复旦附中高三毕业(2016.05)
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。
2024-2025学年上海复旦附中高三上学期数学拓展3及答案
1复旦附中2024学年第一学期高三年级数学拓展32024.09一、填空题（本大题共有12题,满分54分,第1-6题每题4分,第7-12题每题5分） 1.已知集合{}3A x x =>，{B x y ==，则AB = .2.函数()22log 4y x x =−+的增区间为 . 3.已知复数221iz i−+=+，则z 的虚部为 . 4.若对于任意的a R ∈，不等式2122a a b b −++≥−恒成立，则实数b 的取值范围是 .5.已知双曲线1Γ与椭圆222:1166x y Γ+=有相同的焦点，且1Γ的渐近线方程为1,2y x =±则双曲线1Γ的标准方程为 .6.若()60b ⎛> ⎝的展开式中含x 项的系数为60，则2a b +的最小值为 .7.等差数列{}n a 中，12024a =−，20232021220232021S S −=，则2024.S = . 8.如图所示，在正四棱锥P ABCD −中，60APC ∠=︒，则二面角A PB C −−的平面角的余弦值为 .9.某电子设备有两套相互独立的供电系统A 和B ，在时间T 内系统A 和系统B 发生故障的概率分别为0.2和p .若在时间T 内至少有一个系统不发生故障的概率为0.94，则p = .10.若函数()()()()2210f x x x ax b c c =−++−≠的图像关于直线2x =−对称，且()f x 有且仅有7个零点，则a b c ++= . 11.已知平面向量a ，b ，c ，1a b ==，12a b ⋅=，2a c ⋅=，若对向量d ，定义()d f x x d =−，满足()d fc ,a −则d a d b −+−的取值范围是 .212.已知关于x 的不等式()()2ln 340x kx x k x ⎡⎤−−++≤⎣⎦对任意()0,x ∈+∞均成立，则实数k 的取值范围为 .二、选择题（满分18分，13-14每题4分，15-16每题5分） 13.设a 、b 是非零向量，则“0a b ⋅=”是“a b ⊥”的（ ）条件. A.充分必要B.充分非必要C.必要非充分D.既非充分又非必要14.要得到函数23y sin x π⎛⎫=+ ⎪⎝⎭的图像，只需要将函数sin 2y x =的图像（ ）.A.向左平移23π个单位B.向右平移23π个单位 C.向左平移6π个单位 D.向右平移6π个单位 15.已知直线a 、b 和平面α、β，给出以下三个命题： ①若a ∥α，b ⊥a ，则b ⊥α； ②若a ∥α，α⊥β，则a ⊥β；③若a ∥b ，b ⊂α，则a ∥α；其中真命题有（ ）个. A.0B.1C.2D.316.已知定义在R 上的两个函数()y f x =、()y g x =的最大值、最小值分别为f M ，f m 与g M ，g m .给出如下两个命题：①若f g M m <，则“不等式()()f x a g x ≤≤对一切x R ∈恒成立”的充要条件是“f g M a m ≤≤”；②若f g m M <，则“不等式()()f x a g x ≤≤在R 上有解”的充要条件是“f g m a M ≤≤”.关于两个命题的真假，下面判断正确的是（ ） A.命题①、②均为真命题B.命题①为真命题，命题②为假命题3C.命题①、②均为假命题D.命题①为假命题，命题②为真命题三、解答题（满分78分，17-19每题14分，20-21每题18分） 17.（满分14分，第1小题6分，第2小题8分） 已知关于x 的不等式102ax x −<+的解集为M ，不等式211x −<的解集为N . （1）若()123M ,,⎛⎫=−∞−−+∞ ⎪⎝⎭，求实数a 的值和解集N ； （2）若“x N ∈”是“x M ∈”的充分不必要条件，求实数a 的取值范围.18.（满分14分，第1小题6分，第2小题8分） 已知()()322,2f x x sin x sin x x R π⎛⎫=++π−∈ ⎪⎝⎭. （1）求()y f x =的最小正周期及单调递减区间；（2）已知锐角ABC △的内角A 、B 、C 的对边分别为a 、b 、c ，且()f A =4a =，求BC 边上的高的最大值.419.（满分14分，第1小题6分，第2小题8分）如图，在四棱锥P ABCD −中，平面PAD ⊥底面ABCD ，CD ∥AB ，2PA PD AD DC ====，4AB =，60DAB ∠=︒.（1）证明：BD PA ⊥；（λ）求PD 与平面PAB 所成的角的正弦值.20.（满分18分，第1小题4分，第2小题6分，第3小题8分） 已知双曲线Γ：221x y −=的左、右顶点分别为点A 、B ，M 为双曲线Γ上的动点，点()0,2Q .（1）求点M 到Γ的两条渐近线的距离之积； （2）求经过点Q 的双曲线Γ的切线方程；（3）设点P 在第一象限，且在渐近线的上方，直线PA ，PB 分别与y 轴交于点C ，D .过点P 作Γ的两条切线，分别与y 轴交于点E ，F （E 在F 的上方），证明：CE DF =.521.（满分18分，第1小题4分，第2小题6分，第3小题8分） 已知a R ∈，()2sin sin f x x a x =−. （1）当2a =时，求函数()y f x =的值域； （2）若函数()2y f x f x π⎛⎫=−−⎪⎝⎭在区间02,π⎡⎤⎢⎥⎣⎦上是严格增函数，求a 的最大值；（3）设12a =，u R ∈.方程()f x u =的所有正实数解按从小到大的顺序排列后，是否能构成等差数列？若能，求所有满足条件的u 的值；若不能，说明理由.6参考答案一、填空题1.(]3,4;2.(]0,2;3.2;4.[]1,3;5.22182x y −=;6.;7.2024−; 8.17−; 9.0.3; 10.32；11.3⎡⎤⎣⎦ 12.1,1e ⎡⎤⎢⎥⎣⎦12.已知关于x 的不等式()()2ln 340x kx x k x ⎡⎤−−++≤⎣⎦对任意()0,x ∈+∞均成立，则实数k 的取值范围为 . 【答案】1,1e ⎡⎤⎢⎥⎣⎦【解析】当0k …时,x →+∞时,0lnx kx −>,()2340x k x −++>, 左边必然大于0,不满足题意,所以0k >, 令()()1,'f x lnx kx f x k x=−=−,()()234g x x k x =−++, 对称轴为302k x +=>,开口向上,有最小值, 令()'0f x =,解得1x k=为()f x 极大值点, 情况一:()f x 在x 轴下方,()g x 在x 轴上方,即10302f k k g ⎪⎛⎫≤ ⎪⎝⎭+⎛⎫> ⎪⎧⎪⎨⎝⎪⎪⎩⎭,得不等式组的解集为11k e 剟,情况二：()f x 与()g x 有相同的零点，此时10302f k k g ⎪⎛⎫> ⎪⎝⎭+⎛⎫< ⎪⎧⎪⎨⎝⎪⎪⎩⎭,得不等式组的解集为k 无解,综上所述,11k ,e ⎡⎤∈⎢⎥⎣⎦.故答案为:11,e ⎡⎤⎢⎥⎣⎦.二、选择题13. A 14.C 15.A16.B716.已知定义在R 上的两个函数()y f x =、()y g x =的最大值、最小值分别为f M ，f m 与g M ，g m .给出如下两个命题：①若f g M m <，则“不等式()()f x a g x ≤≤对一切x R ∈恒成立”的充要条件是“f g M a m ≤≤”；②若f g m M <，则“不等式()()f x a g x ≤≤在R 上有解”的充要条件是“f g m a M ≤≤”.关于两个命题的真假，下面判断正确的是（ ） A.命题①、②均为真命题B.命题①为真命题，命题②为假命题C.命题①、②均为假命题D.命题①为假命题，命题②为真命题 【答案】B【解析】对命题①，当不等式()()f x a g x 剟对一切x R ∈恒成立时,则f g M a m 剟, 当f g M a m 剟时，不等式()()f x a g x 剟对一切x R ∈恒成立，故①正确;对命题②,当不等式()()f x a g x 剟在x R ∈上有解，则f g m a M 剟， 当f g m a M 剟，则不等式()()f x a g x 剟在x R ∈上有解,故②正确. 三．解答题17.（1）[)3,0,1a N == （2）1a ≤ 18.（1）5,,,1212T k k k Z ππ⎡⎤=π−+π+π∈⎢⎥⎣⎦（2）19.（1）证明略 （220.（满分18分，第1小题4分，第2小题6分，第3小题8分） 已知双曲线Γ：221x y −=的左、右顶点分别为点A 、B ，M 为双曲线Γ上的动点，点()0,2Q .8（1）求点M 到Γ的两条渐近线的距离之积； （2）求经过点Q 的双曲线Γ的切线方程；（3）设点P 在第一象限，且在渐近线的上方，直线PA ，PB 分别与y 轴交于点C ，D .过点P 作Γ的两条切线，分别与y 轴交于点E ，F （E 在F 的上方），证明：CE DF =. 【答案】（1）12（2）2y =+（3）见解析【解析】(1)设点()11M x ,y ,所以22111x y −=,两个渐近线方程为0x y ±=,所以点M 到Γ2211122x y −==(2)由题意得切线方程斜率存在,设经过点Q 的切线方程为2y kx =+, 联立2212x y y kx ⎧−=⎨=+⎩,消去y 得()221450,k x kx −−−= 因为直线与双曲线相切,所以24200k ∆=−+=所以k =所以切线方程为2y =+; (3)证明:设()2222,,0P x y x y −<,因为()()10,10A ,B ,−所以直线PA 的方程为()2211y y x x =++,直线PB 的()2211y y x x =−−,所以22220,011y y C ,D ,x x ⎛⎫⎛⎫− ⎪ ⎪+−⎝⎭⎝⎭, 设过P 且与双曲线相切的直线方程为()00,y k x x y =−+联立()22221y k x x y x y ⎧=−+⎨−=⎩, 消去y 得()()222222222222122210k x k x ky x kx y k x y −+−+−−−= 所以()2222222448440x k x y k y ∆=−−++=,所以()22222221210x k x y k y −−++=, 设直线,PE PF 的斜率分别为12,k k ,所以22122221x y k k x +=−9所以PE 的方程为()122y k x x y =−+,所以(0,E )212y k x − 同理PF 的方程为()222y k x x y =−+,所以(0F )222,y k x − 所以22222222111C D y y yy y x x x +=−=−+−−, ()22221222222221E F x y y y y k k x y x +=−+=−=−22221yx −−所以C D E F y y y y +=+,所以E C D F y y y y −=−,所以E C D F y y y y −=−,所以CE DF =. 21.（满分18分，第1小题4分，第2小题6分，第3小题8分） 已知a R ∈，()2sin sin f x x a x =−. （1）当2a =时，求函数()y f x =的值域； （2）若函数()2y f x f x π⎛⎫=−−⎪⎝⎭在区间02,π⎡⎤⎢⎥⎣⎦上是严格增函数，求a 的最大值；（3）设12a =，u R ∈.方程()f x u =的所有正实数解按从小到大的顺序排列后，是否能构成等差数列？若能，求所有满足条件的u 的值；若不能，说明理由. 【答案】（1）[]1,3−（2）0（3）能，12u =或32u = 【解析】（1）因为()22,a f x sin x asinx ==−,所以()()22211f x sin x sinx sinx =−=−−,因为11sinx −剟,所以210sinx −−剟,所以()13f x −剟,所以()f x 的值域为[]13,−（2）因为()()2,,2f x sin x asinx y f x f x π⎛⎫=−=−− ⎪⎝⎭所以2222y sin x asinx sin x asin x ππ⎛⎫⎛⎫=−−−+− ⎪ ⎪⎝⎭⎝⎭化简得22y sin x asinx cos x acosx =−−+,因为函数()2y f x f x π⎛⎫=−−⎪⎝⎭在区间02,π⎡⎤⎢⎥⎣⎦上是严格增函数，所以'220y sinxcosx acosx cosxsinx asinx =−+−…在02,π⎡⎤⎢⎥⎣⎦上恒成立,所以()40sinxcosx a sinx cosx −+…在02,π⎡⎤⎢⎥⎣⎦上恒成立,10令t sinx cosx =+,则4t x π⎛⎫=+ ⎪⎝⎭,因为02x ,π⎡⎤∈⎢⎥⎣⎦,所以1t ≤≤,又221sinxcosx t =−,所以2220t at −−…在1⎡⎣上恒成立，所以22a t t≤−在1⎡⎣上恒成立, 又函数22y t t =−在1⎡⎣上单调递增,所以当1x =时,22y t t=−取最小值, 最小值为0,所以0a …,所以a 的最大值为0; (3)因为()21,2f x sin x asinx a =−=,所以不等式()f x u =可化为212sin x sinx u −=, 令t sinx =,则21,112t t u t −=−≤≤,作函数()21112y t t t =−−≤≤的图象,又当14t =时,211216t t −=−,由图象可得当116u <−或32t >时,方程2102t t u −−=在[]11,−上没有解,方程()f x u =没有解； 当116u =−时,方程2102t t u −−=的解为14t =,则14sinx =,方程14sinx =的正实数解按从小到大的顺序排列记为1234,,,,x x x x ,如图,则123150,,266x ,x ,x x ππ⎛⎫⎛⎫∈∈π=+π ⎪⎪⎝⎭⎝⎭,所以该数列不是等差数列, 当11162u −<<时,方程2102t t u −−=在[]11,−内有两个解,设方程的解为12,t t ,且12121111,242t t t t −≤<<≤+=，作函数12,,y sinx y t y t ===图象如下,11方程1sinx t =和2sinx t =的正实数解按从小到大的顺序排列记为1234,,,,x x x x ,设数列1234,,,,x x x x 为等差数列,设数列的公差为1d ,因为512x x −=π,所以12,2d x x π=+=π,则14x π=, 所以354x π=,则12t t ==1212t t +=矛盾, 当1322u <<时,方程2102t t u −−=在[]11,−内有一个解，设方程的解为3t ,且3112t −≤<−,作函数3,y sinx y t ==,图象如下,方程3sinx t =的正实数解按从小到大的顺序排列记为1234,,,,x x x x ,设数列1234,,,,x x x x 为等差数列,设数列的公差为1d ,因为312x x −=π,所以12,3d x x =π+=π,则1x =π,所以30t =,与3112t −≤<−矛盾, 若32u =,则方程2102t t u −−=在[]11,−内的解为41t =−,所以1sinx =−,所以322x k =π+π,所以方程()f x u =的正实数解按从小到大的顺序排列后所得数列为22k π⎧⎫π−⎨⎬⎩⎭,该数列为等差数列,满足条件； 当12u =时,方程2102t t u −−=在[]11,−内有两个解5611,2t t ==−,由1sinx =,可得2,2x k k Z π=π+∈,由12sinx =−,可得26x m π=π−或52,6x m m Z π=π−∈ 所以方程()f x u =的所有正实数解按从小到大的顺序排列后满足 ()()3231712,12,26k k x k x k −−ππ=+−π=+−π()311126k x k π=+−π12所以()2123n x n ππ=+−,所以该数列为等差数列, 综上所述,当12u =或32u =时,方程()f x u =的正实数解按从小到大的顺序排列后所得数列为等差数列。
上海市复旦大学附属中学2023-2024学年语文高三上期末考试模拟试题含解析
上海市复旦大学附属中学2023-2024学年语文高三上期末考试模拟试题注意事项1．考生要认真填写考场号和座位序号。
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1．阅读下面的文字，完成下面小题。
材料一古装剧《鹤唳华亭》一上线就收获不少关注。
这部“服饰艺术从北宋，典章制度从明代”的架空剧，其建筑、服饰、器物的华美，以及礼仪、辞赋、规制的严谨，成为许多观众议论的话题。
既有人文内涵又兼具时尚飘逸，新式古装作品近年已形成一股类型：《绣春刀》《琅琊榜》《知否知否应是绿肥红瘦》《长安十二时辰》都是其中典型。
有学者将其定义为“新国风”——用基于当下日常和流行文化的目光去审视、重构源自中华传统的文化元素，在这些影视作品的传播过程中，则体现出年轻一代用古今对话的姿态传播历史文化的新趋势。
这种用当代视角打捞进而传承历史文化的作品，将传统文化推至时尚前沿地带，是激发青年一代亲近传统的有益尝试；同时，如何掌握尺度、如何尊重传统，让审美体验对话严肃历史而非取而代之，这对创作者提出了更高要求。
同时兼具当下青年文化、网络文化以及时尚流行文化的特点，是“新国风”作品最大的创新点，而中国青年一代文化自觉的崛起是其主要推动力。
“当下青年一代具有更强的文化自信与民族文化认同，他们不再把传统文化视作纯粹的审美客体，或遥远的文化想象符号。
”在中国传媒大学学者王茵看来，传统文化正在成为许多年轻人生活中息息相关的“活”的事物，这种充满主动性的审美文化心态，也在塑形影视作品的审美倾向。
（摘编自张祯希《影视剧“新国风”，传统文化正在引领审美时尚》）材料二近年来，不少年轻人喜爱穿戴汉服等传统服饰，在一定范围形成新的“古风”时尚。
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上海市复旦大学附属中学2016届高三下学期5月月考数学试题
绝密★启用前上海市复旦大学附属中学2016届高三下学期5月月考数学试题注意事项：1．答题前填写好自己的姓名、班级、考号等信息2．请将答案正确填写在答题卡上第I 卷（选择题)请点击修改第I 卷的文字说明一、单选题1．等差数列{}n a 的前n 项和记为n S ，若2415a a a ++的值为一个确定的常数，则下列各数中也是常数的是（ ）A ．7SB ．8SC ．13SD ．15S 2．矩阵的一种运算a b x ax by c d y cx dy +⎛⎫⎛⎫⎛⎫= ⎪⎪ ⎪+⎝⎭⎝⎭⎝⎭，该运算的几何意义为平面上的点(,)x y 在矩阵a b c d ⎛⎫ ⎪⎝⎭作用下变换成点(,)ax by cx dy ++，若曲线22421x xy y ++=，在矩阵11a b ⎛⎫ ⎪⎝⎭的作用下变换成曲线2221x y -=，则+a b 的值为（ ） A ．2- B ．2 C ．2± D ．4-3．．函数()y f x =是R 上的增函数，则0()()()()a b f a f b f a f b +>+>-+-是的（ ） A ．充要条件B ．必要不充分条件C ．充分不必要条件D ．既不充分也不必要条件4．有一容积为33a cm 的正方体容器1111ABCD A B C D -，在棱AB 、1BB 和面对角线1BC 的中点各有一小孔E 、F 、G ，若此容器可以任意放置，则其可装水的最大容积是（ ） A ．331a cm B ．337a cm C ．3311a cm D ．3347a cm第II 卷（非选择题)请点击修改第II 卷的文字说明二、填空题5．已知集合{}|lg M x y x ==，{|N x y ==，则M N =I _____________.6．若复数z 满足()3443i z i -=+，则z 的虚部为________.7．在ABC ∆中，角A 、B 、C 所对的边分别为a 、b 、c ，若6a =，4c =，sin23B =，则b =_____.8．如图所示，一家面包销售店根据以往某种面包的销售记录，绘制了日销售量的频率分布直方图，若一个月以30天计算，估计这家面包店一个月内日销售量不少于150个的天数为________.9．现有5个女生和3个男生随机站成一排，则排头和排尾均为女生的概率是________（结果用分数表示）.10．在极坐标系中，圆2sin ρθ=的圆心到极轴的距离为________.11．无穷等比数列{}n a 的前n 项和为n S ，若12a =，且20152016201723S S S +=，则无穷等比数列{}n a 的各项和为________.12．如图，正三棱柱111ABC A B C -中，4AB =，16AA =，若E 、F 分别是棱1BB 、1CC 上的点，则三棱锥1A A EF -的体积是________.13．设直线2310x y ++=和圆22230x y x +--=相交于点A 、B ，则弦AB 的垂直平分线方程是____．14．在平面直角坐标系xOy 中，抛物线()220y px p =>的焦点为F ，双曲线22221x y a b-=()0,0a b >>的两条渐近线分别与抛物线交于A 、B 两点（A 、B 异于坐标原点O ），若直线AB 恰好过点F ，则双曲线的渐近线方程是________.15．在边长为6的等边△ABC 中，点M 满足2BM MA =u u u u r u u u r ，则CM CB ⋅u u u u r u u u r 等于 ．16．已知函数()2xf x =且()()()f xg xh x =+，其中()g x 为奇函数, ()h x 为偶函数，若不等式2()(2)0a g x h x ⋅+≥对任意[1,2]x ∈恒成立,则实数a 的取值范围是 .17．已知圆O ：221x y +=，O 为坐标原点，若正方形ABCD 的一边AB 为圆O 的一条弦，则线段OC 长度的最大值是 .18．如图，在正三棱锥P ABC -中，D 为线段BC 的中点，E 在线段PD 上，23PE PD =，AE l =为定长，则该棱锥的体积的最大值为________.三、解答题19．三角形的三个内角A 、B 、C 所对边的长分别为a 、b 、c ，设向量(,),(,)m c a b a n a b c =--=+r r ，若m r //n r ．（1）求角B 的大小；（2）求sin sin A C +的取值范围．20．如图，空间直角坐标系中，四棱锥P OABC -的正方形，且底面在xOy 平面内，点B 在y 轴正半轴上，PB ⊥平面OABC ，侧棱OP 与底面所成角为45°；（1）若(,,0)N x y 是顶点在原点，且过A 、C 两点的抛物线上的动点，试给出x 与y 满足的关系式；（2）若M 是棱OP 上的一个定点，它到平面OABC 的距离为a （02a <<），写出M 、N 两点之间的距离()d x ，并求()d x 的最小值；（3）是否存在一个实数a （02a <<），使得当()d x 取得最小值时，异面直线MN 与OB 互相垂直？请说明理由；21．已知k ∈R ，0a >且1a ≠，0b >且1b ≠，函数()x xf x a k b =+⋅. （1）设1a >，1ab =，若()f x 是奇函数，求k 的值；（2）设10>>>a b ，0k ≤，判断函数()f x 在R 上的单调性并加以证明；（3）设2a =，12b =，0k >，函数()f x 的图象是否关于某垂直于x 轴的直线对称？如果是，求出该对称轴，如果不是，请说明理由.22．已知A 、B 为椭圆22221x y a b+=（0a b >>）和双曲线22221x y a b -=的公共顶点，P 、Q 分为双曲线和椭圆上不同于A 、B 的动点，且满足()(),1AP BP AQ BQ R λλλ+=+∈>u u u r u u u r u u u r u u u r ，设直线AP 、BP 、AQ 、BQ 的斜率分别为1k 、2k 、3k 、4k .（1）求证：点P 、Q 、O 三点共线；（2）求1234k k k k +++的值；（3）若1F 、2F 分别为椭圆和双曲线的右焦点，且12//QF PF ，求22221234k k k k +++的值.23．已知n S 是数列{}n a 的前n 项和，对任意*n N ∈，都有()()140n n n m S ma m -=-+>；（1）若4m =，求证：数列14n n a -⎧⎫⎨⎬⎩⎭是等差数列，并求此时数列{}n a 的通项公式； （2）若4m ≠，求证：数列344n n a m ⎧⎫+⋅⎨⎬-⎩⎭是等比数列，并求此时数列{}n a 的通项公式；（3）设()4n n n a b n N *=∈，若2n b ≤，求实数m 的取值范围.参考答案1．C【解析】【分析】根据等差数列的性质，有()2415117318363a a a a d a d a ++=+=+=，故7a 为确定常数，再利用()11313713132a a S a +⋅==，可得出选项.【详解】由于题目所给数列为等差数列，根据等差数列的性质，有()2415117318363a a a a d a d a ++=+=+=，故7a 为确定常数，由等差数列前n 项和公式可知()11313713132a a S a +⋅==也为确定的常数，故选C. 