复旦附中高三期中考试试卷201511
复旦附中2015学年第一学期高一数学期中试卷

19. 已知 a R ,设集合 A {x | x 2 (6a 1) x 9a 2 3a 2 0} ,
B {x |1 | x a | 0}
(1)当 a 1 时,求集合 B ; (2)问: a
1 是 A B 的什么条件?并证明你的结论; 2
X Y ( X Y ) (Y X ) , X Y 称为 X 与 Y 的对称差;已知 A { y | y x 2 2 x, x R} , B { y | 3 y 3} ,则 AB 11.
;
已知集合 A {x | x 2 (m 2) x 1 0, x R} ,且 A R ,则实数 m 的取值范围 是 ; ;
20. 设函数 f ( x)
a2 x2 ,aR 且a 0; | xa| a
(1)分别判断当 a 1 及 a 2 时函数的奇偶性; (2)在 a R 且 a 0 的条件下,将(1)的结论加以推广,使命题(1)成为推广后命 题的特例,并对推广的结论加以证明;
21. 已知关于 x 的不等式 (4kx k 2 12k 9)(2 x 11) 0 ,其中 k R ; (1)试求不等式的解集 A ; (2)对于不等式的解集 A ,若满足 A Z B (其中 Z 为整数集),试探究集合 B 能 否为有限集?若能,求出使得集合 B 中元素个数最少时 k 的取值范围,并用列举 法表示集合 B ;若不能,请说明理由;
非空集合 G 关于运算 满足:①对任意 a, b G ,都有 a b G ;②存在 e G 使对 一切 a G 都有 a e e a a ,则称 G 是关于运算 的融洽集;现有下列集合 及运算: ① G 是非负整数集, :实数的加法; ② G 是偶数集, :实数的乘法; ③ G 是所有二次三项式组成的集合, :多项式的乘法; ④ G {x | x a b 2, a, b Q} , :实数的乘法; 其中为融洽集的个数是( A. 1 三. 解答题 17. 已知集合 A {1,1} , B {x | x 2 ax b 0, x R} ,若 B ,且 A B A ,求实 数 a, b 的值; B. 2 C. 3 ) D. 4
上海市浦东复旦附中分校2015学年第一学期

上海市浦东复旦附中分校 2015学年第一学期高二化学期中测试试卷考生注意:1.本卷共4页,满分100分,考试时间60分钟2.试卷包括两部分,第一部分为单项选择题,请将选择题答案填涂在答题卡上;第二部分为综合题,包括多项选择题、填空题、计算题等题型,请将综合题答案填写在答题纸上。
在试卷上作答一律不得分。
3.答题前,务必在答题卡和答题纸的适当位置正确填写班级、姓名和学号。
可能用到的相对原子质量:H 1- C 12- N 14- O 16- Na 23- Mg 24- Al 27- S 32- Cl 35.5-Fe 56- Cu 64-一、单项选择题(每题只有1个正确答案,每题2分。
)1.某古玩爱好者收藏的“商代铝碗”在“鉴宝”时被专家当场否定,其理由是( ) A .铝的导热性较强,不宜做碗B .铝的质地较软,易变形,不宜做碗C .铝元素易导致老年痴呆,不宜盛放食物D .铝的性质较活泼,难提炼,商代不可能有铝制品 2.金属能导电的原因( )A .金属晶体中金属阳离子与自由电子间的相互作用较弱B .金属晶体中的自由电子在外加电场作用下可发生定向移动C .金属晶体中的金属阳离子在外加电场作用下可发生定向移动D .金属晶体在外加电场作用下可失去电子3.美国科学家将两种元素铅和氪的原子核对撞,获得了一种质子数为118、中子数为175的超重元素,该原子核内中子数与核外电子数之差是( ) A .47 B .57 C .61 D .293 4.下列有关铁、铝及其合金的说法正确的是( ) A .铁、铝都属于轻金属 B .生铁的硬度和熔点都比纯铁髙 C .铁、铝的单质都具有银白色金属光泽,都属于有色金属 D .金属形成合金后通常具有更多优良性能,所以用途更广泛 5.下列各组物质的水溶液不用其它试剂无法鉴别的是( )A .NaOH3AlClB .4CuSO 2BaClC .2NaAlO HClD .2MgClNaCl6.铝热剂可以用来冶炼金属,特别是难熔金属,最主要是因为( ) A 、铝具有导热性 B 、铝氧化时放出大量热 C 、铝具有还原性 D 、铝的熔点高7.已知X 、Y 、Z 、W 四种元素在元素周期表中的相对位置如下图所示,其中X 、W 的质子数之和为21,由此可知( )A .X 位于元素周期表中第2周期、第V A 族B .Y 的氢化物(2H Y )不稳定,100C ︒以上即可分解C .Z 的最高价氧化物的水化物是一种强碱D .W 的非金属性比Y 的非金属性弱8.室温下,在强酸性和强碱性溶液中都不能大量共存的离子组是( )A .4NH +、2Cu+、Cl -、3NO - B .K +、Na +、23SO -、2S -C .K +、Na +、2AlO -、24SO -D .2Ba +、2Fe +、3NO -、Br -9.在()32Fe NO 溶液中滴加浓盐酸,下列叙述正确的是( )A .溶液颜色逐渐变浅B .浅绿色逐渐变深C .溶液颜色由浅绿色变成黄色D .溶液颜色不会发生变化10.常温下将等体积的0.1mol /L HAC 溶液与0.1mol /L NaOH 溶液混合。
2023-2024学年上海市复旦大学附属中学高三上学期期中考试英语试题

2023-2024学年上海市复旦大学附属中学高三上学期期中考试英语试题Directions: 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.I received an email from a reader who asked, “Why do some friendships end, no matter how much you want them to last?” She referred to 1 (see) the question in one of my articles, Mystery of Friendship. As I wrote in it, I don’t think easy answers exist as to how friendships start, why some turn into lifetime 2 , and why some end. Although I’ve tried answering the first two questions in other articles (To Have A Friend and Be A Friend), I still get surprised by friendships that endure and disillusi oned by those that slip away. Even so, I’ll try to offer some insights here as to why friendships end.My simple answer is that friendships end because the situations 3 friends are in or even the friends themselves change. First, the realities friends face may change. The decision to relocate 4 a new school or job cannot help but affect a friendship. Likewise, if a friend is in an accident, develops an illness, or loses someone close, these cannot help but affect a friendship. Does a friendship need to end because of these changes? No, but it’ll require adjustments that one or both friends 5 not be willing to make.Second, the friends themselves may change. A significant reason why friendships often end 6 friends are apart for an 7 (extend) period of time (for summer camp, college, etc.) is that one or both of the friends change. I think it 8 (hurt) less when both friends change, because then the breakup is more often mutual and so both friends get closure by both deciding to let go and move forward in their lives without each other. What tends to hurt most is when just one friend changes. One friend might change social circles, become involved in new social organizations, start to date, get a pet, or take on some other venture that consumes more time and passion. Again, a friendship can endure these changes, 9 one or both of the friends for some reason decide not to invest the time and energy involved in the adjustment period. In this situation, breakups may not be mutual and so one or both friends feel betrayed and end up with bitter memories about 10 was a precious friendship to them.Directions: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.A. categoriseB. creationC. goodD. innovativeE. maximumF. packedG. pedestrianise H. processing I. shape J. short-lived K. transformationAll Change in Curitiba!Like many other major world cities, Curitiba in southern Brazil has had to deal with issues such as pollution, poverty, and limited public funding. However, the architect and three-times mayor of the city, Jaime Lerner, has introduced some 11 solutions.As part of his ‘Master Plan’, Lerner hoped to make the city more environmentally friendly. He initiated a recycling scheme. In return for delivering recyclable rubbish to specified 12 points, residents receive a bag of vegetables or bus tickets. As a result, Curitiba now has one of the highest recycling rates in the world. Lerner also ordered the 13 of 26 urban parks. As well as preventing pollution, these control flooding.Lerner did not win over all the city’s residents immediately, however. When his plans to 14 part of the centre were passed, local businesses were up in arms, fearing a reduction in profits. Realising he needed to act quickly, Lerner had the 15 of six blocks completed within three days. When a group of motorists attempted to drive through the new pedestrian area, Lerner arranged for local primary schools to hold a painting workshop on the streets. The drivers were forced to turn back. Luckily for Lerner, this rebellion was 16 . The increase in profit rapidly persuaded shop owners to change their minds.Lerner’s determination helped 17 the Curitiba of today. The average income per capita has risen from a level that was below the Brazilian average in the 1970s to 66% above the average, and surveys indicate high levels of resident satisfaction.So, is it all just one big success story? In some respects, Curitiba may have been too successful for its own 18 . People and businesses have come to the city, which now has more than 1.8 million residents. This has put the city under enormous stress. Forty years ago, buses transported 54,000 passengers a day. Now the number is 2.3 million. According to some experts, the transport system has reached its 19 efficiency capacity. Following a rise in complaints about the noisy and 20 buses, the service is in decline.It started with a bit of casual discomfort on the head, but after a week it had spread to the back of my neck, enough to lead me to my laptop. Annoying as it was, I was ________ to take up my doctor’s time with such a silly complaint and then have a wasted journey only to be informed that it would clear up by itself and that ________ would be of no use at all.As soon as I’d tapped in ‘online self-diagnosis’, the search engine provided me with over 11.5 million results. And during the time normally spent in the clinic’s waiting room reading the Women’s Weekly, I was able to f ind a site that would provide a free ________ in the comfort of my chair, and with no need for an appointment,I answered all the questions until I eventually reached a description exactly matching my ________. As I clicked on ‘More Information’, I was hit with what I’d never anticipated. The worst case scenario was complete hair loss. I couldn’t have been more ________.I headed off to the doctor for what I thought would be a blood test but which turned out to be a valuable lesson in not ________ everything you read on the internet. It took him less than a minute to guess at and locate head lice (虱子). I was relieved to know that I would be ________ my hair, and horrified to know that it was being occupied.I learnt my lesson, but for some the worry caused by ________ every ache has led to a new form of hypochondria (疑病症). Named ‘cyberchondria’ by the print media back in 2000, this particular condition has ________ greatly. Although most people’s main point of call is still the doctor’s surgery, it’s estimat ed that ________ worries are now the second most researched topic on the web. This is truly a serious concern when about 25%of the medical information online is thought to be________.Once upon a time, hypochondria required time and effort: you had to go to the library to research your diseases and ________ go through the books. Now it’s just a matter of a few clicks of a mouse. But while your doctor will make a diagnosis ________ your age, appearance and medical history, a search engine will rely simply on algorithms (算法). These come up with results graded according to popularity or numbers of key words. So the most highly ranked hits might actually be for verygenuine disease, which are nonetheless extremely ________. One minute you think you’ve come down with the flu, the next you’re under attack from sub-tropical, flesh-eating bacteria. Time spent going to the doctor’s for ________ of mind suddenly seems fair enough.21.A.reluctant B.surprised C.able D.sure22.A.knowledge B.association C.evidence D.medication 23.A.sample B.assessment C.subscription D.upgrade24.A.standards B.arguments C.definitions D.symptoms 25.A.fortunate B.touched C.alarmed D.different26.A.believing B.explaining C.questioning D.covering27.A.keeping B.losing C.drying D.washing28.A.taking off B.putting on C.breaking away D.looking up 29.A.dropped B.differed C.increased D.helped30.A.safety B.health C.access D.money31.A.available B.accurate C.misleading D.complex32.A.occasionally B.automatically C.painstakingly D.literally33.A.bringing to light B.taking intoconsideration C.putting intopracticeD.setting on top34.A.rare B.hard C.large D.simple35.A.state B.change C.freedom D.peaceOn 15th June 1996, a huge bomb in Manchester, in the north-west of England, destroyed the city centre, causing nearly a billion pounds’ worth of damage. The bomb, which had been planted by a terrorist group called the IRA, injured over 200 people but remarkably killed no one as police had evacuated the area following a warning from the IRA.Manchester had already undergone some changes as it recovered from the economic depression of the early 1990s that had destroyed much of its industry and created large-scale unemployment. It had won the right to host the Commonwealth Games (a large sporting event) and redeveloped some deserted areas through the building of the National Velodrome, an exhibition centre and an award-winning concert hall. However, at the time of the bombing, the city centre was still badly neglected — dominated by the Arndale Shopping Centre (once described as looking like an enormous public toilet) and squares that were run-down and affected by drug addiction. So, dreadful though the bombing was, it actually provided an opportunity to start again that might not have happened otherwise.Within weeks of the explosion, the government had set up a public-private company to manage the recovery and launched an international competition to design the redevelopment. The winning plan involved restoring the historic buildings that had been damaged, tearing down and rebuilding some of the ugly buildings, creating new public spaces and improving life for pedestrians. Alongside this, the government reduced traffic in the centre by changing the direction of some main roads and developed an integrated public transport system, making access to the centre easier. Since these improvements, the city has attempted to boost tourism by using some of the city’s historical si tes for major public events and by creating the Urbis building, which now houses the National Museum of Football. In turn, these changes have been key in attracting new investors, such as the Qatari royal family who own Manchester City Football Club.Since 1996, the Manchester economy has grown in all areas. However, there are some concerns that inequality has also increased. Nor are all the new spaces appreciated. One new garden square designed by an international architect was rated as the worst attraction in the city. Others argue that in changing market stalls and industry for luxury consumption and glass buildings, the city has lost some of its soul.36. What does the word “evacuate” (paragraph 1)most probably mean?A.Looking for something in a place. B.Estimate the losses in a ruined place.C.Remove people from a place of danger. D.Determine a numerical value of a place. 