2018上海崇明区高三二模卷

崇明区2018届第二次高考模拟考试试卷物理考生注意：1．答题前，务必在试卷与答题纸上填写学校、姓名、准考证号。

2．试卷满分100分，考试时间60分钟。

3．本考试分设试卷和答题纸。

试卷包括三大部分，第一部分为单项选择题，第二部分为填空题，第三部分为综合题。

4．作答必须涂或写在答题纸上相应的位置，在试卷上作答无效。

一、单项选择题（共40分，1至8题每小题3分，9至12题每小题4分。

每小题只有一个正确选项）1．建立完整的电磁场理论并预言电磁波存在的科学家是A ．法拉第B ．奥斯特C ．麦克斯韦D ．赫兹2．由核反应产生，且属于电磁波的射线是A ．阴极射线B ．X 射线C ．a 射线D ．g 射线3．下列能源中属于常规能源的是A ．石油B ．地热能C ．太阳能D ．核能4．在卢瑟福a 粒子散射实验中，金箔中的原子核可以看作静止不动，下列各图画出的是其中两个a 粒子穿过金箔散射过程的径迹（图中的黑点为金箔的原子核），其中正确的是5．万有引力可以理解为：任何有质量的物体都要在其周围空间产生一个引力场，而一个有质量的物体在其他有质量的物体所产生的引力场中，都要受到该引力场的引力（即万有引力）作用，这种情况可以与电场类比，那么，在地球产生的引力场中的重力加速度，可以与电场中下列哪个物理量相类比A ．电场力B ．电场强度C ．电势D．电势能B C D A 6．如图所示，表示一定质量的气体的状态由A 经B 到C 回到A 的图像，其中AB 延长线通过坐标原点．BC 和AC 分别与T 轴和V 轴平行． 则，下列描述正确的是 A ．A →B 过程气体压强增加 B ．B →C 过程气体压强不变 C ．C →A 过程气体分子密度减小 D ．A →B 过程气体分子平均动能增加7．做简谐振动的单摆摆长不变，若摆球质量增加为原来的4倍，摆球经过平衡位置时速度减小为原来的12，则单摆振动的 A ．频率、振幅都不变B ．频率、振幅都改变C ．频率不变、振幅改变D ．频率改变、振幅不变8．如图，用导线将验电器与某种金属板连接，用弧光照射金属板，验电器指针发生明显偏转，在这个过程中A ．金属板上的电子转移到验电器上B ．金属板上光子转移到验电器上C ．金属板上光电子转移到验电器上D ．验电器上电子转移到金属板上9．如图所示的电路中，电源的电动势为E ，内阻0r =，滑片P 在变阻器正中位置时，电灯L正常发光，各电表为理想电表．现将滑片P 向右移动的过程中 A ．电流表示数变小B ．电压表示数变大C ．电灯L 的功率不变D ．电阻R 1的功率变小10．如图，A 、B 两个同轴线圈在同一平面，A 线圈通有顺时针方向逐渐增加的电流I 1，则穿过B 线圈引起感应电流的磁通量f 的方向和B 线圈产生的感应电流I 2的方向分别为 A ．f 垂直纸面向内，I 2逆时针方向B ．f 垂直纸面向内，I 2顺时针方向C ．f 垂直纸面向外，I 2逆时针方向TVO A B C E rA V LPR R 1I 1A B D ．f 垂直纸面向外，I 2顺时针方向11．如图所示是一列简谐横波在0t =时刻的波动图像。

上海市崇明2018届⾼三英语⼆模（含答案）2018崇明⼆模崇明区⾼考英语质量抽查试卷(考试时间120分钟，满分140分。

请将答案填写在答题纸上)I. 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. In a train B. In a theater C. In a meeting room D. In a booking office2. A $2.4 B. $4.8 C. $7.2 D. $9.63. A. A waiters B. A customer C. A secretary D. A saleswoman4. A. The man’s air-conditioner is broken B. The man doesn’t have air-conditioningC. The su mmer has been unusually hotD. The music doesn’t bother her5. A. She’s enjoying the music B. The music doesn’t bother herC. She would prefer different musicD. The music will keep her awake6. A. She acted like a stranger today B. She usually talks quietlyC. She didn’t give the lesson todayD. She usually assigns homework7. A. A job opportunity B. A position as general managerC. A travel experienceD. A sales manager’s experiences8. A. She has had her camera broken B. She hasn’t handed i n her photoC. She has been busy taking photosD. She hasn’t ordered a student’s card9. A. He hasn’t prepared well for his lectureB. He wants the woman to postpone the lectureC. He doesn’t know anything about engineeringD. He regularly gives lectures to high school students10. A. It’s more effective if priority is given to listeningB. It’s more effective if reading comes before listeningC. It’s more effective if listening is combined with readingD. It’s less effective if the learner checks the same informationSection BDirections: In Section B, you will hear two short passages and one longer conversation, and you will be asked several questions on each of them. The passages and the conversation 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. To provide a protective space for giant pandas.B. To stop the loss of giant pandas’ natural habitatsC. To help China to improve its economy on the wholeD. To protect the giant pandas in the proposed territory12. A. About 300 B. Around 1864 C. More than 2,000 D. Less than 156413. A. The park first began to be constructed in January 2017.B. 1.5 billion yuan will be invested in the construction of the parkC. The park will cover a bit more space than Yellowstone National ParkD. The place where the park is to be constructed is a poverty-stricken area.Questions 14 through 16 are based on the following passage.14. A. Smart mirrors than make you look much smarterB. Software apps that allow you to add images to photosC. Virtual mirrors that teach you to use camera functionsD. Special apps that help you see your image after try-on15. A. They can make it easy for customers to make upB. They can help stores avoid damage, loss and theftC. They can teach users how to make smart productsD. The can improve the effect of products on customers16. A. They promote both online and offline businessesB. They have high requirements for mobile devicesC. They enable customers to interact with each otherD. They are quite similar to previous apps like SnapchatQuestions 17 through 20 are based on the following conversation.17. A. Their great food and free drinks for lunchB. The numerous benefits of drinking hot liquidsC. The way to get rid of unhealthy drinking habitsD. Their different perspectives on hot and cold drinks18. A. By causing sweat B. By increasing blood flowC. By helping ease painD. By emitting pleasant smells19. A. It slows down blood flow B. It makes one consume moreC. It helps one become slimmerD. It is good for one’s digestion20. A. The man prefers hot drinks only on very cold daysB. The woman may change her habit of drinking cold liquidsC. The woman believes drinking cold water also helps relieve a coldD. The man is trying losing weight by exercising and drinking hot waterII. 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.China’s Good Samaritan Law (见义勇为法)Takes EffectChina’s Good Samaritan Law went into effect on October 1 to encourage people who are ready to help others. Under the law, people how voluntarily offer emergency assistance to those who are, or who they believe to be, injured, ill or in anger, will not have civil responsibility in the event of harm to the victims.The new law aims to ease the reluctance people feel toward helping strangers for fear of legal consequences if they make mistakes in treatment. It is a response to the phenomenon of people (21)_____ (hesitate) to help fallen senior citizens due to concern that they might be blackmailed(讹诈)later.There has been no shortage of cases over the past decade(22)______people hesitated to offer assistance to those who are in need. And some good Samaritans have been blackmailed for charitable acts. In 2011, a two-year-old girl known as Xiao Yueyue was run over by two cars, and 18 people passed by(23)_____offering emergency help. The girl died after days of medical treatment. In 2014, a man from Guangdong Province aided a senior citizen, but (24)_____(accuse) of knocking him down. The man committed suicide when(25)_____(face)with demands for a large sum of money.These cases(26)____(arouse) debate about morality and heroism in China in recent years. “If you don’t provide help, you will blame yourself, but if you do help, you are likely(27)___(hurt)by the people you help. It is really a difficult choice,” one netizen said on Sina Weibo.(28)______there had been calls for a national Good Samaritan law, only a few cities pushed ahead with such laws before the nationwide law came into effect.However, some experts are concerned (29)____there could be some danger from a nationwide Good Samaritan Law.“Rescuers who know little about first aid could bring serious harm to people in critical conditions,” said Yang Lixin, a professor at the Renmin University of C hina. He hoped the government (30)____introduce details of the policy soon while encouraging people to voluntarily offer assistance.Section BDirections: After reading the passage below, fill in each blank with a proper word given in the box. Each word can only be used once. Note that there is one word more than you need.Bob Dylan Wins a Nobel Prize in LiteratureBob Dylan has won the 2016 Nobel Prize in literature. The productive musician is the first Nobel winner to have followed a career primarily as a singer-songwriter. What’s more, he’s also the first American to have won the prize in more than two decades. Not since novelist Toni Morrison won in 1993 has an American __31__ the prize.Dylan earned the prize “for having __32__ new poetic expressions within the great American song tradition,” according to the statement by the Swedish Academy, the committee that annually decides the winter of the Nobel Prize. The academy’s permanent secretary, Sara Danius, announced the news Thursday.The win comes as something of a(n) __33__. As usual, the Swedish Academy did not announce a shortlist of nominees(被提名者), leaving the betting markets to their best __34__ . And while Dylan has enjoyed favor as an outside shot for the award, the __35__ that the musician would be the one to break the Americans’ long dry period was regarded as unlikely---especially because he made his career mainly on the stage, not the __36__ page.Yet few would argue Dylan has been anything but __37__ , both in the U. S. and beyond its borders. The productive singer, songwriter and multi-instrumentalist has produced dozens of albums. Dylan, who was born Robert Allen Zimmerman in 1941,“has the status of an idol(偶像),” the Swedish Academy wrote. “His influence on contemporary music is significant, and he is the object of a steady stream of __38__ literature.”In an interview following the announcement, Danius __39__ the Swedish Academy’s decision: “He is a great poet in the English-speaking tradition, and he is a wonderful sampler—a very original sampler,” Danius explained. “For 54 years now he has been at it and reinventing himself, constantly creati ng a new identity.”And for his work, he has been __40__ by critical community. Dylan has won Grammys, an Academy Award, a Golden Globe and a Medal of Freedom, the highest civilian honor in the U. S. Now, to the honors Dylan has added a Nobel.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.The Companies Doing the Most to Make Their Employees HappierFat paychecks, light workloads, and endless vacation days don’t necessarily add to happy employee. In fact, the happiest employees in the U. S. owe their happiness to first-rate employee motivations, sufficient benefits, career advancement programs, and great work-life balance. The companies that have been the most devoted to cultivating and advancing these things in the past year have seen employee happiness __41__ .The jobs site /doc/a202d6f9d7bbfd0a79563c1ec5da50e2524dd1af.html just announced the winners of this year’s “Leap Awards,” which honor the companies that have made the biggest leaps to improve employee happiness year-over-year. CareerBliss evaluated more than 250,000 company reviews and ratings it received from __42__ nationwide to determined the top 50 deserving companies. To __43__ the list, each company had to have at least 50 reviews.“The Leap Awards are important because they highlight __44__ in our workforce,” says CareerBliss’s chief executive, Heidi Golledge. CaareerBliss asked the respondents to evaluate t he key factors that __45__ work happiness, including work-life balance, one’s relationship with the boss and co-workers, the work environment, job resources, salary, growth opportunities, company culture, company reputation, daily tasks, and job __46__ .Each respondent valued each of these things on a 1-to-5 scale, and indicated how important each was to their overall happiness at work. These numbers were __47__ to find an average rating of overall employee happiness for each company. These averages were compared to last year’s numbers to find which companies had __48__ the most.“Every employer who receives a Leap Award should __49__ their workplace happiness initiatives,” says Golledge. “Even though we are coming out of a difficult time, it is __50__ to see companies putting their efforts into providing a great environment for their employees. These efforts in workplace happiness will ensure that their employees will be around for years to come, as happiness breeds __51__ .”“We find each year that work-life balance is a key factor in determining employee happiness,” says Golledge. “Employee want to know that they can balance their career with their family and personal life. Often this __52__ over things like salary. Having programs that allow managers to offer employees flexibility can be a key factor in creating a happy work environment. __53__ , we see career advancement programs have a big impact on overall employee happiness. Often employees would rather take a job for a __54__ salary, if the company provides a comprehensive program which will help grow their career. Employees want to learn, develop and sustain a successful career path.”Workplace happiness is the core of CareerBliss’ mission, Miller says. “An individual’s happiness at work will create happiness throughout all areas of their life, and __55__ a company with a happy, motivated workforce will see exceptional results in its products and services.”41. A. soar B. change C. cease D. disappear42. A. netizens B. administrators C. candidates D. employees43. A. make up B. quality for C. count on D. refer to44. A. change B. power C. duty D. variety45. A. lay in B. resulted from C. focused on D. contributed to46. A. analysis B. vacancy C. flexibility D. responsibility47. A. applied B. combined C. compared D. remembered48. A. benefited B. improved C. changed D. produced49. A. approve of B. account for C. take pride in D. get used to50. A. good B. easy C. impossible D. interesting51. A. profit B. honesty C. creativity D. loyalty52. A. turns B. runs C. advantages D. skips53. A. However B. Otherwise C. Besides D. Instead54. A. lower B. fair C. regular D. similar55. A. obviously B. frankly C. fortunately D. similarlySection 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)In the world of higher education in the United States, competition seems more common than schools working together. Every college and university competes for students, as well as the best teachers and money for research programs.But one thing almost every school has in common is the difficulty they face in serving low-income students. The National Center for Education Statistics reports that low-income college students are less likely to complete their study programs than other students.It was only natural that the leaders of Michigan State University and ten other universities discussed this issue when they met in 2014. The 11 schools are spread across the United Sates and serve different populations and needs. But their leaders all saw improving graduation rates for all students as the biggest problem facing American higher education.So the group created an organization called the University Innovation Alliance or UIA for sharing information related to this problem. Its main goal is to get 68,000 more students at the member schools to graduate by 2025, with at least half of those students being low-income. The 11schools now say their number of graduates has increased by over 7,200 in just three years. This includes an almost 25 percent increase in the number of low-income graduates.How were they able to make this happen? It began with each university looking at its own situation and finding out what it had been doing right and what it had been doing wrong.For example, before joining the UIA, academic advising at Michigan State mostly involved reacting to problems students faced after the problems had already arisen. Then school officials heard about a computer program that fellow UIA member Georgia State University was using. This computer program follows decisions students make about their classes and the progress they are making in their studies. It then sends academic advisors messages whenever a student shows signs that they are making mistakes or facing difficulties. Hat way the advisors can try to help students before the problems become too serious. Michigan State began using the computer program and it has meant a world of difference. Michigan States has not only received useful information from its parents. It has also shared helpful information of its own.Bridget Burns, the executive director for the UIA, says efforts like this have never been as successful. “There are rankings that measure all kinds of things,” Burns said. “But how well you do for low-income students has not historically been highlighted.”56. What led to the setting up of the UIA?A. The low graduation ratesB. The great need of low-income students.C. The inefficiency of learningD. The severe competition between schools57. The UIA functions in such a way as the member universities ____.A. find out their own graduation ratesB. share and follow each other’s good practiceC. make joint efforts to aid students financiallyD. popularize computer programs among students58. By “it has meant a world of difference” in paragraph 6, the author means Michigan State__________.A. has found the computer program quite different from theirsB. has discovered the computer program is very difficult to useC. has helped students successfully with the computer programD. has involved more academic advisors in the computer program59. Which of the following might be the best title for the passage?A. Universities Highlighting Their Efforts for Low-IncomesB. Universities Computing for Better Students and TeachersC. Universities Working Together to Help Poor StudentsD. Universities Creating the UIA to Share Information(B)60. The above webpage mainly aims to _________.A. raise funds from readersB. inform readers of quality journalismC. attract more readersD. guarantee readers a secure future61. Which of the following is a difficulty the Guardian is facing?A. It’s losing its editorial independenceB. It’s becoming increasingly reliant on its ownerC. It’s profiting much less from advertisingD. It’s operating in a challenging political climate62. What can be inferred from the webpage?A. Some billionaire owners are the Guardian’s editorsB. The Guardian is independent financially and politicallyC. Shareholders can interfere with the Guardian’s journalismD. Guardian Supporters can put ads on the mobile app for free(C)A new kind of production was underway on the set of the NBC comedy Superstore. Social media stars were crafting 30-second videos to post on their social media channels ahead of the comedy’s second-season return. Each made sure to mention Superstore and its first public show.As networks and studios struggle to reach young audiences in an increasingly fragmented(碎⽚化的)media marketplace, many have turned to so-called influencers—online stars whose is measured by the size of their Internet followings—as a means of generating awareness. Advertisers are seizing on the strategy in an age of commercial-skipping and ad-blockers. Word of mouth in the digital age means messages travel faster by way of social media. The majority of consumers worldwide trust online recommendations from stars. And when Superstore gave its first public show, it did so to higher ratings than the last show of Season 1.Studio and network executives say they work with influencers to build brand awareness and reputation in a more friendly way through the friend-like connections consumers feel toward the online personalities they follow. At the upper level, influencers typically have thousands of followers on social media and online content platforms and count many millions of people who tune in daily to watch them. Some do something that makes themselves look stupid in their daily routine, sharing videos of their trips to the grocery store or dinner dates. Others have built careers on performances—making comedy videos, reviewing video games, performing magic tricks and teaching cooking lessons, among other pursuits.When in the employ of studios, their efforts can be as simple as publicizing a film or more involved attempts like the marketingpush for Superstore. Entertainment companies declined to discuss how much they pay influencers. But several experts said their pay ranges from a few thousand dollars to several million. Some simply receive gift baskets instead of pay.Over the last year or so, some entertainment companies have begun to cast influencers in their TV and film pro jects. The strategy is a bit of gamble: It’s a new business model, and questions remain about the effectiveness of using these personalities to improve a show’s ratings—or helpopen a movie. Just how much influence the influencers have is hard to measure. TV ratings and box-office returns do not reveal what caused a viewer to tune in.What is clear is that these personalities aren’t necessarily getting the work because of their acting skills, but often because of their Internet followings. Yet as social media stars consider whether to take on jobs promoting movies and TV shows, there’s an important consideration for both parties: the credibility of a campaign. “Fans are definitely award when they’re being tempted with promotional posts,” said Zach King, a social media star who performs magic tricks. “It has to be something that is natural and fits with the image of the creator.”63. Why did social media stars post short videos on their channels before Superstore’s second season?A. To attract more influ encersB. To draw audience’s attentionC. To put on better performancesD. To increase the channels’ popularity64. Advertisers like the influencer marketing strategy because ________.A. audiences believe in whatever online stars recommendB. influencers are quite award of the impact of the digital ageC. ordinary advertisements are often ignored by young peopleD. social media platforms are the cheapest place to spread messages65. What is implied in the passage?A. The influencer marketing strategy help build connections between executivesB. Most influencers get paid from gift baskets instead of from their companiesC. Most influencers take on marketing jobs regardless of their reliabilityD. The influencer marketing strategy may not really work well66. The passage mainly wants to tell us that __________.A. most young people like following influencersB. studios are relying more on social media starsC. influencers are gradually replacing movie starsD. social media are filming videos for SuperstoreSection 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.Feel Young at Heart and You’ll Enjoy a Longer LifeAge-liars and birthday-deniers, you’d best learn a thing or two from those who are young at heart. People who feel younger than their actual age may live longer than those who feel older than they truly are, a new study says.____________67____________ Results from the study, published in the Journal of the American Medical Association, suggest that people who feel a year or more older than they truly are could have around 41 percent greater risk for death.Researchers looked at nearly 6,500 older adults, with an average age of 65.8 for they study. Around 70 percent of them felt younger than they were, about a quarter felt their precise age and just under 5 percent felt a year or more older they were, when asked “How old do you feel you are?”Those who felt older than they were had a higher death rate after a follow-up period of 99 months. While just 14.3 and 18.5 percent of people who felt younger or felt their age, respectively, died during those 99 months, 24.6 percent of those who felt aged beyond their years had died.The authors say more research is needed on the topic, but suggest it could be that those who feel “young at heart” have healthier behaviors and a stronger will to live. “____________ 68____________ Individuals who feel older could be targeted with health message promoting positive health behaviors and attitudes toward aging,” the authors write in the study.The good news is that you can change your feeling of how young you are. ____________69____________One recent study found that helping participants have positive feelings toward age, by showing them positive word associations, helped older adults improve in physical tasks like balancing and getting up out of a chair, in as little as four weeks. Another study found that negative feeling of aging and poor memory can make older adults feel up to five years older, regardless of their actual mental abilities.There you have it. ____________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.Do Smartphones Make Us Smarter?Should teachers allow cellphones in a classroom? A recent study on the way smartphones disturb learning might help explain the issue. Researchers published findings showing how students were affected by their phones in the classroom. They explored the differences in student performance in four situations: open phone use allowed, phones allowed in the classroom but could not be used, no phones in the classroom and a no-instruction control group. After watching a 20-minuted video, students took a short quiz. The result was that the students in a room without any cellphones performed significantly better on the test. Scientists believe the way we attach ourselves to our phones could be the problem. Smartphones have become to strongly established in society that many people are lost without them. We are now in an age when many people can’t ima gine life without a phone. There is even a name for the anxiety caused by not having one-monophobia, which is the powerful feeling people get when they don’t have signal, their battery is about to die, or they are separated from their phones. Their fear of missing out on important information or connections can have a controlling effect on their lives and can divide their attention from other important things like learning.So does information technology help or block the way we think? In the past, people relied heavily on specific knowledge and knew how in their circle of friends would be most likely to know things in different subjects. Now, our friend with all the information is the Internet. Indications are that people don’t remember information as wel l if they know they can use a computer of phone to recall it quickly. So it may be more difficult to move information from the Internet into our long-term memory.But the impact of being exposed to so much information isn’t all bad. Reports show that frequent Internet use can strengthen fast-paced problem solving and can speed up the ability to spot patterns in a lot of data.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72.何不利⽤这宜⼈的天⽓出去野餐呢?(advantage)73.当你对情况⼀知半解时，不要随意发表见解。