【点睛】本小题主要考查等差数列的性质，考查对等差数列前n 项和公式的理解和运用.等差数列前n 项和公式有两个，在不同的已知条件下，要学会选择合适的公式的来求解.本小题属于中档题.2．B【解析】【分析】设点(),x y 是曲线22421x xy y ++=上的一点，在矩阵11a b ⎛⎫ ⎪⎝⎭的作用下的点为(),x y ''，可得出x x ay y bx y=+⎧⎨=+''⎩，代入方程2221x y ''-=化简后与方程22421x xy y ++=作比较，可得出关于a 、b 的方程组，解出这两个未知数的值，即可求出+a b 的值.【详解】设点(),x y 是曲线22421x xy y ++=上的一点，在矩阵11a b ⎛⎫ ⎪⎝⎭的作用下的点为(),x y ''， 即11x a x x ay y b y bx y '+⎛⎫⎛⎫⎛⎫⎛⎫== ⎪ ⎪⎪ ⎪'+⎝⎭⎝⎭⎝⎭⎝⎭，代入方程2221x y ''-=，得()()2221x ay bx y +-+=， 即()()()2222122421b x a b xy a y -+-+-=，得2212124422b a b a ⎧-=⎪-=⎨⎪-=⎩，解得20a b =⎧⎨=⎩， 因此，2a b +=.故选：B.【点睛】本题主要考查几种特殊的矩阵变换、曲线与方程等基础知识，解题的关键就是利用待定系数法求出参数的值，考查运算求解能力，属于中等题.3．A【解析】【详解】又在R 上为增函数，则反之，若4．C【解析】【分析】分别讨论水面过直线EF 、FG 、EG时从正方体截去的几何体体积的最小值，即可得出此容器可装水的最大容积.【详解】当水面过直线FG 时，如下图所示，水面截去正方体1111ABCD A B C D -所得几何体为三棱柱MBF NCO -，当点E 在水面上方或水面上时，容器中的水不会漏，且当点M 与点E 重合时，截去的几何体体积最小为()233111228a a a cm ⎛⎫⨯⨯= ⎪⎝⎭； 当水面过直线EF 时，如下图所示，水面截去正方体1111ABCD A B C D -所得几何体为三棱台EBF PCQ -，当点G 在水面上方或水面上时，容器中的水不会漏，且当点G 在直线FQ 上时，截去的几何体为三棱柱，且体积最小为()233111228a a a cm ⎛⎫⨯⨯= ⎪⎝⎭； 当水面过直线EG 时，如下图所示，当点F 在水面上方或水面上时，容器中的水不会漏，此时水面截去正方体1111ABCD A B C D -所得几何体为EBR SCT -，且直线RT 过点G ，易知梯形BCTR 的面积为正方形11BCC B 面积的一半，此时，几何体EBR SCT -的体积为()233111132212EBR SCT E BCTR E SCT E BCTR V V V V a a a cm ----=+>=⨯⨯=. 当RT 与直线1B C 重合时，如下图所示，此时，点F 在水面上方，容器不会漏水，水面截去正方体1111ABCD A B C D -所得几何体为三棱锥1E BB C -， 该三棱锥的体积为()1123311111332212E BB C BB C V BE S a a a cm -∆=⋅=⨯⨯=. 综上可知，水面截去截去正方体1111ABCD A B C D -所得几何体体积的最小值为()33112a cm . 因此，该容器可装水的最大容积是()33331111212a a a cm -=. 故选C.【点睛】本题主要考查几何体体积的计算，根据几何体的几何特征找出水面截去正方体所得几何体体积最小值时的位置是解题的关键，考查推理能力，属于难题. 5．(]0,1 【解析】 【分析】求出集合M 、N ，然后利用交集的定义求出集合M N ⋂. 【详解】{}|lg (0,)M x y x ===+∞，{|[1,1]N x y ===-，(0,)[1,1](0,1].M N ⋂=+∞⋂-=故答案为(]0,1. 【点睛】本题考查集合的交集运算，同时与考查了具体函数的定义域，考查计算能力，属于基础题. 6．45【解析】 【分析】求出复数43i +的模，然后在等式()3443i z i -=+两边同时除以34i -，利用复数的除法可求出复数z ，即可得出复数z 的虚部. 【详解】435i +==Q ，由()34435i z i -=+=，()()()()5345345343434342555i i z i i i i ++∴====+--+，因此，z 的虚部为45. 故答案为45. 【点睛】本题考查复数虚部的求解，同时也考查了复数模的计算以及复数的除法运算，解题的关键就是利用复数的四则运算将复数表示为一般形式，考查计算能力，属于基础题. 7．6 【解析】【分析】利用二倍角公式求出cos B ，然后利用余弦定理求出b 的值. 【详解】由二倍角的余弦公式可得221cos 12sin 1223B B =-=-⨯=⎝⎭. 由余弦定理得2222212cos 64264363b ac ac B =+-=+-⨯⨯⨯=，因此，6b =.故答案为：6. 【点睛】本题考查二倍角余弦公式的应用，同时也考查了利用余弦定理求三角形的边长，考查运算求解能力，属于中等题. 8．9 【解析】 【分析】根据频率分布直方图计算出日销售量不少于150个的频率，然后乘以30即可. 【详解】根据频率分布直方图可知，一个月内日销售量不少于150个的频率为()0.0040.002500.3+⨯=，因此，这家面包店一个月内日销售量不少于150个的天数为300.39⨯=. 故答案为：9. 【点睛】本题考查频率分布直方图的应用，解题时要明确频数、频率和样本容量三者之间的关系，考查计算能力，属于基础题. 9．514【解析】 【分析】计算出基本事件总数为8个学生的全排数，然后考虑排头和排尾均为女生的排法种数，利用古典概型的概率公式即可得出所求事件的概率. 【详解】将5个女生和3个男生随机站成一排，排法种数为88A ，现在考虑排头和排尾都是女生的情况，先从5个女生中选2人进行排列，剩余6个人全排，事件“排头和排尾均为女生”所包含的基本事件数为2656A A ，因此，排头和排尾均为女生的概率是265688514A A A =. 故答案为：514. 【点睛】本题考查利用古典概型概率公式的计算事件的概率，同时也考查了有限制的元素的排列问题，考查计算能力，属于中等题. 10．1 【解析】 【分析】将圆的极坐标方程化为直角坐标方程，求出圆心的坐标，可求出圆心到极轴的距离. 【详解】在圆的极坐标方程两边同时乘以ρ，得22sin ρρθ=，化为普通方程得222x y y +=， 标准方程为()2211x y +-=，圆心坐标为()0,1，因此，圆2sin ρθ=的圆心到极轴的距离为1. 故答案为：1. 【点睛】本题考查圆心到极轴的距离， 解题的关键就是将圆的极坐标方程化为普通方程，考查计算能力，属于基础题. 11．32【解析】 【分析】先求出等比数列{}n a 的公比，然后利用无穷等比数列的和可计算出结果. 【详解】设等比数列{}n a 的公比为q ，由20152016201723S S S +=，得()201720152017201620S S S S -+-=，即2017201630a a +=，310q ∴+=，解得13q =-，因此，无穷等比数列{}n a 的各项和为12311213a q ==-⎛⎫-- ⎪⎝⎭.故答案为：32. 【点睛】本题考查无穷等比数列各项和的计算，解题的关键就是求出等比数列的公比，考查计算能力，属于中等题. 12．【解析】 【分析】用三棱柱111ABC A B C -的体积减去四棱锥111A EFC B -的体积和四棱锥A BCFE -的体积即可得出三棱锥1A A EF -的体积. 【详解】取BC 的中点D ，连接AD ，则AD BC ⊥.Q 平面ABC ⊥平面11BCC B ，平面ABC I 平面11BCC B BC =，AD ⊂平面ABC ，AD ∴⊥平面11BCC B .ABC ∆Q 是等边三角形，4AB =，AD =1//AA Q 平面11BCC B ，且E 、F 分别为1BB 、1CC 的中点.111114333A BCFE A EFCB BCFE V V S AD --∴==⋅=⨯⨯⨯=111122462A A EF ABC A B C A BCFE V V V ---∴=-=⨯-⨯=故答案为：【点睛】本题考查三棱锥的体积的计算，常用的方法有等体积法、间接法、割补法，解题时可充分选择合适的方法来进行计算，考查计算能力，属于中等题. 13．【解析】 【详解】由22230x y x +--=得22(1)4x y -+=，所以圆的圆心为(1,0)，根据圆的相关性质，可知所求的直线过圆心，由直线垂直可得所求直线的斜率为32， 根据直线的点斜式方程化简可得结果为．14．2y x =± 【解析】 【分析】求出抛物线的焦点坐标与双曲线的渐近线方程，代入抛物线的方程可得出点A 、B 的坐标，再由A 、B 、F 三点共线，可得出2222pa pb =，可得出2b a =，由此可得出双曲线的渐近线方程. 【详解】抛物线的焦点F 的坐标为,02p ⎛⎫⎪⎝⎭， 双曲线()222210,0x y a b a b-=>>的渐近线方程为b y x a =±，代入抛物线的方程，可得2222,pa pa A b b ⎛⎫ ⎪⎝⎭、2222,pa pa B b b ⎛⎫- ⎪⎝⎭，由A 、B 、F 三点共线可得2222pa pb =，2214a b ∴=，则2b a =.因此，双曲线的渐近线方程为2y x =±. 故答案为：2y x =±. 【点睛】本题考查抛物线焦点坐标以及双曲线渐近线方程的求解，解题的关键就是利用三点共线得出关系式，考查运算求解能力，属于中等题. 15． 24 【解析】 试题分析：11·()?()?··2433CM CB CA AM CB CA AB CB CACB AB CB =+=+=+=u u u u r u u u r u u u r u u u u r u u u r u u u r u u u r u u u r u u u r u u u r u u u r u u u r考点：本小题考查向量的线性运算及其向量的数量积．点评：解题关键在于向量CM 与AM 的转化,利用数量积定义求题． 16．17[,)12-+∞ 【解析】试题分析：∵h （x ）为定义在R 上的偶函数，g （x ）为定义在R 上的奇函数 ∴g （-x ）=-g （x ），h （-x ）=h （x ）, 又∵由h （x ）+g （x ）=2x， h （-x ）+g∵1≤x ≤2∴2x -2-x＞0,令t=2-x -2x ，整理得：考点：1.函数不等式的恒成立问题；2.换元法；3.基本不等式 17．【解析】试题分析：设,OBA θ∠=则2222cos (sin 2cos )14cos 2sin 23)34OC πθθθθθθ=++=++=++≤+，当且仅当8πθ=取等号，因此OC 长度的最大值是考点：直线与圆位置关系18．3932l【解析】 【分析】设正三棱锥P ABC -的底面边长为a ，则该三棱锥的高为h =求出底面积，并代入三棱锥的体积公式，然后利用基本不等式可求出该棱锥体积的最大值. 【详解】如下图所示，设正三棱锥P ABC -的底面边长为a ，由正弦定理可知，底面ABC ∆的外接圆半径为2sin 60a r =o， 连接AD ，过点P 作PO ⊥平面ABC ，垂足为点O ，过点E 作//EF PO 交AD 于点F ，23PE PD =Q ，22113323OF OD OA r ∴==⨯=，1433AF OA OF r r r ∴=+=+==，EF ∴===23PE PD =Q ，则13DE PD =，又//EF PO Q ，3PO EF ∴==，因此，该三棱锥的体积为221344P ABC V -=⨯⨯===339323232932l ≤===， 当且仅当2221682727l a a -=，即当4a l =时，等号成立. 因此，该三棱锥体积的最大值为3932l . 故答案为3932l . 【点睛】本题考查正三棱锥体积最值的求法，建立关系式是解题的关键，考查数形结合思想的应用，属于中等题.19．（1）3B π=；（2）2⎛ ⎝． 【解析】 【详解】 （1）由m r //n r知c a b aa b c--=+，即得222b a c ac =+-，据余弦定理知 1cos 2B =，得3B π= （2）()sin sin sin sin AC A A B +=++ sin sin 3A A π⎛⎫=++⎪⎝⎭13sin sin cos sin 2222A A A A A =++=+6A π⎛⎫=+ ⎪⎝⎭因为3B π=，所以23A C π+=，得20,3A π⎛⎫∈ ⎪⎝⎭所以5,666A πππ⎛⎫+∈ ⎪⎝⎭，得1sin ,162A π⎛⎫⎛⎤+∈ ⎪ ⎥⎝⎭⎝⎦，即得sin sin A C +的取值范围为⎝． 点睛：本题关键是首先要得出向量平行的等式，再结合余弦定理即可得出B ，对于三角函数范围问题则通常需要将原式化简为sin)A x b ωφ++（的形式再求解答案（需注意范围的变化），此题属于基础题.20．（1）2y x =；（2）()min1,021222a d x a <≤=<<⎩；（3）a =. 【解析】 【分析】（1）根据题意，求出点A 的坐标，代入抛物线方程，即可得出x 与y 的关系式； （2）设点M 和N 的坐标，根据两点间的距离公式，利用二次函数的基本性质，即可得出函数()y d x =的最小值；（3）由（2）可知，当1,22a ⎛⎫∈ ⎪⎝⎭时，当()y d x =取得最小值时，求得2212a x -=，由异面直线MN 与OB 垂直时，M N y y =，代入即可求出a 的值. 【详解】（1）由四棱锥P OABC -()1,1,0A ，可设x 与y 所满足的关系式为22x py =，将点A 横坐标和竖坐标代入该方程得12p =，解得12p =，因此，x 与y 所满足的关系式为2y x =； （2）设点()0,,M a a ，()2,,0N x x ，则()d x MN ===.令20t x =≥，设()()22122f t t a t a =+-+，对称轴为直线212a t -=. ①当022102a a <<⎧⎪⎨-≤⎪⎩时，即当102a <≤时，函数()()22122f t t a t a =+-+在[)0,+∞上单调递增，则()()2min 02f t f a ==，此时()min d x =；②当022102a a <<⎧⎪⎨->⎪⎩时，即当122a <<时，此时函数()()22122f t t a t a =+-+在212a t -=取得最小值，即()()2222min21214412224a a a a f t a --+-⎛⎫=-+=⎪⎝⎭， 此时()mind x =. 因此，()min1,02122a d x a <≤=<<； （3）当10,2a ⎛⎤∈ ⎥⎝⎦时，此时点N 与原点重合，则直线MN 与OB 为相交直线，不符； 当1,22a ⎛⎫∈ ⎪⎝⎭时，则当()y d x =取最小值时，2212a x -=， 当异面直线MN 与OB 垂直时，M N y y =，即2212a a -⎛⎫= ⎪⎝⎭，化简得24810a a -+=.122a <<Q，解得a =【点睛】本题考查抛物线方程、异面直线所成的角、两点间的距离公式以及二次函数基本性质的应用，考查化归与转化思想的应用，属于中等题.21．（1）1k =-；（2）证明见解析；（3）对称轴为4log x k =，理由见解析. 【解析】 【分析】（1）根据已知条件，将1b a=代入函数()y f x =的解析式，得出()x xf x a k a -=+⋅，利用奇函数的定义()()0f x f x +-=，可求出实数k 的值；（2）判断出函数1x y a =和函数2xy b =的单调性，然后利用函数单调性的运算法则，可判断出函数()xxf x a k b =+⋅的单调性，然后利用函数单调性的定义加以证明；（3）根据函数()22xxf x k -=+⋅图象的对称轴为直线x m =，得出()()f m x f m x -=+对任意的实数x 恒成立，即可求出实数m 的值. 【详解】 （1）由已知，1b a=，()x xf x a k a -∴=+⋅，由于函数()y f x =为奇函数， 则()()()()10xxx x x x f x f x a k aa k a k a a ---+-=+⋅++⋅=+⋅+=对任意的x ∈R 恒成立，10k ∴+=，因此，1k =-；（2）当10>>>a b 时，函数1x y a =为增函数，函数2xy b =为减函数，又0k ≤Q ，所以，函数()xxf x a k b =+⋅在R 上是增函数，下面利用定义来证明出函数()y f x =的单调性.任取12x x >，则()()()()()()1122121212x x x x x x x xf x f x a k b a k b a a k b b -=+⋅-+⋅=-+-，1a >Q ，12x x a a ∴>，即120x x a a ->，又01b <<Q ，12x x b b ∴<，0k ≤Q ，()120x xk b b ∴-≥，所以，()()120f x f x ->，即()()12f x f x >.因此，函数()xxf x a k b =+⋅在R 上是增函数；（3）()22xxf x k -=+⋅，若函数()y f x =的图象是轴对称图形，且对称轴为直线x m =，则()()f m x f m x -=+，2222m x x m m x x m k k --+--∴+⋅=+⋅， 即()()22220m xm x x m x m k -+----+⋅-=，即()()2222220m x x m x x k ----+⋅-=， 即()()22220mm x x k --⋅--=对任意的x ∈R 恒成立，22m m k -∴⋅=，即224m m k ==，因此，4log =m k . 【点睛】本题是一道函数综合问题，考查利用函数的奇偶性求参数、利用定义判定函数的单调性以及函数对称性问题，解题时要结合有关定义进行理解，考查分析问题与解决问题的能力，属于中等题.22．（1）见解析；（2）0；（3）8. 【解析】 【分析】（1）由()AP BP AQ BQ λ+=+u u u r u u u r u u u r u u u r ，得到OP OQ λ=u u u r u u u r，由此可证明出点P 、Q 、O 三点共线；（2）设点()11,P x y 、()22,Q x y ，求出2112212x b k k a y +=⋅，2234222x b k k a y +=-⋅，由//OP OQ u u u r u u u r ，可得出1212x x y y =，从而可求出1234k k k k +++的值； （3）由OP OQ λ=u u u r u u u r ，可得222122211212x a y b λλ⎧+=⎪⎪⎨-⎪=⎪⎩，再由12//QF PF ，得出()2124k k +=，()2344k k +=，由此能求出22221234k k k k +++的值.【详解】（1）A Q 、B 为椭圆()222210x y a b a b +=>>和双曲线22221x y a b-=的公共顶点，P 、Q 分别为双曲线和椭圆上不同于A 、B 的动点，且()AP BP AQ BQ λ+=+u u u r u u u r u u u r u u u r ，即22OP OQ λ=⋅u u u r u u u r ，即OP OQ λ=u u u r u u u r，因此，点P 、Q 、O 三点共线； （2）设点()11,P x y 、()22,Q x y ，则21111111122222222111112222y y x y x y x b k k a x a x a x a a y y a a b +=+===⋅+--+-， 同理可得2234222x b k k a y +=-⋅，//OP OQ u u u r u u u r Q ，1221x y x y ∴=，则1212x x y y =，因此，212123421220x x b k k k k a y y ⎛⎫+++=-= ⎪⎝⎭； （3）OP OQ λ=u u u r u u u r Q ，212111x x y y λλ⎧=⎪⎪∴⎨⎪=⎪⎩，2222221x y a b +=Q ，2221122x y a b λ∴+=，又2211221x y a b -=，解得222122211212x a y b λλ⎧+=⎪⎪⎨-⎪=⎪⎩， 又12//QF PF Q ，21OF OF λ∴=⋅，则()22222a b a b λ+=-，则22222a b a b λ+=-. 222412224111x a a y b b λλ+∴=⋅=-，()2444211242441444x b b a k k a y a b∴+=⋅⋅=⋅⋅=， 同理可得()2344k k +=，21111222111y y y k k x a x a x a =⋅=+--Q 且2211221x y a b -=，2222112a x a y b ∴-=，2122b k k a∴=，同理可得2342b k k a=-，因此，()()()22222212341234123428k k k k k k k k k k k k +++=+++-+=.【点睛】本题考查椭圆与双曲线的综合问题，考查整体代换与方程思想，在计算时应充分利用点在曲线上这一条件得出等式进行计算，考查运算求解能力，属于难题. 23．（1）证明见解析，()1314n n a n -=+⋅；（2）1443444n n n m a m m m --=⋅-⋅--；（3）50,2⎛⎤⎥⎝⎦. 【解析】 【分析】（1）将4m =代入()14nn n m S ma -=-+，得344nn n S a =-，令1n =，求出1a ，然后令2n ≥，由344nn n S a =-得出111344n n n S a ---=-，两式作差可得出数列{}n a 的递推公式，然后利用定义证明出数列14n n a -⎧⎫⎨⎬⎩⎭是等差数列，确定该数列的首项，即可求出n a ；（2）令1n =求出14a =，然后令2n ≥，由()14nn n m S ma -=-+得出()11114n n n m S ma ----=-+，两式相减得出数列{}n a 的递推公式，然后利用定义证明出数列344n na m ⎧⎫+⋅⎨⎬-⎩⎭为等比数列，确定该数列的首项和公比，即可求出n a ； （3）结合（1）（2）中的结论，讨论4m =、4m >、01m <<、1m =、14m <<，结合条件2n b ≤，利用数列()41144nm m m m ⎧⎫-⎪⎪⎛⎫⋅⋅⎨⎬ ⎪-⎝⎭⎪⎪⎩⎭的单调性，即可得出实数m 的取值范围. 【详解】（1）将4m =代入()14nn n m S ma -=-+，得344n n n S a -=-+，即344nn n S a =-.当1n =时，则有11344a a =-，得14a =；当2n ≥时， 由344nn n S a =-得出111344n n n S a ---=-，上述两式相减得()11113444444441n n n n n n n n a a a a a ----=---=---，整理得11434n n n a a --=+⋅，等式两边同时除以14n -得112344n n n n a a ---=+，即112344n n n n a a ----=， 所以，数列14n n a -⎧⎫⎨⎬⎩⎭是以首项为1044a =为首项，以3为公差的等差数列， 则()1431314n n a n n -=+-=+，因此，()1314n n a n -=+⋅； （2）对任意*n N ∈，都有()()140nn n m S ma m -=-+>.当1n =时，()1114m S ma -=-+，解得14a =；当2n ≥时，由()14nn n m S ma -=-+得出()11114n n n m S ma ----=-+，两式相减得()111114434nn n n n n n n m a ma ma ma ma -----=-++-=-++⋅，化简得1134n n n a ma --=+⋅，11111111133334344444444333444444n n n n nn n n n n n n n n a ma ma m m m a a a m m m ---------+⋅+⋅+⋅+⋅+⋅---==+⋅+⋅+⋅---Q 1111111111133334444444333444444n n n n n n n n n n n n m ma m a ma m m m m a a a m m m -----------⎛⎫⎛⎫++⋅+⋅+⋅ ⎪ ⎪--⎝⎭⎝⎭-====+⋅+⋅+⋅---， 所以，数列344n n a m ⎧⎫+⋅⎨⎬-⎩⎭是以m 为公比，以()14131244444m a m m m -+⨯=+=---为首项的等比数列，则()1413444nn n m a m m m --+⋅=⋅--，因此，()141344n n n m m a m --⋅-⋅=-； （3）()4n n n a b n N *=∈Q ，且2n b ≤. 当4m =时，314n n b +=，当3n ≥时，2n b >，不满足条件；则4m ≠，可得()4113444nn m m b m m m -⎛⎫=⋅⋅-⎪--⎝⎭， 可得()41313224444nm m m m m m -⎛⎫-+≤⋅⋅≤+⎪---⎝⎭， 显然4m >时，数列()41144nm m m m ⎧⎫-⎪⎪⎛⎫⋅⋅⎨⎬ ⎪-⎝⎭⎪⎪⎩⎭单调递增，不满足条件，04m ∴<<. 当1m =时，则有301-<<显然成立；当01m <<时，若1n =，则数列()41144nm m m m ⎧⎫-⎪⎪⎛⎫⋅⋅⎨⎬ ⎪-⎝⎭⎪⎪⎩⎭的最大项为14m m --，31244m m m -∴+>--，即251m m -<-恒成立； 当512m <≤时，数列()41144nm m m m ⎧⎫-⎪⎪⎛⎫⋅⋅⎨⎬ ⎪-⎝⎭⎪⎪⎩⎭的最大项为104m m -<-， 则3204m +≥-满足条件； 当542m <<时，3204m +<-，数列()41144nm m m m ⎧⎫-⎪⎪⎛⎫⋅⋅⎨⎬ ⎪-⎝⎭⎪⎪⎩⎭的最大项为104m m ->-，不满足条件；综上所述，实数m的取值范围是5 0,2⎛⎤ ⎥⎝⎦.【点睛】本题考查数列的递推公式，等差数列和等比数列的定义，同时也考查了数列不等式问题，考查分析问题和解决问题的能力，属于难题.。