37. What does the writer say about the 1996 IRA bombing?A.It presented an unexpected opportunity for Manchester.B.It destroyed the city centre that used to be busy and crowded.C.It resulted in a lot of people getting hurt or killed in Manchester.D.It cost Manchester its chance to host the Commonwealth Games.38. What did Manchester do for its recovery?A.It set up Manchester City Football Club.B.It organised an international competition to attract new investors.C.It tore down some historical sites to make room for public events.D.It developed a public traffic system to make the city center more accessible.39. What is the passage mainly about?A.Damage Manchester suffered due to the IRA bombing.B.The IRA bombing in Manchester and its consequences.C.Challenges related to the redevelopment of Manchester.D.The long-term effects of the changes made in Manchester.We asked four people who graduated from the Williams Business and Accountancy School what corporate responsibility means to them.JasonI know that some corporations claim to be bringing huge benefits to local people, and maybe some are. However, in other cas es, they’re paying low wages or undercutting small, family-run firms who can’t compete. It may not be a pretty image, but that’s the nature of capitalism. I’d like to hope I won’t end up as part of this process, but I suspect it’s inevitable. Essentially, your biggest responsibility is ultimately to return value to your stakeholders. Positive employee relations are desirable, but not actually a legal requirement in many countries.AnyaThanks to my sister, I’ve recently had a shift in thinking. As far as co rporate responsibility is concerned, I no longer doubt it. Christina recently transferred to an overseas branch. She was surprised and delighted to discover the branch was running local programmes to improve basic literacy skills amongst employees as well as to conserve the environment. She’s now currently retraining as a teacher and moving over to that side of things. Now that I’ve seen this side of corporate responsibility, I’ve been persuaded to give it a go myself in later life, although I’ll stick to Plan A and pursue a solid career in finance for a few years first.AndreFor me, what it comes down to is sustainability. Whatever your product, it shouldn’t have a harmful effect on the planet. Many companies make a big noise about how much cash they give away to charity, but they should make changes in the way they make their profits in the first place. Quite aside from the ethical arguments, there’s also a sound commercial reason here. These days the consumer has access to far more information than ever before thanks to the internet, so if somethingbad goes viral, it’ll destroy a reputation forever. Companies are well aware of that. For that reason, more are starting to face up to their responsibility—or so they claim.LisaIn the USA, corporations often support community development projects by donating books or equipment to schools. However, this apparent altruism (利他主义) is not all it claims to be. There’s a large grey area between corporate giving and company branding. Nowadays every corporate website includes a summary of so-called ‘core values’; vague descriptions of how they’re ‘giving back’ to society. I can’t help thinking they’re unclear for a reason and that it’s all just for good PR. I’m particularly annoyed by the claims of fast-food companies. They pretend to be concerned with obesity (肥胖) levels while promoting special offers on larger portions. The hidden agenda is clearly to boost profit. It’s an insult to consumer intelligence.40. According to Jason, what responsibility is ignored by corporations?A.Bringing benefits to local peopleB.Keeping positive employee relations.C.Returning values to their stakeholders.D.Understanding the nature of capitalism.41. What can be learned about Anya?A.She supports and values corporate responsibility efforts.B.She has been persuaded to work for an overseas corporation.C.She will be devoted to corporate responsibility initiatives soon.D.She believes some corporate responsibility efforts make no sense.42. What do Andre and Lisa have in common?A.Both argue against the necessity of company branding.B.Both think corporations should express their ‘core values’ more clearly.C.Both hold a firm belief that sustainability matters in corporations’ development.D.Both doubt the real purpose of some corporate responsibility efforts.Every decision we make is arrived at through hugely complex neurological processing. Although it feels as though you have a choice, the action that you ‘decide’ to take is entirely directed by automatic neural activity. Brain imaging studies show that a person’s action can be predicted by their brain activity up to 10 seconds before they themselves become aware they are going to act. Multiple neuroscientific studies show that even those important decisions that feel worked out are just as automatic as knee-jerk reactions (膝跳反应) (although more complex).Decision-making starts with the amygdala: a set of two almond-shaped nuclei (杏仁状核) buried deep within the brain, which generate emotion. The amygdala registers the information streaming in through our senses and responds to it in less than a second, sending signals throughout the brain. These produce an urge to run, fight, freeze or grab, according to how the amygdala values various stimuli.Before we act on the amygdala’s si gnals, however, the information is usually processed by other brain areas, including some that produce conscious thoughts and emotions. Areas concerned with recognition work out what’s going on, those concerned with memory compare it with previous experiences, and those concerned with reasoning, judging and planning get to work on constructing various action plans. The best plan—if we are lucky—is then selected and carried out. If any of this process goes wrong, we are likely to hesitate, or do something silly.The various stages of decision-making are marked by different types of brain activity. Fast (gamma)waves, with frequencies of 25 to 100 Hz, produce a keen awareness of the multiple factors that need to be taken into account to arrive at a decision. If you are trying to choose a sandwich, for instance, gamma waves generated in various cells within the ‘taste’ area of the brain bring to mind and compare the taste of ham, hummus, wholemeal, sourdough, and so on. Although it may seem useful to be aware of the full range of choice, too much information makes decision-making more difficult, so irrelevant factors get dismissed quickly and unconsciously.After this comparison stage, the brain switches to slow-wave activity (12 to 30 Hz). This extinguishes most of the gamma activity, leaving just a single ‘hotspot’ of gamma waves which marks the chosen option.Although there is no ‘you’ outside your brain to direct what it’s doing, you can help it to make good decisions by placing yourself in a situation which is likely to make the process run more smoothly. Doing something that is physically or mentally stimulating before making a decision will help your brain produce the initial gamma waves that generate awareness of the competing options. Getting over-excited, on the other hand, will prevent the switch to the slow brainwaves, making it much harder to single out a choice.43. Why does the writer mention “knee-jerk reactions” in the first paragraph?A.To introduce the finding of the latest brain imaging studies.B.To illustrate that decisions are not consciously thought out.C.To call attention to a kind of neural reaction that is not very complex.D.To show the difference between decision-making and other brain activity.44. What does the amygdala do according to the passage?A.It works out conscious thoughts and emotions.B.It selects the best action plan for a given situation.C.It dismisses factors that are irrelevant to the decision to be made.D.It processes sensory information and generates emotional responses.45. What can be concluded from paragraphs 4 and 5?A.Slow-wave activity usually lasts longer than fast-wave activity.B.The brain prioritizes information before settling on a final choice.C.Decision-making is difficult when slow-wave activity occurs first.D.The brain needs as much information as possible to make a decision.46. How does engaging in stimulating activities help the decision-making process?A.By preparing the brain to single out the most reasonable choice.B.By helping the brain switch to slow-wave activity more quickly.C.By getting the brain to focus on those most relevant alternatives.D.By making the brain more aware of the factors and choices involved.Could a New Battery Solve Our Energy Problem?Researchers in the US have made headlines worldwide by developing a new type of battery that charges far faster and holds way more charge than today’s lithium cells (锂电池). It’s not just a terrific technology story, either. The team behind it is led by tech legend Prof John Goodenough of the University of Texas, Austin—the co-inventor of the original lithium-ion battery, and still doing brilliant work at the age of 94.47 That’s why we’re still using 21st-Century gadgetry with one eye on battery, wondering if we can get to a charger before our device goes completely dead.This depressing state of affairs is more than simply inconvenient. If we’re to make the most of renewable energy, we need ways of coping with those times when the wind drops or there’s no sunshine. 48Elo n Musk, the billionaire boss of electric car company Tesla, certainly thinks so. He’s already created a 20 megawatt battery ‘farm’ in California, and is willing to put his money where his batteries are. 49 For example, one wind farm in Hawaii had three f ires in its battery ‘farm’ within a year of opening.But now Goodenough and his team may have found the answer, by switching from lithium to sodium (钠).The lithium batteries that made Goodenough’s reputation contain a liquid electrolyte (电解质) which doesn’t respond well to rapid charging. One of Goodenough’s colleagues, Maria Braga, decided that the answer lay in switching to solid electrolytes. The team has now managed to get a solid glass electrolyte to work with sodium, which is similar to lithium but far more common. 50 The battery has triple the charge of its lithium equivalent, it charges in minutes rather than hours, and it has a longer lifespan.Advances in energy storage are vital if renewable are going to reach their potential. The boundless energy of Goodenough—the Li-ion King himself—may just have found the solution just in time.passage in no more than 60 words. Use your own words as far as possible.Communicating scienceOne of the major problems for scientists lies in communicating the value of research to non-specialists that matter:policymakers and the general public. In recent years, scientific organisations have come a long way in developing ways to make science more accessible to non-specialist groups.The development of blogs has helped substantially in bringing science closer to the public. According to Wikipedia, the ScienceBlogs network is now ranked 37th among the most authoritative blogs worldwide, with two of its sections having won weblog awards. Released from editorial restrictions, science bloggers generally focus on areas of science that they are both passionate and knowledgeable about. They often write about science in an accessible, lively manner, and it is this that p erhaps most attracts members of the public. Ed Yong’s Not Exactly Rocket Science, for instance, is filled with the writer’s enthusiasm and down-to-earth attitude towards the subject. His chatty, youthful style appeals to a wide range of readers.Television has also boosted the image of science. Early pioneers such as Jacques Cousteau, whose beautifully filmed documentaries opened up the oceans to millions, quickly realised the potential of TV to make science come alive for viewers. Other science disciplines have eagerly followed suit. Entertaining presenters carry out daring experiments or explore amazing scientific phenomena in order to attract attention. Celebrities such as Brian Cox, once famous for playing music in D:Ream, have also been instrumental in bringing science into popular culture. Now working in the field of physics, Brian is presenter of the BBC TV series Wonders of the Solar System. His background means that his face is not only well known to younger viewers but is also considered cool. Other organisations have been using the power of visual media through the internet. For example, SciVee offers scientists video services to create online presentations of their research.Nevertheless, despite this progress, communication remains one of science’s biggest obstacle. Perhaps it is time that universities addressed this problem, and thought about adding communications training to the curriculum.________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ___________________________________________________52. 沙漠的温度白天酷热,夜晚极寒。
高中英语真题:2015届高三上学期期中考试试卷 试题.doc

高中英语真题:2015届高三上学期期中考试试卷试题.doc一、阅读理解(共5题)1.When Paul was a boy growing up in Utah, he happened to live near a copper smelter (炼铜厂), and the chemicals that poured out had made a wasteland out of what used to be a beautiful forest. One day a young visitor looked at this wasteland and called it an awful area. Paul knocked him down. From then on, something happened inside him.Years later Paul was back in the area, and he went to the smelter office. He asked if they had any plans or if they would let him try to bring the trees back. The answer from that big industry was “No”.Paul then went to college to study the science of plants. Unfortunately, his teachers said th ere weren’t any birds or squirrels to spread the seeds. It would be a waste of his life to try to do it. Everyone knew that, he was told. Even if he was knowledgeable as he had expected, he wouldn’t get his ideaaccepted.Paul later got married but his dream would not die. And then one night he did what he could with what he had. As Samuel Johnson wrote, “It is common to overlook what is near by keeping the eye fixed on something remote. Attainable good is often ignored by minds busied in wide range s.” Under the cover of darkness, he went secretly into the wasteland and started planting.And every week, he made his secret journey into the wasteland and planted trees and grass. For fifteen years he did this against the plain common sense. Slowly rabbits appeared. Later, as there was legal pressure to clean up the environment, the company actually hired Paul to do what he was already doing.Now the place is fourteen thousand acres of trees and grass and bushes, and Paul has received almost every environmental award Utah has. It took him until his hair turned white, but he managed to keep that impossible vow (誓言) he made to himself as a child.21. When Paul was a boy, _______.A. he had decided never to leave his hometownB. the economy of Utah depended wholly on the copper smelterC. he hit a young visitor because of his comments on the wastelandD. he stopped the copper smelter polluting the area22. Paul went to college to study the science of plants, because _______.A. he wanted to find out the best way to save the area himselfB. he was interested in planting trees since he was youngC. he wanted to get more knowledgeable people to help himD. he thought his knowledge would make his advice more convincing23. W hat does the underlined phrase “the plain common sense” probably mean?A. It was impossible for trees to grow on the wasteland.B. His normal work and life would be greatly affected.C. No one would like to join him in the efforts.D. He had to keep everything he did secret.24. The company hired Paul to plant trees and grass because_______.A. they realized the importance of environmental protectionB. what Paul was doing moved themC. Paul persuaded them to help himD. they had legal pressure2.Music died here last spring, or rather, it was killed by members of the school committee who ignored the importance of music and drama as part of the high-school curriculum (课程).The committee decided that teaching students how to take a standardized test is more important than a curriculum in which students can explore their interests in the arts as well as academics. Because the school system is running out of funding, it needs to make sure that students pass the test or even more money will be lost. If students fail the state standardized test,it is not the fault of drama and music classes—they are failing because the “academic” classes are not sufficient (充足的).It is painful to think of how many students will be discouraged from singing, acting, and playing instruments because school programs are no longer offered. Many