崇明区2018届第二次高考模拟考试试卷英语（考试时间120分钟，满分140分。

请将答案填写在答题纸上）I. 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. In a train. B. In a theater. C. In a meeting room. D. In a booking office.2. A. $2.4. B. $4.8. C. $7.2. D. $9.6.3. A. A waitress. B. A customer. C. A secretary. D. A saleswoman.4. A. The man’s air-conditioner is broken. B. The man doesn’t haveair-conditioning.C. The summer has been unusually hot.D. The man hasn’t been using hisair-conditioner.5. A. She’s enjoying the music. B. The music doesn’t bother her.C. She would prefer different music.D. The music will keep her awake.6. A. She acted like a stranger today. B. She usually talks quietly.C. She didn’t give the lesson today.D. She usually assigns homework.7. A. A job opportunity. B. A position as general manager.C. A travel experience.D. A sales manager’s experiences.8. A. She has had her camera broken. B. She hasn’t handed in her photo.C. She has been busy taking photos.D. She hasn’t ordered a student’s card.9. A. He hasn’t prepared well for his lecture.B. He wants the woman to postpone the lecture.C. He doesn’t know anything about engineering.D. He regularly gives lectures to high school students.10. A. It’s more effective if priority is given to listening.B. It’s less effective if reading comes before listening.C. It’s more effective if listening is combined with reading.范文.范例.指导.参考D. It’s less effective if the learner checks the same information.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 them. The passages and the conversation 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 is the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. To provide a protective space for giant pandas.B. To stop the loss of giant pandas’ natural habitats.C. To help China to improve its economy on the whole.D. To protect the giant pandas in the proposed territory.12. A. About 300. B. Around 1864. C. More than 2,000. D. Less than 1564.13. A. The park first began to be constructed in January 2017.B. 1.5 billion yuan will be invested in the construction of the park.C. The park will cover a bit more space than Yellowstone National Park.D. The place where the park is to be constructed is a poverty-stricken area.Questions 14 through 16 are based on the following passage.14. A. Smart mirrors that make you look much smarter.B. Software apps that allow you to add images to photos.C. Virtual mirrors that teach you to use camera functions.D. Special apps that help you see your image after try-on.15. A. They can make it easy for customers to make up.B. They can help stores avoid damage, loss and theft.C. They can teach users how to make smart products.D. They can improve the effect of products on customers.16. A. They promote both online and offline businesses.B. They have high requirements for mobile devices.C. They enable customers to interact with each other.D. They are quite similar to previous apps like Snapchat.Questions 17 through 20 are based on the following conversation.17. A. Their great food and free drinks for lunch.B. The numerous benefits of drinking hot liquids.C. The way to get rid of unhealthy drinking habits.D. Their different perspectives on hot and cold drinks.18. A. By causing sweat. B. By increasing blood flow.范文.范例.指导.参考C. By helping ease pain.D. By emitting pleasant smells.19. A. It slows down blood flow. B. It makes one consume more.C. It helps one become slimmer.D. It is good for one’s digestion.20. A. The man prefers hot drinks only on very cold days.B. The woman may change her habit of drinking cold liquids.C. The woman believes drinking cold water also helps relieve a cold.D. The man is trying losing weight by exercising and drinking hot water.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.China’s Good Samaritan Law (见义勇为法) Takes Effect China’s Good Samaritan Law went into effect on October 1 to encourage people who are ready to help others. Under the law, people who voluntarily offer emergency assistance to those who are, or who they believe to be, injured, ill or in danger, will not have civil responsibility in the event of harm to the victims.The new law aims to ease the reluctance people feel toward helping strangers for fear of legal consequences if they make mistakes in treatment. It is a response to the phenomenon of people (21)_____ (hesitate) to help fallen senior citizens due to concern that they might be blackmailed (讹诈) later.There has been no shortage of cases over the past decade (22)_____ people hesitated to offer assistance to those who are in need. And some good Samaritans have been blackmailed for charitable acts. In 2011, a two-year-old girl known as Xiao Yueyue was run over by two cars, and 18 people passed by (23)_____ offering emergency help. The girl died after days of medical treatment. In 2014, a man from Guangdong Province aided a senior citizen, but (24)_____ (accuse) of knocking him down. The man committed suicide when (25)_____ (face) with demands for a large sum of money.These cases (26)_____ (arouse) debate about morality and heroism in China in recent years. “If you don’t provide help, you will blame yourself, but if you do help, you are likely (27)_____ (hurt) by the people you help. It is really a difficult choice,”one netizen said on Sina Weibo.(28)_____ there had been calls for a national Good Samaritan law, only a few cities pushed ahead with such laws before the nationwide law came into effect.范文.范例.指导.参考However, some experts are concerned (29)_____ there could be some danger from a nationwide Good Samaritan Law. “Rescuers who know little about first aid could bring serious harm to people in critical conditions,” said Yang Lixin, a professor at the Renmin University of China. He hoped the government (30)_____ introduce details of the policy soon while encouraging people to voluntarily offer assistance.Section BDirections:After reading the passage below, fill in each blank with a proper word given in the box. Each word can only be used once. Note that there is one word more than you need.范文.范例.指导.参考And for his work, he has been 40 by critical community. Dylan has won Grammys, an Academy Award, a Golden Globe and a Medal of Freedom, the highest civilian honor in the U.S. Now, to the honors Dylan has added a Nobel.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.The Companies Doing the Most to Make Their Employees Happier Fat paychecks, light workloads, and endless vacation days don’t necessarily add to happy employees. In fact, the happiest employees in the U.S. owe their happiness to first-rate employee motivations, sufficient benefits, career advancement programs, and great work-life balance. The companies that have been the most devoted to cultivating and advancing these things in the past year have seen employee happiness 41 .The jobs site just announced the winners of this year’s “Leap Awards,” which honor the companies that have made the biggest leaps to improve employee happiness year-over-year. CareerBliss evaluated more than 250,000 company reviews and ratings it received from 42nationwide to determine the top 50 deserving companies. To 43 the list, each company had to have at least 50 reviews.“The Leap Awards are important because they highlight 44 in our workforce,” says CareerBliss’s chief executive, Heidi Golledge. Ca reerBliss asked the respondents to evaluate the key factors that 45 work happiness, including work-life balance, one’s relationship with the boss and co-workers, the work environment, job resources, salary, growth opportunities, company culture, company reputation, daily tasks, and job 46 .Each respondent valued each of these things on a 1-to-5 scale, and indicated how important each was to their overall happiness at work. These numbers were 47 to find an average rating of overall employee happiness for each company. These averages were compared to last year’s numbers to find which companies had 48 the most.“Every employer who receives a Leap Award should 49 their workplace happiness initiatives,” says Golledge. “Even though we are coming out of a difficult time, it is 50 to see companies putting their efforts into providing a great environment for their employees. These efforts in workplace happiness will ensure that their employees will be around for years to come, as happiness breeds 51 .”“We find each year that work-life balance is a key factor in determining employee happiness,” says Golledge. “Employees want to know that they can balance their ca reer with their family and personal life. Often this 52 over things like salary. Having programs that allow managers to offer employees flexibility can be a key factor in creating a happy work environment. 53 , we see career advancement programs have a big impact on overall employee happiness. Often employees would rather take a job for 范文.范例.指导.参考a 54 salary, if the company provides a comprehensive program which will help grow their career. Employees want to learn, develop and sustain a successful career p ath.”Workplace happiness is the core of CareerBliss’ mission, Miller says. “An individual’s happiness at work will create happiness throughout all areas of their life, and 55 a company with a happy, motivated workforce will see exceptional results in its products and services.”41. A. soar B. change C. cease D. disappear42. A. netizens B. administrators C. candidates D. employees43. A. make up B. qualify for C. count on D. refer to44. A. change B. power C. duty D. variety45. A. lay in B. resulted from C. focused on D. contributed to46. A. analysis B. vacancy C. flexibility D.responsibility47. A. applied B. combined C. compared D. remembered48. A. benefited B. improved C. changed D. produced49. A. approve of B. account for C. take pride in D. get used to50. A. good B. easy C. impossible D. interesting51. A. profit B. honesty C. creativity D. loyalty52. A. turns B. runs C. advantages D. skips53. A. However B. Otherwise C. Besides D. Instead54. A. lower B. fair C. regular D. similar55. A. obviously B. frankly C. fortunately D. similarlySection 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）In the world of higher education in the United States, competition seems more common than schools working together. Every college and university competes for students, as well as the best teachers and money for research programs.But one thing almost every school has in common is the difficulty they face in serving low-income students. The National Center for Education Statistics reports that low-income college students are less likely to complete their study programs than other students.范文.范例.指导.参考It was only natural that the leaders of Michigan State University and ten other universities discussed this issue when they met in 2014. The 11 schools are spread across the United States and serve different populations and needs. But their leaders all saw improving graduation rates for all students as the biggest problem facing American higher education.So the group created an organization called the University Innovation Alliance or UIA for sharing information related to this problem. Its main goal is to get 68,000 more students at the member schools to graduate by 2025, with at least half of those students being low-income. The 11 schools now say their number of graduates has increased by over 7,200 in just three years. This includes an almost 25 percent increase in the number of low-income graduates.How were they able to make this happen? It began with each university looking at its own situation and finding out what it had been doing right and what it had been doing wrong.For example, before joining the UIA, academic advising at Michigan State mostly involved reacting to problems students faced after the problems had already arisen. Then school officials heard about a computer program that fellow UIA member Georgia State University was using. This computer program follows decisions students make about their classes and the progress they are making in their studies. It then sends academic advisors messages whenever a student shows signs that they are making mistakes or facing difficulties. That way the advisors can try to help students before the problems become too serious. Michigan State began using the computer program and it has meant a world of difference. Michigan State has not only received useful information from its partners. It has also shared helpful information of its own.Bridget Burns, the executive director for the UIA, says efforts like this have never been as successful. “There are rankings that measure all kinds of things,”Burns said. “But how well you do for low-income students has not historically been highlighted.”56. What led to the setting up of the UIA?A. The low graduation rates.B. The great need of low-income students.C. The inefficiency of learning.D. The severe competition between schools.57. The UIA functions in such a way as the member universities _____.A. find out their own graduation ratesB. share and follow each other’s good practiceC. make joint efforts to aid students financiallyD. popularize computer programs among students58. By “it has meant a world of difference”in paragraph 6, the author means Michigan State _____.A. has found the computer program quite different from theirsB. has discovered the computer program is very difficult to useC. has helped students successfully with the computer program范文.范例.指导.参考D. has involved more academic advisors in the computer program59. Which of the following might be the best title for the passage?A. Universities Highlighting Their Efforts for Low-IncomesB. Universities Competing for Better Students and TeachersC. Universities Working Together to Help Poor StudentsD. Universities Creating the UIA to Share Information（B）We want to make the world a better, fairer place. We want to keep the powerful honest. And we believe that doing so means keeping society informed by producing quality, independent journalism, which discovers and tells readers the truth.It’s essential for the functioning of democracy. And our unique ownership structure means no one can tell us to drop a story.But it’s difficult and expensive work. While more people are reading the Guardian than ever before, far fewer are paying for it. And advertising incomes across the media are falling fast.So if you read us, if you like us, if you value our perspective—then become a Supporter and help make our future more secure.Supporters get closer to the Guardian As a Guardian Supporter, you’ll enjoy a number of benefits, including:◆Exclusive emails from Guardian journalists◆An ad-free experience on our mobile app◆Joining the global Guardian Members community ◆ A welcome giftMost importantly of all, you’ll appreciate every word that you read, in the knowledge that you’ve helped to bring it to the page.Why do we need our Supporters?Like many other media organisations, the Guardian is operating in an incredibly challenging financial climate. Our advertising incomes are falling fast. We have huge numbers of readers, and we are increasingly reliant upon their financial support.范文.范例.指导.参考We don’t have a wealthy owner pulling the strings. Noshareholders, advertisers or billionaire owners can edit oureditor.Our owner, the Scott Trust, protects our editorialindependence from commercial or political interference (干涉). It reinvests income into our journalism, not into shareholders’ pockets.But while the Scott Trust ensures our independence, we need our Supporters, now more than ever before, to help secure our future.We know that not everyone is in a position to become a Supporter. But if you can, you’ll be an essential part of our mission to make the world a better, fairer place, for everyone.60. The above webpage mainly aims to _____.A. raise funds from readersB. inform readers of quality journalismC. attract more readersD. guarantee readers a secure future61. Which of the following is a difficulty the Guardian is facing?A. It’s losing its editorial independence.B. It’s becoming increasingly reliant on its owner.C. It’s profiting much less from advertising.D. It’s operating in a challenging political climate.62. What can be inferred from the webpage?A. Some billionaire owners are the Guardian’s editors.B. The Guardian is independent financially and politically.C. Shareholders can interfere with the Guardian’s journalism.D. Guardian Supporters can put ads on the mobile app for free.（C）A new kind of production was underway on the set of the NBC comedy Superstore. Social media stars were crafting 30-second videos to post on their social media channels ahead of the comedy’s second-season return. Each made sure to mention Superstore and its first public show.As networks and studios struggle to reach young audiences in an increasingly fragmented(碎片化的) media marketplace, many have turned to so-called influencers—online stars whose value is measured by the size of their Internet followings—as a means of generating awareness. Advertisers are seizing on the strategy in an age of commercial-skipping and ad-blockers. Word of mouth in the digital age means messages travel faster by way of social media. The majority of consumers worldwide trust online recommendations from stars. And when Superstore gave its first public show, it did so to higher ratings than the last show of Season 1.Studio and network executives say they work with influencers to build brand awareness and reputation in a more friendly way through the friend-like connections consumers feel范文.范例.指导.参考toward the online personalities they follow. At the upper level, influencers typically have thousands of followers on social media and online content platforms and count many millions of people who tune in daily to watch them. Some do something that makes themselves look stupid in their daily routine, sharing videos of their trips to the grocery store or dinner dates. Others have built careers on performances—making comedy videos, reviewing video games, performing magic tricks and teaching cooking lessons, among other pursuits.When in the employ of studios, their efforts can be as simple as publicizing a film or more involved attempts like the marketing push for Superstore. Entertainment companies declined to discuss how much they pay influencers. But several experts said their pay ranges from a few thousand dollars to several million. Some simply receive gift baskets instead of pay.Over the last year or so, some entertainment companies have begun to cast influencers in their TV and film projects. The st rategy is a bit of a gamble: It’s a new business model, and questions remain about the effectiveness of using these personalities to improve a show’s ratings—or help open a movie. Just how much influence the influencers have is hard to measure. TV ratings and box-office returns do not reveal what caused a viewer to tune in.What is clear is that these personalities aren’t necessarily getting the work because of their acting skills, but often because of their Internet followings. Yet as social media stars consider whether to take on jobs promoting movies and TV shows, there’s an important consideration for both parties: the credibility of a campaign. “Fans are definitely aware wh en they’re being tempte d with promotional posts,” said Zach King, a social media star who performs magic tricks. “It has to be something that is natural and fits with the image of the creator.”63. Why did social media stars post short videos on their channels before Superstore’ssecond season?A. To attract more influencers.B. To draw audience’s attention.C. To put on better performances.D. To increase the channels’popularity.64. Advertisers like the influencer marketing strategy because _____.A. audiences believe in whatever online stars recommendB. influencers are quite aware of the impact of the digital ageC. ordinary advertisements are often ignored by young peopleD. social media platforms are the cheapest place to spread messages65. What is implied in the passage?A. The influencer marketing strategy help build connections between executives.B. Most influencers get paid from gift baskets instead of from their companies.C. Most influencers take on marketing jobs regardless of their reliability.范文.范例.指导.参考D. The influencer marketing strategy may not really work well.66. The passage mainly wants to tell us that _____.A. most young people like following influencersB. studios are relying more on social media starsC. influencers are gradually replacing movie starsD. social media are filming videos for SuperstoreSection 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.Feel Young at Heart and Y ou’ll Enjoy a Longer Life Age-liars and birthday-deniers... you’d best learn a thing or two from those who are young at heart. People who feel younger than their actual age may live longer than those who feel older than they truly are, a new study says.67 Results from the study, published in the Journal of the American Medical Association, suggest that people who feel a year or more older than they truly are could have around 41 percent greater risk for death.Researchers looked at nearly 6,500 older adults, with an average age of 65.8 for the study. Around 70 percent of them felt younger than they were, about a quarter felt their precise age and just under 5 percent felt a year or more older than they were, when asked “How old do you feel you are?”Those who felt older than they were had a higher death rate after a follow-up period of 99 months. While just 14.3 and 18.5 percent of people who felt younger or felt their age, respectively, died during those 99 months, 24.6 percent of those who felt aged beyond 范文.范例.指导.参考their years had died.The authors say more research is needed on the topic, but suggest it could be that those who feel “young at heart”have healthier behaviors and a stronger will to live. “ 68 Individuals who feel older could be targeted with health messages promoting positive health behaviors and attitudes toward aging,”the authors write in the study.The good news is that you can change your feeling of how young you are. 69 One recent study found that helping participants have positive feelings toward age, by showing them positive word associations, helped older adults improve in physical tasks like balancing and getting up out of a chair, in as little as four weeks. Another study found that negative feeling of aging and poor memory can make older adults feel up to five years older, regardless of their actual mental abilities.There you have it. 70IV. 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.Do Smartphones Make Us Smarter?Should teachers allow cellphones in a classroom? A recent study on the way smartphones disturb learning might help explain the issue. Researchers published findings showing how students were affected by their phones in the classroom. They explored the differences in student performance in four situations: open phone use allowed, phones allowed in the classroom but could not be used, no phones in the classroom and a no-instruction control group. After watching a 20-minute video, students took a short quiz. The result was that the students in a room without any cellphones performed significantly better on the test. Scientists believe the way we attach ourselves to our phones could be the problem.Smartphones have become so strongly established in society that many people are lost without them. We are now in an age when many people can’t imagine life without a phone. There is even a name for the anxiety caused by not having one—nomophobia, which is the powerful feeling people get when they don’t have signal, their battery is about to die, or they are separated from their phones. Their fear of missing out on important information or connections can have a controlling effect on their lives and can divide their attention from other important things like learning.So does information technology help or block the way we think? In the past, people relied heavily on specific knowledge and knew who in their circle of friends would be范文.范例.指导.参考most likely to know things in different subjects. Now, our friend with all the information is the Internet. Indications are that people don’t remember information as well if they know they can use a computer or phone to recall it quickly. So it may be more difficult to move information from the Internet into our long-term memory.But the impact of being exposed to so much information isn’t all bad. Reports show that frequent Internet use can strengthen fast-paced problem solving and can speed up the ability to spot patterns in a lot of data.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 何不利用这宜人的天气出去野餐呢？(advantage)73. 当你对情况一知半解时，不要随意发表见解。