上海市复旦大学附属中学2024-2025学年上学期高三年级10月阶段性教学质量评估语文试卷(解析版)
一、积累与运用（10分）
1.按要求填空。
（1）李白的《梦游天姥吟留别》中，描写著名诗人谢灵运住过的地方溪水清澈、猿啼凄凉的句子是：“___________，__________。”
（2）针对魏晋名士崇尚虚无的思想，王羲之在《兰亭集序》中直接批评道：“___________，__________。”
④女性的现代化过程也是一个社会参与的过程。这一时期许多漫画家会把女性描绘得比较强悍，男子比较弱势，这就跟目标读者是女性有关，女性作为读者算是一种（1）。当然画师里也有女性，作家也有女性，这就是一个（2）。三四十年代的女性杂志，比如说《玲珑》，反而是要塑造一种比较淑女型的、准备做良家妇女的女性，这种区别也很有意思。
①文汇报：您在《摩登图释》中用12个词串讲“上海摩登”的报刊图像，帮助大家了解现代女性的由来。百多年前，上海的都市现代景观兴起之际，女性是否其中最直观的表现者？
②陈建华：这本书主要是通过图像来讲故事，里边有比较多的线索：语言、图像、时尚，或者是上海，但女性的确是一个比较贯穿的主题，因为不光像“西方美人”“丝厂女工”，还有其他像“时尚”“时装”“时髦”“摩登”等大部分词条，都跟女性有关。至于是不是一个直接的表现者，这里就牵涉到，谁在表现？
⑤文汇报：“摩登”这个词也很有味。您在书里提到，它最早的来源并不是“modern”？
⑥陈建华：“摩登”是从1920年代末开始流行的，起因却是四大名旦之一尚小云的《摩登伽女》剧。这是一个非常偶然的事件，“摩登伽”一词源于佛经，指游民，跟我们现在说的摩登没有什么关系，但是尚小云在演出时把自己的造型弄得非常洋化。“摩登”这个词，后来很快就被跟英语的modern连接起来，而且一发不可收。这个词本身就包含了上海的一种杂交的文化，所以它的流行有其内在的逻辑。
复旦大学附属中学2025届高三第二次诊断性检测语文试卷含解析
复旦大学附属中学2025届高三第二次诊断性检测语文试卷请考生注意：1．请用2B铅笔将选择题答案涂填在答题纸相应位置上，请用0．5毫米及以上黑色字迹的钢笔或签字笔将主观题的答案写在答题纸相应的答题区内。
写在试题卷、草稿纸上均无效。
2．答题前，认真阅读答题纸上的《注意事项》，按规定答题。
1、阅读下面的散文，完成后面的题目。
枪挑紫金冠李修文谁要看这般的戏?新编《霸王别姬》。
霸王变作了红脸，虞姬的侍女跳的是现代舞，一匹真正的红马扮乌骓。
我先是手足无措，而后生出了深深的羞耻——所谓新编，在许多时候，并不是将我们送往戏里，而是在推我们出去。
它像镜子，只照出两样东西：胆大妻为与匮乏。
羞愧地离席。
出了剧院，二月的北京浸在浓霾里。
没来由想起了甘肃，陇东庆阳，一个叫做小崆峒的地方，黄土上开着一树树的杏花。
三月三，千人聚集，都来看秦腔，《罗成带箭》。
我到时，恰好是武戏，一老一少，两个武生，要翎子，咬牙，甩梢子，一枪扑面，一铜往还，端的是密风骤雨，又配合得滴水不漏。
突然，老武生一声怒喝，一枪挑落小武生头顶的紫金冠。
小武生似乎受到了惊吓，呆立当场。
我以为这是剧情，哪知不是，老武生一卸长髯，手提长枪，对准小的，开始训斥：鼓锣钹之声尴尬地响了一阵，渐至沉默，在场的人都听清了，他是在指责小武生上台前喝过酒。
说到暴怒处，举枪便打。
这出戏是唱不下去了，只好再换一出。
我站在幕布之侧，看见小武生在受罚：时代已至今天，他竟然还在掌自己的嘴。
梨园一行，哪一个的粉墨登场不是从受罚开始的?这台前幕后，遍布着多少不能触犯的律法：玉带不许反上，鬼魂走路要手心朝前，上场要先出将后入相……如此讲究戒律，却是为何?千百年来，多少伶人身上承载着这样的命数：三天两头被人喝了倒彩，砸了场子，不得科举，不得坐上席，甚至不得被娶进门去；在最不堪的年代里，伶人出行，要柬绿巾、扎绿带，单是为了被人认出和不齿；就算身死，也难寿终正寝。
戏台上那烟尘里的救兵、危难之际的观音，实际都不存在。
上海市复旦大学附属中学2016届高三英语下册开学考试卷
复旦附中2014学年第二学期高三年级第一次综合测试英语试卷2015年2月第Ⅰ卷（共103分）Ⅰ.Listening Comprehension.Part A Short ConversationsDirections: In part A, you will hear Len short conversations between two speakers, At the end of each conversation, a third voice will ask a question about what was said, The conversation and the questions 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. In a bank. B. In a train station.C. In a school.D. In a post office.( )2.A. To buy a bunch of flowers.B. To clean their cars.C. To pick up the woman’s parents.D. To drive to meet the man’s parents.( )3.A. He doesn’t need as much sleep as his wife.B. His wife doesn’t sleep well.C. Women need more sleep than men.D. He wants to have more sleep.( )4.A. Winter is his favorite time for sports.B. Sports are quite important to him.C. He plays better now than he used to.D. He should be more enthusiastic for sports.( )5.A. She prefers high-heeled shoes.B. She prefers jogging shoes.C. She has no opinion on it.D. She has different choices for different occasions.( )6.A. Because it needs frequent repairing.B. Because it costs a lot of money.C. Because it doesn’t worth the price.D. Because it needs time to learn.( )7.A. Because it looked funny.B. Because it looked like a post office.C. Because it had a red postbox outside.D. Because the man thought so.( )8.A. Try it on. B. Paint a picture of it.C. Hammer a nail with it.D. Throw it away. ( )9.A. Anger. B. Surprise.C. Confusion.D. Happiness.( )10.A. Go to a lecture. B. Call her sister.C. Attend a planning meeting.D. Go bowling.Part B PassagesDirections: In Part B, you will hear two short passages. And you will be asked t questions on each of the passage. The passage will be read twice but the questions wi. spoken only once. When you hear a question, read the four possible answers in your pc and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the passage you have just heard. ( )11.A. They appear every night in TV weather forecasts.B. The were first employed as women news announcers.C. They are the most attractive women in Britain.D. They are the most popular stars in a TV play.( )12.A. At 10 in the evening. B. At 9 in the evening.C. At 10 in the morning.D. At 9 in the morning.( )13.A. Newspaper reporters still wrote a lot about her.B. People knew that Anna would be the first woman to hold the news gram.C. Independent Television also had a woman news announcer.D. The viewers of her news program that night increased to millions.Questions 14 through 16 are based on the passage you have just heard. ( )14.A. Los Angeles. B. San Francisco.C. Detroit.D. New York.( )15.A. 25,000 dollars. B. 95,000 dollars.C. A million dollars.D. Ten million dollars.( )16.A. He got married.B. He had ten million dollars.C. He had three daughters.D. His wife and daughter were killed in a traffic accident.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 in formation you have heard.Blanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.Blanks 21 through 24 are based on the following conversation.Complete the form. Write NO MORE THAN THREE WORDS for each answer.Ⅱ.Grammar and V ocabularySection 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 from of the given word; for the other blanks, use one word that best fits each blank.（A）Most people know that gold has been used in coins,jewelry and art since before recorded history. But (25) is less well-known is that gold has been and still is used for many other things.Gold (26) (use) in medicine for a long time. In medieval Europe people thought that gold was good for your health. They thought that since gold was so pure and rare it had to be good for you. This isn’t true because gold is inert body. This means that the chemicals in the human body cannot affect gold, therefore, it doesn’t do anything while it is in the body. But gold is used successfully in dentistry. Dentists use gold to fix people’s teeth.Gold is also used in combination with other metals. It gets mixed with these metals. The mixture is better because gold is not affected by air, moisture or corrosive chemicals such as acid. This is one reason (27) it is used for coins and in jewelry.Electricity moves very well through gold. It also does not corrode, (28) means that it lasts a long time without being damaged by the air or chemicals. (29) these two properties, gold is used in electronics. This is the most common industrial use of gold. It is also used in wires that need to carry a lot of electricity. But gold is also used in everyday electronics(30) mobile phones and computers.Gold is also used in other ways. It is used in glass production to change the color of the glass. Gold can also be made so thin(31) you can see through it. Because of this, it can also be put on the glass of the cockpit(where the pilot sits) of some airplanes. When electricity is passed through the gold that is on this glass, it stops ice from forming on the glass. This type of gold plating also prevents some of the instruments in the cockpit from (32) (damage) by radiation. Gold is also used in photography to change the colors of the photograph. It is also used in satellites, cars, CDs and space suits.Although we mostly think of gold as being used in jewelry or for money, it has many other uses. In the future, gold will continue to be very useful for a wide variety of purposes.（B）Cigarette smoking kills. That we know. So, manufactures made electronic cigarettes as a safer smoking choice-safer than tobacco.E-cigarettes contain the drug nicotine like cigarettes. But they do not use tobacco. And you do not light (33) . They are powered by battery.So, if e-cigarettes are so safe, why have poison control centers around the United States seen an increase(34) telephone calls about e-cigarette poisonings? The answer is children.Most of the calls are from people worried about children who have played with the devices. In the period of one month this year, the United States Centers for Disease Control say 215 people called the Center with e-cigarette concerns. More than half of these calls were for children(35) (age) five and younger. The devices apparently had made them sick.Tim McAfee is director of the CDC’s Office on Smoking and Health. He says the problem is regulation, meaning the U.S. Federal government does not control e-cigarettes(36)They contain liquid nicotine. Mr. McAfee adds that liquid nicotine is a well-known danger.“Nicotine historically has been used as a pesticide in the United States. And that’s where we have really had for many, many decades significant poisonings when people got exposed to nicotine that was in liquid solutions.”Mr. McAfee explains that nicotine poisoning happens(37) the substance gets into the skin, gets into the eyes or is swallowed. Even a small amount, he says,(38)make a person sick. Nicotine poisoning can cause stomach pain or a sense of imbalance. Headaches and seizures are also common sighs of nicotine poisoning. And too much nicotine can kill.Tim McAfee says e-cigarettes do not create the level of risk topeople(39)tobacco products do. He notes that almost 500000 Americans die each year from cigarettes. “So, cigarettes are the winner in that contest. And we don’t really know what’s going to happen with e-cigarettes.”E-cigarettes do not contain hundreds of harmful chemicals that are found in real cigarettes. So, the U.S. Surgeon General has suggested that e-cigarettes may be a useful tool for adults(40)(try) to end their tobacco use, or quit.But McAfee worries that teenagers may think electronic cigarettes are harmless. They could become addicted,or hooked, on the nicotine and then start smoking real cigarettes. In other words, he fears that for young people fake e-cigarettes could be a “gateway” to the real thing.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. is testing delivering packages using drones, CEO Jeff Bezos said. The idea would be to deliver packages as quickly as possible using the small, unmanned aircraft, through a service the company is calling Prime Air, the CEO said.The aircraft, also known as octocopters, will pick up packages in small yellow 41 at Amazon’s fulfillment centers and fly through the air to deliver 42 to customers after they hit the buy button online at .The goal of the new delivery system is to get packages into customers’hands in 30 minutes or less, the world’s largest Internet 43 said. Putting Prime Air into commercial use will take “some number of years”as Amazon develops the technology further and waits for the Federal Aviation Administration to come up with rules and regulations, the company added.