families cannot afford private music lessons, and many potential musicians and artists may not find their calling if they are not exposed to it in school. The fact that the school committee thinks the arts are not worth the investment will certainly make some students believe the arts are not worth their time or support and the cycle will continue.Teaching for a test does not shape students into complete,well-rounded people. It blocks the natural sense to create and express feelings through art—there is more to life than the analytical thinking that math and English provide. What happens after a test? Sure, a student might graduate, but they will have limited knowledge—certainly not a good preparation for the real world.25. Music and drama are not included in the high school curriculum mainly because ________.A. the school committee pays no attention to themB. the school is afraid of losing financial supportC. the students are not interested in both of themD. the state standardized test is more important26. Which of the following is TRUE according to the passage?A. The sufficiency of the classes determines students’ performance in the mastery test.B. Quite a few students are discouraged from learning music and art in today’s school system.C. Students can be musicians and artists only if they can afford private music lessons.D. The school committee completely influences students’attitude towards the arts.27. We can learn that music and art can ________.A. motivate students in creativity and expressionB. make students round-shaped people in futureC. provide students with analytical thinkingD. prevent students graduation from high school28. The best title of the passage can be ________.A. Who killed music and drama?B. Can curriculum go without music?C. Why is music so important?D. How to prepare for the real world?3. For more than 40 years, scientists have sought to learn how wellhuman beings can adapt to long periods in space. The International Space Station continues to provide valuable knowledge about spaceflight. But an earlier space station, Skylab, helped make the current space project possible.Canadian astronaut Chris Hadfield sang aboard the International Space Station on May 12, 2013. His music video has become extremely popular. The astronaut played his own version of David Bowie’s so ng Space Oddity. He performed while floating weightlessly, with images of planet earth and space appearing in the window behind him.Chris Hadfield recently returned home after nearly five months on the space station. For him, the long flight produced a hit video on YouTube and no major physical problems. But 40 years ago, scientists did not know how humans would react to long-term spaceflight. To find out, NASA, the American space agency, launched Skylab in May, 1973. Over nearly a year, three teams of astronauts visited Skylab for stays of between 28 to 84 days. They learned how people react to extended periods in space.Gerald Carr commanded Skylab 4. He spoke at a NASA event marking the 40th anniversary of Skylab’s launch. He s aid that the loss of the body’s muscle mass was a main concern. Astronauts on Skylab used exercise equipment to stay strong. The astronauts spent their workdays carrying out experiments, including biomedical (生物医学的) research.Marshall Porterfie ld is the director of NASA’s Space Life and Physical Sciences Division. He says the Skylab astronauts’ understanding of their own ability to deal with long-term spaceflight continues to help current astronauts. NASA says the next step for life away from Earth is a year-longspace station mission, set for 2015.29. Why was Chris Hadfield’s song so special?A. It was performed in space.B. It was created by an astronaut.C. It was a very familiar song.D. It was first sung by a famous singer.30. Which of the following best describes the physical condition of Chris Hadfield after his return?A. Worse.B. Better.C. Normal.D. Weaker.31. For what purpose did NASA launch Skylab?A. To research on whether human beings could stay in space.B. To gather up information on setting up a space station.C. To study the changes in the body when staying long in space.D. To find out the possibility of doing experiments in space.32. What can we learn from the last paragraph?A. Skylab is still in use to explore the space.B. The research results on Skylab are still valuable.C. Skylab is more advanced than the International Space Station.D. The Skylab astronauts made great contributions to biomedical research.4.Suppose you are thinking about attending college in the United States, but perhaps you might not be ready for a university with a four-year program. About 88,000 international students have found solution. They are attending U.S. community colleges. Such colleges are sometimes called junior colleges. They offer two years of education above the secondary or high school level.Community college students can choose from subjects like medical assistance, computer science or law. At the end of their study program, they receive a document of completion, called a certificate. Some students work toward an associate degree in traditional academic subjects like science or history. After getting it, the students can move on to a four-year college or university. They may have only two years of study left before they receive abachelor’s degree.Many educational experts agree that saving money is the major reason to consider a community college. The American Association of Community Colleges (AACC) says that a public two-year college costs 3,000 dollar a year on average. That is true if the student lives in the same state as the school. A student at a four-year public college may pay 8,500 dollars a year for classes and user fees. That does not include books and other materials.Some international students may need more preparation in English before entering a community college in the United States. For example, Istrif Montgomery came to the U.S. from Kosovo in 2006. First, he worked to improve his English at Montgomery College for a year. Then for the next two years, he attended classes in basic subjects in a community college.The international students at two-year colleges need to find a place to live. Most community colleges do not provide student housing on their grounds. But Mr Montgomery had a home nearby. He was able to ride the bicycle, and he was able to walk if he wanted. In fact, most community college students live within five to ten miles off the college.33. What’s the biggest advantage of a community college?A. The classes are free of charge.B. The students can save much time.C. The students can save a lot of money.D. It is convenient for students to live in the college.34. Which of the following is TRUE according to the passage?A. Mr Montgomery usually goes to school on foot.B. Most students in community colleges don’t live far away.C. 8,500 dollars covers all the cost of a four-year public college.D. International students often attend a community college directly.35. What’s the main purpose of the passage?A. To encourage students to study abroad.B. To tell the international students how to save money.C. To tell us it’s a good choice to study in public colleges.D. To give some information about community colleges.5.36 The answer is that the government needs money for many things, for example to pay its army, to build public facilities and to buy goods from abroad, and only the people of the country can supply the money.37 That is, a person pays according to the amount of his income. Whether he is a merchant, a doctor, a lawyer, a shopkeeper, a miner, or anything else, he must pay tax if his income is more than a certain amount. This is called a “direct” tax, because it is paid in money direct to the government.Another tax is paid on goods such as watches, jewelry, tobacco, wine, etc. When they are brought into a country, such a tax is paid as part of the price of these goods if they are later sold in shops. 38People usually complain about having to pay taxes, but they forget that the money is spent on things that they and their families need. We need policemen to catch thieves, and they must be paid what they earn; children need education and there must be schools and teachers; we want our streets to be kept clean, and the wages of men who do this kind of work have to be paid. 39 And we cannot have an army without paying for it.40 We have no real cause to complain when we are asked to pay taxes for the good of ourselves and for our fellow citizens.A. Why must we pay taxes?C. Taxes, therefore, cannot be avoided.D. Taxes, however, should be cancelled.E. One of the most important taxes is income tax.F. We call it “indirect” tax, because it is paid indirectly through the shopkeeper.G. Above all, the country must always be ready to defend itself against attacking enemies.二、完型填空(共1题)1.Starbucks is the biggest coffee shop network in the world with more than 15,000 shops in 44 countries. It was first 41 in Seattle, Washington in 1971 by three people with just a 42 shop that sold selected coffee beans. People 43 the selected coffee beans and ground (碾碎) them in the shop or carried them home. The 44 of Starbucks at the time was to sell quality coffee beans so that consumers could 45 coffee in their own houses.Just after 1987 Starbucks began to show significant 46 after their brand was bought by a former employee of Starbucks, Howard Schultz. He joined Starbucks in 1982 and his 47 to Milan changed his ideas about the coffee shop. Italy, a country that was famous for their coffee consuming habits, inspired Howard to bring these Italian-style coffee shops to theStarbucks because he believed the business of Starbucks should 50 the same. That is, they should 51 selected coffee beans, and not an Italian-style coffee shop.After 52 Starbucks in 1985, Howard Schultz set up his own shop 53 the name of ⅡGiomale. This name 54 was not too good. After he bought the Starbucks brand he quickly changed the name of the shop to Starbucks, and the business 55 to be a great success.People liked to come to Starbucks because the 56 was different and helped to release tiredness after working all 57 long. A shift in American culture was also 58 towards the Starbucks’ success, because before American people liked to go to a 59 and drink alcohol. It was clear that drinking coffee was much healthier than drinking alcohol. Starbucks’ success 60 to many countries, and the culture of drinking coffee has become popular all over the world.41. A. found B. established C. decorated D. formed42. A. clean B. faraway C. modern D. small43. A. booked B. packed C. bought D. grew44. A. center B. concept C. opinion D. theory45. A. admire B. evaluate C. enjoy D.46. A. discovery B. meaning C. future D. growth47. A. trip B. attitude C. flight D. interview48. A. competition B. trade C. market D. economy49. A. purchased B. accepted C. prevented D. rejected50. A. allow B. remain C. believe D. present51. A. provide B. produce C. collect D. advertise52. A. closing B. supporting C. leaving D. moving53. A. in B. at C. as D. by54. A. apparently B. unluckily C. finally D. unexpectedly55. A. showed up B. turned out C. took over D. came out56. A. atmosphere B. situation C. space D. appearance57. A. week B. year C. day D.58. A. strange B. necessary C. hopeful D. influential59. A. hotel B. bar C. park D. hospital60. A. expanded B. added C. rushed D. attached三、单词拼写(共1题)1.61. She leaned over and _____________(低语)something in his ear.62. The reason why he came is not very_____________.(令人信服)63. I paid the cheque into my savings _____________. (账户)64. The author begins by ______________(提到) to the early history of India.65. The room is arranged very ________________.(吸引人)四、阅读填空(共1题)1.Lori: Good morning, Chuck. Are you here 66 (wait) for Professor Johnson?Chuck: Oh, yes. Good morning, Lori. The professor asked me to comeas 68 teacher’s assistant?Lori: Oh, yes. I know all about it 69 I have work experience in this field. Last year, I did it for a long time.Chuck: Really? How did you like 70 ?Lori: Well, actually I think it was 71 (good) I had ever had at school.I was paid nine dollars an hour, which 72 (be) three dollars more than the school post office paid us.Chuck: Yeah, I bet this is a good salary. But what did you do?Lori: My responsibility was to help Professor Johnson grade the students’ homework. It wasn’t hard and the professor was always available 73 there were any questions. I 74 improve myself through doing this job.Chuck: I think I would enjoy this kind of work. But I’m a little worried about how much 75 it might take.Lori: Only about five or six hours a week and you can do that in your room.Chuck: It sounds good.五、短文改错(共1题)1.假定英语课上老师要求同桌之间交换修改作文,请你修改你同桌写的以下作文。
上海市上海中学2015-2016学年高三(上)期中考试数学试卷

2015学年上海市上海中学高三年级期中考试试卷2015/11/6一、填空题(本大题满分56分,总共14题,每小题4分)1、已知()21,02,0x x f x x x ⎧+≤=⎨>⎩,若()10f x =,则x =__________.2、已知函数()131xf x a =++为奇函数,则方程()14f x =的解是_________. 3、已知钝角α的顶点在坐标原点,始边与x 轴的正半轴重合,角α的终边与圆心在原点的单位圆(半径为1的圆)交于第二象限内的点3,5A A x ⎛⎫ ⎪⎝⎭,则sin2α=_________.4、设()f x 是定义在R 上的奇函数,且对任意实数x 满足()()2f x f x +=,当01x <<时,()21f x x =-,则()312f f ⎛⎫-+= ⎪⎝⎭_________.5、已知3cos ,41024x x πππ⎛⎫⎛⎫-=∈ ⎪ ⎪⎝⎭⎝⎭,则cos2x =___________. 6、若函数()0y ax a =<与()0b y b x=-<在()0,+∞上都是减函数,则函数2y ax bx =+在()0,+∞上是单调递__________函数.7、在ABC V 中,若tan tan 122A B +=,则tan 2C的最小值为_________. 8、设函数()21xf x x=+,区间[](),M a b a b =<,集合(){},N y y f x x M ==∈,则使得M N =的实数对(),a b 有___________对.9、若关于x 的方程21x x a x -=有三个不同的实数解,则实数a 的取值范围是_________. 10、当0,2x π⎡⎤∈⎢⎥⎣⎦,满足方程()()322log tan log sin x x =的所有解是__________. 11、设()()()()012015,1n n f x x f x f x n N *-=-=-∈,则函数()2015y f x =的零点个数为___________.12、对于具有相同定义域D 的函数()f x 和()g x ,若存在实常数k 和b ,使得函数()f x 和()g x 对其定义域D 上任意实数x 分别满足:()f x kx b ≥+和()g x kx b ≤+,则称直线:L y kx b =+为()f x 和()g x 的“隔离直线”,给出定义域为{}0D x x =>的四组函数如下:(1)()()tan ,sin f x x g x x ==;(2)()()22,xf xg x x==;(3)()()221,55x x f x g x x x x -+==-+-.(4)()()24,1x x xf x e eg x x -=+=+,其中曲线()f x 和()g x 存在“隔离直线”的所有序号是___________.13、关于x 的不等式220x ax a -+<的解集为A ,若集合A 中恰有两个整数,则实数a 取值组成的集合是__________. 14、已知正实数,x y 满足24310x y x y+++=,则xy 的取值范围是__________. 二、选择题(本大题满分20分,总共4题,每小题5分)15、若a b c <<,则函数()()()()()()()f x x a x b x b x c x c x a =--+--+--的两个零点分别位于区间( ).A (),a b 和(),b c 内 .B (),a -∞和(),a b 内 .C (),b c 和(),c +∞内 .D (),a -∞和(),c +∞内16、存在函数()f x 满足,对任意x R ∈都有( ).A ()cos2sin f x x = .B ()2221f x x x -=- .C ()211f x x +=+ .D ()2cos2f x x x =+17、已知[]1,1x ∈-时,()21f x x =-,又当x R ∈时,()()2f x f x +=,则方程()()log 01a f x x a ora =>≠恰有三个不相等的实数根,则实数a 的取值范围是( ).A ()1,3,4⎛⎫-∞+∞ ⎪⎝⎭U .B ()1,5,2⎛⎫-∞+∞ ⎪⎝⎭U.C ()11,3,542⎛⎫ ⎪⎝⎭U .D []11,3,542⎡⎤⎢⎥⎣⎦U . 18、()f x 是定义在区间[],c c -上的奇函数,其图像如图所示:令()()g x af x b =+,则下列关于函数()g x 的叙述正确的是( ).A若0a<,则函数()g x的图像关于原点对称.B若 1.20a b=--<<,则方程()0g x=有大于2的实根.C若0,2a b≠=,则方程()0g x=有两个实根.D若1,2a b≥<,则方程()0g x=有三个实根三、解答题.(总共74分)19、已知150,tan,sin()22213ααβαβ<<<=+=π,求cosα以及sinβ的值。