2018年上海市崇明区高考数学二模试卷一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1. 已知集合U ={−1, 0, 1, 2, 3}，A ={−1, 0, 2}，则∁U A =________．2. 已知一个关于x 、y 的二元一次方程组的增广矩阵是(1−11012)，则x +y =________3. i 是虚数单位，若复数(1−2i)(a +i)是纯虚数，则实数a 的值为________．4. 若|log 2x−1−42|=0，则x =________．5. 我国古代数学名著《九章算术》有“米谷粒分”题：粮仓开仓收粮，有人送来米1534石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为________石（精确到小数点后一位数字）.6. 已知圆锥的母线长为5，侧面积为15π，则此圆锥的体积为________（结果保留π）．7. 若二项式(2x +a x )7的展开式中一次项的系数是−70，则lim n→∞(a +a 2+a 3+...+a n )=________8. 已知椭圆x 2a 2+y 2=1(a >0)的焦点F 1、F 2，抛物线y 22x 的焦点为F ，若F 1F →=3FF 2→，则a ＝________√29. 设f(x)是定义在R 上以2为周期的偶函数，当x ∈[0, 1]时，f(x)=log 2(x +1)，则函数f(x)在[1, 2]上的解析式是________10. 某办公楼前有7个连成一排的车位，现有三辆不同型号的车辆停放，恰有两辆车停放在相邻车位的概率是________11. 已知x ，y ∈R ，且满足{√3x +y ≤4√3√3x −y ≥0y ≥0，若存在θ∈R 使得xcosθ+ysinθ+1＝0成立，则点P(x, y)构成的区域面积为________12. 在平面四边形中，已知AB =1，BC =4，CD =2，DA =3，则AC →⋅BD →的值为________．二.选择题（本大题共4题，每题5分，共20分）“x >1”是“2x >1”的（ ）A.充分不必要条件B.必要不充分条件C.充分必要条件D.既不充分也不必要条件若1+√2i 是关于x 的实系数方程x 2+bx +c =0的一个复数根，则（ ）A.b =2，c =3B.b =2，c =−1C.b =−2，c =3D.b =−2，c =−1将函数y =sin (2x −π3)图象上的点P (π4,t)向左平移s(s >0)个单位长度得到点P ′．若P ′位于函数y =sin 2x 的图象上，则( )A.t =12，s 的最小值为π6B.t =√32，s 的最小值为π6 C.t =12，s 的最小值为π3D.t =√32，s 的最小值为π3在平面直角坐标系中，定义d(A, B)=max{|x 1−x 2|, |y 1−y 2|}为两点A(x 1y 1)、B(x 2, y 2)的“切比雪夫距离”，又设点P 及l 上任意一点Q ，称d(P, Q)的最小值为点P 到直线l 的“切比雪夫距离”，记作d(P, t)，给出下列三个命题：①对任意三点A 、B 、C ，都有d(C, A)+d(C, B)≥d(A, B)；②已知点P(3, 1)和直线l:2x −y −1=0，则d(P, l)=43；③定点F 1(−c, 0)、F 2(c, 0)，动点P(x, y)满足|d(P, F 1)−d(P, F 2)|=2a(2c >2a >0)，则点P 的轨迹与直线y =k （k 为常数）有且仅有2个公共点；其中真命题的个数是（ ）A.0B.1C.2D.3三.解答题（本大题共5题，共14+14+14+16+18=76分）如图，在四棱锥P −ABCD 中，底面ABCD 为直角梯形，BC // AD ，AB ⊥BC ，∠ADC =45∘，PA ⊥平面ABCD ，AB =AP =1，AD =3．（1）求异面直线PB 与CD 所成角的大小；（2）求点D 到平面PBC 的距离．已知点F 1、F 2依次为双曲线C:x 2a 2−y 2b 2=1(a, b >0)的左右焦点，|F 1F 2|=6，B 1(0, −b)，B 2(0, b)．(1)若a =√5，以d →=(3, −4)为方向向量的直线l 经过B 1，求F 2到l 的距离；(2)若双曲线C 上存在点P ，使得PB 1→⋅PB 2→=−2，求实数b 的取值范围．如图，某公园有三条观光大道AB ，BC ，AC 围成直角三角形，其中直角边BC =200m ，斜边AB =400m ，现有甲、乙、丙三位小朋友分别在AB ，BC ，AC 大道上嬉戏，所在位置分别记为点D ，E ，F ．(1)若甲、乙都以每分钟100m 的速度从点B 出发在各自的大道上奔走，到大道的另一端时即停，乙比甲迟2分钟出发，当乙出发1分钟后，求此时甲乙两人之间的距离；(2)设∠CEF =θ，乙丙之间的距离是甲乙之间距离的2倍，且∠DEF =π3，请将甲乙之间的距离y 表示为θ的函数，并求甲乙之间的最小距离．已知函数f(x)=2x +a2x +1，x ∈R ．（1）证明：当a >1时，函数y ＝f(x)是减函数；（2）根据a 的不同取值，讨论函数y ＝f(x)的奇偶性，并说明理由；（3）当a ＝2，且b <c 时，证明：对任意d ∈[f(c), f(b)]，存在唯一的x 0∈R ，使得f(x 0)＝d ，且x 0∈[b, c]．设数列{a n }的前n 项和为S n ，若12≤a n+1a n ≤2(n ∈N ∗)，则称{a n }是“紧密数列”．（1）已知数列{a n }是“紧密数列”，其前5项依次为1，32,94,x,8116，求x 的取值范围；（2）若数列{a n }的前n 项和为S n =14(n 2+3n)(n ∈N ∗)，判断{a n }是否是“紧密数列”，并说明理由；（3）设{a n }是公比为q 的等比数列，若{a n }与{S n }都是“紧密数列”，求q 的取值范围．参考答案与试题解析2018年上海市崇明区高考数学二模试卷一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1.【答案】{1, 3}【考点】补集及其运算【解析】利用补集定义直接求解．【解答】解：∵ 集合U ={−1, 0, 1, 2, 3}，A ={−1, 0, 2}，∴ ∁U A ={1, 3}．故答案为：{1,3}.2.【答案】5【考点】几种特殊的矩阵变换【解析】根据增广矩阵求得二元一次方程组，即可求得x 和y ，即可求得答案．【解答】由增广矩阵是(1−11012)，则二元一次方程组{x −y =10+y =2 ， 解得：x =3，y =2，∴ x +y =5，3.【答案】−2【考点】虚数单位i 及其性质复数的运算复数的模复数的基本概念【解析】由复数代数形式的乘除运算化简，再由实部等于0且虚部不等于0求得a 的值．【解答】由(1−2i)(a +i)=(a +2)+(1−2a)i 为纯虚数，得{a +2=01−2a ≠0，解得：a =−2． 4.【答案】4【考点】对数的运算性质【解析】由二阶行列式展开式性质得2log2x−4=0，由此利用对数运算法则和性质能求出x．【解答】∵|log2x−1−42|=0，∴2log2x−4=0，∴log2x=2，解得x=4．5.【答案】169.1【考点】简单随机抽样【解析】根据抽样比例求出这批米内夹谷的多少．【解答】解：根据题意，这批米内夹谷为1534×28254≈169.1（石）．故答案为：169.1.6.【答案】12π【考点】旋转体（圆柱、圆锥、圆台）【解析】设圆锥的底面半径为r，母线为l，高为ℎ，根据侧面积公式算出底面半径r=3，用勾股定理算出高ℎ=√l2−r2=4，代入圆锥体积公式即可算出此圆锥的体积．【解答】设圆锥的底面半径为r，母线为l，高为ℎ∵圆锥的母线长为l=5，侧面积为15π，∴12×l×r=15π，解之得底面半径r=3因此，圆锥的高ℎ=√l2−r2=4∴圆锥的体积为：V=13πr2ℎ=13×π×9×4=12π7.【答案】−1 3【考点】数列的极限二项式定理的应用【解析】利用通项公式T r+1=C n r a n−r b r来解决，在通项中令x的指数幂为1可求出含x是第几项，由此算出a．然后利用数列的极限的运算法则求解即可．【解答】由二项式定理的通项公式T r+1=C nr a n−r b r 可设含x 2项的项是 T r+1=C 7r (2x)7−r (a x )r =a r 27−r C 7r x 7−2r ， 令7−2r =1，解得：r =3，∴ 系数为a 324C 73=−70，解得a =−12， lim n→∞(a +a 2+a 3+...+a n )=a 1−a =−121+12=−13， 8.【答案】 √2【考点】圆锥曲线的综合问题【解析】先根据椭圆和抛物线的方程分别求得其焦点坐标，根据F 1F →=3FF 2→，建立等式求得a 的值即可．【解答】依题意可知抛物线的焦点为(12, 0)，椭圆的焦点为(±√a 2−1, 0)，∵ F 1F →=3FF 2→，∴ 12+√a 2−1=3(√a 2−1−12)，整理得a =√2，9.【答案】f(x)=log 2(3−x)【考点】函数解析式的求解及常用方法【解析】设x ∈(1, 2)，则x −2∈(−1, 0)，2−x ∈(0, 1)，由已知表达式可求得f(2−x)，再由f(x)为周期为2的偶函数，可得f(x)=f(x −2)=f(2−x)，从而得到答案．【解答】∵ f(x)是定义在R 上以2为周期的偶函数，当x ∈[0, 1]时，f(x)=log 2(x +1)，∴ 设x ∈(1, 2)，则x −2∈(−1, 0)，2−x ∈(0, 1)，∴ f(2−x)=log 2[(2−x)+1]=log 2(3−x)，又f(x)为周期为2的偶函数，所以f(x)=f(x −2)=f(2−x)=log 2(3−x)．10.【答案】47【考点】古典概型及其概率计算公式【解析】基本事件总数n =C 73=35，恰有两辆车停放在相邻车位包含的基本事件个数m =A 52=20，由此能求出恰有两辆车停放在相邻车位的概率．【解答】某办公楼前有7个连成一排的车位，现有三辆不同型号的车辆停放，基本事件总数n=C73=35，恰有两辆车停放在相邻车位包含的基本事件个数m=A52=20，∴恰有两辆车停放在相邻车位的概率是p=mn =2035=47．11.【答案】4√3−π6【考点】简单线性规划【解析】作出不等式组表示的平面区域，求出xcosθ+ysinθ+1＝0成立的等价条件，利用数形结合求出对应的面积，即可得出正确的结果．【解答】又直线y=√3x的倾斜角为π3，则∠AOB=π3，即扇形的面积为16π⋅12=π6，则P(x, y)构成的区域面积为S＝4√3−π6，故答案为：4√3−π6．12.【答案】10【考点】椭圆中的平面几何问题平面向量数量积的性质及其运算律【解析】方向条件，四边形是椭圆的内接图形，利用椭圆的简单性质以及焦半径公式转化求解即可．【解答】解：∵AB+BC=DA+DC=5，所以把四边形放入椭圆内，AC为左右焦点，不妨令B(x 1, y 1)，D(x 2, y 2)则2a =5，由焦半径公式可得ex 1+a =1，ex 2+a =3，两式相减可得：e(x 2−x 1)=2，而AC →⋅BD →=2c(x 2−x 1)=2c ⋅2e =4a =10． 故答案为：10.二.选择题（本大题共4题，每题5分，共20分）【答案】A【考点】必要条件、充分条件与充要条件的判断【解析】根据不等式的关系，结合充分条件和必要条件的定义进行判断即可．【解答】由2x >1得x >0，则“x >1”是“2x >1”的充分不必要条件，【答案】C【考点】实系数多项式虚根成对定理【解析】利用实系数一元二次的虚根成对原理、根与系数的关系即可得出．【解答】∵ 1+√2i 是关于x 的实系数方程x 2+bx +c =0的一个复数根，∴ 1−√2i 是关于x 的实系数方程x 2+bx +c =0的一个复数根，∴ {1+√2i +1−√2i =−b (1+√2i)(1−√2i)=c，解得b =−2，c =3． 【答案】A【考点】函数y=Asin （ωx+φ）的图象变换【解析】此题暂无解析【解答】解：将x =π4代入y =sin (2x −π3)得t =12，所以P (π4,12)，点P 向左平移s(s >0)个单位长度得到的点的坐标为P ′(π4−s,12)．又因为P ′在y =sin 2x 上，所以sin2(π4−s)=12，所以2s =2kπ+π3或2s =2kπ−π3(k ∈Z)，即s =kπ+π6或s =kπ−π6(k ∈Z)．因为s >0，所以当k =0时，有s min =π6．故选A ．【答案】D【考点】命题的真假判断与应用【解析】①讨论A ，B ，C 三点共线，以及不共线的情况，结合图象和新定义，即可判断； ②设点Q 是直线y =2x −1上一点，且Q(x, 2x −1)，可得d(P, Q)=max{|x −3|, |2−2x|}，讨论|x −3|，|2−2x|的大小，可得距离d ，再由函数的性质，可得最小值； ③讨论P 在坐标轴上和各个象限的情况，求得轨迹方程，即可判断．【解答】①对任意三点A 、B 、C ，若它们共线，设A(x 1, y 1)、B(x 2, y 2)，C(x 3, y 3)，如图，结合三角形的相似可得d(C, A)，d(C, B)，d(A, B)为AN ，CM ，AK ，或CN ，BM ，BK ， 则d(C, A)+d(C, B)=d(A, B)；若B ，C 或A ，C 对调，可得d(C, A)+d(C, B)>d(A, B)；若A ，B ，C 不共线，且三角形中C 为锐角或钝角，如图，由矩形CMNK 或矩形BMNK ，d(C, A)+d(C, B)≥d(A, B)；则对任意的三点A ，B ，C ，都有d(C, A)+d(C, B)≥d(A, B)；故①正确； ②设点Q 是直线y =2x −1上一点，且Q(x, 2x −1)，可得d(P, Q)=max{|x −3|, |2−2x|}，由|x −3|≥|2−2x|，解得−1≤x ≤53，即有d(P, Q)=|x −3|，当x =53时，取得最小值43；由|x −3|<|2−2x|，解得x >53或x <−1，即有d(P, Q)=|2x −2|，d(P, Q)的范围是(3, +∞)∪(43, +∞)=(43, +∞)．无最值，综上可得，P ，Q 两点的“切比雪夫距离”的最小值为43．故②正确；③定点F 1(−c, 0)、F 2(c, 0)，动点P(x, y)满足|d(P, F 1)−d(P, F 2)|=2a(2c >2a >0)，可得P 不y 轴上，P 在线段F 1F 2间成立，可得x +c −(c −x)=2a ，解得x =a ，由对称性可得x =−a 也成立，即有两点P 满足条件；若P 在第一象限内，满足|d(P, F 1)−d(P, F 2)|=2a ，即为x +c −y =2a ，为射线，由对称性可得在第二象限、第三象限和第四象限也有一条射线，则点P 的轨迹与直线y =k （k 为常数）有且仅有2个公共点．故③正确．∴ 真命题的个数是3．三.解答题（本大题共5题，共14+14+14+16+18=76分）【答案】以A 为原点，AB 为x 轴，AD 为y 轴，AP 为z 轴，建立如图所示空间直角坐标系， 则P(0, 0, 1)，B(1, 0, 0)，C(1, 2, 0)D(0, 3, 0)，∴ PB →=(1, 0, −1)，CD →=(−1, 1, 0)，设异面直线PB 与CD 所成角为θ，则cosθ=|PB →∗CD →||PB →|∗|CD →|=12，所以异面直线PB 与CD 所成角大小为π3．设平面PBC 的一个法向量为n →=(x, y, z)，PB →=(1, 0, −1)，BC →=(0, 2, 0)，CD →=(−1, 1, 0)，则{n →∗PB →=x −z =0n →∗BC →=2y =0 ，取x =1，得n →=(1, 0, 1)， ∴ 点D 到平面PBC 的距离d =|n →∗CD →||n →|=√22．【考点】异面直线及其所成的角点、线、面间的距离计算 【解析】（1）以A 为原点，AB 为x 轴，AD 为y 轴，AP 为z 轴，建立空间直角坐标系，利用向量法能求出异面直线PB 与CD 所成角大小．（2）求出平面PBC 的一个法向量，利用向量法能求出点D 到平面PBC 的距离． 【解答】以A 为原点，AB 为x 轴，AD 为y 轴，AP 为z 轴，建立如图所示空间直角坐标系， 则P(0, 0, 1)，B(1, 0, 0)，C(1, 2, 0)D(0, 3, 0)， ∴ PB →=(1, 0, −1)，CD →=(−1, 1, 0)， 设异面直线PB 与CD 所成角为θ， 则cosθ=|PB →∗CD →||PB →|∗|CD →|=12，所以异面直线PB 与CD 所成角大小为π3． 设平面PBC 的一个法向量为n →=(x, y, z)，PB →=(1, 0, −1)，BC →=(0, 2, 0)，CD →=(−1, 1, 0)，则{n →∗PB →=x −z =0n →∗BC →=2y =0 ，取x =1，得n →=(1, 0, 1)， ∴ 点D 到平面PBC 的距离d =|n →∗CD →||n →|=√22．【答案】解：(1)由题意可知：c =3，F 2(3, 0)， c 2=a 2+b 2，a =√5，∴ b =2， 设直线l 的方程为y =kx +m ， d →=(3,−4)为方向向量的直线l ， ∴ k =−43，点B 1(0, −2)在直线l 上，m =−2，∴ 直线方程为4x +3y +6=0， F 2到l 的距离d =√42+32=185.(2)由题意可知：c =3，设P(x 0, y 0)，c 2=a 2+b 2，得a 2=c 2−b 2=9−b 2，① PB 1→=(x 0, y 0+b)，PB 2→=(x 0, y 0−b)，PB 1→⋅PB 2→=−2，整理得：x 02+y 02−b 2=−2， 则：x 02=b 2−y 02−2，② 由点P 在双曲线上：∴x 02a 2−y 02b 2=1，③ 将①②代入③整理得：b 2−y 02−29−b 2−y 02b 2=1， ∴ (b 2−y 02−2)×b 2−y 02×(9−b 2)=(9−b 2)×b 2， 整理得：2b 4−11b 2=9y 02，∵ y 02≥0，∴ 2b 4−11b 2≥0，解得：b ≥√222，∵ b <3，实数b 的取值范围[√222, 3)．【考点】直线与椭圆结合的最值问题 【解析】（1）由题意可知：c ＝3，由a =√5，求得b 的值，根据向量共线定理求得直线的斜率k ，直线过F 2(3, 0)，求得直线方程，根据点到直线的距离公式即可求得F 2到l 的距离； （2）设出P 点坐标，由双曲线的性质可知：a 2＝9−b 2，根据向量数量积的坐标表示求得x 02+y 02−b 2＝−2，由点P 在双曲线上，将P 点坐标代入双曲线上，整理得2b 4−11b 2＝9y 02，由y 02≥0，及b <3，即可求得b 的取值范围． 【解答】解：(1)由题意可知：c =3，F 2(3, 0)， c 2=a 2+b 2，a =√5，∴ b =2， 设直线l 的方程为y =kx +m ， d →=(3,−4)为方向向量的直线l ， ∴ k =−43，点B 1(0, −2)在直线l 上，m =−2， ∴ 直线方程为4x +3y +6=0， F 2到l 的距离d =√42+32=185.(2)由题意可知：c =3，设P(x 0, y 0)，c 2=a 2+b 2，得a 2=c 2−b 2=9−b 2，① PB 1→=(x 0, y 0+b)，PB 2→=(x 0, y 0−b)，PB 1→⋅PB 2→=−2，整理得：x 02+y 02−b 2=−2， 则：x 02=b 2−y 02−2，② 由点P 在双曲线上：∴x 02a 2−y 02b 2=1，③将①②代入③整理得：b 2−y 02−29−b 2−y 02b 2=1，∴ (b 2−y 02−2)×b 2−y 02×(9−b 2)=(9−b 2)×b 2，整理得：2b 4−11b 2=9y 02，∵ y 02≥0，∴ 2b 4−11b 2≥0，解得：b ≥√222，∵ b <3，实数b 的取值范围[√222, 3)．【答案】解：(1)由题意，BD =300，BE =100， △ABC 中，cosB =12，B =π3， △BDE 中，由余弦定理可得：DE =√3002+1002−2×300×100×12=100√7m ； (2)由题意，EF =2DE =2y ，∠BDE =∠CEF =θ． △CEF 中，CE =EFcos∠CEF =2ycosθ △BDE 中，由正弦定理可得200−2ycosθsinθ=ysin60∘，∴ y =√3sinθ+3cosθ=50√3sin(θ+π3)，0<θ<π2，∴ θ=π6，y min =50√3m ．【考点】 解三角形 余弦定理 正弦定理 【解析】（1）由题意，BD =300，BE =100，△BDE 中，由余弦定理可得甲乙两人之间的距离；(2)△BDE 中，由正弦定理可得200−2ysinθsinθ=ysin60∘，可将甲乙之间的距离y 表示为θ的函数，并求甲乙之间的最小距离． 【解答】解：(1)由题意，BD =300，BE =100， △ABC 中，cosB =12，B =π3， △BDE 中，由余弦定理可得：DE =√3002+1002−2×300×100×12=100√7m ；(2)由题意，EF =2DE =2y ，∠BDE =∠CEF =θ． △CEF 中，CE =EFcos∠CEF =2ycosθ △BDE 中，由正弦定理可得200−2ycosθsinθ=y sin60∘，∴ y =√3sinθ+√3cosθ=50√3sin(θ+π3)，0<θ<π2，∴ θ=π6，y min =50√3m ． 【答案】证明：任取x 1，x 2∈R ，设x 1<x 2，则f(x 1)−f(x 2)=(a−1)(2x 2−2x 1)(2x 1+1)(2x 2+1)，∵ x 1<x 2，∴ 2x 1<2x 2，又a >1，∴ f(x 1)−f(x 2)>0，即f(x 1)>f(x 2)． 所以当a >1时，函数y ＝f(x)是减函数．当a ＝1时，f(x)＝1，所以f(−x)＝f(x)＝1，所以函数y ＝f(x)是偶函数， 当a ＝−1时，f(x)=2x −12x +1，f(−x)=2−x −12−x +1=1−2x1+2x=−f(x)， 所以函数y ＝f(x)是奇函数． 当a ≠1且a ≠−1时，f(1)=a+23，f(−1)=2a+13，∴ f(−1)≠f(1)且f(−1)≠−f(1)，所以函数y ＝f(x)是非奇非偶函数．证明：由（1）知，当a ＝2时，函数y ＝f(x)是减函数， 所以函数f(x)在[b, c]上的值域为[f(c), f(b)]，因为d ∈[f(c), f(b)]，所以存在x 0∈R ，使得f(x 0)＝d ． 假设存在x 1∈R ，x 1≠0使得f(x 1)＝d ，若x 1>x 0，由f(x)的单调性可得f(x 1)<f(x 0)，若x 1<x 0，则f(x 1)>f(x 0)， 与f(x 1)＝f(x 0)＝d 矛盾，故x 0是唯一的． 假设x 0∉[b, c]，即x 0<b 或x 0>c ，由单调性可得f(x 0)>f(b)或f(x 0)<f(c)，所以d ∉[f(c), f(b)]，与d ∈[f(c), f(b)]矛盾，故x 0∈[b, c]． 【考点】函数与方程的综合运用 【解析】（1）设x 1<x 2，计算f(x 1)−f(x 2)，判断f(x 1)−f(x 2)的符号得出结论； （2）令f(−x)＝f(x)和f(−x)＝−f(x)分别求出a 的值得出结论； （3）利用反证法得出结论． 【解答】证明：任取x 1，x 2∈R ，设x 1<x 2，则f(x 1)−f(x 2)=(a−1)(2x 2−2x 1)(2x 1+1)(2x 2+1)，∵ x 1<x 2，∴ 2x 1<2x 2，又a >1，∴ f(x 1)−f(x 2)>0，即f(x 1)>f(x 2)． 所以当a >1时，函数y ＝f(x)是减函数．当a ＝1时，f(x)＝1，所以f(−x)＝f(x)＝1，所以函数y ＝f(x)是偶函数， 当a ＝−1时，f(x)=2x −12x +1，f(−x)=2−x −12−x +1=1−2x1+2x=−f(x)， 所以函数y ＝f(x)是奇函数． 当a ≠1且a ≠−1时，f(1)=a+23，f(−1)=2a+13，∴ f(−1)≠f(1)且f(−1)≠−f(1)， 所以函数y ＝f(x)是非奇非偶函数．证明：由（1）知，当a ＝2时，函数y ＝f(x)是减函数， 所以函数f(x)在[b, c]上的值域为[f(c), f(b)]，因为d ∈[f(c), f(b)]，所以存在x 0∈R ，使得f(x 0)＝d ． 假设存在x 1∈R ，x 1≠0使得f(x 1)＝d ，若x 1>x 0，由f(x)的单调性可得f(x 1)<f(x 0)，若x 1<x 0，则f(x 1)>f(x 0)， 与f(x 1)＝f(x 0)＝d 矛盾，故x 0是唯一的． 假设x 0∉[b, c]，即x 0<b 或x 0>c ，由单调性可得f(x 0)>f(b)或f(x 0)<f(c)，所以d ∉[f(c), f(b)]，与d ∈[f(c), f(b)]矛盾，故x 0∈[b, c]． 【答案】 由题意得：12≤x94≤2，12≤8116x≤2，解得98≤x ≤92≤818．由S n =14(n 2+3n)(n ∈N ∗)，n ≥2时，a n =S n −S n−1=14(n 2+3n)−14[(n −1)2+3(n −1)]=12n +12， n =1时，a 1=S 1=1，对于上式也成立． 因此a n =12n +12． ∴a n+1a n=12(n+1)+1212n+12=1+1n+1．因为对任意n ∈N ∗，0<1n+1≤12，即1<1+1n+1≤32， ∴ 12≤a n+1a n≤2(n ∈N ∗)，即数列{a n }是“紧密数列”．由{a n }是公比为q 的等比数列，得q =a n+1a n，∵ {a n }是“紧密数列”，∴ 12≤q ≤2． ①当q =1时，S n =na 1，S n+1S n=n+1n=1+1n ，∵ 1<1+1n+1≤32<2，∴ q =1时，数列{S n }为“紧密数列”，故q =1满足题意． ②当q ≠1时，S n =a 1(1−q n )1−q，则S n+1S n=1−q n+11−q n，∵ 数列{S n }为“紧密数列”， ∴ 12≤1−q n+11−q ≤2，对任意n ∈N ∗恒成立．(ⅰ)当12≤q <1时，12(1−q n )≤1−q n+1≤2(1−q n )， 即{q n (2q −1)≤1q n(q −2)≥−1，对任意n ∈N ∗恒成立．∵ 0<q n ≤q <1，0≤2q −1<1，−32≤q −2<−1，∴ q n (2q −1)<q <1，q n (q −2)≥q(q −2)≥12×(−32)=−34>−1， ∴ 当12≤q <1时，{q n (2q −1)≤1q n (q −2)≥−1，对任意n ∈N ∗恒成立．(ⅱ)当1<q ≤2时，12(q n −1)≤qn+1−1≤2(q n−1)，即{q n (2q −1)≥1q n (q −2)≤−1，对任意n ∈N ∗恒成立．∵ q n ≥q >1，2q −1>1，−1<q −2≤0． ∴ {q(2q −1)≥1q(q −2)≤−1 ，解得q =1，又1<q ≤2，此时q 不存在． 综上所述，q 的取值范围是[12,1]． 【考点】 数列递推式 【解析】（1）由题意得：12≤x94≤2，12≤8116x≤2，解得x 范围．（2）由S n =14(n 2+3n)(n ∈N ∗)，n ≥2时，a n =S n −S n−1，n =1时，a 1=S 1=1，对于上式也成立．可得a n ．a n+1a n=1+1n+1．因为对任意n ∈N ∗，0<1n+1≤12，即1<1+1n+1≤32，即可得出结论．（3）由{a n }是公比为q 的等比数列，得q =a n+1a n，{a n }是“紧密数列”，可得12≤q ≤2．分类讨论：①当q =1时，S n =na 1，S n+1S n=n+1n=1+1n ，即可判断出结论．②当q ≠1时，S n =a 1(1−q n )1−q，S n+1S n=1−q n+11−q n，由数列{S n }为“紧密数列”，可得12≤1−q n+11−q n≤2，对任意n ∈N ∗恒成立．(ⅰ)当12≤q <1时，12(1−q n)≤1−q n+1≤2(1−q n)，即{q n (2q −1)≤1q n (q −2)≥−1，对任意n ∈N ∗恒成立．即可得出结论． (ⅱ)当1<q ≤2时，12(q n −1)≤q n+1−1≤2(q n−1)，即{q n (2q −1)≥1q n (q −2)≤−1，对任意n ∈N ∗恒成立．即可得出结论． 【解答】 由题意得：12≤x94≤2，12≤8116x≤2，解得98≤x ≤92≤818．由S n =14(n 2+3n)(n ∈N ∗)，n ≥2时，a n =S n −S n−1=14(n 2+3n)−14[(n −1)2+3(n −1)]=12n +12，n =1时，a 1=S 1=1，对于上式也成立． 因此a n =12n +12． ∴a n+1a n=12(n+1)+1212n+12=1+1n+1．因为对任意n ∈N ∗，0<1n+1≤12，即1<1+1n+1≤32， ∴ 12≤a n+1a n≤2(n ∈N ∗)，即数列{a n }是“紧密数列”．由{a n }是公比为q 的等比数列，得q =a n+1a n，∵ {a n }是“紧密数列”，∴ 12≤q ≤2． ①当q =1时，S n =na 1，S n+1S n=n+1n=1+1n ，∵ 1<1+1n+1≤32<2，∴ q =1时，数列{S n }为“紧密数列”，故q =1满足题意． ②当q ≠1时，S n =a 1(1−q n )1−q，则S n+1S n=1−q n+11−q n，∵ 数列{S n }为“紧密数列”， ∴ 12≤1−q n+11−q n≤2，对任意n ∈N ∗恒成立．(ⅰ)当12≤q <1时，12(1−q n )≤1−q n+1≤2(1−q n )， 即{q n (2q −1)≤1q n(q −2)≥−1，对任意n ∈N ∗恒成立． ∵ 0<q n ≤q <1，0≤2q −1<1，−32≤q −2<−1，∴ q n (2q −1)<q <1，q n (q −2)≥q(q −2)≥12×(−32)=−34>−1， ∴ 当12≤q <1时，{q n (2q −1)≤1q n (q −2)≥−1，对任意n ∈N ∗恒成立．(ⅱ)当1<q ≤2时，12(q n −1)≤qn+1−1≤2(q n−1)，即{q n (2q −1)≥1q n (q −2)≤−1，对任意n ∈N ∗恒成立．∵ q n ≥q >1，2q −1>1，−1<q −2≤0． ∴ {q(2q −1)≥1q(q −2)≤−1 ，解得q =1，又1<q ≤2，此时q 不存在． 综上所述，q 的取值范围是[12,1]．。