“One day ,Prime Air vehicle will be as __44____ as seeing mail trucks on the road today,”the company said.Drones have _45___ been used by the USA military . However , the cost of these unmanned aircraft has dropped precipitously in recent years ,making them more __46___ to commercial users , such ascompanies ,small businesses and entrepreneurs.However ,the FAA __47___ limits the use of drones in the U.S. to public entities such as police __48___ and hobbyists , meaning the devices cannot be used in return for payment. The regulator said recently that it plans to have regulations __49____ commercial use in place by 2015. “The FAA would not let Amazon do this now,” said Ryan Calo, an expert on robotics , privacy and the law at the University of Washington.” But this is precisely the type of _50____ that Congress had in mind when it told the FAA in 2012 to come up with rules for commercial unmanned aircraft.“We’ll be ready to enter commercial operations as soon as the necessary regulations are in place ,” Amazon said Sunday . “Safety will be our top priority, and our vehicles will be built with multiple redundancies and designed to commercial aviation standards”.III. Reading comprehension.Section ADirections: 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.With tuition rising ever faster --- the average annual coat at a private college is now close to $40,000 and is expected to rise to over $80,000 by 2025 ---- getting financial aid is crucial for many families . if you are one of them , you will want to check out these __51__ from Kalman A . Chany, author of Paying for College Without Going Broke :2011 Edition. Don’t assume you won’t quality . Your income or your grades may or may not make you ineligible , so do your research . And don’t __52___ out a college because you think it’s too expensive . The higher the cost ,the more aid you may __53__.Don’t wait. There’s a limited mount of cash to go __54___. Apply for aid before you are accepted.Apply early. You’ll need to fill out the FAFSA form, which is available online __55__ , or you can order one by calling 800-433-3243. Some colleges __56__additional paperwork , including the College Board’s CSS/PROFILE application , state aid forms ,and forms they themselves provide.Meet the deadline.And don’t ___57___ t here is only one. Different colleges have different deadlines for different forms, which can ___58___ anywhere from late December to March.Know your “expected family contribution.”Use the online tool at /calculators to figure _59____ the colleges you are applying to think you can afford before you apply . That way you canplan accordingly and won’t be unpleasantly surprised.__60__ your aid eligible(资格). Awards to incoming freshman are based in part on income for the year ending Dec.31 of the student’s senior year in high school. Make appropriate adjustments to your assets ,debts , and retirement provisions so that you can get as much ___61_ as you can. Dot your I’s and cross your t’s (一丝不苟). Don’t make ___62__ mistakes . Forgetting to ___63___ financial aid applications , neglecting to fill them out _64___or using the wrong academic year’s version of the form will disqualify you.File your tax returns asap. Some aid deadlines will require you to do a draft version of your income tax return with estimated numbers, so ___65___ your paperwork and be prepared to fill out your tax forms early.For more ideas on saving for college , visit .51. A. changes B. principles C. ideas D. tips52. A. make B. take C. rule D. put53. A. accept B. receive C. capture D. catch54. A. around B. over C. out D. down55. A. of B. on C. at D. from56. A. ask B. require C. claim D. order57. A. assume B. doubt C. desire D. realize58. A. draw B. meet C. set D. fall59. A. how B. where C. which D. what60. A. Qualify B. Maximize C. Minimize D. Disqualify61. A. rescue B. relief C. aid D. promise62. A. genuine B. wise C. honest D. stupid63. A. resign B. sign C. identify D. define64. A. absolutely B. completely C. partly D. partiallySection BDirections:Read the following passages. Each passage is followed by several questions or unfinished statement. 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)Dogs and cats are not for students who live in the dormitory . Just think about the noise, the smell and all that wild behavior , chewing on whatever they can get their teeth on, or knocking over the trash can. But don’t feel sad. There are smaller and less destructive pets to make your dormitory life colorful.Betta fishThey make great pets with theirbig personality and astonishingcolors, ranging from bright red , dark blue to lemon yellow. Unlike many fish, most bettas react to their owner’s presence and become more activethe fish world.ChinchillasWithout bad smell, about the size of a rabbitand with fur so dense that they can’t get petssuch as fleas, the friendly creature originallyfrom the Andes Mountains in South Americamakes an ideal indoor pet. Chinchillas are very social animals, even if you are only alone, you will become its family. In cold winter days, only a glance at its fury pet in a dorm will bring you a lot of warmth.Land hermit crabsIn a society where owners are often asked “Are they tasty?”, land hermit crabs are among the most unlucky anim als commonly kept pets. But they are easy to care for, inexpensive and fascinating to watch. And the factthat they don't cause any allergic reactions makes them perfect for college dormitories.Red-eared slidersIf you're interested in a lifelong friend, a red-eared slider makes a wonderful pet. If well cared for, they can live for around 40 years. But there are a couple of things you should know. Red-eared can grow to an adult size of up to 30 cm! So you may need a larger tank quickly. In addition, you will need to provide UV lighting, water heater, and a swimming area and a basking (晒太阳) area. Housing a red eared slider is not easy.66. All the dormitory pets mentioned in the text are ______.A. active and allergicB. quiet and peacefulC. colorful and tastyD. small and smelly67. Which of the following is not true about these creatures?A. Bettas are active and rich in colors.B. Chinchillas are originally mountain animals.C. Land hermit crabs are allergic but tasty.D. Red-eared sliders need more care from the owner.68. If you want to keep the pet as long as possible, you'd better choose ______ .A. Betta fishB. ChinchillasC. Land hermit crabsD. Red-eared sliders69. The passage is mainly to ______A. introduce the best way to keep petsB. offer useful pictures for choosing petsC. inform students of lifestyle of petsD. recommend some dormitory pets(B)MOOCs (Massive Open Online Courses) are free, but without tutoring, and are open to anyone, anywhere in the world. The courses are flexible – normally three to five hours of study a week – done at any time, short (5 to 10 weeks) and video-rich. They are also heavily dependent on crowd sourcing: you can discuss a course with fellow students through online forums, discussion boards and peer review. Students don't have to finish the courses, pass assessments or do assignments, but, if they do, they get a certification of participation.The Open University launched FutureLearn, the UK's answer to US platforms such as Coursera, EdX and Udacity, which have been offering MOOCs from top US universities for the past two years. The response has been incredible, with more than three million people registering worldwide. Meanwhile, in 2012, Edinburgh University became the first non-US institution to join Coursera's partnership, comprising 13 universities. “We already run 50 online master's degrees, so this was a logical expansion,” says Professor Jeff Haywood, Edinburgh's vice-princi pal. “It's an investment in teaching methods research. How am I going to teach introductory philosophy to 100,000 people? That's what I call educational R&D.” He adds “If you look ahead 10 years,you'd expect all students graduating to have taken some online courses, so you've got to research that. Our MOOCs are no more in competition with our degrees than a lifelong learning course because they don't carry credits.”Cooperation is key, Haywood stresses. It is far better to offer 20-30 courses in your own areas of expertise (专门技能) and let other institutions do likewise. Professor Mike Sharples, FutureLearn's academic lead, goes further: “We've tied the elements available before into a package of courses offered by leading universities worldwide on a new software platform, with a new way of promoting it and also a new social-learning teaching method. You won't just receive an exam, but be able to discuss and mark each other's assignments.”Bath University, one of more than 20 universities working with FutureLearn, launches its first course, Inside Cancer, next January, and regards MOOCs as a way of breaking down age barriers. "There's no reason why someone doing GCSEs should not look at our MOOCs and get quite a way through them, or someone at PhD level and beyond," says Professor Bernie Morley, expert for learning and teaching.70. MOOCs have these features EXCEPT that_______.A. MOOCs are free of charge for anyoneB. MOOCs can be adjusted according to people’s learning paceC. MOOCs provide teachers’ instructions if you have some difficultyD. MOOCs have a platform for learners to share their learning experience71. What can be inferred from Professor Bernie Morley in the last paragraph?A. People with various learning levels will probably show interest in MOOCs.B. People at PhD level have already known everything about MOOCs.C. Inside Cancer will be the most popular course for someone doing GCSEs.D. MOOCs are not so competitive as lifelong learning courses due to the problemsof credits.72. The passage mainly deals with _____.A. the various opinions on FutureLearnB. the advantages of online teaching methodsC. the popularity of no-credit coursesD. the emergence of a new learning platform(C)Healthy knees aren’t the main consideration in choosing high heels, but new research says chunky heels are just as bad for the knees as spindly stilettos(高跟鞋). It takes a long time to feel the effects of knee –osteoarthritis (骨关节炎)–and once you do it is too late,” said Dr. Casey Kerrigan, leading researcher of the study and associate professor at Harvard Medical School’s departmen t of physical medicine. “I compare it to smoking---one cigarette is not painful, butover a lifetime it is. Wide---heeled shoes feel comfortable, so women wear them all day long,”Kerrigan said. “They are better for your feet than stiletto heels, but just a s bad for your knees,”In the study, researchers had twenty women wear two pairs of shoes with three-inch heels, one with a narrow heel and the other with a thick one. The scientists compared how much pressure