19．解：(1) 3[8,1]3[73,136]x y x ⎧∈-⎪=⎨+∈⎪⎩； (2)01 若302t ≤，即0t ≤，则()y f x =在定义域上单调递增，所以具有反函数；02 若3152t≥，即10t ≥，则()y f x =在定义域上单调递减，所以具有反函数；--10分 03 当33122t ≤≤，即28t ≤≤时，由于区间[]0,3关于对称轴32t的对称区间是[]33,3t t -，于是当312332t t <⎧⎪⎨≥⎪⎩或33153122t t->⎧⎪⎨≤⎪⎩，即[)2,4t ∈或(]6,8t ∈时， 函数()y f x =在定义域上满足1-1对应关系，具有反函数． 综上，(,0][2,4)(6,8][10,)t ∈-∞+∞ ． 20．解：(1)设00(,)N x y，由于(A B ，所以223202y k k x ⋅==-，因为00(,)N x y 在椭圆C 上，于是220012x y +=，即220022x y -=-， 所以202320122y k k x ⋅==--.(2)设直线:2MN x my =+，1122(,),(,)M x y N x y，由22222x my x y ⎧=+⎪⎨⎪+=⎩得223(2)02m y ++-=，于是()1212223,222y y y y m m +=-⋅=-++，13k k ⋅==()()2222332212396322222m m m m m --+===---+++．(3)由于直线MN 与x 轴的交点为(,0)t ，于是:MN x my t =+，联立直线:MN x my t =+与椭圆22:12x C y +=的方程，可得 222(2)220m y mty t +++-=，于是212122222,22mt t y y yy m m -+=-⋅=++.因为直线:AM y x =，直线:BN yx =，两式相除，可知2211y y y y===22212221222()222(2t mtm t y m m t m t y m -⋅++--++==-⋅++2==， 于是2xt =，所以2x t =，即直线AM 与直线BN 的交点Q 落在定直线2x t=上． 21．解： (1)因为*11()12n n A A n n n +-=∈+N ，于是数列n A n ⎧⎫⎨⎬⎩⎭是首项为1，公差为12的等差数列，所以1122n A n n =+，即*(1)()2n n n A n +=∈N ， 当2n ≥时，1n n n a A A n -=-=，又因为11a =，所以*()n a n n =∈N . 又因为*2120()n n n b b b n ++-+=∈N ，于是数列{}n b 是等差数列，设{}n b 的前n 项和为n B ，由于95936B b ==，则54b =，由于32b =， 所以1(*)n b n n =-∈N ． (2)数列{}n a 的前n 项和(1)2n n n A +=，数列{}n b 的前n 项和(1)2n n nB -=． 当2(*)n k k =∈N 时，22(1)(1)22n k k k k k k kS S A B k +-==+=+=； 当43(*)n k k =-∈N 时，2432122(21)(23)(1)463n k k k S S A B k k k k k k ---==+=-+--=-+；当41(*)n k k =-∈N 时，241212(21)(21)42n k k k S S A B k k k k k k --==+=-+-=-； 所以2221,243,4341,414n n n k n S n k n n k ⎧=⎪⎪+⎪==-⎨⎪⎪-=-⎪⎩，其中*k ∈N ．(3)由(1)可知，121n c n =-. 若对于任意给定的正整数()2k k ≥，存在正整数,()l m k l m <<，使得,,k l m c c c 成等差数列，则2l k m c c c =+，即211212121l k m =+---， 于是121421212121(21)(21)k l m l k l k --=-=-----，所以222(1)(214)(21)421421kl k l k l k k m k l k l +--+-+-==----2(21)1421k k k l -=-+--，即2(21)1421k m k k l -=+---， 则对任意的()2,k k k N *≥∈，421k l --能整除2(21)k -，且4210k l -->.由于当2k ≥时，21k -中存在多个质数， 所以421k l --只能取1或21k -或()221k -，若4211k l --=，则21l k =-，2452m k k =-+，于是2473(43)(1)0m l k k k k -=-+=-->，符合k l m <<；若42121k l k --=-，则k l =，矛盾，舍去；若2421(21)k l k --=-，则2m k +=，于是0m ≤，矛盾．综上，当2k ≥时，存在正整数221,452l k m k k =-=-+，满足k l m <<，且使得,,k l m c c c 成等差数列．。