高三数学 共4页 第1页崇明区2018学年第二次高考模拟考试试卷数 学考生注意：1． 本试卷共4页，21道试题，满分150分，考试时间120分钟．2． 本试卷分设试卷和答题纸．试卷包括试题与答题要求．作答必须涂（选择题）或写（非选择题）在答题纸上，在试卷上作答一律不得分．3． 答卷前，务必用钢笔或圆珠笔在答题纸正面清楚地填写姓名、准考证号码等相关信息．一、填空题（本大题共有12题，满分54分，其中1～6题每题4分，7～12题每题5分）【考生应在答题纸相应编号的空格内直接填写结果．】1．已知全集{1,2,3,4,5}U =，集合{1,2,3,4}A =，{1,3,5}B =，则()U C A B =I ． 2．函数sin cos y x x =的最小正周期T = ．3．设函数2()(0)f x x x =>的反函数为1()y f x -=，则1(4)f -= ．4．若复数2zi a i =+（i 为虚数单位），且实部和虚部相等，则实数a 的值为 ． 5．已知椭圆的焦点在x 轴上，焦距为2，且经过点(0,2)，则该椭圆的标准方程为 ．6．已知二项式62a x x ⎛⎫+ ⎪⎝⎭的展开式中含3x 项的系数是160，则实数a 的值是 ．7．已知直线1:(3)(4)10l a x a y -+-+=与2:2(3)230l a x y --+=平行，则a = ． 8，母线与底面所成角为3π，则该圆锥的侧面积为 ． 9．已知n S 是公比为q 的等比数列{}n a 的前n 项和．若对任意的*k N ∈，都有1lim()n k k n S S a +→∞-=成立，则q = ．10．甲、乙、丙、丁4名同学参加志愿者服务，分别到三个路口疏导交通，每个路口有1名或2名志愿者，则甲、乙两人在同一路口的概率为 （用数字作答）． 11．已知函数9()f x x a a x=+-+在区间[1,9]上的最大值是10，则实数a 的取值范围 是 ．12．已知点C 是平面ABD 上一点，,1,33BAD CB CD π∠===．若AP AB AD =+u u u r u u u r u u u r ，则AP u u u r的最大值为 ．二、选择题（本大题共有4题，满分20分）【每题有且只有一个正确答案，考生应在答题纸的相应编号上，将代表答案的小方格涂黑，选对得5分，否则一律得零分．】高三数学 共4页 第2页13．下列函数中既是奇函数，又在区间(0,)+∞上单调递减的函数为A．y =B ．12log y x =C ．3y x =-D ．1y x x=+14．对于实数x ，“||1x <”是“1x <”的 A ．充分不必要条件 B ．必要不充分条件C ．充分必要条件D ．既不充分也不必要条件15．已知线段AB 上有一动点D （D 异于A 、B ），线段CD AB ⊥，且满足2CD AD BD λ=⋅（λ是大于0且不等于1的常数），则点C 的运动轨迹为A ．圆的一部分B ．椭圆的一部分C ．双曲线的一部分D ．抛物线的一部分16．在平面直角坐标系中，已知(1,0)A -、(1,0)B ．若对于y 轴上的任意n 个不同的点12,,n P P P L ，总存在两个不同的点,(,1,2,,)i j P P i j n =L ，使得1sin sin 4i jAPB AP B ∠-∠≤，则n 的最小值为 A ．3 B ．4 C ．5 D ．6三、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相应编号的规定区域内写出必要的步骤．】17．（本题满分14分，本题共有2个小题，第(1)小题满分7分，第(2)小题满分7分） 已知在直三棱柱111ABC A B C -中，1901BAC AB BB ∠=︒==，，直线1B C 与平面ABC 成30︒的角．（1）求三棱锥11C AB C -的体积；（2）求二面角1B B C A --的余弦值．18．（本题满分14分，本题共有2个小题，第(1)小题满分6分，第(2)小题满分8分）已知函数12lg ,(6)()5,(6)4a x a x f x x x x ⎧+⎪⎪-=⎨-⎪>⎪-⎩≤ （1）已知(6)3f =，求实数a 的值；（2）判断并证明函数在区间[7,8]上的单调性．B C A 1B 1C 1高三数学 共4页 第3页19．（本题满分14分，本题共有2个小题，第(1)小题满分5分，第(2)小题满分9分） 某公园内有一块以O 为圆心半径为20米的圆形区域．为丰富市民的业余文化生活，现提出如下设计方案：如图，在圆形区域内搭建露天舞台，舞台为扇形OAB 区域，其中两个端点A ，B 分别在圆周上；观众席为等腰梯形ABQP 内且在圆O 外的区域，其中AP AB BQ ==，23PAB QBA π∠=∠=，且AB PQ ，在点O 的同侧．为保证视听效果，要求观众席内每一个观众到 舞台中心O 处的距离都不超过60米（即要求60PO ≤）．设,0,3OAB παα⎛⎫∠=∈ ⎪⎝⎭．（1）当6πα=时，求舞台表演区域的面积； （2）对于任意α，上述设计方案是否均能符合要求？20．（本题满分16分，本题共有3个小题，第(1)小题满分4分，第(2)小题满分6分，第(3)小题满分6分）对于直线l 与抛物线2:4x y Γ=，若l 与Γ有且只有一个公共点且l 与Γ的对称轴不平行（或重合），则称l 与Γ相切，直线l 叫做抛物线Γ的切线．（1）已知00(,)P x y 是抛物线上一点，求证：过点P 的Γ的切线l 的斜率02x k =； （2）已知00(),M x y 为x 轴下方一点，过M 引抛物线的切线，切点分别为1122(,)(,)A x y B x y ，．求证：102,,x x x 成等差数列；（3）如图所示，(,)D m n 、(,)E s t 是抛物线Γ上异于坐标原点的两个不同的点，过点D 、E 的Γ的切线分别是12,l l ，直线12,l l 交于点(,)G a b ，且与y 轴分别交于点1D 、1E ．设12x x 、为方程20(,)x ax b a b R -+=∈的两个实根，max{,}c d 表示实数,c d 中较大的值．求证：“点G 在线段1DD 上”的充要条件是“12||max{||,||}2m x x =”．OABPQD E GE 1 D 1xy高三数学共4页第4页x y21．（本题满分18分，本题共有3个小题，第(1)小题满分4分，第(2)小题满分6分，第(3)小题满分8分）已知数列{}na是公差为(0)d d>的等差数列，如果数列*12,,,(3,)mx x x m m∈NL≥满足11221m ma x a x x a+<<<L≤≤≤，则称数列12,,,mx x xL是“可等距划分数列”．（1）判断数列2, 4, 8, 14是否是“可等距划分数列”，并说明理由；（2）已知,k t R∈，0k>，设nb kn t=+，求证：对任意的*3,m m∈N≥，数列{}(1,2,,)nb n m=L 都是“可等距划分数列”；（3）若数列{2}(1,2,,)n n m=L是“可等距划分数列”，求m的所有可能值．崇明区2018学年第二次高考模拟考试（数学）参考答案及评分标准一、填空题1.{2,4,5}；2. π；3. 2；4. 2-；5.22154x y+=； 6. 2；7.3或5；8. 2π；9.12-+；10.16；11. 8a≤；12.二、选择题13. C；14. A；15. B；16. C.三、解答题17.解：（1）1B B ABC⊥Q平面，130B CB∴∠=︒.....................................................2分又11AB BB==，BC∴=AC=1,BA AC BA AA⊥⊥Q，1BA ACC∴⊥平面，111B A ACC∴⊥平面..........................4分111111113C AB C B ACC ACCV V S B A--∴==⋅=V.....................................................7分（2）建立如图所示空间直角坐标系由题意，得：11,0),(0,0,1)BC BB=-=u u u r u u u r设平面1BB C的一个法向量为1(,,)n u v w=u r，则111n BCn BB⎧⋅=⎪⎨⋅=⎪⎩u r u u u ru r u u u r，即vw-==⎪⎩高三数学 共4页 第5页令1u =，则1n =u r同理，可得：平面1AB C 的一个法向量为2(0,1,1)n =-u u r................................4分设12,n n u r u u r 的夹角为θ，则1212cos 3||||n n n n θ⋅==⋅u r u u ru r u u r 又观察知二面角1B B C A --为锐角，∴二面角1B B C A --的余弦值是3.....................................................7分 18. 解：（1）(6)12lg36af a =+=-................................................3分 lg16aa ∴=-， ∴106a a =-，203a =....................................................6分（2）任取12,[7,8]x x ∈，设12x x <，则有111212121255()()44(4)(4)x x x x f x f x x x x x ----=-=----...................................................3分 因为1278x x ≤<≤，所以上式0<，即12()()f x f x <...................................................6分所以函数在区间[7,8]上单调递增...................................................8分19.解：（1）当6πα=时，23AOB π∠=所以舞台表演区域的面积2140023OABS r απ==扇形平方米.................................................5分（2）作OH AB ⊥于H ，则22cos 40cos AB AH OA αα==⋅= 在OAP V 中，22222cos()3OP OA AP OA AP πα=+-⋅+................................................2分2400(6cos cos 1)ααα=++400(3cos 224)αα=++................................................4分)16003πα=++................................................6分因为(0,)3πα∈，所以当12πα=时，max 60OP =<................................................8分所以对于任意α，上述设计方案均能符合要求................................................9分19. 解：（1）证明：由题意知，l 的斜率必然存在，设l 的方程为00()y y k x x -=-.............................................2分高三数学 共4页 第6页代入抛物线方程，得：2001()04x kx kx y -+-= 由题意，得：2000k kx y ∆=-+=，又2004x y =，所以20()02x k -=，所以02xk =.............................................4分（2）证明：由（1）知，直线MA 的方程是：111()2xy y x x -=-，直线MB 的方程是222()2xy y x x -=-.............................................2分由111222()2()2x y y x x x y y x x ⎧-=-⎪⎪⎨⎪-=-⎪⎩，得：211221()()22x x y y x x x x -=---所以222221211222244x x x x x x x -=-+- 因为12x x ≠，所以1202x x x +=，.............................................5分即102,,x x x 成等差数列.............................................6分（3）证明：由（1）知：1l ：()2my n x m -=-（*），故21(0,)4m D - 由（2）知：2m s a +=，代入（*）中，得：4ms b =，所以(,)24m s msG +.所以方程20x ax b +=-的两个根是12m x =，22sx =............................................2分设1DG GD λ=u u u r u u u u r ()R λ∈，则22(,)(,)244244s m ms m m s ms m λ-+-=-+ 所以22s m m s λ-+=-.............................................3分 ①必要性：当点G 在线段1DD 上时，有0λ≥， 所以()()0s m s m -+≤，所以||||s m ≤所以12||max{||,||}2m x x =②充分性：当12||max{||,||}2m x x =时，所以||||s m ≤，所以()()0s m s m -+≤所以0λ≥，所以点G 在线段1DD 上综上所述：“点G 在线段1DD 上”的充要条件是“12||max{||,||}2m x x =”.................6分21.解：（1）数列2, 4, 8, 14是“可等距划分数列”高三数学 共4页 第7页因为存在等差数列1,3,7,11,15-满足123478111415-≤<≤<≤<≤<................4分 (2) 证明：对任意的*3,m m ∈N ≥，设2n ka kn t =+-(1,2,,1)n m =+L ， 则对任意的{1,2,,}n m ∈L ，有1n n a a k +-=即数列{}n a (1,2,,1)n m =+L 是等差数列...............................................3分 又因为0k >，所以对任意的{1,2,,}n m ∈L ，有(1)22k k kn t kn t k n t +-≤+<++- 即满足11221m m a b a b b a +≤<≤<≤<L所以任意的*3,m m ∈N ≥，数列{}(1,2,,)n b n m =L 都是“可等距划分数列”...................6分（3）当3m =时，对于数列2,4,8存在等差数列0,3,6,9满足条件...................2分 当4m =时，对于数列2,4,8,16存在等差数列3,2.5,8,13.5,19-满足条件...................4分当5m ≥时，若存在等差数列121,,,m a a a +L 满足121242mm m a a a a +≤<≤<<≤<L则有1234562481632a a a a a a ≤<≤<≤<≤<≤<所以32826d a a =-<-=，62442428a a d =+<+=，与632a >矛盾 所以当5m ≥时，若数列{2}(1,2,,)n n m =L 不可能是“可等距划分数列”综上所述，m 的所有可能值是3,4.....................................................................8分更多高考数学信息，请关注。

