硕士研究生招生考试试题格式

2024年全国硕士研究生入学统一考试英语（一）试题Section I Use of EnglishDirections:Read the following text.Choose the best word(s)for each numbered blank and mark A,B,C or D on the ANSWER SHEET.(10points)There’s nothing more welcoming than a door opening for you.1the need to be touched to open or close,automatic doors are essential in2disabled access to buildings and helping provide general3to commercial buildings.Self-sliding doors began to emerge as a commercial product in1960after being invented six years4by Americans Dee Horton and Lew Hewitl.They5as a novelty feature,but as their use has grown,their6have extended within our technologically advanced world. Particularly7in busy locations or during times of emergency,the doors8crowd management by reducing the obstacles put in people’s way.9making access both in and out of buildings easier for people,the difference in the way many of these doors open helps reduce the total area10by them.Automatic doors often open to the side,with the panels sliding across one another.Replacing swing doors,these11smaller buildings to maximise the usable space inside without having to12the way for a large, sticking-out door.There are many different types of automatic door,with each13specific signals to tell them when to open.14these methods differ,the main15remain the same.Each automatic door system16the light,sound weight or movement in their vicinity as a signal to open.Sensor types are chosen to17the different environments they are needed in. 18,a busy street might not19a motion-sensored door,as it would constantly be opening for passers-by.A pressure sensitive mat would be more20to limit the surveyed area.1.[A]Through[B]Despite[C]Besides[D]Without2.[A]revealing[B]demanding[C]improving[D]tracing3.[A]experience[B]convenience[C]guidance[D]reference4.[A]previously[B]temporarily[C]successively[D]eventually5.[A]held on[B]started out[C]settled down[D]went by6.[A]relations[B]volumes[C]benefits[D]sources7.[A]useful[B]simple[C]flexible[D]stable8.[A]call for[B]yield to[C]insist on[D]act as9.[A]As well as[B]In terms of[C]Thanks to[D]Rather than10.[A]connected[B]shared[C]represented[D]occupied11.[A]allow[B]expect[C]require[D]direct12.[A]adopt[B]lead[C]clear[D]change13.[A]adapting to[B]deriving from[C]relying on[D]pointing at14.[A]Once[B]Since[C]Unless[D]Although15.[A]records[B]positions[C]principles[D]reasons16.[A]controls[B]analyses[C]produces[D]mixes17.[A]decorate[B]compare[C]protect[D]complement18.[A]In conclusion[B]By contrast[C]For example[D]Above all19.[A]identify[B]suit[C]secure[D]include20.[A]appropriate[B]obvious[C]impressive[D]delicateSection II Reading ComprehensionPart ADirections:Read the following four texts.Answer the questions below each text by choosing A,B,C or D. Mark your answers on the ANSWER SHEET.(40points)Text1Nearly2000years ago,as the Romans began to pull out of Scotland,they left behind a curious treasure:10tons of nails,nearly a million of the things.The nail hoard was discovered in 1960in a four-metre-deep pit covered by two metres of gravel.Why had the Romans buried a million nails?The likely explanation is that the withdrawal was rushed,and they didn't want the local Caledonians getting their hands on10tons of weapon-grade iron.The Romans buried the nails so deep that they would not be discovered for almost two millennia.Later civilisations would value the skilled blacksmith's labour in a nail even more than the raw material.As Roma Agrawal explains in her new delightful book Nuts and Bolts,early17th-century Virginians would sometimes burn down their homes if they were planning to relocate. This was an attempt to recover the valuable nails,which could be reused after sifting the ashes. The idea that one might burn down an entire house just to reclaim the nails underlines how scarce, costly and valuable the simple-seeming technology was.The price of nails fell by90%between the late1700s and mid-1900s,as economist Daniel Sichel points out in a research paper.According to Sichel,although the falling price of nails was driven partly by cheaper iron and cheaper energy,most of the credit goes to nail manufactures who simply found more efficient ways to turn steel into nails.Nails themselves have changed over the years,but Sichel studied them because they haven't changed much.Roman lamps and Roman chariots are very different from LED strips and sports cars,but Roman nails are still clearly nails.It would be absurd to try to track the changing price of sports cars since1695,but to ask the same question of nails makes perfect sense.I make no apology for being obsessed by a particular feature of these objects:their price.I am an economist,after all.After writing two books about the history of inventions,one thing I've learnt is that while it is the enchantingly sophisticated technologies that get all the hype,it’s thecheap technologies that change the world.The Gutenberg printing press transformed civilisation not by changing the nature of writing but by changing its cost-and it would have achieved little without a parallel collapse in the price of surfaces to write on,thanks to an often-overlooked technology called paper.Solar panels had few niche uses until they became cheap;now they are transforming the global energy system.21.The Romans buried the nails probably for the sake of________.[A]saving them for future use[B]keeping them from rusting[C]letting them grow in value[D]hiding them from the locals22.The example of early17th-century Virginians is used to_____.[A]highlight the thriftiness of early American colonists[B]illustrate the high status of blacksmiths in that period[C]contrast the attitudes of different civilisations toward nails[D]show the preciousness of nail-making technology at that time23.What played the major role in lowering the price of nails after the late1700s?[A]Increased productivity.[B]Wider use of new energies.[C]Fiercer market competition.[D]Reduced cost of raw materials.24.It can be learned from Paragraph5that nails________.[A]have undergone many technological improvements[B]have remained basically the same since Roman times[C]are less studied than other everyday products[D]are one of the world's most significant inventions25.Which of the following best summarises the last two paragraphs?[A]Cheap technologies bring about revolutionary change.[B]Technological innovation is integral to economic success.[C]Technology defines people's understanding of the world.[D]Sophisticated technologies develop from small inventions.Text2Parenting tips obtained from hunter-gatherers in Africa may be the key to bringing up more contented children,researchers have suggested.The idea is based on studies of communities such as the Kung of Botswana,where each child is cared for by many adults.Kung children as young as four will help to look after younger ones and“baby-wearing”,in which infants are carried in slings,is considered the norm.According to Dr Nikhil Chaudhary,an evolutionary anthropologist at Cambridge University, these practices,Known as alloparenting,could lead to less anxiety for children and parents.Dr Annie Swanepoel,a child psychiatrist,believes that there are ways to incorporate them into western life.In Germany,one scheme has paired an old people’s home with a nursery.The residents help to look after the children,an arrangement akin to alloparenting.Another measure could be encouraging friendships between children indifferent school years to mirror the unsupervised mixed-age playgroups in hunter-gatherer communities.In a paper published in the Journal of Child Psychology and Psychiatry,researchers said that the western nuclear family was a recent invention which family broke with evolutionary history.This abrupt shift to an“intensive mothering narrative”,which suggests that mothers should manage childcare alone,was likely to have been harmful.“Such narratives can lead to maternal exhaustion and have dangerous consequences,”they wrote.By contrast,in hunter-gatherer societies adults other than the parents can provide almost half of a child’s care.One previous study looked at the Efépeople of the Democratic Republic of Congo.It found that infants had an average of14alloparents a day by the time they were18 weeks old and were passed between caregivers eight times an hour.Chaudhary said that parents now had less childcare support from family and social networks than during most of humans'evolutionary history,but introducing additional caregivers could reduce stress and maternal depression,which could have a“knock-on”benefit to a child's wellbeing.An infant born to a hunter-gatherer society could have more than ten caregivers-this contrasts starkly to nursery settings in the UK where regulations call for a ratio of one carer to four children aged two to three.While hunter-gatherer children learnt from observation and imitation in mixed-age playgroups,researchers said that western“instructive teaching”,where pupils are asked to sit still, may contribute to conditions such as attention deficit hyperactivity disorder.Chaudhary said that Britain should explore the possibility that older siblings helping their parents“might also enhance their own social development.”26.According to the first two paragraph,alloparenting refers to the practice of_______.[A]sharing child care among community members[B]assigning babies to specific adult caregivers[C]teaching parenting details to older children[D]carrying infants around by their parent27.The scheme in Germany is mentioned to illustrate_______.[A]an attempt to facilitate intergenerational communication[B]an approach to integrating alloparenting into western culture[C]the conventional parenting style in western culture[D]the differences between western African ways of living28.According to Paragraph4,the“intensive mothering narrative”_________.[A]alleviate parenting pressure[B]considerate family relationships[C]results in the child-centered family[D]departs from the course of evolution29.According to paragraph6,what can we learn about nursery in the UK？[A]They tend to fall short of official requirements.[B]They have difficulty finding enough caregivers.[C]They ought to improve their carer-to-child ratio.[D]They should try to prevent parental depression.30.Which of the following would be the best title？[A]Instructive teaching:a dilemma for anxious parents[B]For a happier family,learn from the hunter-gatherers[C]Mix-aged playgroup,a better choice for lonely children[D]Tracing the history of parenting:from Africa to EuropeText3Rutkowski is a Polish digital artist who uses classical painting styles to create dreamy fantasy landscapes.He has made illustrations for games such as Sony’s Horizon Forbidden West, Ubisoft’s Anno,Dungeons&Dragons,and Magic:The Gathering.And he’s become a sudden hit in the new world of text-to-image AI generation.His distinctive style is now one of the most commonly used prompts in the new open-source AI art generator Stable Diffusion,which was launched late last month.The tool,along with other popular image-generation AI models,allows anyone to create impressive images based on text prompts.For example,type in“Wizard with sword and a glowing orb of magic fire fights a fierce dragon Greg Rutkowski,”and the system will produce something that looks not a million miles away from works in Rutkowski’s style.But these open-source programs are built by scraping images from the Internet,often without permission and proper attribution to artists.As a result,they are raising tricky questions about ethics and copyright.And artists like Rutkowski have had enough.According to the website Lexica,which tracks over10million images and prompts generated by Stable Diffusion,Rutkowski’s name has been used as a prompt around93,000times.Some of the world’s most famous artists,such as Michelangelo,Pablo Picasso,and Leonardo da Vinci, brought up around2,000prompts each or less.Rutkowski’s name also features as a prompt thousands of times in the Discord of another text-to-image generator,Midjourney.Rutkowski was initially surprised but thought it might be a good way to reach new audiences.Then he tried searching for his name to see if a piece he had worked on had been published.The online search brought back work that had his name attached to it but wasn’t his.“It’s been just a month.What about in a year?I probably won’t be able to find my work out there because[the internet]will be flooded with AI art,”Rutkowski says.“That’s concerning.”“There is a coalition growing within artist industries to figure out how to tackle or mitigate this,”says Ortiz.The group is in its early days of mobilization,which could involve pushing for new policies or regulation.One suggestion is that AI models could be trained on images in the public domain,and AI companies could forge partnerships with museums and artists,Ortiz says.31.What can be learned about Rutkowski from the first two paragraphs?[A]He is enthusiastic about AI generation painting.[B]He is popular with the users of an AI art generator.[C]He attracts admiration from other illustrators.[D]He specializes in classical painting digitalization.32.The problem with open-source AI art generators is that they____.[A]lack flexibility in responding to prompts[B]produce artworks in unpredictable styles[C]make unauthorized use of online images[D]collect user information without consent33.After searching online,Rutkowski found____.[A]a unique way to reach audiences[B]a new method to identify AI images[C]AI-generated work bearing his name[D]heated disputes regarding his copyright34.According to Ortiz,AI companies are advised to____.[A]campaign for new policies or regulations[B]offer their services to public institutions[C]strengthen their relationships with AI users[D]adopt a different strategy for AI model training35.What is the text mainly about？[A]Artists’responses to Al art generation.[B]AI’s expanded role in artistic creation.[C]Privacy issues in the application of Al.[D]Opposing views on AI development.Text4The miracle of the Chesapeake Bay lies not in its depths,but in the complexity of its natural construction,the interaction of fresh and saline water and the mix of land and water.The shallows provide homes for hundreds of species while storing floodwaters,filtering pollutants from water, and protecting nearby communities from potentially destructive storm surges.All this was put at great risk late last month,when the US Supreme Court issued a ruling in an Idaho case that provides the EPA far less authority to regulate wetlands and waterways. Specifically,a5-4majority decided that wetlands protected by the EPA under it Clean Water Act authority must have a“continuous surface connection”to bodies of water.This narrowing of the regulatory scope was a victory for builders,mining operators and other commercial interests often at odds with environmental rules.And it carries“significant repercussions for water quality and flood control throughout the US,”as Justice Brett Kavanaugh observed.In Maryland,the good news is that there are many state laws in place that provide wetlands protections.But that’s a very shortsighted view,particularly when it comes to the Chesapeake Bay. The reality is that water and the pollutants that so often come with it,don’t respect state boundaries.The Chesapeake draws from a64000-square-mile watershed that extends to Virginia, Pennsylvania,New York,West Virginia,the District of Columbia and Delaware.Will thosejurisdictions extend the same protections now denied under Sackett V.EPA?Perhaps some,but all? That seems unlikely.It is too easy,and misleading,to see such court rulings as merely standing up for the rights of land owners when the consequences can be so dire for their neighbors.And it’s reminder that they EPA’s involvement in the Chesapeake Bay program has long been crucial as the means to transcend the influence of deep-pocketed special interests in neighboring states.Pennsylvania farmers,to use one telling example,aren't thinking about next year's blue crab harvest in Maryland when they decide whether to spread animal waste on their fields,yet the runoff into nearby creeks can have enormous impacts downstream.And so we would also call on state lawmakers from Richmond to Albany to consider reviewing their own wetlands protections and see for themselves the enormous stakes involved. We can’t offer them a trip to the Chesapeake Bay model.It’s been gone since the1980s but perhaps a visit to Blackwater National Wildlife Refuge in Dorchester County where American bald eagles fly over tidal marshes so shallow you could not paddle a boat across them but teaming with aquatic life.It’s worth the scenic drive.36.The Chesapeake Bay is described in Paragraph1as_______.[A]a value natural environment[B]a controversial conservation area[C]a place with commercial potential[D]a headache for nearby communities37.The U.S.Supreme Court's ruling in the Idaho case_________.[A]reinforces water pollution control[B]weakens the EPA's regulatory power[C]will end conflicts among local residents[D]may face opposition from mining operators38.How does the author feel about the future of the Chesapeake Bay?[A]Worried.[B]Puzzled.[C]Relieved.[D]Encouraged.39.What can be inferred about the EPA’s involvement in the Chesapeake Bay Program?[A]It has restored the balance among neighboring jurisdictions.[B]It has triggered a radical reform in commercial fisheries.[C]It has set a fine example of respecting state authorities.[D]It has ensured the coordination of protection efforts.40.The author holds that the state lawmakers should_______.[A]be cautious about the influence of landowners[B]attach due importance to wetlands protections[C]recognize the need to expand wildlife refuges[D]improve the wellbeing of endangered speciesPart BDirections:Read the following comments on a report about American museums returning artifacts to their countries of origin and a list of statements summarizing the comments.Choose the best statement from the list A-G for each numbered name(41—45).There are two extra choices which you do not need to use.Mark your answers on the ANSWER SHEET.(10points)(41)HannahSimply,there are people in Nigeria who cannot travel to the Smithsonian Institution to see that part of their history and culture represented by the Benin Bronzes.These should be available to them as part of their cultural heritage and history and as a source of national pride.There is no good reason that these artifacts should be beyond the ordinary reach of the educational objectives or inspiration of the generations to which they were left.They serve no purpose in a museum in the United States or elsewhere except as curious objects.They cannot be compared to works of art produced for sale which can be passed from hand to hand and place to place by purchase. (42)BuckWe know very exact reproductions of artwork can be and are regularly produced.Perhaps museums and governments might explore some role for the use of nearly exact reproductions as a means of resolving issues relating to returning works of art and antiquities.The context of any exhibit is more important to me than whether the object being displayed is2,000years old or2 months old.In many cases the experts have a hard time agreeing on what is the real object and what is a forgery.Again,the story an exhibit is trying to tell is what matters.The monetary value of the objects on display is a distant second place in importance.(43)SaraWhen visiting the Baltimore Museum of Art,I came across a magnificent15th-century Chinese sculpture.It inspired me to learn more about the culture that it represented.Artifacts in museums have the power to inspire,and perhaps spark that need to learn and understand the nature of their creators.Having said that,I do feel that whatever artifacts find their way to public museums should,in fact,be sanctioned as having been obtained on loan,legally purchased,or obtained by treaty.Stealing artifacts from other peoples’cultures is obscene;it robs not only the physical objects,but the dignity and spirit of their creators.(44)VictorAncient art that is displaced in foreign countries should be returned…(缺失)(45)JuliaTo those of you in the comments section,by all means,who are having strong feeling about artifacts being removed from cities in the US and Britain,I would ask you to consider...(缺失)[A]It is clear that countries of origin have never been compensated for stolen artifacts.[B]It is a flawed line of reasoning to argue against returning artifacts to their countries of origin.[C]Museum visitor can still learn as much from artifacts copies after the originals are returned.[D]Reproductions,even if perfectly made,cannot take the place of the authentic objects.[E]The real value of artifacts can only be recognized in their countries of origin rather than anywhere else.[F]Ways to get artifacts from other countries must be decent and lawful.[G]Concern over security is no excuse for refusing to return artifacts to their countries of origin. Part CDirections:Read the following text carefully and then translate the underlined segments into Chinese.Your translation should be written clearly on the ANSWER SHEET.(10points)“Elephants never forget”—or so they say—and that piece of folklore seems to have some foundation.The African savanna elephant also known as the African bush elephant,is distributed across 37African countries.(46)They sometimes travel more than sixty miles to find food or water,and are very good at working out where other elephants are—even when they are out of ing tracking devices,researchers have shown that they have“remarkable spatial acuity”,when finding their way to waterholes,they headed off in exactly the right direction,on one occasion from a distance of roughly thirty miles.What is more,they almost always seem to choose the nearest water hole.(47)The researchers are convinced that the elephants always know precisely where they are in relation to all the resources they need,and can therefore take shortcuts,as well as following familiar routes.Although the cues used by African elephants for long-distance navigation are not yet understood,smell may well play a part.Elephants are very choosy eaters,but until recently little was known about how they selected their food.(48)One possibility was that they merely used their eyes and tried out the plants they found,but that would probably result in a lot of wasted time and energy,not least because their eyesight is actually not very good.(49)The volatile chemicals produced by plants can be carried a long way,and they are very characteristic:Each plant or tree has its own particular odor signature.What is more,they can be detected even when they are not actually visible.New research suggests that smell is a crucial factor in guiding elephants—and probably other herbivores—to the best food resources.The researchers first established what kinds of plant the elephants preferred either to eat or avoid when foraging freely.They then set up a“food station”experiment,in which they gave elephants a series of choices based only on smell.(50)The experiment showed that elephants may well use smell to identify patches of trees that are good to eat,and secondly to assess the quality of the trees within each patch.Free-ranging elephants presumably also use this information to locate their preferred food.Section III WritingPart A51.Directions:Read the following email from a student.Write a reply.Dear Li Ming,I’ve got a class assignment to make an oral report on an ancient Chinese scientist.I am not sure how to prepare for it.Could you give me some advice?Thanks for your help.Yours,Paul Write your letter in no less than100words.Don’t sign your own name at the end of the e“Li Ming”instead.Part B52.Directions:Write an essay of160-200words based on the pictures below.In your essay,you should1)describe the picture briefly,2)interpret the implied meaning,and3)give your comments.Write your answer on the ANSWER SHEET.(20points)两张图：图一背景信息：在市民健身区两个人在跑，两个人在散步，有一个男生说：“家门口新建的公园真不错。