was put on the women’s knees by both typ es of shoes. The women also walked barefoot to test normal pressure. The scientists found that both types of shoes applied equal amounts of pressure to the knees. Compared with walking barefoot, the heels increased pressure on the inside of the knee by 26 percent. Increased pressure on the knee eventually leads to arthritis, experts say.The idea that high heels are bad for your health isn’t new– scientists have warned women for years that they contribute to problems ranging from corns to hammer toes,knee pain, sprained(扭伤)ankles and back problems. But in 1998 , Kerrigan and a team of Harvard researchers were the first to link high heels and knee osteoarthritis,a painful joint disease that destroys cartilage(软骨) surrounding the knee.The first study looked only at stiletto heels, and Kerrigan said she wanted to study the chunky high-heeled shoes she noticed many women wearing. “This study confirms what we all intuitively(直觉地) know that high-heeled shoes of any kind are not good for our health,”said Dr Gle nn Pfeffer, a San Francisco doctor and member of the American Academy of Orthopaedic Surgeons who was not connected to the study.73.We learn from the passage that women choose chunky heels because_____.A. they want to walk comfortablyB. chunky heeled shoes are cheaper than stiletto heeled pairsC. chunky heels do less harm to kneesD. chunky heels are not painful at all74.The study mentioned in the second paragraph found that_____.A. pressure on the knee is caused by high heelsB. the reading of pressure is abnormal while walking barefootC. arthritis is always caused by pressure on the kneeD. both types of shoe have the same harm to the knees75.It can be inferred that_____.A. people got to know the high heels are had for health recentlyB. people have known the high heels are had for health for yearsC. people haven't known the high heels are had for health yetD. people will be warned that the high heels are had for health soon76.Kerrigan's late study looked at the chunky high-heeled shoes because_____.A. they feel more comfortableB. they are related to knee osteoarthritisC. they are worn by many womenD. they are different from stiletto heels77. The best title for the passage may be_____.A. Taking Healthy Knees into ConsiderationB. High-heels Do Harm to KneesC. Chunky Heels and Stiletto HeelsD. When Wearing High HeelsSection CDirections: Read the passage carefully. Then answer the questions or complete the statements in the fewest possible words.Comprehensive lifestyle changes including a better diet and more exercise can lead not only to a better physique, but also to swift and dramatic changes at the genetic level, U.S. researchers said on Monday. In a small study, the researchers tracked 30 men with low-risk prostate cancer who decided against conventional medical treatment such as surgery and radiation or hormone therapy.The men underwent three months of major lifestyle changes, including eating a diet rich in fruits, vegetables, whole grains, legumes and soy products, moderate exercise such as walking for half an hour a day, and an hour of daily stress management methods such as meditation. As expected, they lost weight, lowered their blood pressure and saw other health improvements. But the researchers found more profound changes when they compared prostate biopsies taken before and after the lifestyle changes. After the three months, the men had changes in activity in about500 genes -- including 48 that were turned on and 453 genes that were turned off. The activity of disease-preventing genes increased while a number of disease-promoting genes, including those involved in prostate cancer and breast cancer, shut down, according to the study published in the journal Proceedings of the National Academy of Sciences.The research was led by Dr. Dean Ornish, head of the Preventive Medicine Research Institute in Sausalito, California, and a well-known author advocating lifestyle changes to improve health. "It's an exciting finding because so often people say, 'Oh, it's all in my genes, what can I do?' Well, it turns out you may be able to do a lot," Ornish, who is also connected with the University of California, San Francisco, said in a telephone interview. "'In just three months, I can change hundreds of my genes simply by changing what I eat and how I live'. That's pretty exciting," Ornish said. "The implications of our study are not limited to men with prostate cancer."(Note: Answer the questions or complete the statements in NO MORE THAN 8 WORDS)78. Apart from eating healthy food and exercising, the men in the study were taught ways to__________.79. In total, ________ genes changed as a result of the healthy lifestyle.80. What happened to some of the disease-causing genes?81. The article basically states that ______________________________.第Ⅱ卷（共47分）I. TranslationDirections: Translate the following sentences into English, using the words given in the brackets.1.我万万没有想到对电脑知识一窍不通的奶奶如今也迷上了网购。
上海复旦附中2025届英语高三第一学期期末学业质量监测模拟试题含解析
上海复旦附中2025届英语高三第一学期期末学业质量监测模拟试题注意事项1．考生要认真填写考场号和座位序号。
2．试题所有答案必须填涂或书写在答题卡上，在试卷上作答无效。
第一部分必须用2B 铅笔作答；第二部分必须用黑色字迹的签字笔作答。
3．考试结束后，考生须将试卷和答题卡放在桌面上，待监考员收回。
第一部分（共20小题，每小题1.5分，满分30分）1．They did everything in their power to save the building dating back to the Qing Dynasty, but their efforts were .A．in turn B．in timeC．in vain D．in need2．It _____ a Saturday afternoon in May ____ Margaret could arrange for me to meet her elder ,sister.A．was until; when B．was until;thatC．was not until; when D．was not until; that3．Please ________ your ashes before it fails on the carpet.A．cut off B．knock offC．get off D．drop off4．While studying, fix your mind on what is really important,or you will _____ remembering nothing.A．end up B．take upC．lead to D．stick to5．—What do you do, Rita？—I’m a clerk in a foreign company now．But I _____ English in a high school for 10 years．A．teach B．have taughtC．taught D．am teaching6．—Your car should be ready next Tuesday．—We were ________ hoping you'd be able to do it by this Friday．A．still B．rather C．always D．even7．The conditions in the local school were fairly _____, no electricity and no basic teaching facilities available.A．unique B．typicalC．Primitive D．Stable8．Which do you prefer, tea or coffee?—_______. I rea lly don’t mind.A．Both B．None C．Neither D．Either9．I'm sorry you ______ so long, but it' ll still be some time before Jim gets back．A．wait B．waited C．had waited D．have been waiting10．_______the weather ,the sports meet will be held on time .A．Instead of B．In relation to C．Regardless of D．In favor of11．A myth is an account of the deeds of a god or supernatural beings, usually expressed in terms of ______ thought.A．primary B．capital C．initial D．primitive12．People believe that the China Dream is not very difficult ________ so long as the whole nation works hard for it.A．realizing B．to be realizedC．realized D．to realize13．––Cathy is not coming to your birthday party tonight.––But she ______!A．promised B．promisesC．will promise D．had promised14．Please don’t make so loud noise．The news of the volcanic eruption in Indonesia____and I want to listen．A．is broadcast B．is being broadcastC．has been broadcast D．had been broadcast15．—Look! Mary is crazily looking for something again!—_____ , she can’t find her keys.A．Typically B．Occasionally C．Accordingly D．Particularly16．Young couples will be happy to see their babies _______ with good health and intelligence when they are born.A．to bless B．blessingC．blessed D．being blessed17．—Uncle Wang is in hospital.—Oh, really? I ____________. I _____________ go and visit her.A．didn’t know; am going to B．hadn’t known; wouldC．haven’t known; will D．didn’t know; will18．________ they’ve managed to get everything finished so quickly is not clear to us. A．Which B．WhatC．That D．How19．The security judge was very _________ when she explained that the driving licence was necessary for her work .A．reasonable B．natural C．ridiculous D．available20．. Some people say more but do less ______ others do the opposite.A．once B．when C．while D．as第二部分阅读理解（满分40分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。
杨浦区2016-2017学年 高三年级上学期期中考试试卷(包括复旦附中)
2017学年 杨浦区 高三年级第一学期 模拟卷2016.11.03一、填空题（每小题4分，共56分）1、命题：若“b a >”则“ba 11<”是________命题（填“真”、“假”） 2、已知集合}5,3,2,1{},5,3{},,3,1{===B A B m A ，则____=m3、函数x x x f -++=211)(的定义域是________ 4、已知32sin =θ，则_____22sin =⎪⎭⎫ ⎝⎛+πθ 5、若函数)(x g 与)0(8)(2<-=x x x f 的图像关于直线x y =对称，则____)1(=g6、一个高为2的圆柱，底面周长为π2，该圆柱的表面积为______7、已知6143+=+n n n C C C （5≥n 且*N n ∈），则_____=n 8、圆锥的侧面展开图为扇形，若其弧长为π2cm ，半径为2cm ，则该圆锥的体积为________3cm9、已知()53cos ,02,20=-<<-<<βαβππα，且43tan =α，则_____sin =β 10、设二项式()n x 13+的展开式的二项式系数的和为p ，各项系数的和为q ，且q p =+6430，则n 的值为________11、若函数xx x f 4)(2+=在],1[a 上的值域为]5,4[，则a 的取值范围是_______ 12、设函数)(1)(Q x x f ∈+=αα的定义域为],[],[b a a b --，其中b a <<0；若函数)(x f 在区间],[b a 上的最大值为5，最小值为2，则)(x f 在区间],[a b --上的最大值与最小值的和为_______13、已知C B A ,,是某个三角形的三个内角，给出下列四组数据：（1）C B A sin ,sin ,sin ；（2）C B A 222sin ,sin ,sin ；（3）C B A sin ,sin ,sin ；（4）C B A sin 1,sin 1,sin 1分别以每组数据作为三条线段的长，其中一定能构成三角形的数组的序号是_________14、设函数)(x f 的定义域为D ，]3,0[π⊆D ，它的对应法则为x x f sin :→，现已知)(x f 的值域为⎭⎬⎫⎩⎨⎧1,21,0，则这样的函数共有_______个 二、选择题（每小题5分，共20分）15、“)(32Z k k x ∈+=ππ”是“23sin =x ”成立的 （ ） A. 充分不必要条件 B. 必要不充分条件C. 充要条件D. 既不充分也不必要条件16、现有5个人排成一排照相，其中甲、乙两人不相邻的排法的种数为 （ ）A. 6B. 36C. 72D. 11617、如图，有一个水平放置的透明无盖的正方体容器，容器高8cm ，将一个球放在容器口，再向容器内注水，当球面恰好接触水平时测得水深为6cm ，如果不计容器的厚度，则球的体积为 （ ）A.33256cm π B. 33500cm π C. 33866cm π D. 331372cm π 18、德国著名数学家狄利克雷在数学领域成就显著，以其名命的函数⎩⎨⎧∈∈=QC x Q x x f R 01)(被命名为狄利克雷函数，其中R 为实数集，Q 为有理数集，则关于函数)(x f 有如下四个命题：（1）函数)(x f 存在反函数； （2）函数)(x f 是偶函数；（3）取一个不为零的有理数T ，)()(x f T x f =+对任意的R x ∈恒成立；（4）存在三个点()()())(,,)(,,)(,332211x f x C x f x B x f x A ，使得ABC ∆为等边三角形，其中真命题的个数是 （ ）A. 1B. 2C. 3D. 4三、解答题（74分）19、（6+6=12分）如图，在四棱锥ABCD P -中，底面ABCD 是矩形，⊥PA 平面ABCD ，2==AD PA ，1=AB ，E 是PB 的中点；（1）求证：BC PB ⊥；（2）求异面直线EC 和AD 所成的角（结果用反三角函数值表示）：20、（8+6=14分） 已知在()nx x 3+的二项展开式中，第三项的二项式系数为66；（1）求二项展开式中所有的有理项；（2）在二项展开式的所有项中选出5项，要求选出的5项中至少有2项是有理项，共有多少种不同的选法？如图，某小区准备在长为8千米的道路OP 的一侧修建一条市民健身跑道，跑道的前一部分为曲线段OSM ，该曲线段为函数)0,0(sin >>=ωωA x A y ，]4,0[∈x 的图像，且图像的最高点为)32,3(S ，跑道的后一部分为折线段MNP ，这保证市民健身的安全，限定32π=∠MNP ；（1）求P M ,两点间的直线距离；（2）求折线段跑道MNP 长度的最大值；设常数R a ∈，已知函数aa x f x x -+=22)(为奇函数； （1）求实数a 的值；（2）判断函数)(x f 在定义域上是否为增函数？并证明你的结论；（3）若0<a ，设⎪⎭⎫⎝⎛+=k x x g 1l og 2)(2，且不等式)()(1x g x f ≤-在区间⎥⎦⎤⎢⎣⎡21,31上恒成立，求实数k 的取值范围；对于函数)(x g ，若存在函数)(x f 和常数a ，使)()()(α+=x f x f x g 成立，则称)(x g 是由)(x f 生成的；（1）设x x x g x x g cos sin )(,2cos )(+==，求证：)(x g 可由)(x f 生成；（2）已知)(,212)(x g x f x x +=由)(x f 生成，若)(x g 的最小值为6，求常数α的值； （3）已知)(,)(x g x x f =是由)(x f 生成的，若对任意]1,1[,21-∈x x ，有4)()(21≤-x g x g ，求α的取值范围；。
江苏省上海市复旦附属中学2008-2009学年度第一学期高三英语质量检测.doc
上海市复旦附属中学2008—2009学年度第一学期高三质量检测英语试题考试诚信宣誓：我已清楚地明白本场考试的一切规则、要求，我以至高的荣誉与诚信保证，在考试的自始至终，我都将诚实无欺地完成每一项答题。