崇明区2018届第二次高考模拟考试试卷语文考生注意：1．本考试设试卷和答题纸两部分，试卷包括试题与答题要求，所有答案必须写在答题纸上，做在试卷上一律不得分。

2．答题纸与试卷在试题编号上是一一对应的，答题时应特别注意，不能错位。

3．考试时间150分钟。

试卷满分150分。

一、积累应用（10分）1．按要求填空。

（5分）（1），断桥头卖鱼人散。

（马致远《双调··远浦帆归》）（2）由是则生而有不用也，。

（孟子《鱼我所欲也》）（3）黄庭坚《登快阁》中用典抒发因世无知己、怀才不遇之感慨的一联是“，”。

2．按要求选择。

（5分）（1）面对不合群、喜欢单打独斗的小明，以下句子最适合劝诫他的是（）（2分）A．君子周而不比，小人比而不周。

B．独学而无友，则孤陋而寡闻。

C．谦者众善之基，傲者众恶之魁。

D．梅须逊雪三分白，雪却输梅一段香。

（2）以下是一份讲座通知中的四句话，其中表述不得体的一句是（）（3分）(甲)为了更好地向同学们普及健康知识，(乙)提高同学们的防病意识，(丙)我们特邀请专家作题为“健康校园，防患未然”的讲座。

(丁)届时欢迎同学们光顾。

A．（甲） B.（乙） C.（丙）D．（丁）二、阅读（一）阅读下文，完成第3－8题。

（16分）面“壁”自视潘飞①从物质形态来看，“壁”是砖的累积物，但在某些特有的情境里，它却是话语和情感流泻的媒介。

比如，佛教第二十八代祖师菩提达摩在少林寺面壁修行长达九年，一言不发，出洞时奇迹般地把自己的影子留在了墙壁上。

他在《入道四行观》中将此举喻为“凝住壁观”，意在提醒人们遇到一切境界，心无贪爱取舍，不生烦恼嗔恨。

这一点．．．足以被新近出版的《壁上观：细读山西古代壁画》所证：死硬的“壁”生发出镜照功能，供人观视自我，感受“诸天宫殿，近处虚空，人天交接，两得相见”的艺术氛围。

在壁画总量已达上万平方米的“佛国圣地”——中国文物大省山西的那一千余座大小不等的庙宇中，古代的画工在墙壁上作画，将信仰、敬畏、崇拜、祈祷等精神内涵付诸于笔下，镌刻于墙上，从而令内心所想固凝为永恒之态，便应和了此意。