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(试题此句删除)一、题型（每小题或每空 分，共 分）……………黑体四号1.A4纸型，上边距3.l 厘米，下边距4.4厘米，左右边距为3.17厘米××××××××××××××××××××××××××××××××××××××××××…………………………………试题内容 宋体小四号 单倍行距2.题与题之间空一行××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××…………………………………试题内容 宋体小四号 单倍行距1．公式规范使用工具：公式编辑器，或者相关的公式编辑工具。

Section I Use of EnglishDirections:Read the following text.Choose the best word(s)for each numbered blank and mark A,B,C or D on the ANSWER SHEET.(10 points)Here's a common scenario that any number of entrepreneurs face today ：you're the CEO of a small business,and though you're making a nice 1,you need to find a way to take it to the next level.What you need to do is 2 growth by establishing a growth team.A growth team is made up of members from different departments within your company,and it harnesses the power of collaboration to focus 3 on finding ways to grow.Let's look at a real-world 4.Prior to forming a growth team,the software company BitTorrent had 50 employees working in the 5 departments of engineering,marketing and product development.This brought them good results until 2012,when their growth plateaued.The 6 was that too many customers were using the basic,free version of their product.And 7 improvements to the premium,paid version,few people were making the upgrade.Things changed,8,when an innovative project-marketing manager came aboard,9 a growth team and sparked the kind of 10 perspective they needed.By looking at engineering issues from a marketing point of view,it became clear that the 11 of upgrades wasn't due to a quality issue.Most customers were simply unaware of the premium version and what it offered.Armed with this 12,the marketing and engineering teams joined forces to raise awareness by prominently 13 the premium version to users of the free version 14,upgrades skyrocketed,and revenue increased by 92 percent.But in order for your growth team to succeed,it needs to have a strong leader.It needs someone who can 15 the interdisciplinary team and keep them on course for improvement.This leader will 16 the target area,set clear goals and establish a time frame for the 17 of these goals.The growth leader is also 18 for keeping the team focused on moving forward and steering them clear of distractions.19 attractive new ideas can be distracting,the team leader must recognize when these ideas don't 20 the current goal and need to be put on the back burner.1.[A]purchase[B]profit[C]connection[D]bet2．[A]define[B]predict[C]prioritize[D]appreciate3．[A]exclusively[B]temporarily[C]potentially[D]initially4．[A]experiment[B]proposal[C]debate[D]example5．[A]identical[B]marginal[C]provisional[D]traditional6．[A]rumor[B]secret[C]myth[D]problem7．[A]despite[B]unlike[C]through[D]besides8．[A]moreover[B]however[C]therefore[D]again9．[A]inspected[B]created[C]expanded[D]reformed10．[A]cultural[B]objective[C]fresh[D]personal11．[A]end[B]burden[C]lack[D]decrease12．[A]policy[B]suggestion[C]purpose[D]insight13．[A]contributing[B]allocating[C]promoting[D]transferring 14．[A]As a result[B]At any rate[C]By the way[D]In a sense 15．[A]unite[B]finance[C]follow[D]choose16．[A]share[B]identify[C]divide[D]broaden17．[A]announcement[B]assessment[C]adjustment[D]accomplishment 18．[A]famous[B]responsible[C]available[D]respectable19．[A]Before[B]Once[C]While[D]Unless20．[A]serve[B]limit[C]summarize[D]alterSection II Reading ComprehensionPart ADirections:Read the followingfour texts.Answer the questions below each text by choosing A,B,C or D.Mark your answers on the ANSWER SHEET.(40points)Text1In the quest for the perfect lawn,homeowners across the country are taking a shortcut-and it is the environment that is paying the price.About eight million square metres of plastic grass is sold each year but opposition has now spread to the highest gardening circles.The Chelsea Flower Show has banned fake grass from this year's event,declaring it to be not part of its ethos.The Royal Horticultural Society(RHS),which runs the annual show in west London,says it has introduced the ban because of the damage plastic grass does to the environment and biodiversity.Ed Horne,of the RHS,said:“We launched our sustainability strategy last year and fake grass is just not in line with our ethos and views on plastic.We recommend using real grass because of its environmental benefits,which include supporting wildlife,alleviating flooding and cooling the environment.”The RHS's decision comes as campaigners try to raise awareness of theproblems fake grass causes.A Twitter account,which claims to“cut through the green-wash”of artificial grass,already has more than 20,000followers.It is trying to encourage people to sign two petitions,one callingfor a ban on the sale of plastic grass and another calling for an“ecologicaldamage”tax on such lawns.They have gathered 7,276 and 11,282signaturesHowever,supporters of fake grass point out that there is also anenvironmental impact with natural lawns,which need mowing andtherefore usually consume electricity or petrol.The industry also pointsout that real grass requires considerable amounts of water,weed killer orother treatments and that people who lay fake grass tend to use theirgarden more.The industry also claims that people who lay fake grassspend an average of£500 on trees or shrubs for their garden,whichprovides habitat for insects.In response to another petition last year about banning fake lawns,which gathered 30,000 signatures,the government responded that it has“no plans to ban the use of artificial grass.It added:"We prefer to help people and organizations make the right choice rather than legislating on such matters,However the use of artificial grass must comply with the legal and policy safeguards in place to protect biodiversity and ensure sustainable drainage,while measures such as the strengthened biodiversity duty should serve to encourage public authorities to consider sustainable alternatives.”21.The RHS thinks that plastic grass________.[A]is harmful to the environment[B]is a hot topic in gardening circles[C]is overpraised in the annual show[D]is ruining the view of west London22.The petitions mentioned in Paragraph 3 reveal the campaigners’________.[A]disappointment with the RHS[B]resistance to fake grass use[C]anger over the proposed tax[D]concern about real grass supply23.In Paragraph 4,supporters of fake grass point out________.[A]the necessity to lower the costs of fake grass[B]the disadvantages of growing real grass[C]the way to take care of artificial lawns[D]the challenges of insect habitat protection24.What would the government do with regard to artificial grass?[A]Urge legislation to restrict its use.[B]Take measures to guarantee its quality.[C]Remind its users to obey existing rules[D]Replace it with sustainable alternatives.25.It can be learned from the text that fake grass______.[A]is being improved continuously[B]has seen a market share decline[C]is becoming increasingly affordable[D]has been a controversial productText2It's easy to dismiss as absurd the federal government's ideas for plugging the chronic funding gap of our national parks.Can anyone really think it's a good idea to allow Amazon deliveries to your tent in Yosemite or food trucks to line up under the redwood trees at Sequoia National Park?But the government is right about one thing:U.S.national parks are in crisis.Collectively,they have a maintenance backlog of more than$12 billion.Roads,trails,restrooms,visitor centers and other infrastructure are crumbling.But privatizing and commercializing the campgrounds would not be a cure-all.Campgrounds are a tiny portion of the overall infrastructure backlog,and businesses in the parks hand over,on average,only about 5%of their revenues to the National Park Service.Moreover,increased privatization would certainly undercut one of the major reasons why 300 million visitors come to the parks each year:to enjoy nature and get a break from the commercial drumbeat that overwhelms daily life.The real problem is that the parks have been chronically starved of funding.An economic survey of 700U.S.taxpayers found that people would be willing to pay a significant amount of money to make sure the parks and their programs are kept intact.Some 81%of respondents said they would be willing to pay additional taxes for the next 10 years to avoid any cuts to the national parks.The national parks provide great value to U.S.residents both as places to escape and as symbols of nature.On top of this,they produce value from their extensive educational programs,their positive impact on the climate through carbon sequestration,their contribution to our cultural and artistic life,and of course through tourism.The parks also help keep America's past alive,working with thousands of local jurisdictions around the country to protect historical sites and to bring the stories of these places to life.The parks do all this on a shoestring.Congress allocates only＄3billion a year to the national park system-an amount that has been flat since 2001(in inflation-adjusted dollars)with the exception of a onetime boost in 2009.Meanwhile,the number of annual visitors has increased by more than50%since 1980,and now stands a t330 million visitors per year. 26.what problem are U.S.national parks facedwith?[A]Decline of business profits[B]Inadequate commercialization[C]Lack of transportation services[D]poorly maintained infrastructure27.Increased privatization of the campgroundsmay________.[A]spoil visitor experience[B]help preserve nature[C]bring operational pressure[D]boost visits to parks28.According to paragraph 5 most respondents in the surveywould[A]go to the national parks on a regular basis[B]advocate a bigger budget for the national parks[C]agree to pay extra for the national parks[D]support the national parks'receive reformsText3The Internet may be changing merely what we remember,not our capacity to do so,suggests Columbia University psychology professor Betsy Sparrow.In 2011,Sparrow led a study in which participants were asked to record 40 factoids in a computer(“an ostrich's eye is bigger than its brain,”for example).Half of the participants were told the information would be erased,while the other half were told it would be saved.Guess what?The latter group made no effort to recall the information when quizzed on it later,because they knew they could find it on their computers.In the same study,a group was asked to remember both the information and the folders it was stored in.They didn't remember the information,but they remembered how to find the folders.In other words,human memory is not deteriorating but“adopting to new communications technology,”Sparrow says.In a very practical way,the Internet is becoming an external hard drive for our memories,a process known as“cognitiveoffloading.”Traditionally,this role was fulfilled by data banks,libraries,and other humans.Your father may never remember birthdays because your mother does,for instance.Some worry that this is having a destructive effect on society,but Sparrow sees an upside.Perhaps,she suggests,the trend will change our approach to learning from a focus on individual facts and memorization to an emphasis on more conceptual thinking something that is not available on the Internet.“I personally have never seen all that much intellectual value in memorizing things,”Sparrow says,adding that we haven’t lost our ability to do it.Still other experts say it’s too soon to understand how the Internet affects our brains.There is no experimental evidence showing that it interferes with our ability to focus,for instance,wrote psychologists Christopher Chabris and Daniel.J.Simons.And surfing the web exercisedthe brain more than reading did among computer-savvy older adults in a 2008 study involving 24 participants at the Semel Institute for Neuroscience and Human Behavior at the University of California,Los Angeles.“There may be costs associated with our increased reliance on the Internet,but I’d have to imagine that overall the benefits are going to outweigh those costs,”observes psychology professor Benjamin Storm.“It seems pretty clear that memory is changing,but is it changing for the better?At this point,we don't know.”31.Sparrow’s study shows that with the Internet,the human brainwill________.[A]analyze information in detail[B]collect information efficiently[C]switch its focus of memory[D]extend its memory duration32.The process of“cognitive offloading”________.[A]helps us identify false information[B]keeps our memory from failing[C]Enables us to classify trivial facts[D]lessens our memory burdens33.Which of the following would Sparrow support about theInternet?[A]It may reform our learning approach[B]It may impact our society negatively[C]It may enhance our adaptability to technology[D]It may interfere with our conceptual thinking34.It is indicated in Paragraph 3 that how the Internet affects our brains[A]requires further academic research[B]is most studied in older adults[C]is reflected in our reading speed[D]depends on our web-surfing habits35.Neither Sparrow nor Storm would agree that________.[A]our reliance on the Internet will be costly[B]the Internet is weakening our memory[C]memory exercise is a must for our brains[D]our ability to focus declines with ageText436.According to Paragraph,children growing into adolescence tend to[A]develop opposite personality traits[B]see the word in an unreasonable way[C]have fond memories of their past[D]show affection for their parents37.It can be learned from 2 that Crone'sstudy________.[A]explores teenagers'socialresponsibilities[B]examines teenagers'emotionalproblems[C]provides a new insight intoadolescence[D]highlights negative adolescentbehavior38.What does crone's study find about prosocialbehavior?[A]It results from the wish to cooperate[B]It is cultivated through education[C]It is subject to family influence[D]It tends to peak in adolescence39.It can be learned from the last two paragraphs that teenagers________.[A]over-stress their influence on others[B]care a lot about social recognition[C]Become anxious about their future[D]Endeavor to live a joyful life40.What is the text mainly about________.[A]Why teenagers are self-contradictory.[B]Why teenagers arerisk-sensitive.[C]How teenagers develop prosociality.[D]How teenagers become independent.Part BDirections:Read the following text and match each of the numbered items in the left column to its corresponding information in the right column.There are two extra choices in the right column.Mark your answers on the ANSWER SHEET.(10points)Net-zero rules set to send cost of new homes and extensionssoaringNew building regulations aimed at improving energy efficiency are set to increase the price of new homes,as well as those of extensions and loft conversions on existing ones.The rules,which came into effect on Wednesday in England,are part of government plans to reduce the UK's carbon emissions to net zero by 2050.They set new standards for ventilation,energy efficiency and heating,and state that new residential buildings must have charging points for electric vehicles.The moves are the most significant change to building regulations in years,and industry experts say they will inevitably lead to higher prices at a time when a shortage of materials and high labour costs are already driving up bills.Brian Berry,chief executive of the Federation of MasterBuilders,saysthe measures will require new materials,testing methods,products and systems to be installed.“All this comes at an increased cost during a time when prices are already sky high.Inevitably,consumers will have to pay more,"he says.Gareth Belsham,of surveyors Naismiths,says people who are upgrading,or extending their home,will be directly affected.“The biggest changes relate to heating and insulation,”he explains.“There are new rules concerning the amount of glazing used in extensions,and any new windows or doors must be highly insulated.”Windows and doors will have to adhere to higher standards,while there are new limits on the amount of glazing you can have to reduce unwanted heat from the sun.Thomas Goodman,of MyJobQuote,says this will bring in newrestrictions for extensions.“Glazing on windows,doors and rooflightsmust cover no more than 25%of the floor area to prevent heat loss,"hesays.As the rules came into effect last Wednesday,property developerswere rushing to file plans just before the deadline.Any plans submittedbefore that date are considered to be under the previous rules,and can goahead as long as work starts before 15 June next year.Builders which have costed projects,but have not filed thepaperwork,may need to go back and submit fresh estimates,says MarcusJefford of Build Aviator.Materials prices are already up 25%in the last two years.How much overall prices will increase as a result of the rule changes is notclear."Whilst admirable in their intentions,they will add to the cost ofhousebuilding at a time when many already feel that they are priced out ofhomeownership,"says Jonathan Rolande of the National Association ofProperty Buyers.“An average extension will probably see around£3,000additional cost thanks to the new regs."John Kelly,a construction lawyer at Freeths law firm,believes priceswill eventually come down.But not in the immediate future."As themarketplace adapts to the new requirements,and the technologies thatsupport them,the scaling up of these technologies will eventually bringcosts down,but in the short term,we will all have to pay the price of the necessary transition.”he says.However,the long-term effects of the changes will be more comfortable and energy-efficient homes,adds Andrew Mellor,of PRP architects.“Homeowners will probably recoup that cost over time in energy bill savings.It will obviously be very volatile at the moment,but they will46.Directions:Translate the following text into Chinese.Write your translation on on the ANSWER SHEET.(15points)In the late 18th century,William Wordsworth became famous for his poems about nature.And he was one of the founders of a movement called Romanticism,which celebrated the wonders of the natural world.Poetry is powerful.Its energy and rhythm can capture a reader,transport them to another world and make them see things differently.Through carefully selected words and phrases,poems can bedramatic,funny,beautiful,moving and inspiring.No one knows for sure when poetry began but it has been around for thousands of years,even before people could write.It was a way to tell stories and pass down history.It is closely related to song and even when written it is usually created to be performed out loud.Poems really come to life when they are recited.This can also help with understanding them too,because the rhythm and sounds of the words become clearer. Section IV WritingPart A47.DirectionsAn art exhibition and a robot show are to be held on Sunday and yourfriend David asks you which one he should go to.Write him an email to1)make a suggestion,and2)give your reason(s)Write your answer in about 100 words on the ANSWER SHEETDo not use your own name in your email,use“Li Ming”instead.(10points)Part B48.Directions:Write an essay based on the chart below.In your writing,youshould 1)describe and interpret the chart and2)give your comments.Write your answer in about 150 words on the ANSWER SHEET.(15 points)health literacy健康素养2011-2021我国居民健康素养水平。

昆明理工大学年硕士研究生招生入学考试试卷(卷)
考试科目代码：考试科目名称：农业知识综合三
考生答题须知
1．所有题目（包括填空、选择、图表等类型题目）答题答案必须做在考点发给的答题纸上，做在本试卷册上无效。

请考生务必在答题纸上写清题号。

2．评卷时不评阅本试卷册，答题如有做在本试卷册上而影响成绩的，后果由考生自己负责。

3．答题时一律使用蓝、黑色墨水笔或圆珠笔作答（画图可用铅笔），用其它笔答题不给分。

4．答题时不准使用涂改液等具有明显标记的涂改用品。

机械设计（分）
是运动的单元体。

论述题（分）
自走式切流型谷物联合收获机由哪些装置组成？说明其工作过程，并分别论述脱粒不净；破碎率高；夹带籽粒；清选损失大；籽粒含杂多的原因。

大学硕士研究生入学考试命题工作管理规定一、命题原则研究生入学考试是选拔性考试，试题应能测试出考生是否具备研究生入学的基本条件。

考试内容应结合研究生培养目标确定，以进入研究生学习必备的专业基础知识、基本理论和基本技能为考查重点，突出考查分析问题及解决问题的能力。

试题中应有用以测验考生灵活运用所学知识分析、解决问题能力的内容，这类题目应区别专业和科目情况，占有适当比重。

试题要有一定的区分度，难易程度要适当，一般应使本学科（类别）、专业（领域）的优秀本科毕业生能取得及格以上成绩。

试题的题量以能够使优秀考生全部答完并有一定的检查时间为宜。

各考试科目均应根据大学本科的教学大纲以及研究生入学的基本要求进行命题，试题应能反映本学科（类别）、专业（领域）主干课程的主要内容和要求，试题应涵盖三门以上本科阶段主干专业基础课程。

试题应避免出现学术界尚有争议的问题，并不得有政治性的错误。

专业学位的自命题科目，命题时应侧重考察考生的实践能力。

二、组织工作招生学院组织相应科目的命题小组，实行命题组长负责制。

每门科目独立成立命题小组。

命题小组由命题组长、命题教师2-3人组成。

命题人员由政治素质好、责任心强、教学经验丰富、学术水平较高并且近期承担教学工作的人员担任。

命题人员原则上应具有副教授及以上职称或相当职称，其中命题组组长应具有教授或相当职称并具有研究生招生考试命题经验。

每位命题人员只能参加一门考试科目的命题工作。

命题小组成员应保持相对稳定。

命题组长全权负责命题内容、质量和保密工作。

三、命题要求1.初试各考试科目均采用笔试形式。

2.相近学科（类别）、专业（领域）的试题难度要尽量保持一致。

3.题意要清晰明确，文字要准确简练，导语要明确，措词要确切，避免引起考生的误解。

命题中应注意考务规则中的有关规定，必要的原始数据、图表和资料须在试卷中提供。

4.每道题的分值须在试卷上注明。

命题时应同时确定试题答案及评分参考。

5.每科考试时间均为3小时。

大连理工大学2019年硕士研究生入学考试大纲科目代码：240 科目名称：英语（二外）试题为五部分（词汇与语法、完形填空、阅读理解、翻译和写作），难度大体相当于大学英语四级水平，考核学生运用各项语言基本技能的能力。