华师大附中高三期中考试试卷

华师大附中高三期中考试试卷第I卷(共110 分)I.Listening ComprehensionPart A Short ConversationsDirections : In Part 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 conversation and the question will be spoken only once.After you hear a conversation and the question about it, read the four possible answers in your paper, and decide which one is the best answer to the question you have heard.1.A.She doesn't like either of them.B.John copied it from Jim.C.Jim copied it from John.D.One is the copy from the other.2.A.She can only use it in the library.B.She is welcome to use it.C.She get one for herself.D.She can check one out.3.A.Andy will help if he's there this summer.B.West Virginia has many unexplored areas.C.Andy would probably be a good person to ask.D.The campers should try to get a lot of information.4.A.The history book. B.The English book.C.The maths book.D.The chemistry book.5.A.She didn't go to the drugstore.B.She couldn't get the medicine.C.She learned that the druggist had been robbed.D.She had a long wait before the druggist arrived.6.A.No, because it's not for sale.B.Yes, because he has plenty of money.C.Yes, if he borrows the money from the woman.D.No, because he didn't bring enough money.7.A.The movie is not good. B.The movie is excellent.C.She wants to see the movie again.D.She doesn't want to stay home.8.A.On a plane. B.On a train. C.In a car. D.On a ship.9.A.At 12 : 45. B.At 12 : 30. C.At 12 : 15. D.At 13 : 00.10.A.At home. B.In a medical center.C.In an office.D.In a shopping center.Part B PassagesDirections: In Part B, you will hear two short passages, and you will be asked three questions on each of the passages.The passages will be read twice but the questions will only be spoken once.When you hear a question, read the four possible answers in 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.Very well. B.All right. C.Disappointingly. D.Badly.12.A.He was not doing anything. B.He painted only one mile.C.He quarreled with his boss.D.He wasted too much paint.13.A.The man got very tired. B.The man made a mess of his work.C.The man never liked the job.D.The man never moved the paint can. Questions 14 through 16 are based on the following passage.14.A.Sitting in front of the TV. B.Too much violence in real life.C.Watching violence on TV.D.Stricter controls on children.15.A.The possible effect on children of violence on TV and video.B.The survey carried in the UK and the US.C.The idea of watching different programmes on TV.D.The fact that more Americans were killed and wounded in a week.16.A.A phone-in programme. B.An online programme.C.A TV series.D.A story-telling programme.Part C Longer ConversationsDirections: In Part C, you will hear two longer conversations.The conversations will be read twice.After you hear each conversation, you are required to fill in the numbered blanks with the information you hear.Student’s Book √(19)Teacher’s Book √ 3Cassette Tapes √(20)Complete the form.Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form.Write ONE WORD for each answer.II.GrammarDirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.25.The Summer Olympics about two weeks and the summer athletic events are five categories.A.RUN FOR...DIVIDED INTO C.GO FOR...SPLIT INTOB.RUN FOR...SEPARATED INTO D.GO ON FOR...BROKEN INTO26.The secretary made a note of it __________ she should forget.A.IN ORDER THATB.IN CASEC.SO THATD.EVERWHEN27.Frank and his team-mates the baseball team often practise in the school gymnasium.A.FORB.ONC.ATD.TO28.I don't know .A.WHOM OF THEM I SHOULD ELECT C.WHO OF THEM I SHOULD ELECTB.WHICH OF THEM I SHOULD CHOOSE D.WHICH OF THEMSHOULD I CHOOSE29.The hotel during our holidays is a grand one with a big garden in front of it.A.WHICH WE STAYED C.WHICH WE STAY ATB.WHERE WE STAY AT D.WHERE WE LIVED30.In our school there is a reading room, _________ the students often go to read newspapers and magazines.A.AT WHICHB.WHICHC.IN WHICHD.TO WHICH31.I regret you that our company has been out of business now.I am afraid that you'll have to go somewhere else.A.TELLINGB.TELLC.TO TELLD.HA VING TOLD32.It is to stare at others.A.BAD MANNERSB.BAD MANNERC.GOOD MANNERD.GOOD MANNERS33.Frank is not quite___________ today.A.HIMB.HIS OWNC.HIMSELFD.HE34 No one is ________ blind _________ those who will not see.A.SO...THATB.SUCH...THATC.SUCH...ASD.SO...AS35.Students are____________.A.prevented to smoke C.forbidden to smokeB.stopped to smoke D.preventing from smoking36.None of the students could answer the teacher's questions.They ____________ the lesson last night.A.would have previewed C.should have previewedB.should previewed D.must have previewed37.The electricity ___________, the light went out.A.cut offB.having cut offC.were cut offD.had cut off38.It was a long time___________ that he graduated from the university.A.sinceB.agoC./D.before39.Mould can grow on all kinds of things food.A.andB.exceptC.besidesD.and on40.China is one of the countries where silkworms ____________.A.riseB.are risingC.are raisedD.feed41.The PLA man spoke about his war experience and .A.listen with great interest C.listened to with great interestB.was listened with great interest D.was listened to with great interest42.It's easier to talk about doing a thing than into practice.A.putting itB.puttingC.to putD.to put it43.Mr.Johnson prefers that to him personally.A.she speaksB.she spokeC.she will speakD.she would speak44.Children usually their parents for food and clothing.A.turn intoB.live onC.ask forD.depend onIII.VocabularyDirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the one answer that best completes the sentence.45.In the advanced course students must take performances at monthly .A.gapsB.lengthC.intervalsD.distance46.Investors seem to be losing in the car industry.A.trustB.relianceC.beliefD.confidence47.He wore a blue silk handkerchief in his pocket.A.shoulderB.breastC.heartD.high48.Sea water can be changed into drinking water by removing the salt in it.A.freshB.cleanC.pureD.clear49.In China it is necessary that a senior high school graduate take an entrance exam to be into a university.A.appointedB.admittedC.acceptedD.agreed50.He a diary the whole time he was in the countryside.A.carried onB.followedC.keptD.put down51.The stream into the fiver just outside the town.A.meetsB.flowsC.unitesD.supplies52She in business as a dressmaker.A.set upB.set offC.set outD.set down53.The American film I saw was .A.not very funnyB.not much funnyC.not very funD.not too much fun54.We have decided to the trip to Beijing until the weather improves.A.put offB.put awayC.delay offD.waitIV.ClozeDirections: For each blank in the following passages 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.(A)Do you read newspapers regularly? Newspaper articles55 important and interesting information for people of all ages.56 , not all information is of 57 to everyone. Fortunately, finding the sections that you particularly want to read is not difficult. There are probably certain sections of the paper that interest you most. 58 , the titles of articles and the pictures give some clues about the contents.Once you have chosen an article to read, you will find the important 59 information 60 the key facts in the first few paragraphs. The rest of mostarticles give 61 . They are usually 62 because they provide valuable supporting ideas to help the reader 63 the key facts better. Sometimes they are simply human-interest details, 64 background information or quotes from people in the news story.55.A.cover B.keep C.record D.contain56.A.Whatever B.Otherwise C.However D.Because57.A.interest B.interesting C.necessary D.important58.A.Above all B.In a word C.Beside D.Apart from thatmon B.ordinary C.general D.detailed60.A.with B.into C.for D.except61.A.facts B.details C.material D.things62.A.including B.included ed D.found63.A.understand B.read C.see D.improveA.so thatB.such asC.insteadD.in spite of(B)Twice-crowned beauty queen Michele Reis may be at most 18 years old, but she is still Mommy’s little girl. Mrs.Reis described her 65 feeling the night when her daughter won the Miss Hong Kong beauty show, “I felt as if I suffered the 66 of something important when they crowned her. Not that I wasn’t happy for her, 67 that I knew my daughter no longer belonged to me alone and I would have to 68 her with everyone else.”Considering her recent fame, the beauty queen said, “Sometimes I have the feeling that I’m 69 myself. My schedule is 70 . I’m not getting enough sleep, and I am always hurrying from one place to another.”Being a famous person has another 71 . “People no longer regard me as an ordinary person. It’s becoming more difficult for me to make friends, ___72 I’ve learned to love old friends because they ___73 treat me as Michele 74 Miss Hong Kong.”65.A.mixed B.mixing C.excited D.exciting66.A.loss B.value C.start D.end67.A.only B.but C.while D.yet68.A.admire B.share C.take D.see69.A.always B.quite C.belong to D.no longer70.A.busy B.full C.long D.covered71.A.price B.advantage C.question D.meaning72.A.and B.but C.unless D.while73.A.never B.forever C.still D.everA.more thanB.instead ofC.in spite ofD.exceptV.Reading ComprehensionDirections: Read the following 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)Handball is a hugely popular sport in Europe and Asia, and it is one of the fastest and most exciting sports in the world. It combines basketball and soccer with the splendid saves of water polo.Handball is played on an indoor court (the size of two basketball courts) and there are goals at each end.There are twelve players on each team, two goal keepers and ten field players, but there is a maximum of one goalkeeper and six field players from each team allowed on the court at any one time.The idea is simple: score more goals than the other team.The ball is made of leather or a synthetic material and it must be of perfectly round shape.The surface must not be shiny or slippery.The size and weight of the ball varies for male and female teams, and adult and junior teams.Handball has the same free-ranging play as basketball, with all players except the goalkeeper constantly moving from attack to defense.The goalkeeper uses hands, feet, head and body to keep out the other team’s shots. The origins of handball are unclear.Many people think that it developed as a training game for soccer, to be played in the off reason, or when it was snowing. Now, in countries where handball is popular, players can earn large sums of money, and indoor stadiums seating over ten thousand people sell out regularly. Handball has been played at the Olympics since 1972.74.The passage tells us that handball was most probably developed________.A.as an alternative to basketball.B.by supporters of water polo.C.for the 1972 Olympics.D.as a training game.75.In which order does the information appear in the passage?A.beginning of the sport; type of ball; court size; team membersB.court size; team members; type of ball; beginning of the sportC.court size; type of ball; team members; beginning of the sportD.beginning of the sport; team members; type of ball; court size76.From the statement “The idea is simple”, we know that in handball the________.A.players can change positionsB.court is clearly markedC.game has only one objectiveD.players can earn a lot of money77.The main purpose of this passage is to ________.A.describe an interesting sportB.show how the rules of handball have changedC.list the world champion handball teamsD.increase the number of teams at the Olympics(B)We find that bright children are seldom held back by mixed-ability teaching.On the contrary, both their knowledge and experience are enriched.We feel that there are many disadvantages in dividing the class of the pupils grouped according to their abilities and intelligence.It doesn’t take into consideration the fact that children develop at different rates.It can have a bad effect on both the bright and the not-so-bright children.After all, it can be quite discouraging to be at the bottom of the top grade!Besides, it is rather unreal to grade people just according to their intellectual ability.This is only one part of their total personality.We are concerned to develop the abilities of all our pupils to the full, not just their study ability.We also value personal qualities and social skills, and we find that mixed-ability teaching helps to bring about all these parts of learning. Sometimes the pupils work in pairs; sometimes they work alone, and they can do this at their own speed.They also have some formal class teaching when this is suitable.We encourage our pupils to use the library, and we teach them the skills they need in order to do this well.An advanced pupil can do advanced work: it does not matter what age the child is.We expect our pupils to do their best, not their least, and we give them every encouragement to achieve this goal.78.In the passage the writer ________ “mixed-ability teaching”A.criticizesB.questions onC.appreciatesD.objects to79.The writer thinks that a teacher’s main concern should be the developmentof the student’s ________.A.social skillsB.total personalityC.learning ability and communicative skillsD.intellectual ability80.The phrase “held back” in the first line means ________.A.“made to remain in the same class”B.“forced to study in the lower classes”C.“drawn to their studies”D.