崇明区2018届第二次高考模拟考试试卷英语（考试时间120分钟，满分140分。

请将答案填写在答题纸上）I. 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. In a train. B. In a theater. C. In a meeting room. D. In a booking office.2. A. $2.4. B. $4.8. C. $7.2. D. $9.6.3. A. A waitress. B. A customer. C. A secretary. D. A saleswoman.4. A. The man’s air-conditioner is broken. B. The man doesn’t have air-conditioning.C. The summer has been unusually hot.D. The man hasn’t been using his air-conditioner.5. A. She’s enjoying the music. B. The music doesn’t bother her.C. She would prefer different music.D. The music will keep her awake.6. A. She acted like a stranger today. B. She usually talks quietly.C. She didn’t give the lesson today.D. She usually assigns homework.7. A. A job opportunity. B. A position as general manager.C. A travel experience.D. A sales manager’s experiences.8. A. She has had her camera broken. B. She hasn’t handed in her photo.C. She has been busy taking photos.D. She hasn’t ordered a student’s card.9. A. He hasn’t prepared well for his lecture.B. He wants the woman to postpone the lecture.C. He doesn’t know anything about engineering.D. He regularly gives lectures to high school students.10. A. It’s more effective if priority is given to listening.B. It’s less effective if reading comes before listening.C. It’s more effective if listening is combined with reading.D. It’s less effective if the learner checks the same information.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 them. The passages and the conversation 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 is the best answer to the question you have heard.第1页/ 共15页Questions 11 through 13 are based on the following passage.11. A. To provide a protective space for giant pandas.B. To stop the loss of giant pandas’natural habitats.C. To help China to improve its economy on the whole.D. To protect the giant pandas in the proposed territory.12. A. About 300. B. Around 1864. C. More than 2,000. D. Less than 1564.13. A. The park first began to be constructed in January 2017.B. 1.5 billion yuan will be invested in the construction of the park.C. The park will cover a bit more space than Yellowstone National Park.D. The place where the park is to be constructed is a poverty-stricken area.Questions 14 through 16 are based on the following passage.14. A. Smart mirrors that make you look much smarter.B. Software apps that allow you to add images to photos.C. Virtual mirrors that teach you to use camera functions.D. Special apps that help you see your image after try-on.15. A. They can make it easy for customers to make up.B. They can help stores avoid damage, loss and theft.C. They can teach users how to make smart products.D. They can improve the effect of products on customers.16. A. They promote both online and offline businesses.B. They have high requirements for mobile devices.C. They enable customers to interact with each other.D. They are quite similar to previous apps like Snapchat.Questions 17 through 20 are based on the following conversation.17. A. Their great food and free drinks for lunch.B. The numerous benefits of drinking hot liquids.C. The way to get rid of unhealthy drinking habits.D. Their different perspectives on hot and cold drinks.18. A. By causing sweat. B. By increasing blood flow.C. By helping ease pain.D. By emitting pleasant smells.19. A. It slows down blood flow. B. It makes one consume more.C. It helps one become slimmer.D. It is good for one’s digestion.20. A. The man prefers hot drinks only on very cold days.B. The woman may change her habit of drinking cold liquids.C. The woman believes drinking cold water also helps relieve a cold.D. The man is trying losing weight by exercising and drinking hot water.第2页/ 共15页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.China’s Good Samaritan Law (见义勇为法) Takes EffectChina’s Good Samaritan Law went into effect on October 1 to encourage people who are ready to help others. Under the law, people who voluntarily offer emergency assistance to those who are, or who they believe to be, injured, ill or in danger, will not have civil responsibility in the event of harm to the victims.The new law aims to ease the reluctance people feel toward helping strangers for fear of legal consequences if they make mistakes in treatment. It is a response to the phenomenon of people (21)_____ (hesitate) to help fallen senior citizens due to concern that they might be blackmailed (讹诈) later.There has been no shortage of cases over the past decade (22)_____ people hesitated to offer assistance to those who are in need. And some good Samaritans have been blackmailed for charitable acts. In 2011, a two-year-old girl known as Xiao Yueyue was run over by two cars, and 18 people passed by (23)_____ offering emergency help. The girl died after days of medical treatment. In 2014, a man from Guangdong Province aided a senior citizen, but (24)_____ (accuse) of knocking him down. The man committed suicide when (25)_____ (face) with demands for a large sum of money.These cases (26)_____ (arouse) debate about morality and heroism in China in recent years. “If you don’t provide help, you will blame yourself, but if you do help, you are likely (27)_____ (hurt) by the people you help. It is really a difficult choice,” one netizen said on Sina Weibo.(28)_____ there had been calls for a national Good Samaritan law, only a few cities pushed ahead with such laws before the nationwide law came into effect.However, some experts are concerned (29)_____ there could be some danger from a nationwide Good Samaritan Law. “Rescuers who know little about first aid could bring serious harm to people in critical conditions,”said Yang Lixin, a professor at the Renmin University of China. He hoped the government (30)_____ introduce details of the policy soon while encouraging people to voluntarily offer assistance.Section BDirections: After reading the passage below, fill in each blank with a proper word given in the box. Each word can only be used once. Note that there is one word more than you need.第3页/ 共15页Bob Dylan has won the 2016 Nobel Prize in literature. The productive musician is the first Nobel winner to have followed a career primarily as a singer-songwriter. What’s more, he’s also the first American to have won the prize in more than two decades. Not since novelist Toni Morrison won in 1993 has an American 31 the prize.Dylan earned the prize “for having 32 new poetic expressions within the great American song tradition,” according to the statement by the Swedish Academy, the committee that annually decides the winner of the Nobel Prize. The academy’s permanent secretary, Sara Danius, announced the news Thursday.The win comes as something of a(n) 33 . As usual, the Swedish Academy did not announce a shortlist of nominees (被提名者), leaving the betting markets to their best 34 . And while Dylan has enjoyed favor as an outside shot for the award, the 35 that the musician would be the one to break the Americans’ long dry period was regarded as unlikely—especially because he made his career mainly on the stage, not the 36 page.Yet few would argue Dylan has been anything but 37 , both in the U.S. and beyond its borders. The productive singer, songwriter and multi-instrumentalist has produced dozens of albums. Dylan, who was born Robert Allen Zimmerman in 1941, “has the status of an idol (偶像),” the Swedish Academy wrote. “His influence on contemporary music is significant, and he is the object of a steady stream of 38 literature.”In an interview following the announcement, Danius 39 the Swedish Academy’s decision: “He is a great poet in the English-speaking tradition, and he is a wonderful sampler—a very original sampler,” Danius explained. “For 54 years now he has been at it and reinventing himself, constantly creating a new identity.”And for his work, he has been 40 by critical community. Dylan has won Grammys, an Academy Award, a Golden Globe and a Medal of Freedom, the highest civilian honor in the U.S. Now, to the honors Dylan has added a Nobel.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.The Companies Doing the Most to Make Their Employees Happier Fat paychecks, light workloads, and endless vacation days don’t necessarily add to happy employees. In fact, the happiest employees in the U.S. owe their happiness to first-rate employee motivations, sufficient benefits, career advancement programs, and great work-life balance. The companies that have been the most devoted to cultivating and advancing these things in the past year have seen employee happiness 41 .The jobs site just announced the winners of this year’s “Leap Awards,” which honor the companies that have made the biggest leaps to improve employee happiness year-over-year. CareerBliss evaluated more than 250,000 company reviews and ratings it received from 42第4页/ 共15页nationwide to determine the top 50 deserving companies. To 43 the list, each company had to have at least 50 reviews.“The Leap Awards are important because they highlight 44 in our workforce,” says CareerBliss’s chief executive, Heidi Golledge. CareerBliss asked the respondents to evaluate the key factors that 45 work happiness, including work-life balance, one’s relationship with the boss and co-workers, the work environment, job resources, salary, growth opportunities, company culture, company reputation, daily tasks, and job 46 .Each respondent valued each of these things on a 1-to-5 scale, and indicated how important each was to their overall happiness at work. These numbers were 47 to find an average rating of overall employee happiness for each company. These averages were compared to last year’s numbers to find which companies had 48 the most.“Every employer who receives a Leap Award should 49 their workplace happiness in itiatives,” says Golledge. “Even though we are coming out of a difficult time, it is 50 to see companies putting their efforts into providing a great environment for their employees. These efforts in workplace happiness will ensure that their employees will be around for years to come, as happiness breeds 51 .”“We find each year that work-life balance is a key factor in determining employee happiness,” says Golledge. “Employees want to know that they can balance their career with their family and pe rsonal life. Often this 52 over things like salary. Having programs that allow managers to offer employees flexibility can be a key factor in creating a happy work environment. 53 , we see career advancement programs have a big impact on overall employee happiness. Often employees would rather take a job for a 54 salary, if the company provides a comprehensive program which will help grow their career. Employees want to learn, develop and sustain a successful career path.”Workplace happiness is the core of CareerBliss’ mission, Miller says. “A n individual’s happiness at work will create happiness throughout all areas of their life, and 55 a company with a happy, motivated workforce will see exceptional results in its products and services.”41. A. soar B. change C. cease D. disappear42. A. netizens B. administrators C. candidates D. employees43. A. make up B. qualify for C. count on D. refer to44. A. change B. power C. duty D. variety45. A. lay in B. resulted from C. focused on D. contributed to46. A. analysis B. vacancy C. flexibility D. responsibility47. A. applied B. combined C. compared D. remembered48. A. benefited B. improved C. changed D. produced49. A. approve of B. account for C. take pride in D. get used to50. A. good B. easy C. impossible D. interesting51. A. profit B. honesty C. creativity D. loyalty52. A. turns B. runs C. advantages D. skips53. A. However B. Otherwise C. Besides D. Instead54. A. lower B. fair C. regular D. similar55. A. obviously B. frankly C. fortunately D. similarly第5页/ 共15页Section 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）In the world of higher education in the United States, competition seems more common than schools working together. Every college and university competes for students, as well as the best teachers and money for research programs.But one thing almost every school has in common is the difficulty they face in serving low-income students. The National Center for Education Statistics reports that low-income college students are less likely to complete their study programs than other students.It was only natural that the leaders of Michigan State University and ten other universities discussed this issue when they met in 2014. The 11 schools are spread across the United States and serve different populations and needs. But their leaders all saw improving graduation rates for all students as the biggest problem facing American higher education.So the group created an organization called the University Innovation Alliance or UIA for sharing information related to this problem. Its main goal is to get 68,000 more students at the member schools to graduate by 2025, with at least half of those students being low-income. The 11 schools now say their number of graduates has increased by over 7,200 in just three years. This includes an almost 25 percent increase in the number of low-income graduates.How were they able to make this happen? It began with each university looking at its own situation and finding out what it had been doing right and what it had been doing wrong.For example, before joining the UIA, academic advising at Michigan State mostly involved reacting to problems students faced after the problems had already arisen. Then school officials heard about a computer program that fellow UIA member Georgia State University was using. This computer program follows decisions students make about their classes and the progress they are making in their studies. It then sends academic advisors messages whenever a student shows signs that they are making mistakes or facing difficulties. That way the advisors can try to help students before the problems become too serious. Michigan State began using the computer program and it has meant a world of difference. Michigan State has not only received useful information from its partners. It has also shared helpful information of its own.Bridget Burns, the executive director for the UIA, says efforts like this have never been as successful. “There are rankings that measure all kinds of things,” Burns said. “But how well you do for low-income students has not historically been highlighted.”56. What led to the setting up of the UIA?A. The low graduation rates.B. The great need of low-income students.C. The inefficiency of learning.D. The severe competition between schools.57. The UIA functions in such a way as the member universities _____.A. find out their own graduation ratesB. share and follow each other’s good practice第6页/ 共15页C. make joint efforts to aid students financiallyD. popularize computer programs among students58. By “it has meant a world of difference” in paragraph 6, the author means Michigan State _____.A. has found the computer program quite different from theirsB. has discovered the computer program is very difficult to useC. has helped students successfully with the computer programD. has involved more academic advisors in the computer program59. Which of the following might be the best title for the passage?A. Universities Highlighting Their Efforts for Low-IncomesB. Universities Competing for Better Students and TeachersC. Universities Working Together to Help Poor StudentsD. Universities Creating the UIA to Share Information（B）We want to make the world a better, fairer place. We want to keep the powerful honest. And we believe that doing so means keeping society informed by producing quality, independent journalism, which discovers and tells readers the truth.It’s essential for the functioning of democracy. And our unique ownership structure means no one can tell us to drop a story.But it’s difficult and expensive work. While more people are reading the Guardian than ever before, far fewer are paying for it. And advertising incomes across the media are falling fast.So if you read us, if you like us, if you value our perspective—then become a Supporter and help make our future more secure.As a Guardian Supporter, you’ll enjoy a number of benefits, Supporters get closer tothe Guardian第7页/ 共15页Why do we need our Supporters?Like many other media organisations, the Guardian is operating in anincredibly challenging financial climate. Our advertising incomes arefalling fast. We have huge numbers of readers, and we are increasinglyreliant upon their financial support.We don’t have a wealthy owner pulling the strings. No shareholders,advertisers or billionaire owners can edit our editor.Our owner, the Scott Trust, protects our editorial independence from commercial or political interference (干涉). It reinvests income into our journalism, not into shareholders’ pockets.But while the Scott Trust ensures our independence, we need our Supporters, now more than ever before, to help secure our future.We know that not everyone is in a position to become a Supporter. But if you can, you’ll be an essential part of our mission to make the world a better, fairer place, for everyone.60. The above webpage mainly aims to _____.A. raise funds from readersB. inform readers of quality journalismC. attract more readersD. guarantee readers a secure future61. Which of the following is a difficulty the Guardian is facing?A. It’s losing its editorial independence.B. It’s becoming increasingly reliant on its owner.C. It’s profiting much less from advertising.D. It’s operating in a challenging political climate.62. What can be inferred from the webpage?A. Some billionaire owners are the Guardian’s editors.B. The Guardian is independent financially and politically.C. Shareholders can interfere with the Guardian’s journalism.D. Guardian Supporters can put ads on the mobile app for free.（C）A new kind of production was underway on the set of the NBC comedy Superstore. Social media stars were crafting 30-second videos to post on their social media channels ahead of the comedy’s second-season return. Each made sure to mention Superstore and its first public show.As networks and studios struggle to reach young audiences in an increasingly fragmented (碎片化的) media marketplace, many have turned to so-called influencers—online stars whose value is measured by the size of their Internet followings—as a means of generating awareness. Advertisers are seizing on the strategy in an age of commercial-skipping and ad-blockers. Word of mouth in the digital age means messages travel faster by way of social media. The majority of consumers worldwide trust online recommendations from stars. And when Superstore gave its first public show, it did so to higher ratings than the last show of Season 1.Studio and network executives say they work with influencers to build brand awareness and reputation in a more friendly way through the friend-like connections consumers feel toward the online personalities they follow. At the upper level, influencers typically have thousands of followers on social第8页/ 共15页media and online content platforms and count many millions of people who tune in daily to watch them. Some do something that makes themselves look stupid in their daily routine, sharing videos of their trips to the grocery store or dinner dates. Others have built careers on performances—making comedy videos, reviewing video games, performing magic tricks and teaching cooking lessons, among other pursuits.When in the employ of studios, their efforts can be as simple as publicizing a film or more involved attempts like the marketing push for Superstore. Entertainment companies declined to discuss how much they pay influencers. But several experts said their pay ranges from a few thousand dollars to several million. Some simply receive gift baskets instead of pay.Over the last year or so, some entertainment companies have begun to cast influencers in their TV and film projects. The strategy is a bit of a gamble: It’s a new business model, and questions remain about the effectiveness of using these personalities to improve a show’s ratings—or help open a movie. Just how much influence the influencers have is hard to measure. TV ratings and box-office returns do not reveal what caused a viewer to tune in.What is clear is that these personalities aren’t necessarily getting the work because of their acting skills, but often because of their Internet followings. Yet as social media stars consider whether to take on jobs promoting movies and TV shows, there’s an important consideration for both parties: the credibility of a campaign. “Fans are definitely aware when they’re being tempted with promotional posts,” said Zach King, a social media star who performs magic tricks. “It has to be something that is natural and fits with the image of the creator.”63. Why did social media stars post short videos on their channels before Superstore’s second season?A. To attract more influencers.B. To draw audience’s attention.C. To put on better performances.D. To increase the channels’ popularity.64. Advertisers like the influencer marketing strategy because _____.A. audiences believe in whatever online stars recommendB. influencers are quite aware of the impact of the digital ageC. ordinary advertisements are often ignored by young peopleD. social media platforms are the cheapest place to spread messages65. What is implied in the passage?A. The influencer marketing strategy help build connections between executives.B. Most influencers get paid from gift baskets instead of from their companies.C. Most influencers take on marketing jobs regardless of their reliability.D. The influencer marketing strategy may not really work well.66. The passage mainly wants to tell us that _____.A. most young people like following influencersB. studios are relying more on social media starsC. influencers are gradually replacing movie starsD. social media are filming videos for Superstore第9页/ 共15页Section 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.Feel Young at Heart and You’ll Enjoy a Longer LifeAge-liars and birthday-deniers... you’d best learn a thing or two from those who are young at heart. People who feel younger than their actual age may live longer than those who feel older than they truly are, a new study says.67 Results from the study, published in the Journal of the American Medical Association, suggest that people who feel a year or more older than they truly are could have around 41 percent greater risk for death.Researchers looked at nearly 6,500 older adults, with an average age of 65.8 for the study. Around 70 percent of them felt younger than they were, about a quarter felt their precise age and just under 5 percent felt a year or more older than they were, when asked “How old do you feel you are?”Those who felt older than they were had a higher death rate after a follow-up period of 99 months. While just 14.3 and 18.5 percent of people who felt younger or felt their age, respectively, died during those 99 months, 24.6 percent of those who felt aged beyond their years had died.The authors say more research is needed on the topic, but suggest it could be that those who feel “young at heart” have healthier behaviors and a stronger will to live. “ 68 Individuals who feel older could be targeted with health messages promoting positive health behaviors and attitudes toward aging,” the authors write in the study.The good news is that you can change your feeling of how young you are. 69 One recent study found that helping participants have positive feelings toward age, by showing them positive word associations, helped older adults improve in physical tasks like balancing and getting up out of a chair, in as little as four weeks. Another study found that negative feeling of aging and poor memory can make older adults feel up to five years older, regardless of their actual mental abilities.There you have it. 70第10页/ 共15页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.Do Smartphones Make Us Smarter?Should teachers allow cellphones in a classroom? A recent study on the way smartphones disturb learning might help explain the issue. Researchers published findings showing how students were affected by their phones in the classroom. They explored the differences in student performance in four situations: open phone use allowed, phones allowed in the classroom but could not be used, no phones in the classroom and a no-instruction control group. After watching a 20-minute video, students took a short quiz. The result was that the students in a room without any cellphones performed significantly better on the test. Scientists believe the way we attach ourselves to our phones could be the problem.Smartphones have become so strongly established in society that many people are lost without them. We are now in an age when many people can’t imagine life without a phone. There is even a name for the anxiety caused by not having one—nomophobia, which is the powerful feeling people get when they don’t have signal, their battery is about to die, or they are separated from their phones. Their fear of missing out on important information or connections can have a controlling effect on their lives and can divide their attention from other important things like learning.So does information technology help or block the way we think? In the past, people relied heavily on specific knowledge and knew who in their circle of friends would be most likely to know things in different subjects. Now, our friend with all the information is the Internet. Indications are that people don’t remember information as well if they know they can use a computer or phone to recall it quickly. So it may be more difficult to move information from the Internet into our long-term memory.But the impact of being exposed to so much information isn’t all bad. Reports show that frequent Internet use can strengthen fast-paced problem solving and can speed up the ability to spot patterns in a lot of data.V. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.72. 何不利用这宜人的天气出去野餐呢？(advantage)73. 当你对情况一知半解时，不要随意发表见解。