一、语法及词汇语法与词汇部分为多项选择题，共50题组成，所占分值比例为25%。

每题有四个选择项。

题目中约60％为词汇题，考查单词、短语及固定搭配等；其余40％为语法题。

二、完形填空完型填空一篇文章，共20题，所占分值比例为10%。

短文长度为220-280词，内容为熟悉的题材。

完型填空的短文有20个空白，有四个选择项，要求考生选择一个最佳答案，使短文的意思和结构恢复完整。

三、阅读理解阅读理解部分由A，B两节组成，共25题，所占分值比例为40%。

Section A快速阅读, 包括1-2篇文章，共10题，每题1分。

考查考生利用略读和查读的技能从文章中快速获取整体和局部信息的能力。

题型包括是非判断，完成句子等。

Section B仔细阅读，三篇文章，共15题，每题2分。

每篇文章后有5个问题或者未完成的表述。

考生根据对文章内容的理解，从每道题的四个选择项中选出最佳答案。

题材广泛，包括人物传记、社会、文化、日常知识、科普常识等。

体裁多样，可以是叙述文、说明文、议论文等；文章中无法猜测而又影响理解的关键词，如超出教学大纲词汇表四级的范围，用汉语注明词义。

四、翻译翻译部分为汉译英和英译汉两部分，所占分值比例为10%。

汉译英部分，共5个句子，所占分值比例为5%。

要求根据全句意思将汉语部分译成英语。

翻译须符合英语的语法结构和表达习惯，要求用词准确。

英译汉部分，共5个句子，所占分值比例为5%。

要求考生根据上下文将段落中的划线部分译成汉语。

五、写作写作部分共1题，所占分值比例为15%。

要求写出一篇120-150词的短文，试卷上可能给出题目，或规定情景，或要求看图作文，或给出段首句要求续写；或给出关键词要求写成短文。

2023年全国硕士研究生招生考试数学试题（数学三）一、选择题:1～10小题,每小题5分,共50分,下列每题给出的四个选项中,只有一个选项是符合题目要求的，请将所选选项前的字母填在答题卡指定位置．(1)已知函数(,)ln(sin )f x y y x y =+，则()(A)(0,1)(0,1)f fx y ∂∂∂∂不存在，存在(B)(0,1)(0,1)f fx y ∂∂∂∂存在，不存在(C)(0,1)(0,1)f fx y ∂∂∂∂，均存在(D)(0,1)(0,1)f fx y ∂∂∂∂，均不存在(2)函数0()(1)cos ,0x f x x x x⎧≤⎪=⎨⎪+>⎩的原函数为()(A)),0()(1)cos sin ,0x x F x x x xx ⎧⎪-≤=⎨+->⎪⎩(B))+1,0()(1)cos sin ,0x x F x x x x x⎧⎪-≤=⎨+->⎪⎩(C)),0()(1)sin cos ,0x x F x x xx x ⎧⎪≤=⎨++>⎪⎩(D))+1,0()(1)sin +cos ,0x x F x x x x x ⎧⎪≤=⎨+>⎪⎩(3)已知微分方程式0y ay by '''++=的解在(,)-∞∞上有界，则()(A)0,0a b <>(B)0,0a b >>(C)0,0a b =>(D)0,0a b =<(4)已知(1,2,)n n a b n <=L ，若级数1nn a∞=∑与1nn b∞=∑均收敛，则“级数1nn a∞=∑绝对收敛”是“级数1nn b∞=∑绝对收敛”的()(A)充分必要条件(B)充分不必要条件(C)必要不充分条件(D)既不充分也不必要条件(5)设,A B 为n 阶可逆矩阵，E 为阶单位矩阵，*M 为矩阵M 的伴随矩阵，则*0A E B ⎛⎫= ⎪⎝⎭()(A)***0*A B B A B A ⎛-⎫⎪⎝⎭(B)***0*B A A B A B ⎛-⎫⎪⎝⎭(C)***0*B A B A A B ⎛-⎫⎪⎝⎭(D)***0*A B A B B A ⎛-⎫⎪⎝⎭(6)二次型()()()222123121323(,,)4f x x x x x x x x x =+++--的规范形为()(A)2212y y +(B)2212y y -(C)2221234y y y +-(D)222123y y y +-(7)已知向量1123α⎛⎫ ⎪= ⎪ ⎪⎝⎭，2211α⎛⎫ ⎪= ⎪ ⎪⎝⎭，1259β⎛⎫ ⎪= ⎪ ⎪⎝⎭，2101β⎛⎫⎪= ⎪ ⎪⎝⎭，若γ既可由12,αα线性表示，也可由与12,ββ线性表示，则γ=()(A)33,4k k R ⎛⎫ ⎪∈ ⎪⎪⎝⎭(B)35,10k k R ⎛⎫ ⎪∈ ⎪⎪⎝⎭(C)11,2k k R -⎛⎫ ⎪∈ ⎪⎪⎝⎭(D)15,8k k R ⎛⎫ ⎪∈ ⎪⎪⎝⎭(8)设随机变量X 服从参数为1的泊松分布，则()E X EX -=()(A)1e(B)12(C)2e(D)1(9)设12,,,n X X X L 为来自总体21(,)N μσ的简单随机样本，12,,,m Y Y Y L 为来自总体22(,2)N μσ的简单随机样本，且两样本相互独立，记11n i i X X n ==∑，11m i i Y Y m ==∑，22111(1n i i S X X n ==--∑，22211(1mi i S Y Y m ==--∑，则()(A)2122(,)S F n m S :(B)2122(1,1)S F n m S --:(C)21222(,)S F n m S :(D)21222(1,1)S F n m S --:(10)设12,X X 为来自总体()2,Nμσ的简单随机样本，其中()0σσ>是未知参数，记12ˆa x x σ=-，若()ˆE σσ=，则a =()(A)2(B)2(C)(D)二、填空题:11～16小题，每小题5分，共30分．(11)2_11l _im o ____(2si s __nc x x x x x→∞--=.(12)已知函数os p 满足22(,)xdy ydx df x y x y -=+,()1,14f π=,则)f =.(13)()2n=02!nx n ∞=∑.(14)设某公司在t 时刻的资产为()f t ，从0时刻到t 时刻的平均资产等于()f t t t-.假设()f t 连续且()00f =，则()f t =.(15)已知线性方程组13123123121202ax x x ax x x x ax ax bx +=⎧⎪++=⎪⎨++=⎪⎪+=⎩有解，其中,a b 为常数，若0111412a a a=,则11120a a ab =.(16)设随机变量X 与Y 相互独立，且()1,X B p :，()2,Y B p :，(0,1)p ∈,则X Y +与X Y -的相关系数为.三、解答题:17～22小题,共70分.解答应写出文字说明、证明过程或演算步骤.(17)(本题满分10分)已知可导函数()y y x =满足2ln(1)cos 0,xae y y x y b ++-++=且(0)0,(0)0y y '==.（Ⅰ）求,a b 的值.（Ⅱ）判断0x =是否为()y x 的极值点.(18)（12分）已知平面区域(),01D x y y x ⎧⎫⎪⎪=≤≤≥⎨⎬⎪⎪⎩⎭（Ⅰ）求D 的面积.（Ⅱ）求D 绕x 轴旋转所成旋转体的体积.(19)（12分）已知平面区域22{(,)(1)1}D x y x y =-+≤，计算二重积分1Ddxdy .(20)（12分）设函数()f x 在[],a a -上具有2阶连续倒数，证明：(Ⅰ)若(0)0f =，则存在(,)a a ξ∈-，使得[]21()()()ξ''=+-f f a f a a.(Ⅱ)若()f x 在(,)a a -内取得极值，则存在(,)a a η∈-使得21()()()2f f a f a aη''≥--.(21)（12分）设矩阵A 满足对任意123,,x x x 均有112321233232--x x x x A x x x x x x x ++⎛⎫⎛⎫ ⎪ ⎪=+ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭.(I)求A .(II)求可逆矩阵P 与对角矩阵Λ，使得1-=ΛP AP .(22)（12分）设随机变量X 的概率密度为2(),,(1)xx e f x x e =-<<+∞+∞令.x Y e =（Ⅰ）求X 的分布函数（Ⅱ）求Y 的概率密度（Ⅲ）Y 的期望是否存在？2023年答案及解析（数学三）一、选择题:1～10小题,每小题5分,共50分,下列每题给出的四个选项中,只有一个选项是符合题目要求的，请将所选选项前的字母填在答题卡指定位置．(1)【答案】(A)【解析】(0,1)0=f ，由偏导数的定义000(0,1)ln(1sin1)(,1)(0,1)lim lim sin1lim →→→+∂-===∂x x x x x f f x f x x xx ，因为0lim 1+→=x x x，0lim 1-→=-x x x ，所以(0,1)∂∂fx 不存在，111(0,1)(0,)(0,1)ln 1lim lim lim 1111→→→∂--====∂---y y y f f y f y y y y y y ，所以(0,1)∂∂fy 存在.(2)【答案】(D)【解析】当0≤x时，1()ln(==+⎰f x dx x C 当0>x 时，()(1)cos (1)sin (1)sin sin =+=+=+-⎰⎰⎰⎰f x dx x xdx x d x x x xdx2(1)sin cos =+++x x x C 原函数在(,)-∞+∞内连续，则在0=x处110lim ln(-→++=x x C C ，22lim(1)sin cos 1+→+++=+x x x x C C 所以121=+C C ，令2=C C ，则11=+C C，故ln(1,0()(1)sin cos ,0⎧⎪++≤=⎨+++>⎪⎩⎰x C x f x dx x x x C x ，结合选项，令0=C ，则()f x的一个原函数为)1,0().(1)sin cos ,0⎧⎪++≤=⎨++>⎪⎩x x F x x x x x (3)【答案】(C)【解析】微分方程0'''++=y ay by 的特征方程为20++=a b λλ，当240∆=->a b 时，特征方程有两个不同的实根12,λλ，则12,λλ至少有一个不等于零，若12,C C 都不为零，则微分方程的解1212--=+xx y C eC e λλ在(,)-∞+∞无界；当240∆=-=a b 时，特征方程有两个相同的实根，1,22=-aλ，若20≠C ，则微分方程的解2212--=+a x a x y C eC xe 在(,)-∞+∞无界；当240∆=-<a b时，特征方程的根为1,222=-±a i λ，则通解为212(cos sin )22-=+a x y eC x C x ，此时，要使微分方程的解在(,)-∞+∞有界，则0=a ，再由240∆=-<a b ，知0.>b (4)【答案】(A)【解析】由条件知1()nn n ba ∞=-∑为收敛的正项级数，进而绝对收敛；设1nn a∞=∑绝对收敛，则由n n n n n n n b b a a b a a =-+≤-+与比较判别法，得1nn b∞=∑绝对收敛；设1nn b∞=∑绝对收敛，则由n n n n n n n a a b b b a b =-+≤-+与比较判别法，得1nn a∞=∑绝对收敛.(5)【答案】(B)【解析】结合伴随矩阵的核心公式，代入(B)计算知*********A EB A A B B AA AA B A B O B OA B O A BB ⎛⎫⎛⎫--+⎛⎫= ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭**B A EOB A E A B A B A B E OA B E OA B E ⎛⎫⎛⎫-+=== ⎪⎪⎝⎭⎝⎭，故(B)正确.(6)【答案】(B)【解析】由已知()222123123121323,,233228f x x x x x x x x x x x x =--+++，则其对应的矩阵211134143A ⎛⎫ ⎪=- ⎪⎪-⎝⎭由()()211134730143E A λλλλλλλ----=-+-=+-=--+,得A 的特征值为3,7,0-故选(B).