“prevented from advancing”81.The purpose of the writer in writing the passage is to ________.A.argue for teaching bright and not-so-bright pupils in the same classB.recommend pair work and group work for classroom activitiesC.offer advice on the proper use of the libraryD.put emphasis on the importance of proper formal classroom teaching(C)It moved without a ripple, a moon-white circle beneath the surface, and in a few seconds it was as far away as it had been when he had first sighted it.Then it broke the top of the water.Jonsai was astonished.It was a turtle.Jonsai rubbed his eyes, thinking that the sun had weakened them. It was not unusual to find turtle feeding near the edge of the reef.But this was not an ordinary turtle.It stayed there on the surface, white and shining.The creature stayed still for some time.So did the boy.Leaning forward, he stared without moving, disbelief giving way to a small fear.His heart was beating wildly.There was no such thing as a white turtle!His mind moved first.Tonight the men would return from the pig hunt.Samu and Aesake would be at the feast with the men.He, Jonsai, would have to sit with the women and children. But what would happen if, at the height of the feasting, Jonsai brought forward a gift for Chief Vueti, something he had never seen before, a present that would make him the envy of every chief on the island?His heart beat fast, but steady now, as he got closer, moving swiftly like a thief. He would leave his spear hidden under the raft. That wonderful shell must not be pierced. The only way to catch the turtle was by stealth.82.Jonsai was surprised when he saw the turtle because the turtle ________.A.was the Chief’s favoriteB.moved very slowly through the waterC.was whiteD.was not afraid of him83.Jonsai’s main reason for wanting to catch the turtle is to ________.A.provide food for his familyB.make the other people envy himC.get the shell for jewelryD.impress the chief of his village84.In the last paragraph, as Jonsai moves towards the turtle, he feels ______.A.determined but sadB.unsure but excitedC.jealous and unsureD.worried and upset(D)Mrs.White was 67 when she moved out of the house where she had lived most of her life.The house was pulled down and a new block of flats was built there instead.At about the same time her only son was offered a job in Canada.Since the shopping and the housework had become too much for her, and her son and his wife were not able to look after her any more, Mrs.White had to be taken to Homefield Old People’s Home.She still had some friends near her old home, but now she was separated from them.During the first few months she was visited by friends and former neighbours, but Homefield was a long way from where they lived, too far away for old people.At Homefield Mrs.White was given a small room of her own, and she was well looked after.But she knew no one when she arrived, and she was not able to make friends there.She was well liked by the people who worked there, but she kept apart from the other old people and spent most of her time in her room.After a time she was hardly ever seen at meetings and social evenings.Although she was in poor health and had to be treated for a weak heart, she did not complain.“After all,”she said, “lots of people are worse off than I am.”What she disliked most was the “quietness” in the home, and what was even worse was that her son was not able to see her, not even at Christmas.A.Mrs.White was moved out of her old house mainly because ________.B.her son was going to work in CanadaC.she didn’t want to do housework any moreD.her house was to be replaced by a new buildingE.her friends had all moved away from the area85.She was ________ the people who worked there.A.criticized byB.disliked byC.popular withD.kept away from86.Which of the following words can best describe her life in the old people’shome?A.BusyB.UnhappyC.VariedD.Happy87.Which of the following is incorrect?A.She suffered from a heart trouble.B.Her son didn’t wish to see her at Christmas.C.She didn’t like the atmosphere in the home.D.She was quite satisfied with her living conditions.第II卷(共40 分)I. TranslationDirections: Translate the following sentences into English, using the wordsgiven in the brackets.1.十人中有九人会同意你刚才说的话。
2015-2016年上海市复旦大学附中高三(上)期中数学试卷及参考答案(理科)

2015-2016学年上海市复旦大学附中高三(上)期中数学试卷(理科)一、填空题:1.若集合A={x|x2﹣2x>0,x∈R},B={x||x+1|<0,x∈R},则A∩B=.2.函数f(x)=log2x+1(x≥4)的反函数f﹣1(x)的定义域是.3.满足等式=0的复数z为.4.甲校有3600名学生,乙校有5400名学生,丙校有1800名学生.为统计三校学生某方面的情况,计划采用分层抽样法,抽取一个样本容量为90人的样本,则应在甲校抽取的学生数是.5.(x2﹣)9的二项展开式中,含x3项的系数是.6.直线l1:(a+3)x+y﹣3=0与直线l2:5x+(a﹣3)y+4=0,若l1的方向向量是l2的法向量,则实数a=.7.阅读程序框图,如果输出的函数值y在区间内,则输入的实数x的取值范围是.8.已知圆锥的母线长为5cm,侧面积为20πcm2,则此圆锥的体积为cm3.9.在△ABC中,内角A,B,C所对的边分别是a,b,c,已知b﹣c=a,2sinB=3sinC,则cosA的值为.10.数列{a}中,若a1=1,(n∈N*),则=.11.甲、乙两人参加法律知识竞赛,共有10道不同的题目,其中选择题有6道,判断题4道,甲、乙两人依次各抽一题(不能抽同一题).则甲、乙中至少有一人抽到选择题的概率等于.(用数字作答)12.已知等差数列{a n}满足:,且它的前n项和S n有最大值,则当S n 取到最小正值时,n=.13.已知f(x)是定义在R上且周期为3的函数,当x∈[0,3)时,f(x)=|x2﹣2x+|,若函数y=f(x)﹣a在区间[﹣3,4]上有10个零点(互不相同),则实数a的取值范围是.14.若X是一个非空集合,M是一个以X的某些子集为元素的集合,且满足:(1)X∈M,Φ∈M;(2)对于X的任意子集A,B,当A∈M,B∈M时,A∪B∈M,A∩B∈M.则称M是集合X的一个“M﹣集合类”.例如:M={Φ,{b},{c},{b,c},{a,b,c}}是集合X={a,b,c}的一个“M﹣集合类”.已知集合X={a,b,c},则所有含{b,c}的“M﹣集合类”的个数为.二、选择题15.若f(x)和g(x)都是定义在R上的函数,则“f(x)与g(x)同是奇函数或同是偶函数”是“f(x)•g(x)是偶函数”的()A.充分非必要条件 B.必要非充分条件C.充要条件D.既非充分又非必要条件16.已知数列{a n}前n项和满足S n﹣S n﹣1=+(n≥2),a1=1,则a n=()A.n B.2n﹣1 C.n2D.2n2﹣117.若对任意x∈R,都有f(x)<f(x+1),那么f(x)在R上()A.一定单调递增B.一定没有单调减区间C.可能没有单调增区间D.一定没有单调增区间18.设S,T是R的两个非空子集,如果存在一个从S到T的函数y=f(x)满足:(i)T={f(x)|x∈S};(ii)对任意x1,x2∈S,当x1<x2时,恒有f(x1)<f(x2),那么称这两个集合“保序同构”,以下集合对不是“保序同构”的是()A.A=N*,B=NB.A={x|﹣1≤x≤3},B={x|x=﹣8或0<x≤10}C.A={x|0<x<1},B=RD.A=Z,B=Q三、解答题19.(12分)已知函数f(x)=|x﹣1|,g(x)=﹣x2+6x﹣5.(1)若g(x)≥f(x),求实数x的取值范围;(2)求g(x)﹣f(x)的最大值.20.(14分)已知向量(m∈R),且.设y=f(x).(1)求f(x)的表达式,并求函数f(x)在上图象最低点M的坐标.(2)若对任意,f(x)>t﹣9x+1恒成立,求实数t的范围.21.(14分)如图所示,一种医用输液瓶可以视为两个圆柱的组合体.开始输液时,滴管内匀速滴下球状液体,其中球状液体的半径毫米,滴管内液体忽略不计.(1)如果瓶内的药液恰好156分钟滴完,问每分钟应滴下多少滴?(2)在条件(1)下,设输液开始后x(单位:分钟),瓶内液面与进气管的距离为h(单位:厘米),已知当x=0时,h=13.试将h表示为x的函数.(注:1cm3=1000mm3)22.(16分)如图,椭圆C1:+y2=1,x轴被曲线C2:y=x2﹣b截得的线段长等于C1的长半轴长.(1)求实数b的值;(2)设C2与y轴的交点为M,过坐标原点O的直线l与C2相交于点A、B,直线MA、MB分别与C1相交于D、E.①证明:•=0;②记△MAB,△MDE的面积分别是S1,S2.若=λ,求λ的取值范围.23.(18分)已知数列{a n}满足:a1=1,|a n+1﹣a n|=p n,n∈N*,S n为数列{a n}的前n项和.(1)若{a n}是递增数列,且a1,2a2,3a3成等差数列,求p的值;(2)若p=,且{a2n}是递增数列,{a2n}是递减数列,求数列{a n}的通项公式;﹣1(3)若p=1,对于给定的正整数n,是否存在一个满足条件的数列{a n},使得S n=n,如果存在,给出一个满足条件的数列,如果不存在,请说明理由.2015-2016学年上海市复旦大学附中高三(上)期中数学试卷(理科)参考答案与试题解析一、填空题:1.若集合A={x|x2﹣2x>0,x∈R},B={x||x+1|<0,x∈R},则A∩B=∅.【解答】解:由集合A中的不等式变形得:x(x﹣2)>0,解得:x<0或x>2,即A=(﹣∞,0)∪(2,+∞);由集合B中的不等式,根据绝对值的意义得:x∈∅,即B=∅,所以A∩B=∅.故答案为:∅.2.函数f(x)=log2x+1(x≥4)的反函数f﹣1(x)的定义域是[3,+∞).【解答】解:函数f(x)=log2x+1(x≥4)的值域为[3,+∞),∴f﹣1(x)的定义域是[3,+∞),故答案为:[3,+∞).3.满足等式=0的复数z为﹣1.【解答】解:∵等式=0,∴z(1+i)+i(1﹣i)=0,∴z(1+i)(1﹣i)+i(1﹣i)(1﹣i)=0,∴2z+2=0,解得z=﹣1.故答案为:﹣1.4.甲校有3600名学生,乙校有5400名学生,丙校有1800名学生.为统计三校学生某方面的情况,计划采用分层抽样法,抽取一个样本容量为90人的样本,则应在甲校抽取的学生数是30.【解答】解:∵甲校,乙校,丙校的学生的人数之比为:3600:5400:1800=2:3:1,∴抽取一个样本容量为90人的样本,则应在甲校抽取的学生数为:,故答案为:30.5.(x2﹣)9的二项展开式中,含x3项的系数是﹣126.【解答】解:(x2﹣)9的二项展开式中,通项公式为T r+1=•(﹣1)r•x18﹣3r,令18﹣3r=3,求得r=5,故展开式中含x3项的系数为﹣=﹣126.故答案为:﹣126.6.直线l1:(a+3)x+y﹣3=0与直线l2:5x+(a﹣3)y+4=0,若l1的方向向量是l2的法向量,则实数a=﹣2.【解答】解:∵直线l1:(a+3)x+y﹣3=0与直线l2:5x+(a﹣3)y+4=0,∴直线l1的方向向量为=(1,﹣(a+3)),直线l2的方向向量为=(1,),∵l1的方向向量是l2的法向量,∴两直线的方向向量垂直,即•=1×1+(﹣a﹣3)×=0,解得a=﹣2,∴实数a=﹣2.故答案为:﹣2.7.阅读程序框图,如果输出的函数值y在区间内,则输入的实数x的取值范围是[﹣2,0] .【解答】解:由程序框图可得分段函数:y=,∴令2x∈[,1],则x∈[﹣2,0],满足题意;∴输入的实数x的取值范围是[﹣2,0].故答案为:[﹣2,0].8.已知圆锥的母线长为5cm,侧面积为20πcm2,则此圆锥的体积为16πcm3.【解答】解:∵圆锥的母线长是5cm,侧面积是20πcm2,设圆锥的半径为r,∴有πr×5=20π⇒r=4,∴圆锥的高为=3,∴圆锥的体积为×π×r2×3=16πcm3.故答案:16πcm3.9.在△ABC中,内角A,B,C所对的边分别是a,b,c,已知b﹣c=a,2sinB=3sinC,则cosA的值为﹣.【解答】解:在△ABC中,∵b﹣c= a ①,2sinB=3sinC,∴2b=3c ②,∴由①②可得a=2c,b=.再由余弦定理可得cosA===﹣,故答案为:﹣.10.数列{a}中,若a1=1,(n∈N*),则=.+a2n)=【解答】解:由,得(a1+a2)+(a3+a4)+…+(a2n﹣1==,∴==,故答案为:.11.甲、乙两人参加法律知识竞赛,共有10道不同的题目,其中选择题有6道,判断题4道,甲、乙两人依次各抽一题(不能抽同一题).则甲、乙中至少有一人抽到选择题的概率等于.(用数字作答)【解答】解:甲、乙两人参加法律知识竞赛,共有10道不同的题目,其中选择题有6道,判断题4道,甲、乙两人依次各抽一题(不能抽同一题).基本事件总数n=10×9=90,甲、乙都抽到判断题包含的基本事件个数m=4×3=12,∴甲、乙中至少有一人抽到选择题的概率:p=1﹣=1﹣=.故答案为:.12.已知等差数列{a n}满足:,且它的前n项和S n有最大值,则当S n取到最小正值时,n=19.【解答】解:由题意知,S n有最大值,所以d<0,由,所以a10>0>a11,且a10+a11<0,所以S20=10(a1+a20)=10(a10+a11)<0,则S19=19a10>0,又a1>a2>…>a10>0>a11>a12所以S10>S9>…>S2>S1>0,S10>S11>…>S19>0>S20>S21又S19﹣S1=a2+a3+…+a19=9(a10+a11)<0,所以S19为最小正值.故答案为:19.13.已知f(x)是定义在R上且周期为3的函数,当x∈[0,3)时,f(x)=|x2﹣2x+|,若函数y=f(x)﹣a在区间[﹣3,4]上有10个零点(互不相同),则实数a的取值范围是(0,).【解答】解:f(x)是定义在R上且周期为3的函数,当x∈[0,3)时,f(x)=|x2﹣2x+|,若函数y=f(x)﹣a在区间[﹣3,4]上有10个零点(互不相同),在同一坐标系中画出函数f(x)与y=a的图象如图:由图象可知.故答案为:(0,).14.若X是一个非空集合,M是一个以X的某些子集为元素的集合,且满足:(1)X∈M,Φ∈M;(2)对于X的任意子集A,B,当A∈M,B∈M时,A∪B∈M,A∩B∈M.则称M是集合X的一个“M﹣集合类”.例如:M={Φ,{b},{c},{b,c},{a,b,c}}是集合X={a,b,c}的一个“M﹣集合类”.已知集合X={a,b,c},则所有含{b,c}的“M﹣集合类”的个数为10.【解答】解:依题意知,M中至少含有这几个元素:∅,{b,c},{a,b,c},将它看成一个整体;剩余的{a}、{b}、{c}、{a,c}、{a,b}共5个,{a,b}和{b}必须同时在M中,{a,c}和{c}必须同时在M中;①{a}、{b}、{c}、{a,c}、{a,b}添加0个的集合为{∅,{b,c},{a,b,c}},一种②{a}、{b}、{c}、{a,c}、{a,b}添加1个的集合为{∅,{a},{b,c},{a,b,c}},{∅、{b},{b,c},{a,b,c}},{∅、{c},{b,c},{a,b,c}},共三种③{a}、{b}、{c}、{a,c}、{a,b}添加2个的集合共3种即{b}、{c};{c}、{a,c};{b}、{a,b}三种添加方式④{a}、{b}、{c}、{a,c}、{a,b}添加3个的集合共2种,即:{b}、{c}、{a,c};④{a}、{b}、{a,b}二种⑤{a}、{b}、{c}、{a,c}、{a,b}添加4个的集合共0种⑥{a}、{b}、{c}、{a,c}、{a,b}添加5个的集合共1种综上讨论知,共10种故答案为:10.二、选择题15.若f(x)和g(x)都是定义在R上的函数,则“f(x)与g(x)同是奇函数或同是偶函数”是“f(x)•g(x)是偶函数”的()A.充分非必要条件 B.必要非充分条件C.充要条件D.既非充分又非必要条件【解答】解:由“f(x)与g(x)同是奇函数”可得“f(x)•g(x)是偶函数”;反之不成立,例如可能f(x)与g(x)同是偶函数.因此“f(x)与g(x)同是奇函数”是“f(x)•g(x)是偶函数”的充分不必要条件.故选:A.16.已知数列{a n}前n项和满足S n﹣S n﹣1=+(n≥2),a1=1,则a n=()A.n B.2n﹣1 C.n2D.2n2﹣1【解答】解:由S n﹣S n=+,得=+,﹣1∴,∴数列{}是一个首项为1公差为1的等差数列.∴=1+(n﹣1)×1=n,∴S n=n2.当n≥2,a n=S n﹣S n﹣1=n2﹣(n﹣1)2=2n﹣1;a1=1适合上式,∴a n=2n﹣1,故选:B.17.若对任意x∈R,都有f(x)<f(x+1),那么f(x)在R上()A.一定单调递增B.一定没有单调减区间C.可能没有单调增区间D.一定没有单调增区间【解答】解:若f(x)是增函数,则由x<x+1可知f(x)<f(x+1)一定成立,但F(x)<F(x+1)并不能保证f(x)<f(x+0.5),比如令f(x)=x+sin2πx则f(x+1)=x+1+sin2πx=f(x)+1>f(x)但显然它不单调,因此,无法证明f(x)是增函数,同理,函数f(x)可能没有单调增区间,可能没有单调减区间.故选:C.18.设S,T是R的两个非空子集,如果存在一个从S到T的函数y=f(x)满足:(i)T={f(x)|x∈S};(ii)对任意x1,x2∈S,当x1<x2时,恒有f(x1)<f(x2),那么称这两个集合“保序同构”,以下集合对不是“保序同构”的是()A.A=N*,B=NB.A={x|﹣1≤x≤3},B={x|x=﹣8或0<x≤10}C.A={x|0<x<1},B=RD.A=Z,B=Q【解答】解:对于A=N*,B=N,存在函数f(x)=x﹣1,x∈N*,满足:(i)B={f (x)|x∈A};(ii)对任意x1,x2∈A,当x1<x2时,恒有f(x1)<f(x2),所以选项A是“保序同构”;对于A={x|﹣1≤x≤3},B={x|x=﹣8或0<x≤10},存在函数,满足:(i)B={f(x)|x∈A};(ii)对任意x1,x2∈A,当x1<x2时,恒有f(x1)<f(x2),所以选项B是“保序同构”;对于A={x|0<x<1},B=R,存在函数f(x)=tan(),满足:(i)B={f(x)|x∈A};(ii)对任意x1,x2∈A,当x1<x2时,恒有f(x1)<f(x2),所以选项C是“保序同构”;前三个选项中的集合对是“保序同构”,由排除法可知,不是“保序同构”的只有D.故选:D.三、解答题19.(12分)已知函数f(x)=|x﹣1|,g(x)=﹣x2+6x﹣5.(1)若g(x)≥f(x),求实数x的取值范围;(2)求g(x)﹣f(x)的最大值.【解答】解:(1)当x≥1时,f(x)=x﹣1;∵g(x)≥f(x),∴﹣x2+6x﹣5≥x﹣1;整理,得(x﹣1)(x﹣4)≤0,解得x∈[1,4];当x<1时,f(x)=1﹣x;∵g(x)≥f(x),∴﹣x2+6x﹣5≥1﹣x,整理,得(x﹣1)(x﹣6)≤0,解得x∈[1,6],又,∴x∈∅;综上,x的取值范围是[1,4].(2)由(1)知,g(x)﹣f(x)的最大值在[1,4]上取得,∴g(x)﹣f(x)=(﹣x2+6x﹣5)﹣(x﹣1)=﹣+≤,∴当x=时,g(x)﹣f(x)取到最大值是.20.(14分)已知向量(m∈R),且.设y=f(x).(1)求f(x)的表达式,并求函数f(x)在上图象最低点M的坐标.(2)若对任意,f(x)>t﹣9x+1恒成立,求实数t的范围.【解答】解:(1)∵,即,消去m,得,即,时,,,即f(x)的最小值为1,此时∴函数f(x)的图象上最低点M的坐标是(2)∵f(x)>t﹣9x+1,即,当时,函数单调递增,y=9x单调递增,∴在上单调递增,∴的最小值为1,为要恒成立,只要t+1<1,∴t<0为所求.21.(14分)如图所示,一种医用输液瓶可以视为两个圆柱的组合体.开始输液时,滴管内匀速滴下球状液体,其中球状液体的半径毫米,滴管内液体忽略不计.(1)如果瓶内的药液恰好156分钟滴完,问每分钟应滴下多少滴?(2)在条件(1)下,设输液开始后x(单位:分钟),瓶内液面与进气管的距离为h(单位:厘米),已知当x=0时,h=13.试将h表示为x的函数.(注:1cm3=1000mm3)【解答】解:(1)设每分钟滴下k(k∈N*)滴,则瓶内液体的体积cm3,k滴球状液体的体积cm3,∴,解得k=75,故每分钟应滴下75滴.(2)由(1)知,每分钟滴下πcm3药液,当4≤h≤13时,xπ=π•42•(13﹣h),即,此时0≤x≤144;当1≤h<4时,xπ=π•42•9+π•22•(4﹣h),即,此时144<x≤156.综上可得.22.(16分)如图,椭圆C1:+y2=1,x轴被曲线C2:y=x2﹣b截得的线段长等于C1的长半轴长.(1)求实数b的值;(2)设C2与y轴的交点为M,过坐标原点O的直线l与C2相交于点A、B,直线MA、MB分别与C1相交于D、E.①证明:•=0;②记△MAB,△MDE的面积分别是S1,S2.若=λ,求λ的取值范围.【解答】(1)解:由题意知:半长轴为2,则有2=2 …(3分)∴b=1 …(4分)(2)①证明:由题意知,直线l的斜率存在,设为k,则直线的方程为y=kx.与抛物线方程联立,消去y可得x2﹣kx﹣1=0,…(6分)设A(x1,y1),B(x2,y2),则x1,x2是上述方程的两个实根,于是x1+x2=k,x1x2=﹣1.…(7分)又点M的坐标为(0,﹣1),所以k MA k MB=×==﹣1…(9分)故MA⊥MB,即MD⊥ME,故…(10分)②设直线的斜率为k1,则直线的方程为y=k1x﹣1,代入抛物线方程可得x2=k1x,解得x=0或x=k1,则点A的坐标为(k1,)…(12分)同理可得点B的坐标为.于是==直线的方程为y=k1x﹣1,代入椭圆方程,消去y,可得()x2﹣8k1x=0,解得x=0或x=,则点D的坐标为;…(14分)同理可得点E的坐标于是S2==因此,…(16分)又由点A,B的坐标可知,k==,平方后代入上式,所以λ=故λ的取值范围为[).…(18分)23.(18分)已知数列{a n}满足:a1=1,|a n+1﹣a n|=p n,n∈N*,S n为数列{a n}的前n项和.(1)若{a n}是递增数列,且a1,2a2,3a3成等差数列,求p的值;(2)若p=,且{a2n﹣1}是递增数列,{a2n}是递减数列,求数列{a n}的通项公式;(3)若p=1,对于给定的正整数n,是否存在一个满足条件的数列{a n},使得S n=n,如果存在,给出一个满足条件的数列,如果不存在,请说明理由.【解答】解:(1){a n}是递增数列,且a1,2a2,3a3成等差数列,4a2=a1+3a3,又a2﹣a1=p,a3﹣a2=p2,所以3p2﹣p=0,解得p=或者p=0(舍去)(2)p=,且{a2n﹣1}是递增数列,{a2n}是递减数列,所以a2n﹣a2n﹣1>0,a2n+1﹣a2n<0,,,所以a n=a1+(a2﹣a1)+(a3﹣a2)+…(a n﹣a n﹣1)=1﹣+…+=;(3)由题意得|a n+1﹣a n|=1,而a1=1,所以a2=2,0;a3=3,1,﹣1;a4=4,2,0,﹣2…所以S1=1,S2=3,1;S3=6,4,2,0;S4=10,8,6,4,0,﹣2…即S4k﹣3为奇数;S4k﹣2为偶数;S4k为偶数;因此只有S4k﹣3,S4k满足S n=n.。
复旦附中高三期中考

上海复旦附中08届期中II. Multiple Choice (35/150)25.Well over eighty years of age, and thus _____ to walk without support, he now rarely leaves his room.A. unableB. disableC. failedD. incapable26.The little bird was so beautiful and lovely ___ we filmed him waddling here and there until he disappeared from sight.A. asB. whileC. evenD. that27.Untouched by any human activity, the valley hidden in the mountains _____ a natural sanctuary for wild animals.A. remainsB. remainC. is remainedD. are remained28._____, yellow-eyed penguins were reducing sharply.A. Killing the parent birdsB. Attacked the nestsC. Deprived of their natural habitatD. Clearing the forest to make grassland29.It is wrong for our society to be completely _____, the result of which may be that we are rapidly _____ our limited natural resources.A. consumer-orienting, exhaustedB. consumer-oriented, exhaustedC. consumer-orienting, exhaustingD. consumer-oriented, exhausting30.All the money and clothes raised in this charity show will be _____ to people living in poor inland areas.A. belongedB. goneC. givenD. entitled31.As an environmentalist, I made my new century wish to everyone in china –say no to _____ everyday articles like toothbrushes and chopsticks.A. profitableB. recyclableC. portableD. disposable32.Considered the primary wrong doer of environmental pollution, automobiles in many big modern cities are _____ with pollution-control devices.A. mixedB. equippedC. installedD. stocked33.Scientists are increasingly _____ that the earth is getting hotter because of the buildup of the atmosphere of carbon dioxide and other gases.A. convincedB. determinedC. expectedD. relieved34.If there were no subjunctive mood, English _____ much easier.A. will beB. would haveC. shall have beenD. would be35.When the autumn fashions arrive in August, shops will _____ away the summer clothes at discount prices. w.w.w.k.s.5.u.c.o.mA. stumbleB. clearC. driveD. dump36.What is tragic is that, on average, one of every four fish _____ is dead and unnecessarily thrown overboard.A. being caughtB. is caughtC. caughtD. which caught37._____ fish stocks overexploited, or seriously destroyed, the ocean, the last great piece of wilderness on this planet, is _____ serious trouble.A. That … out ofB. With … inC. Because … noD. For … of38.Supplying food and employment, regulating our climate and providing transportation, the ocean is _____ to our lives in many ways.A. basicB. accessibleC. dramaticD. known39.Because of the birth peak 20 years ago, a(n) _____ number of young people find themselves facinga full job market.A. growingB. failingC. upcomingD. decreased40.His life is in such a mess as leads to _____ in a vicious cycle.A. him caughtB. his being caughtC. him to be caughtD. his caught41. A lot of countries have benefited a lot economically from _____ the scientific discoveries made in their universities or even middle schools.A. expandingB. explodingC. exploitingD. exposing42.The journalist has developed the habit of having his camera at hand, _____ he should see something that would make a good news picture.A. just in caseB. in any caseC. in no caseD. in which case43.The revolutionary system of robot-controlled farming developed by the Israeli inventor was _____ he believed could change the face of modern agriculture.A. whenB. whichC. howD. what44.Once, a _____ portion of poor families had their children deprived of higher education, but now students having economic difficulties can receive loan from the government.A. acceptableB. sizableC. feasibleD. suitable45. A