崇明区2018届第二次高考模拟考试试卷英语（考试时间120分钟，满分140分。

请将答案填写在答题纸上）I.ListeningComprehension5.A.She’8.A.Shehashadhercamerabroken. B.Shehasn’thandedinherphoto.C.Shehasbeenbusytakingphotos.D.Shehasn’torderedastudent’scard.9.A.Hehasn’tpreparedwellforhislecture.B.Hewantsthewomantopostponethelecture.C.Hedoesn’tknowanythingaboutengineering.仅供个人学习参考D.Heregularlygiveslecturestohighschoolstudents.10.A.It’smoreeffectiveifpriorityisgiventolistening.B.It’slesseffectiveifreadingcomesbeforelistening.C.It’smoreeffectiveiflisteningiscombinedwithreading.D.It’slesseffectiveifthelearnerchecksthesameinformation. SectionBB.Softwareappsthatallowyoutoaddimagestophotos.C.Virtualmirrorsthatteachyoutousecamerafunctions.D.Specialappsthathelpyouseeyourimageaftertry-on.15.A.Theycanmakeiteasyforcustomerstomakeup.仅供个人学习参考B.Theycanhelpstoresavoiddamage,lossandtheft.C.Theycanteachusershowtomakesmartproducts.D.Theycanimprovetheeffectofproductsoncustomers.16.A.Theypromotebothonlineandofflinebusinesses.B.Theyhavehighrequirementsformobiledevices.C.Theyenablecustomerstointeractwitheachother.SectionADirections:Afterreadingthepassagebelow,fillintheblankstomakethepassagecoherentandgrammaticallycorr ect.Fortheblankswithagivenword,fillineachblankwiththeproperformofthegivenword;fortheotherblanks,use onewordthatbestfitseachblank.China’s GoodSamaritanLaw(见义勇为法)TakesEffect仅供个人学习参考China’sGoodSamaritanLawwentintoeffectonOctober1toencouragepeoplewhoarereadytohelpothers.U nderthelaw,peoplewhovoluntarilyofferemergencyassistancetothosewhoare,orwhotheybelievetobe,injured,i llorindanger,willnothavecivilresponsibilityintheeventofharmtothevictims.Thenewlawaimstoeasethereluctancepeoplefeeltowardhelpingstrangersforfearoflegalconsequencesifth eymakemistakesintreatment.Itisaresponsetothephenomenonofpeople(21)_____(hesitate)tohelpfallensenior citizensduetoconcernthattheymightbe blackmailed(讹诈)later.Therehasbeennoshortageofcasesoverthepastdecade(22)_____peoplehesitatedtoofferassistancetothose whoareinneed.AndsomegoodSamaritanshavebeenblackmailedforcharitableacts.In2011,atwo-year-oldgirlk仅供个人学习参考仅供个人学习参考50.A.good B.easy C.impossible D.interesting51.A.profit B.honesty C.creativity D.loyalty52.A.turns B.runs C.advantages D.skips53.A.However B.Otherwise C.Besides D.Instead仅供个人学习参考54.A.lower B.fair C.regular D.similar55.A.obviously B.frankly C.fortunately D.similarlySectionBDirections:Readthefollowingthreepassages.Eachpassageisfollowedbyseveralquestionsorunfinishedstatem ents.ForeachofthemtherearefourchoicesmarkedA,B,CandD.Choosetheonethatfitsbestaccordingtotheinform ationgiveninthepassageyouhavejustread.（A）仅供个人学习参考56.WhatledtothesettingupoftheUIA?A.Thelowgraduationrates.B.Thegreatneedoflow-incomestudents. Wewanttomaketheworldabetter,fairerplace.Wewanttokeepthepowerfulhonest.Andwebelievethatdoingsomeanskeepingsocietyinformedbyproducingquality,independentjournalism,whichdiscoversandtellsreadersthetruth.It’sessentialforthefunctioningofdemocracy.Andouruniqueownershipstructuremeansnoon ecantellustodropastory.akeourfuturemoresecure.仅供个人学习参考Likemanyothermediaorganisations,theGuardianisoperatinginanincrediblychallengingfin ancialclimate.Ouradvertisingincomesarefallingfast.Wehavehugenumbersofreaders,andw Wedon’thaveawealthyownerpullingthestrings.Noshareholders,advertisersorbillionaireo60.Theabovewebpagemainlyaimsto_____.A.raisefundsfromreadersrmreadersofqualityjournalismC.attractmorereadersD.guaranteereadersasecurefuture61.WhichofthefollowingisadifficultytheGuardianisfacing?仅供个人学习参考A.It’slosingitseditorialindependence.B.It’sbecomingincreasinglyreliantonitsowner.C.It’sprofitingmuchlessfromadvertising.D.It’soperatinginachallengingpoliticalclimate.62.Whatcanbeinferredfromthewebpage?A.SomebillionaireownersaretheGuardian’seditors.B.TheGuardianisindependentfinanciallyandpolitically.C.ShareholderscaninterferewiththeGuardian’sjournalism.仅供个人学习参考63.Whydidsocialmediastarspostshortvideosontheirchannelsbefore Superstore’ssecondseason?A.Toattractmoreinfluencers.B.Todrawaudience’sattention.C.Toputonbetterperformances.D.Toincreasethechannels’popularity.64.Advertisersliketheinfluencermarketingstrategybecause_____.A.audiencesbelieveinwhateveronlinestarsrecommendB.influencersarequiteawareoftheimpactofthedigitalage仅供个人学习参考FeelYoungatHeartandY ou’ll EnjoyaLongerLife67Resultsfromthestudy,publishedintheJournaloftheAmericanMedicalAssociation,suggestthatpeoplewThereyouhaveit.70IV.SummaryWritingDirections:?Readthefollowingpassage.Summarizethemainideaandthemainpoint(s)ofthepassageinnomoret eyourownwordsasfaraspossible.?仅供个人学习参考DoSmartphonesMakeUsSmarter?Shouldteachersallowcellphonesinaclassroom?Arecentstudyonthewaysmartphonesdisturblearningmigh thelpexplaintheissue.Researcherspublishedfindingsshowinghowstudentswereaffectedbytheirphonesinthecl assroom.Theyexploredthedifferencesinstudentperformanceinfoursituations:openphoneuseallowed,phonesa llowedintheclassroombutcouldnotbeused,nophonesintheclassroomandano-instructioncontrolgroup.Afterw atchinga20-minutevideo,studentstookashortquiz.Theresultwasthatthestudentsinaroomwithoutanycellphone sperformedsignificantlybetteronthetest.Scientistsbelievethewayweattachourselvestoourphonescouldbethep roblem.72.73.74.到底是什么促使你放弃了这么稳定的工作，来到这个偏远地区保护野生动物？(it)75.人工智能正以如此快的速度改变着整个世界，你很难预测未来的生活究竟会是什么样子。