第I卷（共105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 conversations and the questions will be spoken only once. After you hear a conversation and the question about it. Read the four possible answers on your paper, and decide which one is the best answer to the question your have heard.1．A．At a boat dock. B．At a weather stationC．At a stadium D．At an airport.2．A．At two o‘clock.B．At four o‘clockC．At six o‘clockD．At eight o‘clock3．A．Her exams have already begun.B．She has finished two papers.C．She‘s trying to complete her papers.D．She‘s too busy to work on her papers.4．A．She doesn‘t have any time.B．It doesn‘t bother her to wait.C．She‘s never had to wait before.D．She hasn‘t seen anyone at all.5．A．Go to the beach with her friends.B．Postpone her meeting with Professor Jones.C．See Professor Jones after class.D．Give a speech in Professor Jones‘s class.6．A．He spends too much money.B．He bought an expensive watch.C．He really does like television.D．He should watch more television.7．A．It has a large yard.B．It is bigger.C．It has a prettier yard.D．It has a prettier color.8．A．Daryl doesn‘t like picnics after all.B．Daryl had previously said he wouldn‘t come.C．Daryl doesn‘t mind arriving late.D．Daryl is always changing his mind.9．A．Laura really needs full – time job.B．Laura already has a job working for the school.C．Laura needs to spend her time studying.D．Laura should think about becoming a teacher.10．A．His car‘s in quite good condition.B．He‘s willing to lend them the car.C．He would prefer to go to the game on foot.D．He will take them if he can.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 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．He knew he was wrong.B．He was too angry to speak.C．He couldn‘t speak in front of a judge.D．He thought the judge would usually believe a rich man.12．A．The poor man finally told him.B．The rich man told him.C．The poor man gave him a clue.D．He knew it at once.13．A．He was poor and couldn‘t pay for the horse.B．He was a reasonable man.C．He usually hated the rich people.D．He was proud of his horse.Questions 14 through 16 are based on the following passage.14．A．The US president will visit Korea soon.B．The US and Korea will have talks.C．There used to be talks between US and Korea.D．The issue of human rights will be discussed.15．A．Russia. B．Yemen. C．France D．The US. 16．A．12 B．14 C．76 D．88Part 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 me numbered blanks with the information you have heard. Write your answers on your answer sheetBlanks 17 through 20 are based on the following conversation.Complete the form. Write ONE WORD for each answer.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．A clear, warm day suddenly grew chill a dark curtain of rolling dust advancedacross the plains. A ．until B ．as C ．so D ．since26．Whether or not man ‘s understanding of social conflicts in any way ―scientific ‖remains an annoying question.A ．areB ．isC ．beingD ．to be27．Just as the soil is part of the earth, the atmosphere.A ．as it isB ．the same asC ．so isD ．and so is28．Some companies have introduced flexible working time with less emphasis onpressure .A ．than more on efficiencyB ．and more efficiencyC ．and more on efficiencyD ．than efficiency29．In Martin Luther King ‘s time, the money spent in educating a black child was just one fourthofon each white child.A ．that spentB ．what to be spentC ．it had beenD ．which was spent30．is more likely to create deep – seated anxieties in people than the falseconsumption that life should be free from anxieties.A ．NoneB ．No oneC ．NothingD ．Nowhere31．The chief manager has decided to put he thinks is energetic and has good qualitiesin the position of leadership of the company.A．who B．anyone C．whomever D．whoever32．We are ignorant of the degree his experiments have supplied forceful evidence for his idea.A．at which B．in that C．to which D．for which 33．Catherine bought a postcard of the place she was visiting, addressed to and then posted it at the nearby post office.A．it; her B．it; herself C．herself, her D．herself; it34．The speech which he made that football match bored a lot of fans to death.A．being concerned B．concerned C．concerned D．concerning35．the city lies the famous beautiful mountain.A．Southeast 40 miles to B．To 40 miles southeast ofC．40 miles southeast of D．To southeast 40 miles of36．This is the most important assignment facing American journalism –to to the readers the problems of the day, and make international news as understandable as community news.A．make it clear B．make that clearC．make this clear D．make clear37．people in western countries think we Muslim women are controlled by men is wrong and it makes me sad people won‘t learn the truth by asking us how we feel.A．That; why B．/; why C．/; what D．That; that38．in her life Jennie gained a clear idea of how large the world isA．The first time B．For the first timeC．At first D．At the first time39．These days the Internet is an integral part of the way we work, invest money, stay and have .A．informed; a fun B．informing; fun C．to inform; a fun D．informed; fun III．Cloze(A)Directions: There is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. You may not use any of the words in the bank more than once.Growing up as an Asian in Britain is much more than a question of facing discrimination and trying to find a decent job – especially for a girl. She has to keep a delicate 40 between two cultures: her own and the British.Seetha Crishna has written a booklet called Girls of Asian Origin in Britain. In it the girls she is most concerned with are those who are 41 different because they have gone through the British educational system and have therefore emerged with an 42 which is distinct from that of their parents.They speak English with regional English accents, they look 43 in Western clothes, and they so not necessarily choose to work in a factory. But they are unmistakably Asian and they are still held by their Asian 44 roots. At home, Asian girl may find herself conforming to the traditions and values of her parents , while at school she tends to 45 the attitudes and appetites of her British contemporaries.As a result , Seetha Crishna found girls existing at two levels-and inclined to 46 both. ―But unless they can successfully accept both, t hey will 47 constantly from one level to the other, feeling trapped. between the two-at 48 cost to their own confidence and happiness,‖For teenage girls, the main 49 is to match the social life which their parents expect them to live with that enjoyed by their schoolmates.(B)Directions: 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 contextRiding a motorcycle is a popular way to travel. A motorcycle often has better acceleration than the fastest 50 . A motorcycle is easier to 51 than a car, most parts of the engine are not too difficult to 52 . A motorcycle is faster in 53 traffic. It‘s smaller than a car, so it can avoid traffic jams and can speed ahead while the cars 54 . A motorcycle is cheaper to run – you 55 less petrol per mile for a motorcycle than for most cars.But this doesn‘t 56 why, for some people, motorcycles are 57 just a way to travel, they are a 58 of life. Everybody knows about the 59 of riding a motorcycle. It‘s far 60 than driving a car. It‘s often very uncomfortable too. However well dressed for a ride the motorcycle is, wind and rain make the 61 difficult and tiring. And then, motorcycles often 62 . There‘s nowhere to sleep, or to shelter from bad 63 when this happens.But the enthusiastic motorcyclist doesn‘t care!Take a look at any motorcycle magazine and you will have an idea of what motorcycling means to the fanatic. The 64 motorcyclist may sometimes think about the dangers of his way of life. But he will still go ‗on the read‘ whenever he can with his bike!50．A．bike B．car C．bus D．train 51．A．mend B．drive C．clean D．operate 52．A．carry B．touch C．oil D．reach 53．A．busy B．heavy C．large D．complex 54．A．park B．move C．wait D．stop55．A．fill B．save C．need D．add 56．A．indicate B．say C．express D．explain 57．A．more than B．less than C．nothing but D．something of 58．A．kind B．type C．way D．fashion 59．A．safety B．excitement C．difficulties D．problems 60．A．quicker B．cheaper C．safer D．more dangerous 61．A．road B．journal C．trip D．journey62．A．go bad B．bread down C．break up D．break in 63．A．day B．weather C．climate D．condition 64．A．mad B．fond C．keen D．crazyIV．Reading ComprehensionDirections: Read the following four passages. Each passage is followed by several questions orunfinished statements. For each of them there are four choices marked A, B, C, and D. Choose the one that fits best according to me information given in me passage you have just read.(A)D day is a term used to stand for the starting day of a campaign or planned series of actions. When the secret starting date is unknown, secret or subject to change, D day is the reference point which helps planners arrange every step of a campaign. For example, the day before D day is D - ; the day after: D+1,D+2 and so on.The letter D here stands for Day, so D day actually means Day day. More commonly the term has a military usage. In fact, it came into being during the First World War, but it was during the Second that D day got its common usage.The beginning of the end of the Second World War was the allied landing of Europe, and D day was its starting date. After months of careful planning, the exact day was fixed for June 5,1994. Because of impossible weather conditions, at the minute the landing was put off until the following day.65．If a man –made satellite is planned to launch on August 1 st, but for some reason, it is launched of July 29 th, then according to the passage, the day is ,A．D – 2 B．D – 3 C．D+2 D．D+366．The allied landing of Europe .A．brought the Second World War to an endB．started the Second World WarC．took place on the day D - 1D．was the end of the Second World War67．Why was the landing of Europe put off in the Second World War?A．Because it had been carelessly plannedB．Because it was fine that day.C．Because it wasn‘t suitable for attacking that day.D．Because it was raining that day.68．Which of the following is true according to the passage?A．D day is a term used only in a campaign.B．D day is helpful for people to plan something to be happening.C．In fact, the term D day is June 5, not June 6D．June 1 st, Children‘s Day can be called D day.