(7)【答案】(D)【解析】设11221122r x x y y ααββ=+=+则112211220x x y y ααββ+--=又()121212211003,,,2150010131910011ααββ--⎛⎫⎛⎫ ⎪ ⎪--=-→- ⎪ ⎪⎪ ⎪--⎝⎭⎝⎭故()()1212,,,3,1,1,1,TTx x y y c c R=--∈所以()()()121,5,81,5,81,5,8,TTTr c c c c k k R ββ=-+=---=-=∈(8)【答案】(C)【解析】法一：由题可知1EX =，所以1,0||1,1,2,X X EX X X =⎧-=⎨-=⎩L，故，1||1{0}(1){}k E X EX P X k P X k ∞=-=⋅=+-=∑01(1){}(01){0}k k P X k P X e ∞==+-=--=∑112(1)(01)E X e e e=+---=，选（C ）法二：随机变量X 服从参数为1泊松分布，即()()110,1,2,...!P X k e k k -===期望()1E X =()()()()111111111101...1..0!1!2!!E X E X E X e e k e k -----=-=⋅+⋅+⋅++-⋅+()()111111112222211111!!!1!!k k k k k k e k e e e e e e e k k k k k ∞∞∞∞∞--------======+-⋅=+-=+--∑∑∑∑∑()()11111112e e e e e e ----=+----=选(C).(9)【答案】(D)【解析】12,,...,n X X X 的样本方差()221111n i i S X Xn ==--∑12,,...,n Y Y Y 的样本方差()222111mi i S Y Y m ==--∑则()()221211n S n χσ--:()()2222112m S m χσ--:，两个样本相互独立所以()()()()()21222211222212221121,11212n S n S S F n m m S S S m σσσσ--==----:选择(D).(10)【答案】(A)【解析】由题可知212~(0,2)X X N σ-.令12Y X X =-，则Y 的概率密度为2222()y f y σ-⋅=.22222240(||)||y y E Y y dy yedy σσ--+∞+∞⋅-∞===⎰⎰，12(||)(||)E a X X aE Y -==.由ˆ()E σσ=，得2a =.选(A).二、填空题:11～16小题，每小题5分，共30分．(11)【答案】23.【解析】2233221111111lim (2sincos 2(())(1())62x x x x x x x x x x x x οο→∞⎡⎤--=--+--+⎢⎥⎣⎦22221112(623x x xx ο⎡⎤=++=⎢⎥⎣⎦.(12)【答案】3π.【解析】由题意可得22(,),x y f x y x y -'=+则1(,)arctan ()arctan ()x xf x y y c y c y y y y=-⋅⋅+=-+,又因为22(,)y x f x y x y '=+可得()c y c '=，由(1,1)4f π=可得2c π=，即(,)arctan 2xf x y y π=-+，即3f π=.(13)【答案】1122x xe e -+【解析】令20()(2)!n n x s x n ∞==∑,则211()(21)!n n x s x n -∞='=-∑,22210()()(22)!(2)!n nn n x x s x s x n n -∞∞==''===-∑∑.即有()()0s x s x ''-=,解得12()x x s x C e C e -=+.又由(0)1,(0)0s s '==有121C C +=,120C C -=,解得1212C C ==.故11()22x x s x e e -=+.(14)【答案】222te t --【解析】由题意可得方程()()tf x dx f t t tt=-⎰，即20()()t f x dx f t t =-⎰.两边同时t 对求导得()()2f t f t t '=-,即()()2f t f t t '-=.由一阶线性微分方程通解公式有：11()2dt dtf t e te dt C -⎛⎫⎰⎰=+ ⎪⎝⎭⎰()2tte tedt C-=+⎰()22t te t e C -⎡⎤=-++⎣⎦22t Ce t =--.又由于(0)0f =,则20C -=，即2C =.故()222tf t e t =--.(15)【答案】8【解析】由已知()(),34r A r A b =≤<，故,0A b =即()()1444011110111110,1112211112240120012002a a a a a Ab a a a a a baa ba b++==⋅-+⋅-=-+⋅=故111280a a a b=.(16)【答案】13-【解析】因为()1,X B p ~，所以(1)DX p p =-.因为()2,Y B p ~，所以2(1)DY p p =-.ov(,)ov(,)ov(,)C X Y X Y C X Y X C X Y Y +-=+-+ov(,)ov(,)ov(,)ov(,)C X X C Y X C X Y C Y Y =+--(1)2(1)(1)DX DY p p p p p p =-=---=--因为X 与Y 相互独立,所以()3(1)D X Y DX DY p p +=+=-,()3(1)D X Y DX DY p p -=+=-故13ρ==-三、解答题:17～22小题,共70分.解答应写出文字说明、证明过程或演算步骤.(17)【解析】（1）在题设方程两边同时对x 求导得，cos 2ln(1)sin 01x yae y y y x y y x'''+⋅+-++⋅⋅=+①将0x =，0y =代入题设方程得，0a b +=；将0x =，0y =，(0)0y '=代入①式得，10a -=综上：1a =，1b =-.（2）在等式①两边再对x 求导得，()22sin (1)cos 2()2ln(1)sin 0(1)x y y x yae y y y y x y y x '-⋅⋅+-'''''''++⋅+-++⋅⋅=+②将0x =，0y =，(0)0y '=代入②式得，(0)12y a ''=--=-.由于(0)0y '=，(0)2y ''=-，故0x =是()y x 的极大值点.(18)【解析】（1）面积2tan 2221444sec csc ln csc cot ln(1tan sec x ttS dt tdt t tt t ππππππ=+∞====-=+⋅⎰⎰⎰.（2）旋转体体积为2222211111111arctan (1)(1)14x V y dx dx dx x x x x x x ππππππ+∞+∞+∞+∞⎛⎫⎛⎫===-=--=- ⎪ ⎪++⎝⎭⎝⎭⎰⎰⎰.(19)【解析】本题目先利用奇偶对称性化简，再切割积分区域，把积分区域分为三块，分别采用极坐标进行计算：σσσσσd y x d y x d y x d y x d y x D D D D D D D 1212121213213212222222222-+++-++-=-+=-+⎰⎰⎰⎰⎰⎰⎰⎰⎰⎰++分别采用极坐标进行计算：18613)1(13010221ππθσπ=⋅=-=+-⎰⎰⎰⎰dr r r d d y x D 3439166cos 38cos 2)1(1233223cos 20222+-=-=-=+-⎰⎰⎰⎰⎰ππππθπθθθθσd dr r r d d y x D 18334361cos 2cos 38)1(1302330cos 21223ππθθθθσππθ+-=+-=-=-+⎰⎰⎰⎰⎰d dr r r d d y x D 所以：33932121212132122222222++-=-+++-++-=-+⎰⎰⎰⎰⎰⎰⎰⎰πσσσσd y x d y x d y x d y x D D D D (20)【解析】（1）证明：22()()()(0)(0)(0),02!2!f f f x f f x x f x x x ηηη''''''=++=+介于与之间，则211()()(0),02!f f a f a a a ηη'''=+<<①()222()()(0),02!f f a f a a a ηη'''-=-+-<<②①+②得：[]212()()()()2a f a f a f f ηη''''+-=+③又()f x ''在[]21,ηη上连续，则必有最大值M 与最小值m ，即()()12;;m f M m f M ηη''''≤≤≤≤从而()()12;2f f m M ηη''''+≤≤由介值定理得：存在[]()21,,a a ξηη∈⊂-，有()()()122f f f ηηξ''''+''=，代入③得：()2()(),f a f a a f ξ''+-=即()2()()f a f a f aξ+-''=.（2）证明：设()0(),f x x x a a =∈-在取极值，且0()f x x x =在可导，则0()0f x '=.又()()()22000000()()()()()(),02!2!f f f x f x f x x x x x f x x x x γγγ'''''=+-+-=+-介于与之间，则()21001()()(),02!f f a f x a x a γγ''-=+---<<()22002()()(),02!f f a f x a x aγγ''=+-<<从而()()()()22020111()()22f a f a a x f a x f γγ''''--=--+()()()()2202011122a x f a x f γγ''''≤-++又()f x ''连续，设(){}()12max ,M f f γγ''''=，则()()()222200011()()22f a f a M a x M a x M a x --≤++-=+又()0,x a a ∈-，则()2220()()2f a f a M a x Ma --≤+≤，则21()()2M f a f a a ≥--，即存在()12,a a ηγηγ==∈-或，有()21()()2f f a f a a η''≥--(21)【解析】(I)因为112312123232331112211011x x x x x A x x x x x x x x x ++⎛⎫⎛⎫⎛⎫⎛⎫⎪ ⎪ ⎪⎪=-+=- ⎪ ⎪ ⎪⎪ ⎪ ⎪ ⎪⎪--⎝⎭⎝⎭⎝⎭⎝⎭对任意的1x ，2x ，3x 均成立，所以111211011A ⎛⎫⎪=- ⎪ ⎪-⎝⎭(II)1111111211(1)21111011E A λλλλλλλλ---+----=-+-=-⋅+⋅-+-+-+2(1)(2)2(2)(2)(2)(1)0λλλλλλλ=-+-+=+-+=.所以A 的特征值为1232,2,1λλλ=-==-.12λ=-时，1311100211011011000E A λ---⎛⎫⎛⎫ ⎪ ⎪-=---→ ⎪ ⎪⎪ ⎪--⎝⎭⎝⎭，可得特征向量1(0,1,1)Tα=-；22λ=时，2111104231013013000E A λ---⎛⎫⎛⎫ ⎪ ⎪-=--→- ⎪ ⎪ ⎪ ⎪-⎝⎭⎝⎭，可得特征向量2(4,3,1)T α=；31λ=-时，3211201201010010000E A λ---⎛⎫⎛⎫ ⎪ ⎪-=--→ ⎪ ⎪ ⎪ ⎪-⎝⎭⎝⎭，可得特征向量3(1,0,2)T α=-；令123041(,,)130112P ααα⎛⎫ ⎪==- ⎪ ⎪-⎝⎭，则1200020001P AP --⎛⎫ ⎪= ⎪ ⎪-⎝⎭.(22)【解析】（I ）21(),(1)11xx x x x x x e e F x dx x R e e e -∞-∞==-=∈+++⎰（II ）【法一】分布函数法(){}{}X Y F y P Y y P e y =≤=≤当0y <时，()0Y F y =；当0y ≥时，(){ln }(ln )1Y y F y P X y F y y=≤==+；所以Y 的概率密度为21,0(1)()0,Y y y f y ⎧>⎪+=⎨⎪⎩其他.【法二】公式法因为xy e =在(,)-∞+∞上单调且处处可导，当(,)x ∈-∞+∞，0y >，此时ln x y =，所以Y 的概率密度为ln 2ln 211,0,0(ln )(ln ),0(1)()(1)0,0,0,y y Y e y y f y y y y f y e y ⎧⎧>'⋅>>⎧⎪⎪+===+⎨⎨⎨⎩⎪⎪⎩⎩其他其他其他.（III ）2001ln(1)(1)1y EY dy y y y +∞+∞⎛⎫==++=∞ ⎪++⎝⎭⎰，所以不存在.。