2018年上海市崇明区高考数学二模试卷一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1．（4分）已知集合U={﹣1，0，1，2，3}，A={﹣1，0，2}，则∁U A=．2．（4分）已知一个关于x、y的二元一次方程组的增广矩阵是，则x+y= 3．（4分）i是虚数单位，若复数（1﹣2i）（a+i）是纯虚数，则实数a的值为．4．（4分）若=0，则x=．5．（4分）我国古代数学名著《九章算术》有“米谷粒分”题：粮仓开仓收粮，有人送来米1534石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为石（精确到小数点后一位数字）6．（4分）已知圆锥的母线长为5，侧面积为15π，则此圆锥的体积为（结果保留π）．7．（5分）若二项式（2x+）7的展开式中一次项的系数是﹣70，则（a+a2+a3+…+a n）=8．（5分）已知椭圆（a＞0）的焦点F1、F2，抛物线y22x的焦点为F，若=3，则a=9．（5分）设f（x）是定义在R上以2为周期的偶函数，当x∈[0，1]时，f（x）=log2（x+1），则函数f（x）在[1，2]上的解析式是10．（5分）某办公楼前有7个连成一排的车位，现有三辆不同型号的车辆停放，恰有两辆车停放在相邻车位的概率是11．（5分）已知x，y∈R，且满足，若存在θ∈R使得xcosθ+ysinθ+1=0成立，则点P（x，y）构成的区域面积为12．（5分）在平面四边形ABCD中，已知AB=1，BC=4，CD=2，DA=3，则的值为．二.选择题（本大题共4题，每题5分，共20分）13．（5分）“x＞1”是“2x＞1”的（）A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件14．（5分）若1是关于x的实系数方程x2+bx+c=0的一个复数根，则（）A．b=2，c=3B．b=2，c=﹣1C．b=﹣2，c=3D．b=﹣2，c=﹣1 15．（5分）将函数y=sin（2x﹣）图象上的点P（，t）向左平移s（s＞0）个单位长度得到点P′，若P′位于函数y=sin2x的图象上，则（）A．t=，s的最小值为B．t=，s的最小值为C．t=，s的最小值为D．t=，s的最小值为16．（5分）在平面直角坐标系中，定义d（A，B）=max{|x1﹣x2|，|y1﹣y2|}为两点A（x1y1）、B（x2，y2）的“切比雪夫距离”，又设点P及l上任意一点Q，称d（P，Q）的最小值为点P到直线l的“切比雪夫距离”，记作d（P，t），给出下列三个命题：①对任意三点A、B、C，都有d（C，A）+d（C，B）≥d（A，B）；②已知点P（3，1）和直线l：2x﹣y﹣1=0，则d（P，l）=；③定点F1（﹣c，0）、F2（c，0），动点P（x，y）满足|d（P，F1）﹣d（P，F2）|=2a（2c＞2a＞0），则点P的轨迹与直线y=k（k为常数）有且仅有2个公共点；其中真命题的个数是（）A．0B．1C．2D．3三.解答题（本大题共5题，共14+14+14+16+18=76分）17．（14分）如图，在四棱锥P﹣ABCD中，底面ABCD为直角梯形，BC∥AD，AB⊥BC，∠ADC=45°，PA⊥平面ABCD，AB=AP=1，AD=3．（1）求异面直线PB与CD所成角的大小；（2）求点D到平面PBC的距离．18．（14分）已知点F1、F2依次为双曲线C：（a，b＞0）的左右焦点，|F1F2|=6，B1（0，﹣b），B2（0，b）．（1）若a=，以=（3，﹣4）为方向向量的直线l经过B1，求F2到l的距离；（2）若双曲线C上存在点P，使得=﹣2，求实数b的取值范围．19．（14分）如图，某公园有三条观光大道AB，BC，AC围成直角三角形，其中直角边BC=200m，斜边AB=400m，现有甲、乙、丙三位小朋友分别在AB，BC，AC大道上嬉戏，所在位置分别记为点D，E，F．（1）若甲、乙都以每分钟100m的速度从点B出发在各自的大道上奔走，到大道的另一端时即停，乙比甲迟2分钟出发，当乙出发1分钟后，求此时甲乙两人之间的距离；（2）设∠CEF=θ，乙丙之间的距离是甲乙之间距离的2倍，且∠DEF=，请将甲乙之间的距离y表示为θ的函数，并求甲乙之间的最小距离．20．（16分）已知函数f（x）=，x∈R．（1）证明：当a＞1时，函数y=f（x）是减函数；（2）根据a的不同取值，讨论函数y=f（x）的奇偶性，并说明理由；（3）当a=2，且b＜c时，证明：对任意d∈[f（c），f（b）]，存在唯一的x0∈R，使得f（x0）=d，且x0∈[b，c]．21．（18分）设数列{a n}的前n项和为S n，若（n∈N*），则称{a n}是“紧密数列”．（1）已知数列{a n}是“紧密数列”，其前5项依次为1，，求x的取值范围；（2）若数列{a n}的前n项和为S n=（n2+3n）（n∈N*），判断{a n}是否是“紧密数列”，并说明理由；（3）设{a n}是公比为q的等比数列，若{a n}与{S n}都是“紧密数列”，求q的取值范围．2018年上海市崇明区高考数学二模试卷参考答案与试题解析一.填空题（本大题共12题，1-6每题4分，7-12每题5分，共54分）1．（4分）已知集合U={﹣1，0，1，2，3}，A={﹣1，0，2}，则∁U A={1，3} ．【考点】1F：补集及其运算．【专题】11：计算题；37：集合思想；4O：定义法；5J：集合．【分析】利用补集定义直接求解．【解答】解：∵集合U={﹣1，0，1，2，3}，A={﹣1，0，2}，∴∁U A={1，3}．故答案为：{1，3}．【点评】本题考查补集的求法，考查补集定义等基础知识，考查运算求解能力，考查函数与方程思想，是基础题．2．（4分）已知一个关于x、y的二元一次方程组的增广矩阵是，则x+y= 5【考点】OC：几种特殊的矩阵变换．【专题】35：转化思想；4R：转化法；5R：矩阵和变换．【分析】根据增广矩阵求得二元一次方程组，即可求得x和y，即可求得答案．【解答】解：由增广矩阵是，则二元一次方程组，解得：x=3，y=2，∴x+y=5，故答案为：5．【点评】本题考查二元一次方程组的增广矩阵的求法，考查转化思想，属于基础题．3．（4分）i是虚数单位，若复数（1﹣2i）（a+i）是纯虚数，则实数a的值为﹣2．【考点】A1：虚数单位i、复数．【专题】5N：数系的扩充和复数．【分析】由复数代数形式的乘除运算化简，再由实部等于0且虚部不等于0求得a的值．【解答】解：由（1﹣2i）（a+i）=（a+2）+（1﹣2a）i为纯虚数，得，解得：a=﹣2．故答案为：﹣2．【点评】本题考查了复数代数形式的乘法运算，考查了复数为纯虚数的条件，是基础题．4．（4分）若=0，则x=4．【考点】4H：对数的运算性质．【专题】11：计算题；35：转化思想；49：综合法；51：函数的性质及应用．【分析】由二阶行列式展开式性质得2log2x﹣4=0，由此利用对数运算法则和性质能求出x．【解答】解：∵=0，∴2log2x﹣4=0，∴log2x=2，解得x=4．故答案为：4．【点评】本题考查对数性质及行列式性质的应用，是基础题，解题时要认真审题，注意行列式展开法则及对数性质、运算法则的合理运用．5．（4分）我国古代数学名著《九章算术》有“米谷粒分”题：粮仓开仓收粮，有人送来米1534石，验得米内夹谷，抽样取米一把，数得254粒内夹谷28粒，则这批米内夹谷约为169.1石（精确到小数点后一位数字）【考点】B2：简单随机抽样．【专题】38：对应思想；4O：定义法；5I：概率与统计．【分析】根据抽样比例求出这批米内夹谷的多少．【解答】解：根据题意，这批米内夹谷为1534×≈169.1（石）．故答案为：169.1．【点评】本题考查了频率、频数与样本容量的应用问题，是基础题．6．（4分）已知圆锥的母线长为5，侧面积为15π，则此圆锥的体积为12π（结果保留π）．【考点】L5：旋转体（圆柱、圆锥、圆台）．【专题】11：计算题；5F：空间位置关系与距离．【分析】设圆锥的底面半径为r，母线为l，高为h，根据侧面积公式算出底面半径r=3，用勾股定理算出高h==4，代入圆锥体积公式即可算出此圆锥的体积．【解答】解：设圆锥的底面半径为r，母线为l，高为h∵圆锥的母线长为l=5，侧面积为15π，∴×l×r=15π，解之得底面半径r=3因此，圆锥的高h==4∴圆锥的体积为：V=πr2h=×π×9×4=12π故答案为：12π【点评】本题给出圆锥母线长和侧面积，求它的体积，着重考查了圆锥的侧面积公式和体积公式等知识，属于基础题．7．（5分）若二项式（2x+）7的展开式中一次项的系数是﹣70，则（a+a2+a3+…+a n）=【考点】8J：数列的极限；DA：二项式定理．【专题】11：计算题；34：方程思想；49：综合法；55：点列、递归数列与数学归纳法；5P：二项式定理．=C n r a n﹣r b r来解决，在通项中令x的指数幂为1可求出【分析】利用通项公式T r+1含x是第几项，由此算出a．然后利用数列的极限的运算法则求解即可．【解答】解：由二项式定理的通项公式T r=C n r a n﹣r b r可设含x2项的项是+1T r+1=C7r（2x）7﹣r（）r=a r27﹣r C7r x7﹣2r，令7﹣2r=1，解得：r=3，∴系数为a324C73=﹣70，解得a=﹣，（a+a2+a3+…+a n）===，故答案为：．【点评】本题主要考查二项式定理中通项公式的应用，属于基础题型，数列的极限的运算法则的应用，考查计算能力．8．（5分）已知椭圆（a＞0）的焦点F1、F2，抛物线y22x的焦点为F，若=3，则a=【考点】KI：圆锥曲线的综合．【专题】11：计算题；34：方程思想；49：综合法；5D：圆锥曲线的定义、性质与方程．【分析】先根据椭圆和抛物线的方程分别求得其焦点坐标，根据=3，建立等式求得a的值即可．【解答】解：依题意可知抛物线的焦点为（，0），椭圆的焦点为（±，0），∵=3，∴=3（﹣），整理得a=，故答案为：．【点评】本题主要考查了椭圆和抛物线的简单性质．考查了学生基础知识的理解和应用以及基本的运算能力．9．（5分）设f（x）是定义在R上以2为周期的偶函数，当x∈[0，1]时，f（x）=log2（x+1），则函数f（x）在[1，2]上的解析式是f（x）=log2（3﹣x）【考点】36：函数解析式的求解及常用方法．【专题】11：计算题；33：函数思想；4O：定义法；51：函数的性质及应用．【分析】设x∈（1，2），则x﹣2∈（﹣1，0），2﹣x∈（0，1），由已知表达式可求得f（2﹣x），再由f（x）为周期为2的偶函数，可得f（x）=f（x﹣2）=f （2﹣x），从而得到答案．【解答】解：∵f（x）是定义在R上以2为周期的偶函数，当x∈[0，1]时，f（x）=log2（x+1），∴设x∈（1，2），则x﹣2∈（﹣1，0），2﹣x∈（0，1），∴f（2﹣x）=log2[（2﹣x）+1]=log2（3﹣x），又f（x）为周期为2的偶函数，所以f（x）=f（x﹣2）=f（2﹣x）=log2（3﹣x）．故答案为：f（x）=log2（3﹣x）．【点评】本题考查函数解析式的求解及函数的周期性、奇偶性，考查学生灵活运用所学知识解决问题的能力，属中档题．10．（5分）某办公楼前有7个连成一排的车位，现有三辆不同型号的车辆停放，恰有两辆车停放在相邻车位的概率是【考点】CB：古典概型及其概率计算公式．【专题】11：计算题；34：方程思想；4O：定义法；5I：概率与统计．【分析】基本事件总数n==35，恰有两辆车停放在相邻车位包含的基本事件个数m==20，由此能求出恰有两辆车停放在相邻车位的概率．【解答】解：某办公楼前有7个连成一排的车位，现有三辆不同型号的车辆停放，基本事件总数n==35，恰有两辆车停放在相邻车位包含的基本事件个数m==20，∴恰有两辆车停放在相邻车位的概率是p==．故答案为：．【点评】本题考查概率的求法，考查古典概型概率计算公式等基础知识，考查运算求解能力，考查函数与方程思想，是基础题．11．（5分）已知x，y∈R，且满足，若存在θ∈R使得xcosθ+ysinθ+1=0成立，则点P（x，y）构成的区域面积为4﹣【考点】7C：简单线性规划．【专题】31：数形结合；44：数形结合法；56：三角函数的求值；5T：不等式．【分析】作出不等式组表示的平面区域，求出xcosθ+ysinθ+1=0成立的等价条件，利用数形结合求出对应的面积，即可得出正确的结果．【解答】解：画出不等式组对应的平面区域如图所示：对应区域为三角形OAB，若存在θ∈R，使得xcosθ+ysinθ+1=0成立，则（cosθ+sinθ）=﹣1，令sinα=，则cosα=，则方程等价为sin（α+θ）=﹣1，即sin（α+θ）=﹣，∵存在θ∈R，使得xcosθ+ysinθ+1=0成立，∴|﹣|≤1，即x2+y2≥1，则对应的区域为单位圆的外部，由，解得，即B（2，2），又A（4，0），则△OAB的面积为S=×4×2=4；又直线y=x的倾斜角为，则∠AOB=，即扇形的面积为π•12=，则P（x，y）构成的区域面积为S=4﹣，故答案为：4﹣．【点评】本题主要考查了线性规划的应用问题，根据条件作出对应的图象，求出对应的面积是解题的关键．12．（5分）在平面四边形ABCD中，已知AB=1，BC=4，CD=2，DA=3，则的值为10．【考点】9O：平面向量数量积的性质及其运算；9S：数量积表示两个向量的夹角．【专题】11：计算题；34：方程思想；35：转化思想；49：综合法；5A：平面向量及应用；5D：圆锥曲线的定义、性质与方程．【分析】方向条件，四边形是椭圆的内接图形，利用椭圆的简单性质以及焦半径公式转化求解即可．【解答】解：AB+BC=DA+DC=5，所以把四边形放入椭圆内，AC为左右焦点，不妨令B（x1，y1），D（x2，y2）则2a=5，由焦半径公式可得ex1+a=1，ex2+a=3，两式相减可得：e（x1﹣x2）=2，而=2c（x1﹣x2）=2c=4a=10．故答案为：10．【点评】本题考查四边形对角线系列的数量积，椭圆的简单性质的应用，考查转化思想以及计算能力．二.选择题（本大题共4题，每题5分，共20分）13．（5分）“x＞1”是“2x＞1”的（）A．充分不必要条件B．必要不充分条件C．充分必要条件D．既不充分也不必要条件【考点】29：充分条件、必要条件、充要条件．【专题】35：转化思想；4O：定义法；5L：简易逻辑．【分析】根据不等式的关系，结合充分条件和必要条件的定义进行判断即可．【解答】解：由2x＞1得x＞0，则“x＞1”是“2x＞1”的充分不必要条件，故选：A．【点评】本题主要考查充分条件和必要条件的判断，结合不等式的关系是解决本题的关键．14．（5分）若1是关于x的实系数方程x2+bx+c=0的一个复数根，则（）A．b=2，c=3B．b=2，c=﹣1C．b=﹣2，c=3D．b=﹣2，c=﹣1【考点】&S：实系数多项式虚根成对定理．【专题】11：计算题；35：转化思想；49：综合法；5N：数系的扩充和复数．【分析】利用实系数一元二次的虚根成对原理、根与系数的关系即可得出．【解答】解：∵1+i是关于x的实系数方程x2+bx+c=0的一个复数根，∴1﹣i是关于x的实系数方程x2+bx+c=0的一个复数根，∴，解得b=﹣2，c=3．故选：C．【点评】本题考查了实系数一元二次的虚根成对原理、根与系数的关系，属于基础题．15．（5分）将函数y=sin（2x﹣）图象上的点P（，t）向左平移s（s＞0）个单位长度得到点P′，若P′位于函数y=sin2x的图象上，则（）A．t=，s的最小值为B．t=，s的最小值为C．t=，s的最小值为D．t=，s的最小值为【考点】HJ：函数y=Asin（ωx+φ）的图象变换．【专题】35：转化思想；4R：转化法；57：三角函数的图像与性质．【分析】将x=代入得：t=，进而求出平移后P′的坐标，进而得到s的最小值．【解答】解：将x=代入得：t=sin=，将函数y=sin（2x﹣）图象上的点P向左平移s个单位，得到P′（﹣s，）点，若P′位于函数y=sin2x的图象上，则sin（﹣2s）=cos2s=，则2s=+2kπ，k∈Z，则s=+kπ，k∈Z，由s＞0得：当k=0时，s的最小值为，故选：A．【点评】本题考查的知识点是函数y=Asin（ωx+φ）（A＞0，ω＞0）的图象和性质，难度中档．16．（5分）在平面直角坐标系中，定义d（A，B）=max{|x1﹣x2|，|y1﹣y2|}为两点A（x1y1）、B（x2，y2）的“切比雪夫距离”，又设点P及l上任意一点Q，称d（P，Q）的最小值为点P到直线l的“切比雪夫距离”，记作d（P，t），给出下列三个命题：①对任意三点A、B、C，都有d（C，A）+d（C，B）≥d（A，B）；②已知点P（3，1）和直线l：2x﹣y﹣1=0，则d（P，l）=；③定点F1（﹣c，0）、F2（c，0），动点P（x，y）满足|d（P，F1）﹣d（P，F2）|=2a（2c＞2a＞0），则点P的轨迹与直线y=k（k为常数）有且仅有2个公共点；其中真命题的个数是（）A．0B．1C．2D．3【考点】2K：命题的真假判断与应用．【专题】34：方程思想；48：分析法；5L：简易逻辑；5M：推理和证明．【分析】①讨论A，B，C三点共线，以及不共线的情况，结合图象和新定义，即可判断；②设点Q是直线y=2x﹣1上一点，且Q（x，2x﹣1），可得d（P，Q）=max{|x﹣3|，|2﹣2x|}，讨论|x﹣3|，|2﹣2x|的大小，可得距离d，再由函数的性质，可得最小值；③讨论P在坐标轴上和各个象限的情况，求得轨迹方程，即可判断．【解答】解：①对任意三点A、B、C，若它们共线，设A（x1，y1）、B（x2，y2），C（x3，y3），如图，结合三角形的相似可得d（C，A），d（C，B），d（A，B）为AN，CM，AK，或CN，BM，BK，则d（C，A）+d（C，B）=d（A，B）；若B，C或A，C对调，可得d（C，A）+d（C，B）＞d（A，B）；若A，B，C不共线，且三角形中C为锐角或钝角，如图，由矩形CMNK或矩形BMNK，d（C，A）+d（C，B）≥d（A，B）；则对任意的三点A，B，C，都有d（C，A）+d（C，B）≥d（A，B）；故①正确；②设点Q是直线y=2x﹣1上一点，且Q（x，2x﹣1），可得d（P，Q）=max{|x﹣3|，|2﹣2x|}，由|x﹣3|≥|2﹣2x|，解得﹣1≤x≤，即有d（P，Q）=|x﹣3|，当x=时，取得最小值；由|x﹣3|＜|2﹣2x|，解得x＞或x＜﹣1，即有d（P，Q）=|2x﹣2|，d（P，Q）的范围是（3，+∞）∪（，+∞）=（，+∞）．无最值，综上可得，P，Q两点的“切比雪夫距离”的最小值为．故②正确；③定点F1（﹣c，0）、F2（c，0），动点P（x，y）满足|d（P，F1）﹣d（P，F2）|=2a（2c＞2a＞0），可得P不y轴上，P在线段F1F2间成立，可得x+c﹣（c﹣x）=2a，解得x=a，由对称性可得x=﹣a也成立，即有两点P满足条件；若P在第一象限内，满足|d（P，F1）﹣d（P，F2）|=2a，即为x+c﹣y=2a，为射线，由对称性可得在第二象限、第三象限和第四象限也有一条射线，则点P的轨迹与直线y=k （k为常数）有且仅有2个公共点．故③正确．∴真命题的个数是3．故选：D．【点评】本题考查新定义的理解和运用，考查数形结合思想方法，以及运算能力和推理能力，属于难题．三.解答题（本大题共5题，共14+14+14+16+18=76分）17．（14分）如图，在四棱锥P﹣ABCD中，底面ABCD为直角梯形，BC∥AD，AB⊥BC，∠ADC=45°，PA⊥平面ABCD，AB=AP=1，AD=3．（1）求异面直线PB与CD所成角的大小；（2）求点D到平面PBC的距离．【考点】LM：异面直线及其所成的角；MK：点、线、面间的距离计算．【专题】11：计算题；31：数形结合；41：向量法；5F：空间位置关系与距离；5G：空间角．【分析】（1）以A为原点，AB为x轴，AD为y轴，AP为z轴，建立空间直角坐标系，利用向量法能求出异面直线PB与CD所成角大小．（2）求出平面PBC的一个法向量，利用向量法能求出点D到平面PBC的距离．【解答】解：（1）以A为原点，AB为x轴，AD为y轴，AP为z轴，建立如图所示空间直角坐标系，则P（0，0，1），B（1，0，0），C（1，2，0）D（0，3，0），∴=（1，0，﹣1），=（﹣1，1，0），……（3分）设异面直线PB与CD所成角为θ，则cosθ==，……（6分）所以异面直线PB与CD所成角大小为．……（7分）（2）设平面PBC的一个法向量为=（x，y，z），=（1，0，﹣1），=（0，2，0），=（﹣1，1，0），则，取x=1，得=（1，0，1），……（4分）∴点D到平面PBC的距离d==．……（7分）【点评】本题考查异面直线所成角的余弦值的求法，考查点到直线的距离的求法，考查空间中线线、线面、面面间的位置关系等基础知识，考查运算求解能力，考查函数与方程思想，是中档题．18．（14分）已知点F1、F2依次为双曲线C：（a，b＞0）的左右焦点，|F1F2|=6，B1（0，﹣b），B2（0，b）．（1）若a=，以=（3，﹣4）为方向向量的直线l经过B1，求F2到l的距离；（2）若双曲线C上存在点P，使得=﹣2，求实数b的取值范围．【考点】KH：直线与圆锥曲线的综合．【专题】35：转化思想；49：综合法；5D：圆锥曲线的定义、性质与方程．【分析】（1）由题意可知：c=3，由，求得b的值，根据向量共线定理求得直线的斜率k，直线过F2（3，0），求得直线方程，根据点到直线的距离公式即可求得F2到l的距离；（2）设出P点坐标，由双曲线的性质可知：a2=9﹣b2，根据向量数量积的坐标表示求得x02+y02﹣b2=﹣2，由点P在双曲线上，将P点坐标代入双曲线上，整理得2b4﹣11b2=9y02，由y02≥0，及b＜3，即可求得b的取值范围．【解答】解：（1）由题意可知：c=3，F2（3，0），c2=a2+b2，，∴b=2，设直线l的方程为y=kx+m，为方向向量的直线l，∴k=﹣，点B1（0，﹣2）在直线l上，m=﹣2，∴直线方程为4x+3y+6=0，F2到l的距离d==（2）由题意可知：c=3，设P（x0，y0），c2=a2+b2，得a2=c2﹣b2=9﹣b2，①=（x0，y0+b），=（x0，y0﹣b），，整理得：x02+y02﹣b2=﹣2，则：x02=b2﹣y02﹣2，②由点P在双曲线上：∴，③将①②代入③整理得：，∴（b2﹣y02﹣2）×b2﹣y02×（9﹣b2）=（9﹣b2）×b2，整理得：2b4﹣11b2=9y02，∵y02≥0，∴2b4﹣11b2≥0，解得：b≥，∵b＜3，实数b的取值范围[，3）．【点评】本题考查双曲线的性质及应用，考查求直线的方程、点到直线的距离公式及向量数量积的坐标表示，考查分析问题及解决问题的能力，综合性较强，属于中档题．19．（14分）如图，某公园有三条观光大道AB，BC，AC围成直角三角形，其中直角边BC=200m，斜边AB=400m，现有甲、乙、丙三位小朋友分别在AB，BC，AC大道上嬉戏，所在位置分别记为点D，E，F．（1）若甲、乙都以每分钟100m的速度从点B出发在各自的大道上奔走，到大道的另一端时即停，乙比甲迟2分钟出发，当乙出发1分钟后，求此时甲乙两人之间的距离；（2）设∠CEF=θ，乙丙之间的距离是甲乙之间距离的2倍，且∠DEF=，请将甲乙之间的距离y表示为θ的函数，并求甲乙之间的最小距离．【考点】HU：解三角形．【专题】15：综合题；35：转化思想；4G：演绎法；58：解三角形．【分析】（1）由题意，BD=300，BE=100，△BDE中，由余弦定理可得甲乙两人之间的距离；（2）△BDE中，由正弦定理可得=，可将甲乙之间的距离y表示为θ的函数，并求甲乙之间的最小距离．【解答】解：（1）由题意，BD=300，BE=100，△ABC中，cosB=，B=，△BDE中，由余弦定理可得DE==100m；（2）由题意，EF=2DE=2y，∠BDE=∠CEF=θ．△CEF中，CE=EFcos∠CEF=2ycosθ△BDE中，由正弦定理可得=，∴y==，0，∴θ=，y min=50m．【点评】本题考查利用数学知识解决实际问题，考查正弦、余弦定理的运用，考查学生分析解决问题的能力，属于中档题．20．（16分）已知函数f（x）=，x∈R．（1）证明：当a＞1时，函数y=f（x）是减函数；（2）根据a的不同取值，讨论函数y=f（x）的奇偶性，并说明理由；（3）当a=2，且b＜c时，证明：对任意d∈[f（c），f（b）]，存在唯一的x0∈R，使得f（x0）=d，且x0∈[b，c]．【考点】57：函数与方程的综合运用．【专题】33：函数思想；49：综合法；51：函数的性质及应用．【分析】（1）设x1＜x2，计算f（x1）﹣f（x2），判断f（x1）﹣f（x2）的符号得出结论；（2）令f（﹣x）=f（x）和f（﹣x）=﹣f（x）分别求出a的值得出结论；（3）利用反证法得出结论．【解答】（1）证明：任取x1，x2∈R，设x1＜x2，则f（x1）﹣f（x2）=，∵x1＜x2，∴2＜2，又a＞1，∴f（x1）﹣f（x2）＞0，即f（x1）＞f（x2）．所以当a＞1时，函数y=f（x）是减函数．（2）解：当a=1时，f（x）=1，所以f（﹣x）=f（x）=1，所以函数y=f（x）是偶函数，当a=﹣1时，f（x）=，f（﹣x）===﹣f（x），所以函数y=f（x）是奇函数．当a≠1且a≠﹣1时，f（1）=，f（﹣1）=，∴f（﹣1）≠f（1）且f（﹣1）≠﹣f（1），所以函数y=f（x）是非奇非偶函数．（3）证明：由（1）知，当a=2时，函数y=f（x）是减函数，所以函数f（x）在[b，c]上的值域为[f（c），f（b）]，因为d∈[f（c），f（b）]，所以存在x0∈R，使得f（x0）=d．假设存在x1∈R，x1≠0使得f（x1）=d，若x1＞x0，由f（x）的单调性可得f（x1）＜f（x0），若x1＜x0，则f（x1）＞f（x0），与f（x1）=f（x0）=d矛盾，故x0是唯一的．假设x0∉[b，c]，即x0＜b或x0＞c，由单调性可得f（x0）＞f（b）或f（x0）＜f（c），所以d∉[f（c），f（b）]，与d∈[f（c），f（b）]矛盾，故x0∈[b，c]．【点评】本题考查了函数单调性的判断与证明，函数奇偶性的判断，属于中档题．21．（18分）设数列{a n}的前n项和为S n，若（n∈N*），则称{a n}是“紧密数列”．（1）已知数列{a n}是“紧密数列”，其前5项依次为1，，求x的取值范围；（2）若数列{a n}的前n项和为S n=（n2+3n）（n∈N*），判断{a n}是否是“紧密数列”，并说明理由；（3）设{a n}是公比为q的等比数列，若{a n}与{S n}都是“紧密数列”，求q的取值范围．【考点】8H：数列递推式．【专题】34：方程思想；49：综合法；54：等差数列与等比数列；59：不等式的解法及应用．【分析】（1）由题意得：≤2，≤2，解得x范围．（2）由S n=（n2+3n）（n∈N*），n≥2时，a n=S n﹣S n﹣1，n=1时，a1=S1=1，对于上式也成立．可得a n．=1+．因为对任意n∈N*，，即≤，即可得出结论．（3）由{a n}是公比为q的等比数列，得q=，{a n}是“紧密数列”，可得2．分类讨论：①当q=1时，S n=na1，==1+，即可判断出结论．②当q≠1时，S n=，=，由数列{S n}为“紧密数列”，可得≤2，对任意n∈N*恒成立．（ⅰ）当1时，≤1﹣q n+1≤2（1﹣q n），即，对任意n∈N*恒成立．即可得出结论．（ⅱ）当1＜q≤2时，（q n﹣1）≤q n+1﹣1≤2（q n﹣1），即，对任意n∈N*恒成立．即可得出结论．【解答】解：（1）由题意得：≤2，≤2，解得≤．（2）由S n=（n2+3n）（n∈N*），n≥2时，a n=S n﹣S n﹣1=（n2+3n）﹣[（n﹣1）2+3（n﹣1）]=n+，n=1时，a1=S1=1，对于上式也成立．因此a n=n+．∴==1+．因为对任意n∈N*，，即≤，∴（n∈N*），即数列{a n}是“紧密数列”．（3）由{a n}是公比为q的等比数列，得q=，∵{a n}是“紧密数列”，∴2．①当q=1时，S n=na1，==1+，∵≤＜2，∴q=1时，数列{S n}为“紧密数列”，故q=1满足题意．②当q≠1时，S n=，则=，∵数列{S n}为“紧密数列”，∴≤2，对任意n∈N*恒成立．（ⅰ）当1时，≤1﹣q n+1≤2（1﹣q n），即，对任意n∈N*恒成立．∵0＜q n≤q＜1，0≤2q﹣1＜1，﹣≤q﹣2＜﹣1，∴q n（2q﹣1）＜q＜1，q n（q﹣2）≥q（q﹣2）≥=＞﹣1，∴当1时，，对任意n∈N*恒成立．（ⅱ）当1＜q≤2时，（q n﹣1）≤q n+1﹣1≤2（q n﹣1），即，对任意n∈N*恒成立．∵q n≥q＞1，2q﹣1＞1，﹣1＜q﹣2≤0．∴，解得q=1，又1＜q≤2，此时q不存在．综上所述，q的取值范围是．【点评】本题考查了等比数列的通项公式与求和公式、不等式的性质、分类讨论方法、新定义，考查了推理能力与计算能力，属于难题．。