(B)Two hours from the tall buildings of Manhattan and Philadelphia live – some of the world‘s largest black bears. They are in Northern Pennsylvania‘s Pocono Mountains, a home they share with an abundance of other wildlife.The streams, lakes, meadows, mountain ridges and forests that make the Poconos an ideal place for black bears have attracted more people to the region. Open spaces are threatened by plans for housing estates and important habitats are endangered by highway construction . To protect the Pocono‘s natural beauty from irresponsible development, the Nature Conservancy（大自然保护协会）named the area one of America‘s ―Last Great Places‖.Operating out of a century-old schoolhouse in the village of Long Pond , Pennsylvania, the conservancy‘s head Cook is working with local people and business leaders to balance economic growth with environmental protection. By creating partnership with people like Francis Altemose ,the Conservancy has been able to protect more than 14,000 acres of environmentally important land in the area .Altemose‘s family has farmed in the Pocono area for ge nerations. Two years ago Francis worked with the conservancy to include his farm in a county farmland protection program . As a result, the family‘s land can be protected from development and the Altemoses will be better able to provide a secure financial future for their 7-year-old grandson .Cook attributes the Conservancy‘s success in the Poconos to having a local presence and a commitment to working with local residents,―The key to protecting these remarkable lands is connecting with the local community,‖ Cook said. ―The people who live there respect the land.‖ They value quiet forests , clear streams and abundant wildlife . They are eager to help with conservation effort.For more information on how you can help The Nature Conservancy protect the Poconos and the world‘s other ―Last Great Places,‖ please call 1-888-5646864, or visit us on the World Wide Web at www. tnc. org.69．We learn from the passage that .A．the population in the Pocono area is growingB．wildlife in the Pocono area is dying out rapidlyC．the security of the Pocono residents is being threatenedD．farmlands in the Pocono area are expanding70．What is important in protecting the Poconos according to Cook ?A．The setting up of an environmental protection website .B．Support from organizations like the Nature Conservancy .C．Cooperation with the local residents and business leaders .D．Inclusion of farmlands in the region‘s protection system.71．What does Cook mean by ―having a local presence‖ (in Para. 5)?A．Financial contributions from local business leadersB．Consideration of the interests of the local residentsC．The establishment if a wild protection foundation in the area.D．The setting up of a local Nature Conservancy branch in the Pocono area72．The passage most probably is .A．an official document B．a news storyC．an advertisement D．a research report(C)For years, doctors advised their patients that the only thing taking multivitamins does is to give them extensive urine (尿). After all, true vitamin deficiencies (缺乏) are practically unheard of in industrialized countries. Now it seems those doctors may have been wrong. The results of a growing number of studies suggest that even a modest vitamin shortfall can be harmful to your health. Although proof of the benefits of multivitamins is still far from certain, the few dollars you spend on them is probably a good investment.Or at least that‘s the argument put forward in the New England Journal of Medicine. Ideally, say Dr. Walter Willett and Dr. Meir Stampfer of Harvard, all vitamin supplements would be evaluated in scientifically rigorous clinical trials. But those studies can take a long time and often raise more questions than they answer. At some point, while researchers work on figuring out where the truth lies, it just makes sense to say the potential benefit outweighs (超过) the cost.Despite vitamin C‘s great popularity, consuming large amounts of it still has not been positively linked to any great benefit. The body quickly becomes filled with C and simply excretes (排泄) any excess.The multivitamins question boils down to this: Do you need to wait until all the evidence is in before you take them, or are you willing to accept that there‘s enough evidence that they don‘t hurt and could help? If the latter, there‘s no need to go to extremes and buy the biggest horse pills or the most expensive bottles. Large doses can cause trouble, including excessive bleeding and nervous system problems.Multivitamins are no substitute for exercise and a balanced diet, of course. As long as you understand that any potential benefit is modest and subject to further refinement, taking a daily multivitamin makes a lot of sense.73．At one time doctors discouraged taking multivitamins because they believed that multivitamins__ __.A．could not easily be absorbed by the human bodyB．were potentially harmful to people‘s healthC．were too expensive for daily consumptionD．could not provide any cure for vitamin deficiencies74．It can be seen that large doses of multivitamins .A．may bring about serious side effectsB．may help prevent excessive bleedingC．are likely to induce the blockage of arteriesD．are advisable for those with vitamin deficiencies75．The author concludes the passage with the advice that___ _.A．the benefit of daily multivitamin intake outweighs that of exercise and a balanced diet B．it‘s risky to take multivitamins without knowing their specific functionC．the potential benefit of multivitamins can never be overestimatedD．it‘s reasonable to take a rational (合理的) dose of multivitamins daily(D)As soon as it was revealed that a reporter for Progressive magazine had discovered how to make a hydrogen bomb, a group of firearm fans formed the National Hydrogen Bomb Association, and they are now lobbying against any legislation (立法) to stop Americans from owning one.―The Constitution(宪法),‖ said the association‘s spokesman, ―gives everyone the right to own arms. It doesn‘t spell out what kind of a rms. But since anyone can now make a hydrogen bomb, the public should be able to buy it to protect themselves.‖―Don‘t you think it‘s dangerous to have one in the house, particularly where there are children around?‖―The National Hydrogen Bomb Association hopes to educate people in the safe handling of this type of weapon. We are instructing owners to keep the bomb in a locked cabinet and the fuse (导火索) separately in a drawer.‖―Some people consider the hydrogen bomb a very fatal weapon which could kill somebody.‖The spokesman said, ―Hydrogen bombs don't kill people—people kill people. The bomb is for self protection and it also has a deterrent effect. If somebody knows you have a nuclear weapon in your house, they're going to think twice about breaking in.‖―But those who want to ban the bomb for American citizens claim that if you have one locked in the cabinet, with the fuse in a drawer, you would never be able to assemble it in time to stop an intruder.‖―Another argument against allowing people to own a bomb is that at the moment it is very expensive to build one. So what your association is backing is a program which would allow the middle and upper classes to acquire a bomb while poor people will be left defenseless with just handguns.‖76．According to the passage, some people started a national association so as to .A ．block any legislation to ban the private possession of the bombB ．support the mass production of the destructive weaponC ．instruct people how to keep the bomb safe at homeD ．promote the large-scale sale of this newly invented weapon77．By saying that the bomb also ―has a deterrent effect ‖ the spokesman means that it .A ．will frighten away any possible intrudersB ．can show the special status of its ownersC ．will threaten the safety of the owners as wellD ．can kill those entering others' houses by force78．According to the passage, opponents of the private ownership of H-bombs are very muchworried that .A ．the influence of the association is too powerful for common people to overcomeB ．poorly-educated Americans will find it difficult to make use of the weaponC ．the wide use of the weapon will push up living expenses tremendouslyD ．the cost of the weapon will put citizens on an unequal basis79．From the tone of the passage we know that the author is .A ．strongly doubtful about the necessity of keeping H-bombs at home for safetyB ．unhappy with those who vote against the ownership of H-bombsC ．not serious about the private ownership of H-bombsD ．concerned about the spread of nuclear weapons(E)Directions: Read the following text and choose the most suitable heading from A – F for each paragraph. There is one extra heading which you do not need.80．Navigation computers, now sold by most car – makers, cost $ 2,000 and up. No surprise, then,that they are most often found in luxury cars, like Lexus, and Audi. But it is a developing technology –meaning prices should eventually drop market does seem. growing.81．Even at current prices, a navigation computer is impressive. It can guide you from point to point in most major cities with precise turn – by – turn directions spoken by a clear human –sounding voice, and written on a screen in front of the driver.82．The computer woks an antenna that takes signals from no fewer than three of the 24 global positioning system (GPS) satellites. By measuring the time required for a signal to travel between the satellites and the antenna, the car‘s location can be pinned down within 200 meters.83．The satellite signals, along with inputs on speed from a wheel – speed sensor and direction from a meter, determine the car‘s position even as it moves. This information is combined with a map database. Street, landmarks and points of interest are included.84．Most system are basically the same. The differences come in hardware –the way the computer accepts the driver‘s request for directions and the way it presents the driving instructions. On most systems, a driver enters a desired address, motorway junction or point of interest by a torch screen or disc. But the Lexus screen goes a step further: you can point to any spot on the map screen and get directions to it.第Ⅱ卷（共45分）I．TranslationDirections: Translate the following sentences into English, using the words given in the Brackets. 1．在夏天，人们可以用空调和电扇来调节室内温度。
2016-2017年上海市复旦附中高三上第一次月考
一. 填空题
1. 不等式 1 1 的解为 x3
2. 已知集合 A {y | y x2 1, x R} ， B {x | y lg(1 x)} ，则 A B
3. 已知奇函数 g(x) ，当 x 0 时， g(x) x2 x ，则 x 0 时， g(x) 4. 函数 y x3 4 ， x [1, 4] 的值域为
18. 已知函数 f (x) a x x （ a 为常数，且 a N * ），对于定义域内的任意两个实数
x1 、 x2 ，恒有 | f (x1) f (x2 ) | 1 成立，则正整数 a 可以取的值有（ ）个
A. 4
B. 5
C. 6
D. 7
三. 解答题
19. 设复数 z a bi (a, b R) ，若 z 是纯虚数，求| z 2 | 的取值范围； z 1
3x
9. 已知方程 x2 px 4 0 ( p R) 有两个虚根,，则2 2 的取值范围是
10. 从集合{1,2,3,4,5,6, 7,8, 9,10} 中任取两个数，要使取到的一个数大于 k ，另一个数小 2
于 k （其中 k {5, 6, 7,8,9} ）的概率是 ，则 k 5
11. 已知命题 p : x 1或 x 3 ，命题 q : x 3m 1 或 x m 2 ，若 p 是 q 的充分非必要 条件，则实数 m 的取值范围是
的子数组，求C( A, S ) 的最大值；
（3）若数组 A (a , a , a ) 中的“元”满足 a 2 a 2 a 2 1，设数组 B (m N *) 含有
123
1
2
3
m
四个“元” b ,b ,b ,b ，且b 2 b 2 b 2 b 2 m ，求 A 与 B 的所有含有三个“元”
2025届上海市复旦附中高三数学第一学期期末学业质量监测试题含解析