2017-2018学年第二学期徐汇区学习能力诊断卷高三数学 2018.4一、填空题（本大题共有12题，满分54分，第1-6题每题4分，第7-12题每题5分） 考生应在答题纸的相应位置直接填写结果．1．已知全集R U =，集合{}0322>--=x x x A ，则=A C U .2．在61x x ⎛⎫+ ⎪⎝⎭的二项展开式中，常数项是.3．函数()lg(32)x xf x =-的定义域为_____________．4．已知抛物线2x ay =的准线方程是14y =-，则a =.5．若一个球的体积为323π，则该球的表面积为_________．6．已知实数x y ，满足001x y x y ≥⎧⎪≥⎨⎪+≤⎩，，．则目标函数z x y =-的最小值为___________．7．函数()2sin cos 1()11x x f x +-=的最小正周期是___________．8．若一圆锥的底面半径为3，体积是12π，则该圆锥的侧面积等于.9．将两颗质地均匀的骰子抛掷一次，记第一颗骰子出现的点数是m ，记第二颗骰子出现的点数是n ，向量()2,2a m n =--，向量()1,1b =，则向量a b ⊥的概率．．是. 10．已知直线12:0,:20l mx y l x my m -=+--=.当m 在实数范围内变化时，1l 与2l 的交点P 恒在一个定圆上，则定圆方程是.11．若函数222(1)s i n()1x x f x x ++=+的最大值和最小值分别为M 、m ，则函数()()()s i n 1g x M m x M m x =+++-⎡⎤⎣⎦图像的一个对称中心是． 12．已知向量,a b 的夹角为锐角，且满足||15a =、||b =，若对任意的{}(,)(,)||1,0x y x y xa yb xy ∈+=>，都有||1x y +≤成立，则a b ⋅的最小值为.二、选择题（本大题共有4题，满分20分，每题５分）每题有且只有一个正确选项。

2018学年第二学期徐汇区学习能力诊断卷 高三数学 试卷 2019.4【考生注意】考试设试卷和答题纸两部分，所有答案必须填涂（选择题）或书写（非选择题）在答题纸上，做在试卷上一律不得分。

考试时间120分钟，试卷满分150分。

一、填空题（本大题共有12题，满分54分，第1~6题每题4分，第7~12题每题5分）考生应在答题纸的相应位置直接填写结果.1. 设全集U R =，若集合{1,2,3,4},{|23}A B x x ==≤≤，则=U A B I ð___________.2. 已知点(2,5)在函数x a x f +=1)((0a >且1a ≠)的图像上，则()f x 的反函数1()=f x -______________.3. 不等式+11x x>的解为___________. 4. 已知球的主视图所表示图形的面积为9π，则该球的体积是 .5.函数cos 2sin ()cos x xf x x-=在区间0,2π⎡⎤⎢⎥⎣⎦上的最小值为___________. 6. 若2+i （i 是虚数单位）是关于x 的实系数方程20x mx n ++=的一个根，则圆锥曲线221x y m n+=的焦距为 . 7.设无穷等比数列{}n a 的公比为q .若{}n a 的各项和等于q ，则首项1a 的取值范围是 .8.已知点(0,0),(2,0),(1,O A B -，P是曲线y =则OP BA ⋅u u u r u u u r 的取值范围是 .9. 甲、乙两队进行排球决赛，现在的情形是甲队只要再赢一局就获冠军，乙队需要再赢两局才能得冠军.若两队在每局赢的概率都是0.5，则甲队获得冠军的概率为________.（结果用数值表示）10.已知函数4()1f x x x =+-，若存在121,,,,44n x x x ⎡⎤∈⎢⎥⎣⎦L ，使得121()()()()n n f x f x f x f x -+++=L ，则正整数n 的最大值是___________.11.在平面直角坐标系中，设点00O （，），(3,A ，点(,)P x y的坐标满足0200y x y -≤-+≥⎨⎪≥⎪⎩，则OA u u u r 在OP uuu r上的投影的取值范围是 .12.函数()sin (0)f x x ωω=>的图像与其对称轴在y 轴右侧的交点从左到右依次记为123,,,,,,n A A A A L L 在点列{}n A 中存在三个不同的点,,k l p A A A ，使得k l p A A A ∆是等腰直角三角形.