powerful inland earthquake, _____ a magnitude of 6.3, rattled the Indonesian island of Sumatratoday, leveling hundreds of buildings and killing at least 70 people.A. measuredB. to measureC. measuringD. measure46.Though this was an original or creative invention, it turned out that it was not _____ useful in real life for various reasons. WHICH IS NOT PROPER?A. a littleB. nearlyC. at allD. exactly47.Entitled “One World, One Dream, Universal Human Rights”, the lett er _____ China's leaders as well as heads of international organizations including the UN and the IOC.A. was addressed toB. was addressedC. addressedD. addressed to48.With house prices soaring, having a house of their own seems to be _____ of most young white collars. w.w.w.k.s.5.A. fairly within the meansB. far beyond the meansC. quite by means ofD. rather without the means49._____ they listened quietly and then came up with many great ideas and suggestions.A. That impressed on meB. What impressed me was thatC. What impressed on me thatD. As was impressed me that50.With that calm and _____ smile of hers, our anxiety almost disappeared into thin air.A. confusingB. reassuringC. opposingD. demanding51.The Minister’s refusal to meet the press _____ j ust how serious the crisis is.A. detectedB. relievedC. revealedD. concealed52.I’m afraid what happens in the historical film bears little ______ to what actually happened.A. coincidenceB. influenceC. inferenceD. resemblance53.Many people have the _____ idea that AIDS virus spreads through physical touch.A. criticalB. faintestC. mistakenD. original54.The keen competition in on-line game industry forced the firms with poor performance to _____ from the market.A. withdrawB. benefitC. adaptD. remove55.We'd better leave things _____ they are until the police arrive.A. whichB. whatC. anywhereD. as56.Opinion polls suggested that only 10% of the population _____ their government.A. should trustB. trustC. trustsD. trusted57. A drama _____ some basic elements such as a complete and dramatic plot, characters interactingwith each other and a thought provoking theme.A. is involved inB. involvesC. involves inD. is involved58.The peace talks are being held _____ a background of increasing violence.A. despiteB. behindC. againstD. within59.At the news of China’s success in the bid for the next Olympics, the whole country was _____ with joy.A. overlookedB. undergoneC. overcomeD. undertakenIII. Cloze Test(A)The room was dark except for the spotlight, which felt to Jeff like a heat lamp beaming on his face. He felt time stand still. He glanced down at his notes, and then, with hands shaking almost uncontrollably, launched into his speech.Afterward, as his mental acuity returned to _60_, he asked his wi fe how he did. He really didn’t know. It was as if he wasn’t there during the speech, _61_ not as the confident and secure CEO that he knew himself to be. Jeff knew instinctively that something was _62_ when he spoke in front of a group. After observing the confidence and poise of the guest speaker that followed him, he finally put a name to it: his power.Does that happen to you? _63_, it’s time to learn an important skill that will make sure you regain your power on the platform: strategic storytelling.Storytelling is a powerful leadership tool. It puts you in touch with your authentic power so you can motivate and inspire your _64_. Professional speakers have learned how to turn storytelling into an art form. They know they can both connect with their audience and _65_ vital messages using the power of storytelling. Stories are the perfect form of communication working on many _66_. Because they are inherently visual and _67_ the imagination, stories cause the non-linear (非直线型的) right brain to get _68_; because the sequence of the story is linear, they also involve the left linear brain. Stories are _69_ as well as educational, thus connecting the heart and the head. They are well received by auditory, visual learners becausewell-crafted stories can combine all modes of learning. In short, stories are the window through which audience members see their own truth.60. A. the public B. conscience C. normal D. excitement61. A. in all B. even so C. at least D. at all62. A. resistant B. present C. upcoming D. missing63. A. If so B. at the same time C. What’s more D. If not64. A. boss B. audience C. lecturers D. teammates65. A. read B. receive C. deliver D. decline66. A. examples B. levels C. performances D. interests67. A. stimulate B. dismiss C. imitate D. escape68. A. threatened B. entaintained C. exhausted D. engaged69. A. ideal B. formal C. impersonal D. emotional(B)A play is a dramatic composition in verse or prose that has been written for theatrical performance and tells a story of conflict and emotion using action and dialogue.Drama is the literature of plays. It is one of three literary genres (drama, epic史诗, and lyric poetry) _70_ by the Greeks. Drama is different than other genres because the author's or dramatist's intention is _71_ by the presentation of actors and theatrical devices, not reading or reciting. It is an oral and visual creation whose written form, which is called the script, is first a(n) _72_, secondly an aid to performance, (actors’ lines), and lastly a printed text for critical and educational reflection. _73_ the words of a dramatic text remain unchanged, the effect of the play varies with each interpretation.Like a short story, a play has time constraints (约束) that require continuous action _74_ into new situations and relationships. This makes an economical _75_ essential. Divisions of acts and scenes mark the _76 _ of time and emphasize major developments.Although some types of drama deliberately avoid a human focus, the focus of most drama is human and characterization is the device. The characters must be _77_ presented and become familiar to the audience in a short time. The method of achieving this is through the primary _78_ of drama; dialogue. Dialogue represents people communicating through speech. Therefore, characterization in drama is _79_ on the dialogue the characters speak, the actions they perform, and what other characters report.70. A. celebrated B. developed C. specified D. observed71. A. initiated B. fulfilled C. mastered D. withdrawn72. A. resolution B. background C. preparation D. influence73. A. Each time B. As C. When D. While74. A. moving B. interpreting C. condensing D. melting75. A. lyrics B. element C. conflict D. plot76. A. limit B. passage C. departure D. worth77. A. quickly B. musically C. merely D. fairly78. A. climax B. spectacle C. clue D. medium79. A. dependent B. reflected C. effective D. carriedIV. Reading Comprehension (35/ 150)(A)According to Alvin Toffler, author of the best seller Future Shock, America has become a throwaway society. Cardboard milk containers and rockets are only two examples. Such products are made for short-term or one-time use. They are becoming larger in number and more important to modern living. Toffler thinks that man’s relationships with things will grow increasingly short in time. w.w.w.k.s.5.u.c.o.mAs proof of this trend, Toffler names products as disposable diapers(织物), bibs, paper napkins, and non-returnable bottles. Vegetables are wrapped in plastic bags. They can be dropped into a pan of boiling water and thrown away after the meal. TV dinners are cooked in throwaway plates. They are even served in them.All the se things are quickly used up. Then they are thrown away without any pity. In Toffler’s view, the American home has become little more than a large processing plant.Toffler further believes that his countrymen are developing throwaway values to go with their throwaway products. He says that easy disposability leads to shorter man-thing relationships. People were once linked with a few objects for a long time. Now they are linked with a lot of objects for a short period.80. Which of the following shows th at man’s relationship with things will grow increasingly short in time? A.Poor quality leads to the short-term use of products. B.People do not like products made for one-time use.C.Products tend to be made to be thrown away after one use. D.Consumer goods are well wrapped or over wrapped.81. Examples in the second paragraph are given to immediately ______.A. show the growing trend toward disposability in AmericaB. warn people of the damage of disposable principleC. appeal for people’s reacti on to anti-pollution movementD. arouse the country’s attention to environmentally friendly products82.The article is written mainly to _____.A.introduce Alvin Toffler’s best seller Future ShockB.present the throwaway problem in AmericaC.talk about the relationship between man and thingsD.boast the throwaway products made in USA83.What does the sentence “the American home has become little more than a large processing plant” mean? A.In America there are a large number of plants in the neighborhood.B.The American home is consuming products in large numbers.C.The American home can process raw materials to make products.D.Each home is in the process of becoming a large factory.(B) What is the Big Schools' Birdwatch?In 2007, over 30,000 UK school children stuck black paper with eye-slits on classroom windows, put up bird posters, borrowed binoculars, made bird feeders out of old plastic bottles, and stared out of their classroom windows. Why? They were taking part in the RSPB Big Schools’ Birdwatch.What is the Big Schools’ Birdwatch?➢The Big Schools’ Birdwatch is simple t o set up and fun for children of all ages to take part in. Children are asked to watch the birds in their school grounds or local parks and record the highest number of each species they see at any one time.➢ A free resource pack is available for teachers and provides information about the host of curriculum-linked activities that can be incorporated into this event.➢Teachers, or children, can return their results via online or postal forms to receive a certificate and letter of thanks for their school.➢The Big Schools’ Birdwatch is part of the world’s biggest annual bird watching event; the RSPB’s Big Garden Birdwatch.➢The Big Schools’ Birdwatch provides an opportunity for thousands of children to join in, discover the birdlife within their local environment whilst at school, and join the nearly half a million people that took part in the Big Garden Birdwatch 2007.Big Schools’ Birdwatch 2008➢The Big Schools’ Birdwatch has grown steadily over the past five years and 2008 will be our biggest and best year, with exciting new incentives and awards.Join in➢To request your Big Schools’ Birdwatch teachers’ pack, please e-mail us (details below) with your name and address. You will receive your pack later in the year.The next Big Schools’ Birdwatch will take place in 2008, for two weeks during January and February. Contact E-mail: Education@ Last modified: 30 May 200784.The purpose of the Big Schools’ Birdwatch is _____.A. to take full advantage of buildings of UK schools to observe birdsB. to teach school children how to set up birdwatch organizationC. to do scientific research of birds within and out of the countryD. to engage school children in watching and making records about local birds85.To take part in the activity, one needs _____.A. to send out his personal information before 20 May, 2007B. to give his name and address by emailC. to be a member of the Big Garden BirdwatchD. to be a school student in UK 86.Participants of The Big Scho ols’ Bridwatch do all the things EXCEPT _____.A. watching birds with binocularsB. putting up bird postersC. giving away resource pack to the localsD. making records about bird species87.The Big Schools’ Birdwatch ______.A. is an annual eventB. has half a million participants in 2008C. is to attract participants from all over the worldD. will be the biggest event in UK in 2008(C)★This Week’s Highlights● Visit the new College of Engineering Alu mni Web forcoming events, photo collections, and career services.● Reunion Weekend 2007 is just around the corner, and weinvite you back to BU to take part in all the fun.★BU Breaking News□ Boston University Professor demands Napping at the W orkplace in His Speech.(3/18)□ Boston University Hosts Discussion on Putin, U.S.-Russian ties for Future. (3/11)□ BU Physicist Receives Boltzmann Award For Excellent Work In Physics at the Conference.(3/8)★Features□ Learn more about the Young Alumni C ouncil, serving alumni up to 15 years out of BU.□ Offer students jobs for earning income to pay their taxes.★□ Four BU students share their home schooling experiences,and the lessons they learned.□ Scientists at the South End will study the world’s mostdangerous microbes, and develop measures to bioterrorism88. Which of the following statements is true according to the webpage? A. Alumni Web cares only about BU’s scientific research. B. BU provides its teaching staff with napping break.C. Reunion Weekend 2007 is one of the most important news of this week.D. This is a webpage of an engineering club.89. The underlined word “around the corner” probably means “______”.A. in the immediate future B . at present C. in the distant futureD. around here90. If you are a biology student at BU, what is most probably your first choice after you finish reading thewebpage? 高. A. Watch the video of the Discussion. B. Buy the magazine Bostonia.C. Watch the video of the Conference.D. Book tickets for the Reunion Weekend.(D) GHI Hosts Delhi Colleagues in CaliforniaMillions of people in urban areas throughout India stand to benefit from a pilot project now underway in Delhi, India to improve the seismic safety of existing buildings there. India has one of the greatest seismic risks in the world. About 610 million people reside in the area of highest seismic risk in the north, where there have been seven large-magnitude earthquakes during the last 100 years.To help reduce this risk, USAID funded GeoHazards International (GHI), a non-profit serving earthquake-threatened communities world wide, would work with the Government of India on the transfer of American earthquake retrofit (翻新) technology and experience. The pilot project, US Assistance to Seismic Retrofitting of Lifeline Buildings in Delhi, India, will analyze five groups of buildings in Delhi and facilitate a potential nation-wide movement to reduce earthquake risk in India. "Lifeline" buildings are needed after earthquakes. They include hospitals, schools, police headquarters and key government buildings. The 3-year project includes preparing designs for retrofit of the selected lifeline buildings, developing decision-making procedures, building capacity for similar work elsewhere in India, and fostering relationships among Indian and US engineers.In April, American experts participated in a review panel meeting held in Delhi. Now GHI will host 14 Indian earthquake engineers and government officials responsible for earthquake safety who are coming from Delhi to the San Francisco Bay Area in August for the second review panel meeting. The visitors will collaborate withThe Alumni MagazineWinter 2006their California counterparts and participate in on-site tours of earthquake retrofit projects at the University of California campus. "Local experts will serve as guides to demonstrate the lessons Californians learned when retrofitting buildings during the last 30 years," according to L. Thomas Tobin of GHI. "Improved seismic safety requires cutting-edge engineering 'know how' and wise facilities management practices." says Tobin.91.The underlined word in the first paragraph means _____.A. relating to or caused by earthquakesB. relating to the energy of the earthC. of the study of retrofit of buildingsD. causing physical or mental pain92.The pilot project of GHI will _____.A. host another two review meetings both in Delhi and CaliforniaB. help to reduce the damage of the recent earthquakes throughout IndiaC. make design to retrofit some lifeline buildings and plan specific proceduresD. strengthen the diplomatic relationship between India and US93.Lifeline Buildings include the following buildings EXCEPT _____.A. schools and hospitalsB. government buildingsC. air ports and train stationsD. police headquarters94.According to the expert of GHI, improving seismic safety needs _____.A. the positive and determined public actionB. rich experience in earthquake preventionC. to rebuild the whole cityD. the most advanced knowledge in engineeringVI. Translation1.家庭的和谐基于理解和尊重。