2023年全国硕士研究生招生考试英语(二)试题全文共3篇示例，供读者参考篇12023 National Master's Postgraduate Entrance Examination (Part 2) English Test QuestionsPart A: Reading Comprehension (60 minutes)Questions 1-5Read the following passage and answer the questions below.The North Pole is known for its icy landscapes and freezing temperatures. It is a place that many people dream of visiting, but very few ever get the chance to experience. The North Pole is located in the Arctic Ocean at the northernmost point of the Earth. It is covered by a thick layer of ice that is constantly shifting and changing.1. What is the North Pole known for?2. Where is the North Pole located?3. Describe the climate at the North Pole.4. Why do few people get the chance to visit the North Pole?5. What covers the North Pole?Questions 6-10Read the following passage and answer the questions below.In recent years, there has been a growing interest ineco-friendly transportation options. Electric cars, bicycles, and public transportation are just a few examples of environmentally friendly ways to get around. These options not only help reduce pollution and greenhouse gas emissions but also promote a healthier lifestyle for individuals.6. What is the focus of recent interest in transportation options?7. Name two examples of eco-friendly transportation options.8. How do eco-friendly transportation options benefit the environment?9. In what way do eco-friendly transportation options promote a healthier lifestyle?10. Explain why eco-friendly transportation options are important.Part B: Writing (60 minutes)Essay Question:In recent years, the importance of sustainable living has become more evident in our society. Discuss the ways in which individuals can contribute to environmental sustainability in their daily lives. Provide examples to support your argument.End of ExamThis document is a practice test for the 2023 National Master's Postgraduate Entrance Examination English (Part 2). Do not write on this document.篇22023 National Postgraduate Entrance Examination (II) English TestPart I Reading Comprehension (40%)Directions: There are four passages in this part. Each passage is followed by some questions or unfinished statements. For each of them, there are four choices marked A, B, C, and D. You should decide on the best choice and mark the corresponding letter on the Answer Sheet with a single line through the center.Passage 1Questions 1-5Q1. What is the main topic of the passage?A. The importance of sleep for overall healthB. The effects of sleep deprivation on cognitive functionC. The link between sleep and memoryD. The role of dreams in the sleep cycleQ2. According to the passage, what are some of the consequences of sleep deprivation?A. Increased focus and attentionB. Improved mood and emotional regulationC. Impaired decision-making and memoryD. Enhanced creativity and problem-solving skillsQ3. What does the author suggest is the best way to improve memory and cognitive function?A. Taking naps throughout the dayB. Practicing mindfulness meditationC. Getting enough quality sleepD. Consuming caffeine and stimulantsQ4. Which of the following is NOT mentioned as a potential benefit of dreaming?A. Emotional processingB. Memory consolidationC. Problem-solvingD. Physical healingQ5. What is the purpose of the last paragraph?A. To recommend specific techniques for improving sleep qualityB. To explain the role of sleep in the brain's restorative processesC. To outline the stages of the sleep cycleD. To highlight the importance of prioritizing sleep for cognitive healthPassage 2Questions 6-10Q6. According to the passage, what factor has contributed to the decline in bee populations?A. Climate changeB. Pesticide useC. Habitat lossD. All of the aboveQ7. How do bees benefit the environment?A. By providing honey for human consumptionB. By pollinating plants and cropsC. By controlling the insect populationD. By producing beeswax for commercial useQ8. What is the main idea of the second paragraph?A. The importance of protecting bees for human healthB. The decline in bee populations and its causesC. The economic value of honey productionD. The role of bees in food productionQ9. According to the passage, what is one way individuals can help protect bees?A. Planting bee-friendly flowers and plantsB. Avoiding honey consumptionC. Using chemical pesticides in the gardenD. Destroying beehives found on private propertyQ10. What is the author's main message in the passage?A. Bees are an essential part of ecosystems and human survivalB. Bees are a nuisance and should be eradicatedC. Pesticides are necessary for crop productionD. Declining bee populations will not impact food securityPart II Usage (10%)Directions: There are ten incomplete sentences in this part. For each sentence, there are four choices marked A, B, C, and D. You should choose the ONE that best completes the sentence. Mark your answer on the Answer Sheet.11. _______, he managed to finish the project on time.A. However busy was heB. Busy as he wasC. As he was busyD. He was however busy12. The guests were ________ by the variety of dishes at the banquet.A. impressB. impressedC. impressedlyD. impression13. It is essential that you _______ the terms of the contract before signing it.A. understandB. understandsC. understoodD. understanding14. The teacher asked the students to work ________ on the assignment.A. independentB. independentlyC. independentliestD. independence15. She showed me _______ dog she had adopted from the shelter.A. thatB. whatC. whichD. whoPart III Writing (50%)Directions: Write an essay of about 600 words on the following topic:"It is often said that technology has greatly influenced the way we communicate with each other. Discuss the advantages and disadvantages of using technology to communicate. Provide examples to support your argument."Remember to:1. State your opinion clearly in the introduction.2. Support each point with relevant examples.3. Summarize your points and restate your opinion in the conclusion.---This is just a sample of the type of questions you may encounter in the 2023 National Postgraduate Entrance Examination (II) English Test. The actual test may vary in format and content. Good luck to all the test-takers.篇32023 National Graduate Entrance Examination (English) TestPart I. Reading Comprehension (40 points)Section ADirections: In this section, there are four passages followed by questions or incomplete statements. For each of them, choose the one most suitable answer from the options given.Passage 1Recent studies have shown the positive impact of meditation on mental health. It has been found that regular meditation can reduce stress levels, improve focus and concentration, and increase overall well-being. Some researchers even believe that meditation can help in the treatment of anxiety and depression.1. What is the main topic of the passage?A. The history of meditationB. The benefits of meditationC. The negative effects of meditationD. The types of meditation techniques2. According to the passage, how can meditation benefit mental health?A. By increasing stress levelsB. By decreasing focus and concentrationC. By improving well-beingD. By causing anxiety and depression3. Which of the following is NOT mentioned as a benefit of meditation?A. Reduce stress levelsB. Improve focus and concentrationC. Increase anxiety and depressionD. Treat mental health issuesPassage 2The concept of artificial intelligence (AI) has become increasingly popular in recent years. Many industries are now using AI technology to streamline processes and improve efficiency. However, concerns have been raised about the ethical implications of AI and its potential impact on jobs.4. What is the main point of the passage?A. The benefits of AI technologyB. The popularity of AI technologyC. The ethical concerns of AI technologyD. The impact of AI technology on jobs5. According to the passage, why are concerns being raised about AI technology?A. Its potential impact on jobsB. Its efficiency in streamlining processesC. Its popularity in recent yearsD. Its lack of ethical implications6. Which of the following is NOT mentioned as a use of AI technology?A. Streamline processesB. Improve efficiencyC. Replace human jobsD. Ethical implicationsSection BDirections: Read the following passage and answer the questions that follow.The tourism industry plays a significant role in the global economy, generating billions of dollars in revenue each year. As more people travel for leisure and business, the demand for travel services such as flights, accommodation, and tours has increased. However, there are growing concerns about the impact of mass tourism on the environment and local communities.7. What is the main focus of the passage?A. The economic impact of the tourism industryB. The demand for travel servicesC. The benefits of mass tourismD. The concerns about the impact of mass tourism8. Why has the demand for travel services increased?A. More people are traveling for leisure and businessB. The tourism industry is failingC. The impact of mass tourism on the environmentD. The decrease in revenue each year9. Which of the following is NOT mentioned as a concern of mass tourism?A. Environmental impactB. Economic benefitsC. Impact on local communitiesD. Cultural preservationPart II. Cloze Test (20 points)Directions: For each blank in the passage below, there are four words or phrases marked a, b, c, and d. Choose the one that best fits the context and write the corresponding letter on your answer sheet.Cities around the world are facing the challenges of rapid urbanization. As the population continues to (10)______ in urban areas, cities are struggling to provide adequate housing, transportation, and infrastructure. One of the key issues facingurban planners is (11)______ to balance economic growth with environmental sustainability. The rise of mega-cities has led to increased traffic congestion and pollution, (12)______ creating a strain on resources and public services. Without sustainable planning and development, cities will (13)______ to meet the needs of their growing populations.10. a. gatherb. concentratec. dispersed. distribute11. a. decideb. determiningc. decidingd. decision12. a. consequentiallyb. consequentlyc. consequentlyd. consequent13. a. failureb. succeedc. forgetd. preparePart III. Writing (40 points)Directions: Write an essay of at least 300 words on one of the following topics. Make sure to use examples and arguments to support your ideas.1. The impact of technology on education2. The importance of environmental conservation3. The role of social media in societyThis concludes the 2023 National Graduate Entrance Examination (English) Test. Good luck to all the candidates!。