将满足上述条件的ω值从小到大组成的数列记为{}n ω，则2019ω=___________.二、选择题（本大题共有4题，满分20分，每题5分）每题有且只有一个正确选项.考生应在答题纸的相应位置，将代表正确选项的小方格涂黑.13. 满足条件i 34i z -=+（i 是虚数单位）的复数z 在复平面上对应的点的轨迹是（ ）（A ）直线 （B ）圆 （C ）椭圆 （D ）双曲线14. 设*n N ∈，则“数列{}n a 为等比数列”是“数列{}n a 满足312n n n n a a a a +++⋅=⋅”的（ ）（A ）充分非必要条件 （B ）必要非充分条件 （C ）充要条件 （D ）既非充分也非必要条件15. 已知直线1:4360l x y -+=和直线2:1l x =-，则抛物线24y x =上一动点P 到直线1l 和直线2l 的距离之和的最小值是（ ） （A ）3716（B ）115 （C ）2 （D ）7416. 设()f x 是定义在R 上的函数，若存在两个不等实数12,x x R ∈,使得1212()()()22x x f x f x f ++=，则称函数()f x 具有性质P ,那么以下函数： ①1(0)()0(0)x f x xx ⎧≠⎪=⎨⎪=⎩； ②3()f x x =； ③2()1f x x =-； ④2()f x x =中，不具有性质P 的函数为（ ）（A ）① （B ）② （C ）③ （D ）④三、解答题（本大题共有5题，满分76分）解答下列各题必须在答题纸的相应位置写出必要的步骤.17.（本题满分14分，第1小题满分6分，第2小题满分8分）在△ABC 中，角A ，B ，C 的对边分别是a ，b ，c ，且2cos 2+4cos()30A B C ++=. （1）求角A 的大小； （2）若3=a ，3=+c b ，求b 和c 的值.18.（本题满分14分，第1小题满分6分，第2小题满分8分）如图：正四棱柱1111ABCD A B C D -中，底面边长为2，1BC 与底面ABCD 所成角的大小为arctan 2，M 是1DD 的中点，N 是BD 上的一动点，设(01)DN DB λλ=<<u u u r u u u r.（1）当1=2λ时，证明：MN 与平面11ABC D 平行；（2）若点N 到平面BCM 的距离为d ，试用λ表示d ，并求出d 的取值范围.19.（本题满分14分，第1小题满分6分，第2小题满分8分）2018年世界人工智能大会已于2018年9月在上海徐汇西岸举行，某高校的志愿者服务小组受大会展示项目的启发，会后决定开发一款“猫捉老鼠”的游戏.如下图：A 、B 两个信号源相距10米，O 是AB 的中点，过O 点的直线l 与直线AB 的夹角为045.机器猫在直线l 上运动，机器鼠的运动轨迹始终满足：接收到A 点的信号比接收到B 点的信号晚8v 秒(注：信号每秒传播0v 米).在时刻0t 时，测得机器鼠距离O 点为4米. （1）以O 为原点，直线AB 为x 轴建立平面直角坐标系（如图），求时刻0t 时机器鼠所在位置的坐标；（2）游戏设定：机器鼠在距离直线l 不超过1.5米的区域运动时，有“被抓”的风险.如果机器鼠保持目前的运动轨迹不变，是否有“被抓”风险？20.（本题满分16分，第1小题满分4分，第2小题满分6分，第3小题满分6分）对于项数为(3)m m ≥的有穷数列{}n a ，若存在项数为1m +，公差为d 的等差数列{}n b ，使得1k k k b a b +<<，其中1,2,,k m =…，则称数列{}n a 为“等差分割数列”. （1）判断数列{}:1,4,8,13n a 是否为“等差分割数列”，并说明理由；（2）若数列{}n a 的通项公式为2(1,2,,)nn a n m ==L ，求证：当5m ≥时，数列{}n a 不是“等差分割数列”；（3）已知数列{}n a 的通项公式为43(1,2,,)n a n n m =+=L ，且数列{}n a 为“等差分割数列”.1A若数列{}n b 的首项13b =，求数列{}n b 的公差d 的取值范围（用m 表示） .21.（本题满分18分，第1小题满分4分，第2小题满分6分，第3小题满分8分）已知函数()1y f x =，()2y f x =，定义函数()()()()()()()112212,,f x f x f x f x f x f x f x ≤⎧⎪=⎨>⎪⎩.（1）设函数()()()11210,2x f x f x x -⎛⎫==≥ ⎪⎝⎭求函数()y f x =的值域；（2）设函数()1lg(1)f x p x =-+（10,2x p <≤为实常数），()21lg f x x= 102x ⎛⎫<≤⎪⎝⎭，当102x <≤时，恒有()()1,f x f x =求实常数p 的取值范围； （3）设函数12()2,()32,x x pf x f x -==⋅p 为正常数，若关于x 的方程()f x m =(m 为实常数）恰有三个不同的解，求p 的取值范围及这三个解的和（用p 表示）.