上海市复旦附中2015届高三最后一卷数学文理试题 Word版无答案

2015年考前最后一卷(文理科)时间120分钟,满分150分2015.05.28一、填空题(每题4分,共56分)1.若复数z 满足2i z i z =-(i 是虚数单位),则z =________.2.直线12:3l y x=的一个单位法向量n =________. 3.函数cos cos 3y x x π⎛⎫=+- ⎪⎝⎭的最大值为________.4.若圆锥的侧面积与其底面积之比为2,则该圆锥的轴与母线的夹角大小为________.5.若曲线C 为到点()0,1和()0,1-距离之和为4的动点的轨迹,则曲线C 的方程为________.6.设等差数列{}n a 的公差d 不为0,若对于任意*N i ∈,行列式1+23ii i i a a a a ++的值恒等于公差d ,则d =________.7.(理科)两本书随机给甲、乙、丙三人,则甲拿到的书的数目ξ的数学期望E ξ=________. (文科)若集合{}1,2,3,4,,A a A b A =∈∈,那么方程221x y a b+=表示中心在原点,焦点在y轴的椭圆的概率为________.8.在1时15分时,时针与分针所成的最小正角是________弧度.9.定义:区间[]()1212,x x x x <的长度为21x x -,若函数2log 2xy =的定义域为[],m n ,值域为[]0,2,则区间[],m n 长度的最小值为________.10.设12,e e 为单位向量,非零向量12,,b xe ye x y R =+∈,若12,e e 的夹角为6π,则x b的最大值等于________.11.已知运算按下面的方式定义:2a b a ab =-,若整数,x y 使()2400x y =成立,则在所有满足条件的整数对(),x y 中,x y +的最大值为________.12.设()f x 是定义在正整数集上的函数,且()f x 满足:“当()2f k k ≥成立时,总可推出()()211f k k +≥+成立”.那么,下列四个命题中,正确的是________.(填写命题序号)①若()24f <成立,则()10100f <;②若()39f >成立,则当4k ≥时,均有()2f k k >成立;③若()425f ≥成立,则当4k ≥时,均有()2f k k ≥成立;④若()525f <成立,则()11f ≤;13.在n 行n 列矩阵12321234113451212321n n n n n nn n n n --⎛⎫ ⎪- ⎪⎪ ⎪ ⎪⎪---⎝⎭中,记位于第i 行j 列的数为(),1,2,,ij a i j n =,当7n =时,表中所有满足2i j <的ij a 和为________.14.设,R a b ∈,且对一切0x ≤,不等式()()2220ax x b ++≤恒成立,则2a b -的最小值为________.二、选择题(共4大题,满分20分,每小题中只有一个正确选项,选对得5分,否则0分) 15.已知集合1,Z 2P x x k k ⎧⎫==+∈⎨⎬⎩⎭,,Z 2k Q x x k ⎧⎫==∈⎨⎬⎩⎭,记原命题:“x P ∈,则x Q ∈”.那么,在原命题及其逆命题、否命题、逆否命题中,真命题的个数是( )A.0B.1C.2D.416.(理科)已知极坐标中圆C 的方程为2cos 4πρθ⎛⎫=- ⎪⎝⎭,则圆心的极坐标为( )A. 1,4π⎛⎫ ⎪⎝⎭B. 31,4π⎛⎫ ⎪⎝⎭C. 1,4π⎛⎫- ⎪⎝⎭D. 31,4π⎛⎫- ⎪⎝⎭(文科)把函数()2log 234y x =-+的图像按向量a 平移后得到函数()2log 2y x =的图像,则a =( )A. 3,42⎛⎫- ⎪⎝⎭B. 3,42⎛⎫-- ⎪⎝⎭C. 3,42⎛⎫- ⎪⎝⎭D. ()3,4-- 17.若干个平面把一个长方体分成k 个四面体,这些四面体的体积之和等于长方体的体积,则k 的最小值为( ) A.3 B.4 C.5 D.618.定理:若0,2x π⎛⎫∈ ⎪⎝⎭,则sin x x <.设,,0,2a b c π⎛⎫∈ ⎪⎝⎭,其中a 是函数y x =与cos y x =图像交点的横坐标,()sin cos b b =,()cos sin c c =,则,,a b c 的大小关系是( ) A.a b c <<B. a c b <<C. b a c <<D. b c a <<三、解答题(共5大题,满分74分,写出必要的文字说明与步骤) 19.(本题满分12分,第1小题6分,第2小题6分)已知正方体1111ABCD A B C D -的棱长为1,点O 是1BD 的中点,M 是棱1AA 上的一点,请问:(1)若M 是1AA 的中点,求直线MO 与1AD 所成角的大小;(2)若M 在线段1AA (不为点A )上运动,试求三棱锥1M ABD -体积的最大值.20. (本题满分14分,第1小题6分,第2小题8分) 在ABC ∆中,3A π∠=,1BC =.(1)若4B π∠=,求AC 的长;(2)若ABC ∆1,求ABC ∠的值.21. (本题满分14分,第1小题7分,第2小题7分) 设常数R a ∈,若函数()()f x a x x =-存在反函数()1f x -. (1)求证:0a =,并求出反函数()1f x -;(2)若关于x 的不等式()()12f x m f x -+<对一切[]2,2x ∈-恒成立,求实数m 的取值范围.ABCD 1A 1B 1C 1D MO22. (本题满分16分,第1小题4分,第2小题6分,第3小题6分)已知直线l 过点()2,1A --,直线l 的一个方向向量为()1,1,抛物线Γ的方程为2y ax =. (1)求直线l 的方程;(2)若直线l 与抛物线Γ交于,B C 两点,且BC 是AB 和AC 的等比中项,求抛物线Γ的方程;(3)设抛物线Γ的焦点为F ,问:是否存在正整数a ,使得抛物线Γ上至少有一点P ,满足PF PA =?若存在,求出所有这样的正整数a 的值;若不存在,说明理由.23. (本题满分18分,第1小题4分,第2小题6分,第3小题8分)对于给定数列{}n x ,若存在一个常数*k N ∈,对于任意的*n N ∈,使得n k n x x +=成立,则称数列{}n x 是周期数列,k 是数列{}n x 的一个周期,若k 是数列{}n x 的周期,且1,2,,1k -均不是数列{}n x 的周期,则称k 为数列{}n x 的最小周期.已知数列{}n a 的最小周期为4,前n 项和为n S ,且()241n n S a =+.(1)求1a 的值;(2)求数列{}n a 通项公式n a 和前n 项和n S ;(3)已知数列{}n b 是首项为135,公比为13的等比数列,记数列{}n n a b ⋅的前n 项和为n T ,求n T 的取得最大值和最小值时n 的值.。
上海市复旦大学附属中学2024届高三上学期期中数学试题

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复旦大学附属中学2015学年第一学期高三年级英语期中考试试卷第I卷(共103分)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 conversation and the question 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. This afternoon. B. Tomorrow. C. Next week. D. Next month.2. A. She doesn’t play tennis well. B. She likes other sports as well.C. She is an enthusiastic tennis player.D. She is a professional athlete.3. A. At a paint store. B. At an oil market.C. At a science museum.D. At a gallery.4. A. Work in the yard. B. Buy some wood.C. Go to the bookstore.D. Take a walk.5. A. A taxi driver. B. A passenger. C. A car cleaner. D. A mechanic.6. A. Call a repairman. B. Get out the paper stuck.C. Turn to her colleague for help.D. Restart the machine.7. A. There are not enough gardens. B. Parking areas are full before 10:00.C. Parking areas are closed after 10:00.D. All classes begin at 10:00.8. A. The presentation will begin at noon.B. She’ll present her work to the man.C. She’d like to invite the man for lunch.D. She suggests working on the presentation at 12:00.9. A. The dormitory hours. B. The problem with the rules.C. The door number of the dormitory.D. The time to open the dormitory.10. A. The chairs didn’t need to be painted.B. He doesn’t like the color of the chairs.C. The park could have avoided the problem.D. The woman should have been more careful.Section BDirections: In section B, you will hear two short passages, and you will be asked three questions on each of the passages. The passages 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. Worried B. Surprised. C. Satisfied. D. Uninterested.12. A. It spoiled Juana’s reputation. B. It copied her ideas without permission.C. It bought Juana’s dishwashers.D. It wanted to share the dishwasher market.13. A. A successful business case. B. Juana’s waterless laundry.C. A case against a global company.D. The worldwide dishwasher market.Questions 14 through 16 are based on the following passage.14. A. Footprints. B. Food. C. Living insects. D. Orange seeds.15. A. Don’t touch animals under any circumstances.B. Don’t take away any natural objects from the park.C. Don’t leave litter in the park or throw any off the boat.D. Don’t transport animals from one island to another.16. A. To protect the guide’s interest. B. To improve the unique environment.C. To ensure a trouble-free visit.D. To get rid of illegal behaviors.Section CDirections: In section C, you will hear two longer conversations. The conversations will be read twice. After you hear each conversation, you are required to fill in the numbered blanks with the information you have heard. (本题做在答题纸上)Write onlyII. Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages 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.(A)Libraries are my world. I've been a patron all my life, and for the past nine years I (25) ______ (work) at multiple libraries and archives in and around Detroit. The library (26) ______ an institution has many roles, but as our country struggles through an economic crisis, I have watched the library where I work evolve into a career and business center, a community gathering place and a bastion for hope.In the spring of 2007 I got a library internship at the Southfield Public Library, just north of Detroit. Summers at SPL (27) ______ (be) usually slow, but that year, we experienced a library that hustled and bustled like science-fair project week, midterms or tax season. Yet patrons weren't looking for Mosby's Nursing Drug Reference or 1040 forms. They were coming for information on entrepreneurship and growing their small business.I interpreted people's interest in our business collection as the first step to (28) ______ (pursue) their dreams, but these patrons were not motivated by dreams. They were responding to reality, and they were looking for Plan B.Things worsened in 2008, and in 2009 the economic crisis continues to suffocate Michigan. Last year, we put up a display with a variety of job resources that we restocked every hour. Each night the library closed, the display was bare. (29) ______ we normally keep displays up for a week, we kept the job resources display up for months.Then there's the tightening credit market. People see the writing on the wall and they want to get educated. They can't afford a financial adviser, but checking books out is free. Some of (30) ______(popular) titles now are "Rich Dad, Poor Dad," "Think and Grow Rich," and "Suze Orman's 2009 Action Plan."The economic downturn affects us all. I have had to work long hours and don't get to see (31) ______ of my boyfriend or experience any kind of social life lately, but I am thankful to be in a position where I can help people overcome this struggle. In Michigan, we haven't lost hope. (32) ______ ______ ______ there are libraries here, there will always be hope.(B)It’s estimated that 300 million people in China are studying, or (33) ______ (study), English. That’s an impressive number and I can’t think of any other country in the world where one quarter of the population is so dedicated to (34) ______ (learn) a second language. But some people are questioning whether this “craze” for studying English is worthwhile.Professor Zhang Shuhua of the Chinese Academy of Social Sciences says that too much emphasis is placed on learning English and that it is a waste of education resources as well as a threat to the study of Chinese. He says that having English as a compulsory course in university “has distracted much of students’attention (35) ______ specialized subjects,”and that some students have been denied access to postgraduate education because they failed English. Others have admitted that studying so much English has made them (36) ______ (poor) Chinese speakers.Both of these criticisms are legitimate, but they beg the question of why so many Chinese still want to learn English. English, (37) ______ recognize, is the lingua franca of the modern world. It is the language of business and has become the language of international relations and culture. When people from different countries get together, they frequently speak in English rather than try to translate their native languages. It seems that everyone everywhere can speak at least some English.For China to be part of that international conversation, it is necessary that some level ofEnglish proficiency (38) ______ be achieved. But what, you may ask, about those who will never speak a word of English once they leave school? Well, for good or ill, they will still be surrounded by English. It is there in signs, in music, in movies and in the casual conversations they overhear of the increasing number of foreigners on the city streets. To know English is to be included in the rest of the world, (39) ______ ______ your world is limited to China.I agree with Professor Zhang on one point, (40) ______. English should not be a compulsory subject in university. For most, passing the CET is just the endless drudgery of memorizing word lists. There is little emphasis placed on communication. And if you can’t communicate in English after years of study in primary school, middle school and high school, a few more years in university probably won’t help.Section BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.For writers in Western cultures, autumn is a difficult season to describe. On the one hand, it is the end of the summer, and therefore a little sad. The nights draw in, and when you wake in the morning, ther e’s mist and it’s cooler: Winter is around the ___41___. American writer Ernest Hemingway wrote in his book A Moveable Feast: “You expected to be sad in the fall. Part of you died each year when the leaves fell from the trees and their branches were ___42___against the wind and the cold, wintry light.”On the other hand, autumn has its good side. There are so many changes in nature at this time of year, such as the reds and browns that the leaves change to, and the ___43___ they fall from the trees. French writer Albert Camus even though autumn was a second spring: “Autumn is a second spring when every leaf is a flower.” It’s a view you can also find in the most famous autumn poem in English literature, To Autumn by John Keats. In that poem Keats says that the autumn has its own songs, just like spring.Another autumn theme is wisdom. The arrival of the season is thought to be similar to a person becoming ___44___. Their summer peak may have been and gone, but old age has not yet come. At this time it’s thoug ht that people have ___45___ a thing or two about life. The great Irish poet W.B. Yeats takes up this theme in his poem The Wild Swans at Coole. Yeats puts together a picture for the reader out of the ___46___ of the changing seasons in Coole Park in the west of Ireland, a place he knew well. Seeing and counting 59 swans, he remembers first making the count 19 years ago. He ___47___ whether he can still love like the lover swans do.Of course, many other themes and subject matters can play a part in the literature of autumn. For example, it’s the beginning of a new term of the school year. As you would expect, autumncan___48___ in writing for children and young people. But autumn writing usually ___49___ on the changes in nature that we see, which writers often use as a ___50___ for changes in human life.