2023年全国硕士研究生招生考试数学试题（数学一）一、选择题:1～10小题,每小题5分,共50分,下列每题给出的四个选项中,只有一个选项是符合题目要求的，请将所选选项前的字母填在答题卡指定位置．(1)曲线1ln(1y x e x =+-的渐近线方程为()(A)y x e=+(B)1y x e =+(C)y x=(D)1y x e=-(2)若微分方程0y ay by '''++=的解在(,)-∞+∞上有界，则()(A)0,0a b <>(B)0,0a b >>(C)0,0a b =>(D)0,0a b =<(3)设函数()y f x =由2sin x t ty t t⎧=+⎪⎨=⎪⎩确定，则()(A)()f x 连续，(0)f '不存在(B)(0)f '存在，()f x '在0x =处不连续(C)'()f x 连续，(0)f ''不存在(D)(0)f ''存在，()f x ''在0x =处不连续(4)已知(1,2,)n n a b n <=L ，若级数1nn a∞=∑与1nn b∞=∑均收敛，则“1nn a∞=∑绝对收敛”是“1nn b∞=∑绝对收敛的”()(A)充分必要条件(B)充分不必要条件(C)必要不充分条件(D)既不充分也不必要条件(5)已知n 阶矩阵,,A B C 满足0ABC =，E 为n 阶单位矩阵，记矩阵0A BC E ⎛⎫⎪⎝⎭，0AB C E ⎛⎫ ⎪⎝⎭，0E AB AB⎛⎫⎪⎝⎭的秩分别为123,,γγγ，则()(A)123γγγ≤≤(B)132γγγ≤≤(C)312γγγ≤≤(D)213γγγ≤≤(6)下列矩阵中不能相似于对角矩阵的是()(A)11022003a ⎛⎫ ⎪ ⎪⎪⎝⎭(B)1112003a a ⎛⎫⎪ ⎪⎪⎝⎭(C)11020002a ⎛⎫ ⎪ ⎪⎪⎝⎭(D)11022002a ⎛⎫ ⎪ ⎪⎪⎝⎭(7)已知向量1123α⎛⎫ ⎪= ⎪ ⎪⎝⎭，2211α⎛⎫ ⎪= ⎪ ⎪⎝⎭，1259β⎛⎫ ⎪= ⎪ ⎪⎝⎭，2101β⎛⎫⎪= ⎪ ⎪⎝⎭，若γ既可由12,αα线性表示，也可由12,ββ线性表示，则γ=()(A)33,4k k R⎛⎫⎪∈ ⎪ ⎪⎝⎭(B)35,10k k R⎛⎫ ⎪∈ ⎪ ⎪⎝⎭(C)11,2k k R-⎛⎫ ⎪∈ ⎪ ⎪⎝⎭(D)15,8k k R⎛⎫ ⎪∈ ⎪ ⎪⎝⎭(8)设随机变量X 服从参数为1的泊松分布，则()E X EX -=()(A)1e(B)12(C)2e(D)1(9)设12,,,n X X X L 为来自总体21(,)N μσ的简单随机样本，12,,,m Y Y Y L 为来自总体22(,2)N μσ的简单随机样本，且两样本相互独立，记11n i i X X n ==∑，11m i i Y Y m ==∑，22111(1n i i S X X n ==--∑，22211(1mi i S Y Y m ==--∑，则()(A)2122~(,)S F n m S (B)2122~(1,1)S F n m S --(C)21222~(,)S F n m S (D)21222~(1,1)S F n m S --(10)设12,X X 为来自总体2(,)N μσ的简单随机样本，其中(0)σσ>是未知参数.若12ˆa X X σ=-为σ的无偏估计，则a =()(A)2(B)2(C)(D)二、填空题:11～16小题，每小题5分，共30分．(11)当0x →时，函数2()ln(1)f x ax bx x =+++与2()cos x g x e x =-是等价无穷小，则ab =____.(12)曲面222ln(1)z x y x y =++++在点(0,0,0)处的切平面方程为________.(13)设()f x 为周期为2的周期函数，且()1,[0,1]f x x x =-∈，若01()+cos 2n n a f x a n x π∞==∑，则21nn a∞==∑_______.(14)设连续函数()f x 满足2(2)(),()0f x f x x f x dx +-==⎰，则31()f x dx =⎰_______.(15)已知向量12311223311010111,,,,10111111k k k αααβγααα-⎛⎫⎛⎫⎛⎫⎛⎫⎪ ⎪ ⎪ ⎪-=====++ ⎪ ⎪ ⎪ ⎪- ⎪ ⎪ ⎪ ⎪-⎝⎭⎝⎭⎝⎭⎝⎭，若(1,2,3)TTi i i γαβα==，则222123k k k ++=________.(16)设随机变量与Y 相互独立，X 且11~(1,),~(2,)32X B Y B 则{}P X Y ==________.三、解答题:17～22小题,共70分.解答应写出文字说明、证明过程或演算步骤.(17)(本题满分10分)设曲线)()(0y x x y =>经过点(1,2)，该曲线上任一点(,)P x y 到y 轴的距离等于该点处的切线在y 轴上的截距.(I)求()y x ;(II)求函数1()()xf x y t dt =⎰在(0,)+∞上的最大值.(18)(本题满分12分)求函数23(,)()()f x y y x y x =--的极值.(19)(本题满分12分)设空间有界区域Ω中，柱面221x y +=与平面0z =和1x z +=围成，∑为Ω边界的外侧，计算曲面积分2cos 3sin I xzdydz xz ydzdx yz xdxdy ∑=++⎰⎰Ò.(20)设函数()f x 在[,]a a -上具有二阶连续导数，证明：(I)若(0)0f =，则存在(,)a a ξ∈-，使得21()[()()]f f a f a a ξ''=+-;(II)若()f x 在(,)a a -内取得极值，则存在(,)a a η∈-使得21()()()2f f a f a a η''≥--.(21)已知二次型2221231231213(,,)2222f x x x x x x x x x x =+++-,22212312323(,,)2g y y y y y y y y =+++(I)求可逆变换x Py =，将123(,,)f x x x 化为123(,,)g y y y ;(II)是否存在正交变换x Qy =，将123(,,)f x x x 化为123(,,)g y y y .(22)设二维随机变量(,)X Y 的概率密度为22222(),1(,)0,x y x y f x y π⎧++≤⎪=⎨⎪⎩其它(I)求X 与Y 的斜方差;(II)求X 与Y 是否相互独立;(IIi)求22Z X Y =+的概率密度.答案及解析(1)【答案】(B)【解析】1limlim ln()11x x y k e x x →∞→∞==+=-，11lim()lim[ln(]lim [ln()1]11→∞→∞→∞=-=+-=+---x x x b y kx x e x x e x x 11lim ln[1]lim .(1)(1)→∞→∞=+==--x x x x e x e x e所以斜渐近线方程为1.=+y x e(2)【答案】(C)【解析】微分方程0'''++=y ay by 的特征方程为20++=a b λλ，当240∆=->a b 时，特征方程有两个不同的实根12,λλ，则12,λλ至少有一个不等于零，若12,C C 都不为零，则微分方程的解1212--=+xx y C eC e λλ在(,)-∞+∞无界；当240∆=-=a b 时，特征方程有两个相同的实根，1,22=-a λ，若20≠C ，则微分方程的解2212--=+a x a x y C eC xe 在(,)-∞+∞无界；当240∆=-<a b时，特征方程的根为1,222=-±a i λ，则通解为212(cos sin )22-=+ax y eC x C x ，此时，要使微分方程的解在(,)-∞+∞有界，则0=a ，再由240∆=-<a b ，知0.>b (3)【答案】(C)【解析】0t ≥时，3sin x t y t t =⎧⎨=⎩，得sin 33x xy =；0t <时，sin x t y t t=⎧⎨=-⎩，得sin y x x =-；综上，sin ,033sin ,0xx x y x x x ⎧≥⎪=⎨⎪-<⎩，从而由00sin 0sin 033(0)lim 0,(0)lim 0x x x xx x y y x x +-+-→→---''====，得(0)0y '=；于是1sin cos ,033930,0sin cos ,0x x x x y x x x x x ⎧+>⎪⎪'==⎨⎪--<⎪⎩，得y '连续；又由001sin cos 02sin cos 03393(0)lim ,(0)lim 29x x x x x x x x y y x x+++-→→+----''''====-，得(0)y ''不存在.(4)【答案】(A)【解析】由条件知1()nn n ba ∞=-∑为收敛的正项级数，进而绝对收敛；设1nn a∞=∑绝对收敛，则由n n n n n n n b b a a b a a =-+≤-+与比较判别法，得1nn b∞=∑绝对收敛；设1nn b∞=∑绝对收敛，则由n n n n n n n a a b b b a b =-+≤-+与比较判别法，得1nn a∞=∑绝对收敛.(5)【答案】(B)【解析】因初等变换不改变矩阵的秩，10000,A ABC r r r r n BC E BC E BC E -⎛⎫⎛⎫⎛⎫====⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭20(),00AB C AB r r r r AB n E E ⎛⎫⎛⎫===+ ⎪⎪⎝⎭⎝⎭300EAB Er r r AB AB ABAB ⎛⎫⎛⎫==⎪ ⎪-⎝⎭⎝⎭0()()0E r r ABAB n r AB nABAB ⎛⎫==+≤+ ⎪-⎝⎭故选(B).(6)【答案】(D)【解析】选项(A)矩阵的特征值为三个不同特征值，所以必可相似对角化；选项(B)矩阵为实对称矩阵，所以必可相似对角化；选项(C)矩阵特征值为1,2,2，二重特征值的重数()232r C E =--，所以必可相似对角化；选项(D)矩阵特征值为1,2,2，二重特征值的重数()232r D E ≠--，所以不可相似对角化.故选(D).(7)【答案】(D)【解析】设11221122r x x y y ααββ=+=+,则112211220x x y y ααββ+--=.又()121212211003,,,2150010131910011ααββ--⎛⎫⎛⎫ ⎪ ⎪--=-→- ⎪ ⎪ ⎪ ⎪--⎝⎭⎝⎭,故()()1212,,,3,1,1,1,TTx x y y c c R =--∈.所以()()()121,5,81,5,81,5,8,T T Tr c c c c k k R ββ=-+=---=-=∈.(8)【答案】(C)【解析】由题可知()1E X =，所以1,0||1,1,2,X X EX X X =⎧-=⎨-=⎩L，故()1||1{0}(1){}k E X EX P X k P X k ∞=-=⋅=+-=∑01(1){}(01){0}k k P X k P X e ∞==+-=--=∑112(1)(01)E X e e e=+---=，故选(C).(9)【答案】(D)【解析】12,,...,n X X X 的样本方差()221111n i i S X Xn ==--∑，12,,...,n Y Y Y 的样本方差()222111mi i S Y Y m ==--∑，则()()21221~1n S n χσ--，()()22221~12m S m χσ--，两个样本相互独立，所以()()()()()2122221122222222112~1,11212n S n S S F n m m S S S m σσσσ--==----，故选(D).(10)【答案】(A)【解析】由题可知212~(0,2)X X N σ-.令12Y X X =-，则Y 的概率密度为2222()y f y σ-⋅=.22222240(||)||y y E Y y dy yedy σσ--+∞+∞⋅-∞===⎰，12(||)(||)E a X X aE Y -==.由12ˆ||)a X X σ=-为σ的无偏估计，有^()E σσ=，得2a =.故选(A).二、填空题:11～16小题，每小题5分，共30分．(11)【答案】2-【解析】2200()ln(1)lim lim ()cos x x x f x ax bx x g x e x →→+++=-222022221()2lim 11()1()2x ax bx x x x x x x x οοο→++-+=⎡⎤++--+⎢⎥⎣⎦1=,可得10a +=，1322b -=，即1,2a b =-=,故2ab =-.(12)【答案】20x y z +-=【解析】22(,,)2ln(1)F x y z x y x y z =++++-,222222(,,)(1,2,1)11x y z x yF F F x y x y'''==++-++++n ，即在点(0,0,0)处的法向量为()1,2,1-，即切平面方程为20x y z +-=.(13)【答案】0【解析】由()f x 展开为余弦级数知，()f x 为偶函数.由傅里叶系数计算公式有12(1)cos n a x n xdxπ=-⎰()112cos cos n xdx x n xdx ππ=-⎰⎰1100112sin sin n x xd n x n n ππππ⎛⎫=- ⎪ ⎪⎝⎭⎰102sin xd n x n ππ=-⎰()11002sin sin x n x n xdxn πππ-=-⎰102sin n xdx n ππ=⎰12202cos n x n ππ-=()222cos 1n n ππ-=-.故()()2222211cos 2111022n a n n n πππ--=-=-=.(14)【答案】12【解析】323112()()()f x dx f x dx f x dx=+⎰⎰⎰()211()(2)2f x dx f t dt x t =++=+⎰⎰令211()(2)f x dx f x dx=++⎰⎰[]211()()f x dx f x x dx=++⎰⎰2111()()f x dx f x dx xdx=++⎰⎰⎰21()f x dx xdx=+⎰⎰1xdx=⎰12=.(15)【答案】119【解析】11111221331123111130013TTTTTk k k k k k k γαβααααααα==⇒++=⇒⋅+⋅+⋅=⇒=.同理2311,3k k =-=-.所以，222123119k k k ++=.(16)【答案】13【解析】因为1~1,3X B ⎛⎫ ⎪⎝⎭，所以0,1X =;1~2,2Y B ⎛⎫⎪⎝⎭，所以0,1,2Y =.又因为X 与Y 相互独立，所以{}{0,0}{1,1}P X Y P X Y P X Y ====+=={0}{0}{1}{1}P X P Y P X P Y ===+==2201222111132323C C ⎛⎫⎛⎫=+= ⎪ ⎪⎝⎭⎝⎭.三、解答题:17～22小题,共70分.解答应写出文字说明、证明过程或演算步骤.(17)【解析】(I)设点(,)x y 处的切线方程为()Y y y X x '-=-，故y 轴的截距为y y x '-，则x y y x '=-，解得(ln )y x C x =-，其中C 为任意常数.由(1)2y C ==，故()(2ln )y x x x =-.(II)由(I)知1()(2ln )xf x t t dt =-⎰，故()(2ln )0f x x x '=-=，则驻点为2x e =.当20x e <<时，()0f x '>；当2x e >时，()0f x '<,故()f x 在2x e =处取得极大值，同时也取得最大值，且最大值为224115()(2ln )44e f e x x dx e =-=-⎰.(18)【解析】323(235)020x y f x y xy x f y x x '⎧=-+-=⎪⎨'=--=⎪⎩，得驻点为(0,0)，(1,1)，210(,)327.32(235)(315)xxf y xy x x y x ''=-+---,(23)xy f x x ''=-+，2yy f ''=.代入(0,0)，002xxxyyyA fB fC f ''⎧==⎪''==⎨⎪''==⎩，则20AC B -=，故充分条件失效，当0x →时，取23(0)y x kx k =+>，2332355(,)()()[(1)]()f x y y x y x kx x k x kx o x =--=+-=+，则555500(,)()lim lim 0x x f x y kx o x k x x →→+==>，由极限的局部保号性：存在0δ>，当(,0)x δ∈-时，5(,)0f x y x >，(,)0(0,0)f x y f <=，当(0,)x δ∈时，5(,)0f x y x>，(,)0(0,0)f x y f >=，故(0,0)不是极值点；代入(1,1)，1252xxxyyy A f B f C f ''⎧==⎪''==-⎨⎪''==⎩，则20AC B -<，故(1,1)不是极值点；代入210(,327的10027832xx xyyyA fB fC f ⎧''==⎪⎪⎪''==-⎨⎪''==⎪⎪⎩，则20AC B ->且0A >，故210(,)327是极小值点；故2104(,)327729f =-为极小值.(19)【解析】由高斯公式可得：()2sin 3sin I z xz y y x dVΩ=-+⎰⎰⎰2zdV Ω=⎰⎰⎰102xy x D dxdy zdz -=⎰⎰⎰()21xy D x dxdy =-⎰⎰()22:1xy D x y +≤()212xy D x x dxdy =-+⎰⎰()2212xyD x y dxdy π=++⎰⎰2130012d r dr ππθ=+⎰⎰544πππ=+=.(20)【解析】(I)证明：22()()()(0)(0)(0),02!2!f f f x f f x x f x x x ηηη''''''=++=+介于与之间，则211()()(0),02!f f a f a a a ηη'''=+<<.①()222()()(0),02!f f a f a a a ηη'''-=-+-<<.②①+②得：[]212()()()()2a f a f a f f ηη''''+-=+.③又()f x ''在[]21,ηη上连续，则必有最大值M 与最小值m ，即,()()12,,m f M m f M ηη''''≤≤≤≤从而()()122f f m M ηη''''+≤≤.由介值定理得：存在[]()21,,a a ξηη∈⊂-，有()()()122f f f ηηξ''''+''=，代入③得：()()22()()()(),f a f a f a f a a f f a ξξ+-''''+-==即.(II)设()0(),f x x x a a =∈-在取极值，且0()f x x x =在可导，则0()0f x '=.又()()()22000000()()()()()(),02!2!f f f x f x f x x x x x f x x x x γγγ'''''=+-+-=+-介于与之间，则()21001()()(),02!f f a f x a x a γγ''-=+---<<.()22002()()(),02!f f a f x a x a γγ''=+-<<.从而()()()()22020111()()22f a f a a x f a x f γγ''''--=--+()()()()2202011122a x f a x f γγ''''≤-++.又()f x ''连续，设(){}()12max ,M f f γγ''''=，则()()()222200011()()22f a f a M a x M a x M a x --≤++-=+又()0,x a a ∈-，则()2220()()2f a f a M a x Ma --≤+≤，则21()()2M f a f a a ≥--，即存在()12,a a ηγηγ==∈-或，有()21()()2f f a f a aη''≥--.(21)【解析】(I)利用配方法将123(,,)f x x x 和123(,,)g y y y 化为规范形,从而建立两者的关系.先将123(,,)f x x x 化为规范形.2221231231213(,,)222f x x x x x x x x x x =+++-2221232323()2x x x x x x x =+-+++2212323()()x x x x x =+-++令112322333z x x x z x x z x =+-⎧⎪=+⎨⎪=⎩,则2212312(,,)f x x x z z =+.即112233*********z x z x z x -⎛⎫⎛⎫⎛⎫ ⎪ ⎪⎪= ⎪ ⎪⎪ ⎪ ⎪⎪⎝⎭⎝⎭⎝⎭,使得2212312(,,)f x x x z z =+.再将123(,,)g y y y 化为规范形.2222212312323123(,,)2()g y y y y y y y y y y y =+++=++令1122333z y z y y z y =⎧⎪=+⎨⎪=⎩,则2212312(,,)g y y y z z =+.即112233100011001z y z y z y ⎛⎫⎛⎫⎛⎫ ⎪ ⎪⎪= ⎪ ⎪⎪ ⎪ ⎪⎪⎝⎭⎝⎭⎝⎭,使得2212312(,,)g y y y z z =+.从而有112233*********z x z x z x -⎛⎫⎛⎫⎛⎫ ⎪ ⎪⎪= ⎪ ⎪⎪ ⎪ ⎪⎪⎝⎭⎝⎭⎝⎭123100011001y y y ⎛⎫⎛⎫ ⎪⎪= ⎪⎪ ⎪⎪⎝⎭⎝⎭,于是可得112233x y x P y x y ⎛⎫⎛⎫ ⎪ ⎪= ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭,其中1111100111011011010001001001P ---⎛⎫⎛⎫⎛⎫ ⎪ ⎪ ⎪== ⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎝⎭⎝⎭⎝⎭为所求矩阵，可将化为.(II)二次型和的矩阵分别为111120102A -⎛⎫ ⎪= ⎪ ⎪-⎝⎭,100011011B ⎛⎫ ⎪= ⎪ ⎪⎝⎭.由题意知,若存在正交变换x Qy =，则1T Q AQ Q AQ B -==，可得和相似.易知()5,()3tr A tr B ==，从而和不相似，于是不存在正交变换x Qy =，使得化为.(22)设二维随机变量(,)X Y 的概率密度为【解析】(I)()222()0D E X xx y d σπ=+=⎰⎰，()222()0D E Y yx y d σπ=+=⎰⎰，()222()0DE XY xyx y d σπ=+=⎰⎰，所以(,)()()()0Cov X Y E XY E X E Y =-=.(II)22),11()0X x y dy x f x ⎧+-<<⎪=⎨⎪⎩，其他24(121130x x π⎧+-<<⎪=⎨⎪⎩，其他同理，得：24(1211()30Y y y f y π⎧+-<<⎪=⎨⎪⎩，其他.因为，()()(,)X Y f x f y f x y ≠,所以X 与Y 不相互独立.(III)22(){}{}Z F z P Z z P X Y z =≤=+≤当0z <时，()0Z F z =；当01z ≤<时，222320022()()z Z D F z x y d d dr z πσθππ=+==⎰⎰⎰⎰；当1z ≥时，()1Z F z =；所以，Z 的概率密度为2,01()0,Z z z f z <<⎧=⎨⎩其他.。