参考答案一、填空题：(共54分，第1~6题每题4分；第7~12题每题5分)1. {}14，2. 2log (1)x -3. (0,+)∞4. 36π5.6. 67. 1(2,0)0,4⎛⎤-⋃ ⎥⎝⎦ 8. []2,4- 9. 34 10. 611. [3,3]- 12.40372π 二、 选择题：(共20分，每题5分)13. B 14. A 15. C 16. D 三、 解答题17、解：（1）由2cos 2+4cos()30A B C ++=，得01)cos(4cos 42=+++C B A ，…（2分） 因为π=++C B A ，所以A C B cos )cos(-=+，故0)1cos 2(2=-A ，…………（4分）所以，21cos =A ，3π=A ． ………………（6分） （2）由余弦定理，A bc c b a cos 2222-+=，得322=-+bc c b ， ………………（8分）33)(2=-+bc c b ，得2=bc ， ………………（10分）由⎩⎨⎧==+,2,3bc c b 解得⎩⎨⎧==,1,2c b 或⎩⎨⎧==.2,1c b ……………（14分）18、解：(1) 因为1C 是1BC 上的点，且1C 在平面ABCD 上的射影是C ，即BC 是1BC 在平面ABCD 上的射影，于是1C BC ∠是1BC 与底面ABCD 所成的角，而111tan 22CC CC C BC BC ∠===,所以14CC =. ………（2分） 如图，以D 为原点，直线DA 为x 轴，直线DC 为y 直线1DD 为z 轴，建立空间直角坐标系.连结1BD ，因为M 是1DD 的中点，N 是BD 中点， 所以1//MN BD ， ………（4分）于是1//MN BD u u u u r u u u u r ，令1()MN tBD t R =∈u u u u r u u u u r. 设1n u r 是平面11ABC D 的法向量，则11n BD ⊥u r u u u u r ，于是11111()0n MN n tBD tn BD ⋅=⋅=⋅=u r u u u u r u r u u u u r u r u u u u r ，即1n MN ⊥u r u u u u r ，又因为MN 不在平面11ABC D 内，所以MN 与平面11ABC D 平行. (2)由于(2,2,0),(0,2,0),(0,0,2)B C M ，于是(2,0,0),(0,2,2)CB CM ==-u u u r u u u u r. ………（设平面BCM 的法向量2(,,)n x y z =u u r，因为220,0n CB n CM ⋅=⋅=u u r u u u r u u r u u u u r ，于是20220x y z =⎧⎨-+=⎩，取1y =，则平面BCM 的一个法向量为2(0,1,1)n =u u r.………（10分） 因为(01)DN DB λλ=<<u u u r u u u r，于是(2,2,0)(01)N λλλ<<，则(2,2,2)MN λλ=-u u u u r， ………（11分）所以点N 到平面BCM的距离22,(0,1)||MN n d n λ⋅==∈u u u u r u u r u u r ，………（13分） 从而d的取值范围是. ………（14分） 19、解：（1）设机器鼠在点(,)P x y 处，则由题意，得0088PA PB v AB v -=⋅=< 所以，P 为以A 、B 为焦点，实轴长为8，焦距为10 的双曲线右支上的点，……（2分）该双曲线的方程为()2214169x y x -=≥， ………（4分）又4PO =，解得(4,0)P ，即在时刻0t 时，机器鼠所在位置的坐标为40（，）. ………（6分） （2）与直线l 平行且距离不超过1.5的直线方程为(2y x m m =+≤……（8分）考虑(2y x m m =+≤与()2214169x y x -=≥是否有交点， 2222217321614405764032169x y x mx m m y x m ⎧-=⎪⇒+++=⇒∆=-⎨⎪=+⎩……（10分）因为2m ≤，所以0∆< ……（12分）所以，(2y x m m =+≤与()2214169x y x -=≥没有交点， 即机器鼠保持目前的运动轨迹不变，没有“被抓”风险. ……（14分） 20、解：(1)因为存在等差数列1,3,7,11,15-， ……（2分） 满足113478111315-<<<<<<<<，所以数列{}:1,4,8,13n a 是“等差分割数列”. ……（4分） (2)当5m ≥时，若存在公差为d ，项数为1m +项的等差数列{}n b 满足：1k k k b a b +<<， 