2025届上海市复旦附中高三数学第一学期期末学业质量监测试题注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置． 3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B 铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效． 5．如需作图，须用2B 铅笔绘、写清楚，线条、符号等须加黑、加粗．一、选择题：本题共12小题，每小题5分，共60分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1．已知向量()1,2a =，()2,2b =-，(),1c λ=-，若()//2c a b +，则λ=（ ） A ．2-B ．1-C ．12-D ．122．如图，将两个全等等腰直角三角形拼成一个平行四边形ABCD ，将平行四边形ABCD 沿对角线BD 折起，使平面ABD ⊥平面BCD ，则直线AC 与BD 所成角余弦值为（ ）A ．223B ．63C ．33D ．133．已知向量(,4)a m =-，(,1)b m =（其中m 为实数），则“2m =”是“a b ⊥”的（ ） A ．充分不必要条件 B ．必要不充分条件 C ．充要条件D ．既不充分也不必要条件4．如图在直角坐标系xOy 中，过原点O 作曲线()210y x x =+≥的切线，切点为P ，过点P 分别作x 、y 轴的垂线，垂足分别为A 、B ，在矩形OAPB 中随机选取一点，则它在阴影部分的概率为（ ）A ．16B ．15C ．14D ．12A ．60B ．120C ．60或150D ．60或1206．如图，圆锥底面半径为2，体积为223π，AB 、CD 是底面圆O 的两条互相垂直的直径，E 是母线PB 的中点，已知过CD 与E 的平面与圆锥侧面的交线是以E 为顶点的抛物线的一部分，则该抛物线的焦点到圆锥顶点P 的距离等于（ ）A ．12B ．1C ．104D 5 7．已知函数1()cos 22f x x x π⎛⎫=++ ⎪⎝⎭，,22x ππ⎡⎤∈-⎢⎥⎣⎦，则()f x 的极大值点为( ) A ．3π-B ．6π-C ．6π D ．3π 8．甲乙两人有三个不同的学习小组A ， B ， C 可以参加，若每人必须参加并且仅能参加一个学习小组，则两人参加同一个小组的概率为（ ） A ．13 B ．14 C ．15 D ．169．已知变量的几组取值如下表：x1 2 3 4 y2.4 4.3 5.37若y 与x 线性相关，且ˆ0.8yx a =+，则实数a =（ ） A ．74B ．114C ．94D ．13410．设正项等比数列{}n a 的前n 项和为n S ，若23S =，3412a a +=，则公比q =（ ） A ．4±B ．4C ．2±D ．211．点P 为棱长是2的正方体1111ABCD A B C D -的内切球O 球面上的动点，点M 为11B C 的中点，若满足DP BM ⊥，则动点P 的轨迹的长度为（ ） A ．5πB ．5πC ．45πD ．85π12．双曲线的渐近线与圆(x －3)2＋y 2＝r 2(r ＞0)相切，则r 等于( )A ．B ．2C ．3D ．6二、填空题：本题共4小题，每小题5分，共20分。
上海复旦大学附属中学2025届高三考前热身语文试卷含解析
上海复旦大学附属中学2025届高三考前热身语文试卷考生须知：1．全卷分选择题和非选择题两部分，全部在答题纸上作答。
选择题必须用2B铅笔填涂；非选择题的答案必须用黑色字迹的钢笔或答字笔写在“答题纸”相应位置上。
2．请用黑色字迹的钢笔或答字笔在“答题纸”上先填写姓名和准考证号。
3．保持卡面清洁，不要折叠，不要弄破、弄皱，在草稿纸、试题卷上答题无效。
1、下列对漫画的理解和推论，不正确的一项是（）A．国家关心贫困群众，开展了扶贫攻坚工作，帮助他们走向脱贫之路。
B．少数贫困户把帮扶措施当做慈善，产生了“等靠要”的思想和行为。
C．贫困群众都是因为自身懒情、好逸恶劳和缺乏进取心而导致贫穷的。
D．在扶贫过程中，要教育群众，让贫困群众从被动接受变为主动创造。
2、下列各句中，表达得体的一句是A．我在朋友的书房里坐下来，书桌上摆着我惠赠的《红楼梦》，我翻了翻，随手丢开。
B．在那样艰难的情形下，你自己过得并不好，却还能对我鼎力相助，我现在怎能忘记？C．您这么优秀，您推荐的舍妹也一定很优秀，这次去和外商洽谈合作事宜，非她莫属。
D．我家千金明年参加高考，我们也只能尽可能满足她物质上的需求，学习上拜托老师。
3、阅读下面的文字完成下面小题。
近日，美国商务部悍然宣布将对我国44家企业采取出口管制措施，其霸权主义行径暴露无遗。
这虽然会对我国高新技术产业的发展带来一定的影响，但绝不会滞缓我国高新技术产业快速发展的步伐。
相反，这一事件促使很多企业和科技界以更长远的眼光，围绕核心技术为目标，谋求更自主自强的发展。
近年来，我国在全球高科技领域________的态势愈发突出，在不少领域实现“并跑”乃至“领跑”。
但我国高科技企业走向世界的进程不会_________，难免会遭遇这样或那样的掣肘，尤其是在核心技术上落后，就难免__________，出现意想不到的困难。
“核心技术靠化缘是要不来的，必须靠自力更生”。
（）。
突破核心技术，要有“十年磨一剑”的定力，在芯片、发动机等很多方面,需要咬紧牙关,攻坚克难。
2023届上海市复旦大学附中高三三模语文试题(解析版)
7.本文第⑦段指出“以文为戏”具有“跨进跨出”的艺术特征，指叙述者的评论打破了沉浸，具有游戏性（或中国小说时常有干预叙述，人物视角与说话人视角呈现流动性）。《红楼梦》的这段文字先是站在宝钗的视角叙述其赏鉴通灵宝玉的经过，随后转换为叙述者视角评论，告诉读者后文在画下通灵宝玉形状时进行了放大，是为了方便读者观看，让读者不要怀疑宝玉大小等真实性问题。叙述视角“跨进跨出”，起到真假难辨、游戏笔墨的效果。
【4题详解】
本题考查学生筛选并辨析信息的能力。
C.“网络文学的游戏性是接受美学等理论的产物”错。接受美学等理论是后现代文学的理论主张，原文第五段说“数字时代也并不只是后现代小说、超文本的精英文学，也可能是中国网络文学、日本轻小说这种流行文艺”，可见两者并无直接关联。
故选C。
【5题详解】
本题考查学生根据文本内容进行判断推理的能力。
B.最早的文学作品都与游戏密不可分。
C.网络文学的游戏性是接受美学等理论的产物。
D.“以文为戏”体现在中国传统文学的多种体裁中。
5.在视频网站上，以下视频标题不能体现“数字时代文学消费的游戏性”的一项是（ ）
A.《××中学〈红楼梦〉课本剧实况录像》
B.《××大学（红楼梦〉公开课全集》
C.《×××教授揭秘〈红楼梦〉后四十回真相》
2023复旦附中高三语文毕业考试（三模）
2023.5
一积累应用10分
1.填空题。
（1）携来百侣曾游，_____________。（毛泽东《沁园春·长沙》）
（2）《六国论》中，作者描绘诸侯先祖创业艰难的两句是：_____________，_____________。（苏洵《六国论》）
上海市复旦大学附属中学2023-2024学年英语高三第一学期期末考试试题含解析
上海市复旦大学附属中学2023-2024学年英语高三第一学期期末考试试题注意事项1．考试结束后，请将本试卷和答题卡一并交回．2．答题前，请务必将自己的姓名、准考证号用0．5毫米黑色墨水的签字笔填写在试卷及答题卡的规定位置．3．请认真核对监考员在答题卡上所粘贴的条形码上的姓名、准考证号与本人是否相符．4．作答选择题，必须用2B铅笔将答题卡上对应选项的方框涂满、涂黑；如需改动，请用橡皮擦干净后，再选涂其他答案．作答非选择题，必须用05毫米黑色墨水的签字笔在答题卡上的指定位置作答，在其他位置作答一律无效．5．如需作图，须用2B铅笔绘、写清楚，线条、符号等须加黑、加粗．第一部分（共20小题，每小题1.5分，满分30分）1．It’s certainly hard work.But, a man who wishes to have a career has to make a great many sacrifices.A．on the contrary B．in addition C．on the other hand D．in that case2．Let Harry play with your toys as well, Clare — you must learn to ________. A．support B．careC．spare D．share3．Mr. Green was very famous when he lived there. There is ______ to be someone in this district who remembers him.A．content B．opposedC．bound D．restricted4．The little girl ________ a foreign language fairly quickly.A．picked up B．got up C．stepped up D．made up5．As I opened my eyes, in ______ direction I looked, I could see smiling, peaceful, calm and content faces.A．whatever B．however C．whichever D．wherever6．—What do you think of your preparations for the final exams?—Not so good. Actually I feel like ______ for I’ve made little progress in Maths. A．Daniel in the lion’s den B．Achilles’ heelC．a good Samaritan D．a sacred cow7．Della turned all of her pockets inside out only to find $ 1.87 buy Jim a present for Christmas.A．with what to B．with that she can C．in which to D．with which to8．－Could you possilby take to the railway station tomorrow?A．No way B．Never mind C．Not at all D．No problem9．— You should have helped your mom wash the dishes．—I meant ．But she is always telling me to study．A．to do B．to C．doing so D．doing10．The conference aims to develop business and let people think about _______ they can have a positive influence on the planet.A．why B．thatC．what D．how11．The room ______ 10 metres across is large enough for a single man to live in．A．measuring B．measures C．to be measured D．measured12．I like such houses with beautiful gardens in front, but I don’t have enoug h money to buy .A．it B．one C．that D．this13．Good food，good sleep，no exercise．That's he gained weight．A．how B．when C．what D．whether14．Parents often tell their children that they __________ take candy from strangers. A．needn't B．wouldn't C．shouldn't D．daren't15．—What’s up? Y ou look down. —I have piles of papers ________, but I type so slowly.A．to be typed B．typed C．to type D．being typed16．—Mum, is the pair of gloves ________ mine?—Yes. You have to wear another pair.A．washing B．have washedC．being washed D．having washed17．Thanks to the efforts in environmental protection, the wetland has been _____ to its original appearance.A．restored B．deliveredC．transferred D．drafted18．Star skater Wu Dajing won China’s firs t gold medal at the 2018 PyeongChang Olympic Winter Games breaking world record in short track men’s 500m. A．to B．byC．with D．in19．The dining room is clean and tidy, with a table already ______for a big meal．A. being laid B．laying C．to lay D．laid20．--- Do you think I should join the singing group, Mary?--- ______ If I were in your shoes, I certainly would.A．None of your business．B．It depends.C．Why not? D．I don’t think so.第二部分阅读理解（满分40分）阅读下列短文，从每题所给的A、B、C、D四个选项中，选出最佳选项。
复旦大学附属中学高三年级9月月考作文试题导写
高三年级 ９月月考作 文试题导 写
复旦大学附属中学 王 召强
圈圈
阅 读 以下 材料 ，自选 角度 。自拟题 目，
写一篇不 少于 ８ ０ ０字的文章 。 （ ７ ｒ ） 分）
月 夜
文／ 沈尹默
霜风 呼 呼 的 吹 着
月光 朗 朗的 照 着
我和一株顶高的树 并排 立着 而不是靠着
分 析 。毕 竟 。“ 善 假 于物 ” 也 是 成 功 人 士 必 备 的 要 素 。 不 过 ， 这 道 题 目不 宜 写 成 “ 翻案文章” ，一 则 翻起 案来 有 相 当 的 难 度 ， 很 难 自圆其 说 ；二 则材 料 中 暗 含 了 “ 立 着 而 不 是 靠着 ”的 主 旨 ， 只要对 “ 立 着 ”加 以 诠 释 、论证 即可 ，无 须 花 太 多 笔墨 在 辨 析
底 线 了 ，就 没 有普 世 价 值 了 ，这 是 所 有恩 辨 性 写 作 最 容 易 出现
的 问题 。
这 方 面 的 例 子 是 不 胜 枚 举 的 ，只 是 不 要 列 举 大 家 司 空 见 惯 的
例子就行 。
这 道 题 目也 不 宜 从 “ 人 格 ”迁 移 到 “ 国格” 。从 “ 个人 ” 迁 移到 “ 国 家 ”。这 完 全 是 两 个 层 面 的 问 题 ， 单 写 其 中 任 何
《 礼记 ・ 礼 运 》有 云 ：“ 故 人 者 。天 地 之 心 也 ， 五 行 之 端 也 。 ” 人 是 社会 的人 ， 依 附于 社 会 而存 在 ， 但个性造就人格 ， 每个人又是独立存在的。
少 。跟 随 “ 顶 高 的树 ” 固然 没 有什 么错 ，但 失 去 自我 就 得 不偿 失 了 。 不 论 身 处 何 方 ，心 向 何 处 ，即 使 身 前 是 泥 泞 沼 泽 ，身 后 是 荆 棘 丛 林保持 “ 立着” 的姿态 （ 怎 么办 ） 。理
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N 两点之间的距离 d ( x ) ，并求 d ( x ) 的最小值；
（3）是否存在一个实数 a （ 0 a 2 ） ，使得当 d ( x ) 取得最小值时，异面直线 MN 与 OB 互相垂直？请说明理由；
21. 已知 k R ， a 0 且 a 1 ， b 0 且 b 1 ，函数 f ( x ) a k b ； （1）设 a 1 ， ab 1 ，若 f ( x ) 是奇函数，求 k 的值； （2）设 a 1 b 0 ， k 0 ，判断函数 f ( x ) 在 R 上的单调性并加以证明； （3）设 a 2 ， b
5. 现有 5 个女生和 3 个男生随机站成一排，则排头和排尾均为女生的概率是 果用分数表示）
（结
P52 P66 5 【解析】 P88 14
6. 在极坐标系中，圆 2sin 的圆心到极轴的距离为 【解析】标准方程为 x 2 y 2 2 y ，圆心 (0,1) ，距离为1 7. 无穷等比数列 {an } 的前 n 项和为 S n ，若 a1 2 ，且 S 2015 2 S 2016 3S 2017 ，则无穷等比 数列 {an } 的各项和为 【解析】 S 2015 2S 2016 3S2017 a2016 3a2017 q 资料整理 sh-maths
18. 有一容积为 a3 cm3 的正方体容器 ABCD A1 B1C1 D1 ， 在棱 AB 、BB1 和面对角线 BC1 的 中点各有一小孔 E 、 F 、 G ，若此容器可以任意放置，则其可装水的最大容积是（ A. ）
1 3 3 a cm 2
B.
7 3 3 a cm 8
C.
11 3 3 a cm 12
| | 1 ） ，设直线 AP 、 BP 、 AQ 、 BQ 的斜率分别为 k1 、 k2 、 k3 、 k4 ；
（1）求证：点 P 、 Q 、 O 三点共线； （2）求 k1 k 2 k3 k4 的值；
2 （3）若 F1 、 F2 分别为椭圆和双曲线的右焦点，且 QF1 ∥ PF2 ，求 k12 k2 k32 k42 的值；
二. 选择题 15. 等差数列 {an } 的前 n 项和为 S n ，若 a2 a4 a15 的值为定值，则下列各数中为定值的是 （ ） A. S7 16. 矩阵的一种运算 B. S8 C. S13 D. S15
a b x ax by ，该运算的几何意义为平面上的点 ( x, y ) 在矩 c d y cx dy a b 1 a 阵 作用下变换成点 (ax by , cx dy ) ，若曲线 x 2 4 xy 2 y 2 1 ，在矩阵 c d b 1
【解析】焦点 F ( 12. 已知函数 f ( x) 2 （ x R ），且 f ( x) g ( x) h( x ) ，其中 g ( x) 为奇函数， h( x) 为 偶函数，若不等式 2a g ( x) h(2 x) 0 对任意 x [1, 2] 恒成立，则实数 a 的取值范围是
D.
47 3 3 a cm 48
三. 解答题
19. 三角形的三内角 A 、 B 、 C 所对边的长分别为 a 、 b 、 c ，设向量 m (c a, b a) ，
n (a b, c ) ，若 m ∥ n ；
（1）求角 B 的大小； （2）求 sin A sin C 的取值范围；
10. 在平面直角坐标系 xOy 中， 抛物线 y 2 px（ p 0 ） 的焦点为 F ， 双曲线
2
若直线 AB 恰好过点 F ，则双曲线的渐近线方程是
ቤተ መጻሕፍቲ ባይዱ
p p p , 0) ，∴ A( , p ) ， B( , p ) ，即渐近线 y 2 x 2 2 2 11. 在边长为 6 的等边 ABC 中，点 M 满足 BM 2MA ，则 CM CB 等于 【解析】 CM 在 CB 方向的投影为 4，∴ CM CB 4 6 24
13. 已知圆 O : x 2 y 2 1 ， O 为坐标原点，若正方形 ABCD 的一边 AB 为圆 O 的一条弦， 则线段 OC 长度的最大值是 14. 如图，在正三棱锥 P ABC 中， D 为线段 BC 的中点，
E 在线段 PD 上， PE
的体积的最大值为
2 PD ， AE l 为定长，则该棱锥 3
FunshineMaths
峰行数学
复旦附中高三毕业考试数学试卷
2016.05 一. 填空题 1. 已知集合 M {x | y lg x} ， N {x | y 1 x 2 } ，则 M N 2. 若复数 z 满足 (3 4i) z | 4 3i | ，则 z 的虚部为 3. 在 ABC 中，角 A 、B 、C 所对的边分别为 a 、b 、c ，若 a 6 ，c 4 ，sin 则b 4. 如图所示，一家面包销售店根据以往某种面包的销售记录，绘制了日销售量的频率分布 直方图，若一个月以 30 天计算，估计这家面包店一个月内日销售量不少于 150 个的天数为
x2 y2 1 a2 b2 （ a 0 ，b 0 ）的两条渐近线分别与抛物线交于 A 、 B 两点（ A 、 B 异于坐标原点 O ），
10. 在平面直角坐标系 xOy 中， 抛物线 y 2 2 px（ p 0 ） 的焦点为 F ， 双曲线 若直线 AB 恰好过点 F ，则双曲线的渐近线方程是
11. 在边长为 6 的等边 ABC 中，点 M 满足 BM 2MA ，则 CM CB 等于 资料整理 sh-maths
FunshineMaths
x
峰行数学
12. 已知函数 f ( x) 2 （ x R ），且 f ( x) g ( x) h( x ) ，其中 g ( x) 为奇函数， h( x) 为 偶函数，若不等式 2a g ( x) h(2 x) 0 对任意 x [1, 2] 恒成立，则实数 a 的取值范围是
的作用下变换成曲线 x 2 y 1 ，则 a b 的值为（ A. 2 B. 2 C. 2
2 2
） D. 4
17. 函数 y f ( x ) 是 R 上的增函数，则 a b 0 是 f (a) f (b) f ( a) f ( b) 的 （ ） A. 充分不必要条件 C. 充要条件 B. 必要不充分条件 D. 既不充分又不必要条件
5 3 4 4 i ，虚部为 ，注意虚部为实数 3 4i 5 5 5
3. 在 ABC 中，角 A 、B 、C 所对的边分别为 a 、b 、c ，若 a 6 ，c 4 ，sin 则b 【解析】 cos B 1 2sin 2
B 3 ， 2 3
62 42 b 2 1 B 1 ，余弦定理 cos B ，解得 b 6 2 3 26 4 3
x
x
1 ， k 0 ，函数 f ( x ) 的图像是否关于某垂直于 x 轴的直线对称？如 2
果是，求出该对称轴，如果不是，请说明理由；
资料整理
sh-maths
FunshineMaths
22. 已知 A 、B 为椭圆
峰行数学
x2 y2 x2 y2 1 （ ） 和双曲线 1 的公共顶点，P 、Q a b 0 a2 b2 a2 b2 分为双曲线和椭圆上不同于 A 、 B 的动点，且满足 AP BP ( AQ BQ) （ R ，
（1）若 m 4 ，求证：数列 {
资料整理
sh-maths
FunshineMaths
峰行数学
复旦附中高三毕业考试数学试卷
2016.05 一. 填空题 1. 已知集合 M {x | y lg x} ， N {x | y 1 x 2 } ，则 M N 【解析】 M (0, ) ， N [1,1] ，∴ M N (0,1] 2. 若复数 z 满足 (3 4i) z | 4 3i | ，则 z 的虚部为 【解析】 (3 4i) z 5 ， z
4. 如图所示，一家面包销售店根据以往某种面包的销售记录，绘制了日销售量的频率分布 直方图，若一个月以 30 天计算，估计这家面包店一个月内日销售量不少于 150 个的天数为
【解析】频率依次为 0.15、0.25、0.3、0.2、0.1，不少于 150 个的天数 30 (0.2 0.1) 9
1 3 ，∴各项和为 3 2
FunshineMaths
峰行数学
8. 如图，正三棱柱 ABC A1 B1C1 中， AB 4 ， AA1 6 ，若 E 、 F 分别是棱 BB1 、 CC1 上的点，则三棱锥 A A1 EF 的体积是 【解析】 VF A1 AE
1 1 S A1AE h 12 2 3 8 3 3 3
资料整理
sh-maths
FunshineMaths
峰行数学
20. 如图，空间直角坐标系中，四棱锥 P OABC 的底面是边长为 2 的正方形，且底面在
xOy 平面内，点 B 在 y 轴正半轴上， PB 平面 OABC ，侧棱 OP 与底面所成角为 45°；
（1）若 N ( x, y , 0) 是顶点在原点，且过 A 、 C 两点的抛物线上的动点，试给出 x 与 y 满足 的关系式； （2）若 M 是棱 OP 上的一个定点，它到平面 OABC 的距离为 a （ 0 a 2 ） ，写出 M 、
2 2
9. 设直线 2 x 3 y 1 0 和圆 x y 2 x 3 0 相交于 A 、 B 两点，则弦 AB 的垂直平 分线方程是 【解析】设垂直平分线为 3 x 2 y c 0 ，经过圆心 (1, 0) ，∴方程为 3 x 2 y 3 0