广西科技大学 2023 年硕士研究生招生考试初试专业课试卷考试科目代码： 806 考试科目名称：普通化学考试时间：180分钟（本试题共 4 页）一、选择题（每题2分，共计30分）1.为了提高CO在反应CO(g)＋H2O(g) CO2(g)＋H2(g)中的转化率，可以采取的措施是( )A. 增加CO的分压B. 增加水蒸汽的分压C. 按比例增加H2O(g)和CO的分压D. 增加H2的分压2.使下列液态物质沸腾，只需克服色散力的是( )A. O2B. HFC. CH3CH2OHD. H2O3. NCl3分子的空间构型是( )A. 直线形B. 三角锥形C. 正四面体D.平面三角形4.由实验测得2ICl＋H2＝I2＋2HCl 的反应速率与[ICl]成正比，可知此反应是( )A. 三级反应B. 二级反应C. 一级反应D. 零级反应5.下列分子中，属于极性分子的是（）A．H2S B．CO2C．BBr3D．CCl46. 已知某难溶盐AB2的溶解度为S（单位为mol·dm-3），其溶度积为（）A. S3B. S2C. 4S3D. S3/47. 下面电对中，E 最大的为哪一种( )A. E (AgI/Ag)B. E (AgCl/Ag)C. E (AgBr/Ag)D. E (Ag+/Ag)8.催化剂加快反应速率的根本原因是( )A.改变了反应的平衡常数B.改变了反应途径，使反应变成了一步就能完成的简单反应C.催化剂为反应补充了额外的能量D.改变了反应的途径，降低了反应的活化能9.质量作用定律只能直接适用于( )A. 基元反应B. 复杂反应C. 化合反应D. 分解反应10. 向HAc溶液中，加入少许固体物质，使HAc解离度减小的是（）A. NaClB. NaAcC. FeCl3D. KCN11.按照酸和碱的质子理论，下述物质中，哪一种属于弱酸( )A. NO3-B. Cl-C. NH4+D. CO32-12. 基态11Na原子最外层电子的四个量子数可能是( )A. 3，0，0，+12 B. 3，1，0，+12C. 3，1，0，-12 D. 3，2，1，-1213. 血浆中K+的平均质量浓度为0.195g·dm-3(K的相对原子质量39.10)，则其物质的量浓度是( )A. 1.6mmol·dm-3B. 7.6mmol·dm-3C. 5mmol·dm-3D. 5×10-3 mmol·dm-3 14．下列说法正确的是( )A. ∆H< 0的反应均为自发反应B. ∆S > 0的反应均为自发过程C. ∆H< 0，∆S> 0的反应均为自发过程D. ∆H> 0，∆S< 0的反应均为自发过程15. 过氧化氢(H2O2) （）A. 是一种碱B. 是一种酸C. 是一种氧化剂D. 既是酸，又是碱，既是氧化剂，又是还原剂二、填空题（每题2分，共计20分）1.在一定温度下，难溶混合气体在水中的溶解度与该气体的①成正比。