其中1,2,,k m =…，则有1234562481632m b b b b b b b <<<<<<<<<<<<…，……（6分） 于是32826d b b =-<-=，所以633681826b b <+⨯<+=，与632b >矛盾， ……（8分） 即5m ≥时，{}n a 不是“等差分割数列”. ……（10分） (3)由题意知,111213141512345b a b d a b d a b d a b d a b d <<+<<+<<+<<+<<+<… 11(1)m b m d a b md <+-<<+，于是一方面11213111114,()4,()4,,()423m d a b d a b d a b d a b m>-=>-=>-=>-=…，所以4d >. ……（11分）另一方面，2131411111,(),(),,()231m d a b d a b d a b d a b m <-<-<-<--…， ……（13分）由于111114()()12(1)(2)m m a b a b m m m m -----=----，又因为3m ≥， 于是11111()()12m m a b a b m m --<---，所以114()11m md a b m m <-=--.……（15分） 综上所述，441md m <<-. ……（16分）21、解：（1）因为()()12111f f ==，当[]0,1x ∈时，()1f x 单调递增；当()1,x ∈+∞时，()1212x f x -⎛⎫= ⎪⎝⎭单调递减.所以 ()111,12x x f x x -≤≤=⎨⎛⎫>⎪ ⎪⎝⎭⎩ ……（2分）当01x ≤≤时，()[]0,1f x ∈；当1x >时，()()0,1f x ∈()y f x ∴=值域为[]0,1……（4分）（2）102x <≤时，()()1f x f x =恒成立，等价于()()12,f x f x ≤对102x <≤恒成立，即()1lg 1lg ,p x x -+≤ 11p x x -+≤，11,p x x -≤-1111p x x x-+≤-≤-即1111x p x x x -+≤≤+-对102x <≤恒成立， ……（5分）11x x ⎛⎫-+ ⎪⎝⎭Q 在10,2x ⎛⎤∈ ⎥⎝⎦上递增12x ∴=时，max 11+12x x ⎛⎫-=- ⎪⎝⎭……（7分）又11 xx⎛⎫+- ⎪⎝⎭Q在10,2 x⎛⎤∈⎥⎝⎦上递减，12x∴=时，min1312xx⎛⎫+-=⎪⎝⎭……（9分）1322p∴-≤≤……（10分）（3）11()(),f x f x=-Q22()()f p x f p x+=-∴函数12(),()f x f x图像分别关于直线0,x x p==对称.当x R∈时，若1()()f x f x=恒成立，等价于12()()f x f x≤恒成立，即232x x p-≤⋅即23x x p--≤，即2log3x x p--≤恒成立.当0p>时，设(),(0)2,(0),()p xg x x x p x p x pp x p-<⎧⎪=--=-≤≤⎨⎪>⎩max()g x p∴=，故20log3p<≤成立.……（12分）当20log3p<≤时，1()()f x f x=()(][)1,00+f x-∞∞Q为偶函数，且在上递减、，上递增，方程()f x m=最多有两个解.如下图.故关于x的方程()f x m=恰有三个不同的解，则2log3p>……（14分）当0x≤时，()()()()12122,x p xf x f x f x f x--=<<=从而当x p≥时，1()222x p x pf x-==⋅>2log3222()x p f x-⋅=从而2()().f x f x=当0x p<<时，1()2xf x=及2()32p xf x-=⋅由00232,x p x-=⋅得2log32px+=显然2log32px p+<=<表明x在0与p之间Q在(]00,x x∈时，1()2xf x=递增，2()32p xf x-=⋅递减；在(),x x p∈时，1()2xf x=递增，2()32p xf x-=⋅递减1020(),(0)()(),()f x x x f x f x x x p <≤⎧∴=⎨<<⎩综上可知，1020(),()()(),()f x x x f x f x x x ≤⎧=⎨>⎩……（16分）()f x 在(][]0,0,,x p -∞上单调减，在[][)00,,,x p +∞上单调增. 如下图故关于x 的方程()f x m =恰有三个不同的解，则3m =或20log 3210()22p x m f x +===01当3m =时，三个解的和为p ……（17分） 02当20log 3210()22p x m f x +===时，三个解的和为203log 32.2p p x --=……（18分）更多高考数学信息，请关注。