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.After the college-board examinations in June, Basil Duke Lee and five other boys from St. Regis School ___51___ the train for the West. Two got out at Pittsburgh, one slanted south toward St. Louis and two stayed in Chicago; from then on Basil was alone. It was the first time in his life that he had ever felt the need of tranquility, but now he took long breaths of it; for, though things had gone better toward the end, he had had a / an ___52___ year at school.He wore one of those extremely flat derbies (常礼帽) in vogue during the twelfth year of the century, and a blue business suit became a little too short for his constantly ___53___ body. Within he was by turns a disembodied (空洞的) spirit, almost ___54___ of his person and moving in a mist of impressions and emotions, and a fiercely competitive individual trying ___55___ to control the rush of events that were the steps in his own ___56___ from child to man. He believed that everything was a matter of ___57___ — the current principle of American education — and his fantastic ___58___ was continually leading him to expect too much. He wanted to be a great athlete, popular, brilliant and always happy. During this year at school, where he had been punished for his “freshness,” for fifteen years of thor ough spoiling at home, he had grown uselessly introspective, and this ___59___ with that observation of others which is the beginning of wisdom. It was apparent that before he obtained much success in dealing with the world he would know that he’d been in a fight.Fifteen is of all ages the most difficult to ___60___———to put one’s fingers on and say, “That’s the way I was.” And all one can know is that somewhere between thirteen, boyhood’s___61___, and seventeen, when one is a sort of counterfeit young man, there is a time when youth ___62___ hourly between one world and another —— pushed ceaselessly forward into unprecedented experiences and ___63___ trying to struggle back to the days when nothing had to be ___64___ for. Fortunately none of our contemporaries remember much more than we do of how we behaved in those days; nevertheless the ___65___ is about to be drawn aside for an inspection of Basil’s madness that summer.51. A. boarded B. missed C. jumped D.followed52. A. happy B. unhappy C.memorableD.favourable53. A. swelling B. bending C. lengthening D.strengthening54. A. aware B.fond C. critical D.unconscious55. A. randomly B. desperately C. particularly D.indifferently56. A. evolution B. revolution C. solutionD.introduction57. A. fact B. opinion C. course D. effort58. A. fashion B. ambition C. character D.treasure59. A. contacted B. associated C. interfered D.smashed60. A. digest B.describe C. deal D. locate61. A. majority B. minority C. senior D. junior62. A. floats B. varies C. fluctuates D. ranges63. A. successfully B. vainly C. wildly D. gently64. A. hunted B. provided C. compensated D. paid65. A.curtain B. adolescence C. portrait D. ceilingSection 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)There are people in Italy who can’t stand soccer. Not all Canadians love hockey. A similar situation exists in America, where there are those individuals you may be one of them who yawn or even frown when somebody mentions baseball. Baseball to them means boring hours watching grown men in funny tight outfits standing around in a field staring away while very little of anything happens. They tell you it’s a game better suited to the 19th century, slow, quiet, gentlemanly. These are the same people you may be one of them who love football because there’s the sport that glorifies “the hit”.By contrast, baseball seems abstract, cool, silent, still.On TV the game is fractured into a dozen perspectives, replays, close ups. The geometry of the game, however, is essential to understanding it. You will contemplate the game from one point as a painter does his subject; you may, of course, project yourself into the game. It is in this projection that the game affords so much space and time for involvement. The TV won’t do it for you.Take, for example, the third baseman. You sit behind the third base dugout and you watch him watching home plate. His legs are apart, knees flexed. His arms hang loose. He does a lot of this. The skeptic still cannot think of any other sports so still, so passive. But watch what happens every time the pitcher throws: the third baseman goes up on his toes, flexes his arms or brings the glove to a point in front of him, takes a step right or left, backward or forward, perhaps he glances across the field to check his first baseman’s position. Suppose the pitch is a ball. “Nothing happened,” you say. “I could have had my eyes closed.”The skeptic and the innocent must play the game. And this involvement in the stands is no more intellectual than listening to music is. Watch the third baseman. Smooth the dirt in front of you with one foot; smooth the pocket in your glove; watch the eyes of the batter, the speed of the bat, the sound of horsehide on wood. If football is a symphony of movement and theatre, baseball is chamber music, a spacious interlocking of notes, chores and responses.66. Those who don’t like baseball may complain that ______.A. it is only to the taste of the oldB. it involves fewer players than footballC. it is not exciting enoughD. it is pretentious and looks funny67. The author admits that ______.A. baseball is too peaceful for the youngB. baseball may seem boring when watched on TVC. football is more attracting than baseballD. baseball is more interesting than football68. By stating ‘I could have had my eyes closed.’ the author means (4th paragraph last sentence):A. The third baseman would rather sleep than play the game.B. Even if the third baseman closed his eyes a moment ago, it could make no difference to theresult.C. The third baseman is so good at baseball that he could finish the game with eyes closed allthe time and do his work well.D. The consequence was too bad he could not bear to see it.69. We can safely conclude that the author ______.A. likes footballB. hates footballC. hates baseballD. likes baseball(B)Some of the world’s most significant problems never hit headlines. One example comes from agriculture. Food riots and hunger make news. But the trend lying behind these matters is rarely talked about. This is the decline in the growth in yields of some o f the world’s major crops. A new study by the University of Minnesota and McGill University in Montreal looks at where, and how far, this decline is occurring.The authors take a vast number of data points for the four most important crops: rice, wheat corn and soybeans. They find that on between 24% and 39% of all harvested areas, the improvement in yields that took place before the 1980s slowed down in the 1990s and 2000s.There are two worrying features of the slowdown. One is that it has been particularly sharp in the world’s most populous countries, India and China. Their ability to feed themselves has been an important source of relative stability both within the countries and on world food markets. That self-sufficiency cannot be taken for granted if yields continue to slow down or reverse.Second, yield growth has been lower in wheat and rice than in corn and soya beans. This is problematic because wheat and rice are more important as foods, accounting for around half of all calories consumed. Corn and soybeans are more important as feed grains. The authors note that “we have preferentially focused our crop improvement efforts on feeding animals and ca rs rather than on crops that feed people and are the basis of food security in much of the world.”The report qualifies the more optimistic findings of another new paper which suggests that the world will not have to dig up a lot more land for farming in order to feed 9 billion people in 2050, as the Food and Agriculture Organization has argued.Instead, it says, thanks to slowing population growth, land currently ploughed up for crops might be able to revert to forest or wilderness. This could happen. The trouble is that the forecast assumes continued improvements in yields, which may not actually happen.70. What does the author try to draw attention to?A. Food riots and hunger in the world.B. News headlines in the leading media.C. The decline of the grain yield growth.D. The food supply in populous countries.71. Why does the author mention India and China in particular?A. Their self-sufficiency is vital to the stability of world food markets.B. Their food yields have begun to decrease sharply in recent years.C. Their big populations are causing worldwide concerns.D. Their food self-sufficiency has been taken for granted.72. What does the new study by the two universities say about recent crop improvement efforts?A. They fail to produce the same remarkable results as before the 1980s.B. They contribute a lot to the improvement of human food production.C. They play a major role in guaranteeing the food security of the world.D. They focus more on the increase of animal feed than human food grains.73. What does the Food and Agriculture Organization say about world food production in the coming decades?A. The growing population will greatly increase the pressure on world food supplies.B. The optimistic prediction about food production should be viewed with caution.C. The slowdown of the growth in yields of major food crops will be reversed.D. The world will be able to feed its population without increasing farmland.(C)Among the more colorful characters of Leadville’s golden age were H.A.W. Tabor and his second wife, Elizabeth McCourt, better known as “Baby Doe”. Their history is fast be coming one of the legends of the Old West. Horace Austin Warner Tabor was a school teacher in Vermont. With his first wife and two children he left Vermont by covered wagon in 1855 to homestead in Kansas. Perhaps he did not find farming to his liking, or perhaps he was tempted by rumors of fortunes to be made in Colorado mines. At any rate, a few years later he moved west to the small Colorado mining camp known as California Gulch, which he later renamed Leadville when he became its leading citizen. “Great deposits of lead are sure to be found here.” he said.As it turned out, it was silver, not lead, that was to make Leadville’s fortune and wealth. Tabor knew little about mining himself, so he opened a general store, which sold everything from boots to salt, flour, and tobacco. It was his custom to “grubstake” prospective miners, in other words, to supply them with food and supplies, or “grub”, while they looked for ore, in return for which he would get a share in the mine if one was discovered. He did this for a number of years, but no one that he aided ever found anything of value.Finally one day in the year 1878, so the story goes, two miners came in and asked for “grub”. Tabor had decided to quit supplying it because he had lost too much money that way. These werepersistent, however, and Tabor was too busy to argue with them. “Oh help yourself. One more time won’t make any difference,” He said and went on selling shoes and hats to other customers. The two miners took $17 worth of supplies, in return for which they gave Tabor a one-third interest in their findings. They picked a barren place on the mountain side and began to dig. After nine days they struck a rich vein of silver. Tabor bought the shares of the other two men, and so the mine belonged to him alone. This mine, known as the “Pittsburgh Mine,” made 1 300 000 for Tabor in return for his $17 investment.Later Tabor bought the Matchless Mine on another barren hillside just outside the town for $117 000. This turned out to be even more fabulous than the Pittsburgh, yielding $35 000 worth of silver per day at one time. Leadville grew. Tabor became its first mayor, and later became lieutenant governor of the state.74. Leadville got its name for the following reasons EXCEPT ______.A. because Tabor became its leading citizenB. because great deposits of lead is expected to be found thereC. because it could bring good fortune to TaborD. because Tabor renamed it so75. The word “grubstake” in paragraph 2 means ______.A. to supply miners with food and suppliesB. to open a general storeC. to do one’s contribution to the development of the mineD. to supply miners with food and supplies and in return get a share in the mine, if one wasdiscovered76. Tabor made his first fortune ______.A. by supplying two prospective miners and getting in return a one-third interest in the findingsB. because he was persuaded by the two miners to quit supplyingC. by buying the shares of the otherD. as a land speculator77. The underlying reason for Tabor’s life career is ______.A. purely accidentalB.based on the analysis of miner’s being very poor and their possibility of discoveringprofitable mining siteC. through the help from his second wifeD. he planned well and accomplished targets step by stepSection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.When the Internet powerhouse Yahoo wanted to teach ethics to its employees, it faced a challenge familiar to multinational companies.Yahoo employs nearly 14,000 people at 25 sites worldwide. They would feel bored at sitting down in front of a dated video in which actors with 1980s haircuts tell them what to do. So it hired a company called The Network to design a game. In the game, the truck where Yahoo wasfounded traveled the world, turning into a boat and a helicopter along the way as it visited some of Yahoo's foreign offices. Participants play in game show-like scenarios that quiz them about conflicts of interest and doing business fairly. And employees note: Yahoo is tracking how well they do.Such activities draw more enthusiastic participation and teach more effectively than traditional methods. They are described as alternative-reality games (ARGs), involving both interactive and real-world elements. Besides teaching employees, ARGs have also been used in many areas for a number of different purposes.From a marketing perspective, a number of very successful ARGs have been written as a way to build product awareness. A very popular ARG called I Love Bees was produced to market the 2004 video game Halo 2. At its height, I Love Bees received between two to three million unique visitors over the course of three months.ARGs are more than just a fun way to learn. They have also been used to solve real world problems. An ARG called World Without Oil was created to obtain collective input from players about dealing with the world's dependency on oil. World without Oil simulates the first 32 days of a global oil crisis and anybody could play by creating a personal story that recorded the imagined reality of their life in the crisis. World Without Oil's success on a small budget has opened the door for similar games to engage mainstream Internet users with climate change, education reform, governmental policy and other timely, vital issues.(Note: Answer the questions or complete the statements in NO MORE THAN TEN WORDS.)78.What challenge did face in teaching ethics to its employees?79.In the game designed for , participants had to answer questions about ________.80.What are the three major functions of ARG mentioned in the passage?81.The success of World Without Oil suggests that ARGs can ________.第II卷(共47分)I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.没有人不希望和平。