2023年全国硕士研究生招生考试英语（二）试题Section I Use of EnglishDirections:Read the following text.Choose the best word(s)for each numbered blank and mark A,B,C or D on the ANSWER SHEET.(10points)Here's a common scenario that any number of entrepreneurs face today：you're the CEO of a small business,and though you're making a nice1,you need to find a way to take it to the next level.What you need to do is2growth by establishing a growth team.A growth team is made up of members from different departments within your company,and it harnesses the power of collaboration to focus3on finding ways to grow.Let's look at a real-world4.Prior to forming a growth team,the software company BitTorrent had50employees working in the5departments of engineering,marketing and product development.This brought them good results until2012,when their growth plateaued.The6was that too many customers were using the basic,free version of their product.And7improvements to the premium,paid version,few people were making the upgrade.Things changed,8,when an innovative project-marketing manager came aboard,9a growth team and sparked the kind of10perspective they needed.By looking at engineering issues from a marketing point of view,it became clear that the11of upgrades wasn't due to a quality issue.Most customers were simply unaware of the premium version and what it offered.Armed with this12,the marketing and engineering teams joined forces to raise awareness by prominently13the premium version to users of the free version14,upgrades skyrocketed,and revenue increased by92percent.But in order for your growth team to succeed,it needs to have a strong leader.It needs someone who can15the interdisciplinary team and keep them on course for improvement.This leader will16the target area,set clear goals and establish a time frame for the17of these goals.The growth leader is also18for keeping the team focused on moving forward and steering them clear of distractions.19attractive new ideas can be distracting,the team leader must recognize when these ideas don't20the current goal and need to be put on the back burner.1.[A]purchase[B]profit[C]connection[D]bet 2．[A]define[B]predict[C]prioritize[D]appreciate 3．[A]exclusively[B]temporarily[C]potentially[D]initially 4．[A]experiment[B]proposal[C]debate[D]example 5．[A]identical[B]marginal[C]provisional[D]traditional 6．[A]rumor[B]secret[C]myth[D]problem 7．[A]despite[B]unlike[C]through[D]besides 8．[A]moreover[B]however[C]therefore[D]again9．[A]inspected[B]created[C]expanded[D]reformed 10．[A]cultural[B]objective[C]fresh[D]personal 11．[A]end[B]burden[C]lack[D]decrease 12．[A]policy[B]suggestion[C]purpose[D]insight 13．[A]contributing[B]allocating[C]promoting[D]transferring 14．[A]As a result[B]At any rate[C]By the way[D]In a sense 15．[A]unite[B]finance[C]follow[D]choose 16．[A]share[B]identify[C]divide[D]broaden 17．[A]announcement[B]assessment[C]adjustment[D]accomplishment 18．[A]famous[B]responsible[C]available[D]respectable 19．[A]Before[B]Once[C]While[D]Unless 20．[A]serve[B]limit[C]summarize[D]alterSection II Reading ComprehensionPart ADirections:Read the following four texts.Answer the questions below each text by choosing A,B, C or D.Mark your answers on the ANSWER SHEET.(40points)Text1In the quest for the perfect lawn,homeowners across the country are taking a shortcut-and it is the environment that is paying the price.About eight million square metres of plastic grass is sold each year but opposition has now spread to the highest gardening circles.The Chelsea Flower Show has banned fake grass from this year's event,declaring it to be not part of its ethos.The Royal Horticultural Society(RHS),which runs the annual show in west London,says it has introduced the ban because of the damage plastic grass does to the environment and biodiversity.Ed Horne,of the RHS,said:“We launched our sustainability strategy last year and fake grass is just not in line with our ethos and views on plastic.We recommend using real grass because of its environmental benefits,which include supporting wildlife,alleviating flooding and cooling the environment.”The RH S's decision comes as campaigners try to raise awareness of the problems fake grass causes.A Twitter account,which claims to“cut through the green-wash”of artificial grass,already has more than20,000followers.It is trying to encourage people to sign two petitions,one calling for a ban on the sale of plastic grass and another calling for an“ecological damage”tax on such lawns. They have gathered7,276and11,282signaturesHowever,supporters of fake grass point out that there is also an environmental impact with natural lawns,which need mowing and therefore usually consume electricity or petrol.The industryalso points out that real grass requires considerable amounts of water,weed killer or other treatments and that people who lay fake grass tend to use their garden more.The industry also claims that people who lay fake grass spend an average of£500on trees or shrubs for their garden,which provides habitat for insects.In response to another petition last year about banning fake lawns,which gathered30,000 signatures,the government responded that it has“no plans to ban the use of artificial grass.It added:"We prefer to help people and organizations make the right choice rather than legislating on such matters,However the use of artificial grass must comply with the legal and policy safeguards in place to protect biodiversity and ensure sustainable drainage,while measures such as the strengthened biodiversity duty should serve to encourage public authorities to consider sustainable alternatives.”21.The RHS thinks that plastic grass________.[A]is harmful to the environment[B]is a hot topic in gardening circles[C]is overpraised in the annual show[D]is ruining the view of west London22.The petitions mentioned in Paragraph3reveal the campaigners’________.[A]disappointment with the RHS[B]resistance to fake grass use[C]anger over the proposed tax[D]concern about real grass supply23.In Paragraph4,supporters of fake grass point out________.[A]the necessity to lower the costs of fake grass[B]the disadvantages of growing real grass[C]the way to take care of artificial lawns[D]the challenges of insect habitat protection24.What would the government do with regard to artificial grass?[A]Urge legislation to restrict its use.[B]Take measures to guarantee its quality.[C]Remind its users to obey existing rules[D]Replace it with sustainable alternatives.25.It can be learned from the text that fake grass______.[A]is being improved continuously[B]has seen a market share decline[C]is becoming increasingly affordable[D]has been a controversial productText2It's easy to dismiss as absurd the federal government's ideas for plugging the chronic funding gap of our national parks.Can anyone really think it's a good idea to allow Amazon deliveries to your tent in Yosemite or food trucks to line up under the redwood trees at Sequoia National Park?But the government is right about one thing:U.S.national parks are in crisis.Collectively,they have a maintenance backlog of more than$12billion.Roads,trails,restrooms,visitor centers and other infrastructure are crumbling.But privatizing and commercializing the campgrounds would not be a cure-all.Campgrounds are a tiny portion of the overall infrastructure backlog,and businesses in the parks hand over,on average, only about5%of their revenues to the National Park Service.Moreover,increased privatization would certainly undercut one of the major reasons why300 million visitors come to the parks each year:to enjoy nature and get a break from the commercial drumbeat that overwhelms daily life.The real problem is that the parks have been chronically starved of funding.An economic survey of700U.S.taxpayers found that people would be willing to pay a significant amount of money to make sure the parks and their programs are kept intact.Some81%of respondents said they would be willing to pay additional taxes for the next10years to avoid any cuts to the national parks.The national parks provide great value to U.S.residents both as places to escape and as symbols of nature.On top of this,they produce value from their extensive educational programs,their positive impact on the climate through carbon sequestration,their contribution to our cultural and artistic life, and of course through tourism.The parks also help keep America's past alive,working with thousands of local jurisdictions around the country to protect historical sites and to bring the stories of these places to life.The parks do all this on a shoestring.Congress allocates only＄3billion a year to the national park system-an amount that has been flat since2001(in inflation-adjusted dollars)with the exception of a onetime boost in2009.Meanwhile,the number of annual visitors has increased by more than50% since1980,and now stands a t330million visitors per year.26.what problem are U.S.national parks faced with?[A]Decline of business profits[B]Inadequate commercialization[C]Lack of transportation services[D]poorly maintained infrastructure27.Increased privatization of the campgrounds may________.[A]spoil visitor experience[B]help preserve nature[C]bring operational pressure[D]boost visits to parks28.According to paragraph5most respondents in the survey would________.[A]go to the national parks on a regular basis[B]advocate a bigger budget for the national parks[C]agree to pay extra for the national parks[D]support the national parks'receive reforms29.The National Parks are valuable in that they____.A.lead the way in tourismB.have historical significanceC.sponsor research on climateD.provide an income for the locals30.It can be concluded from the text that national park system____A.is able to cope with staff shortageB.is able to meet visitor demandsC.is in need of new pricing policyD.is in need of funding increaseText3The Internet may be changing merely what we remember,not our capacity to do so,suggests Columbia University psychology professor Betsy Sparrow.In2011,Sparrow led a study in which participants were asked to record40factoids in a computer(“an ostrich's eye is bigger than its brain,”for example).Half of the participants were told the information would be erased,while the other half were told it would be saved.Guess what?The latter group made no effort to recall the information when quizzed on it later,because they knew they could find it on their computers.In the same study,a group was asked to remember both the information and the folders it was stored in.They didn't remember the information,but they remembered how to find the folders.In other words,human memory is not deteriorating but“adopting to new communications technology,”Sparrow says.In a very practical way,the Internet is becoming an external hard drive for our memories,a process known as“cognitive offloading.”Traditionally,this role was fulfilled by data banks,libraries, and other humans.Your father may never remember birthdays because your mother does,for instance. Some worry that this is having a destructive effect on society,but Sparrow sees an upside.Perhaps,she suggests,the trend will change our approach to learning from a focus on individual facts and memorization to an emphasis on more conceptual thinking something that is not available on the Internet.“I personally have never seen all that much intellectual value in memorizing things,”Sparrow says,adding that we haven’t lost our ability to do it.Still other experts say it’s too soon to understand how the Internet affects our brains.There is no experimental evidence showing that it interferes with our ability to focus,for instance,wrote psychologists Christopher Chabris and Daniel.J.Simons.And surfing the web exercised the brain more than reading did among computer-savvy older adults in a2008study involving24participants at the Semel Institute for Neuroscience and Human Behavior at the University of California,Los Angeles.“There may be costs associated with our increased reliance on the Internet,but I’d have to imagine that overall the benefits are going to outweigh those costs,”observes psychology professor Benjamin Storm.“It seems pretty clear that memory is changing,but is it changing for the better?At this point,we don't know.”31.Sparrow’s study shows that with the Internet,the human brain will________.[A]analyze information in detail[B]collect information efficiently[C]switch its focus of memory[D]extend its memory duration32.The process of“cognitive offloading”________.[A]helps us identify false information[B]keeps our memory from failing[C]Enables us to classify trivial facts[D]lessens our memory burdens33.Which of the following would Sparrow support about the Internet?[A]It may reform our learning approach[B]It may impact our society negatively[C]It may enhance our adaptability to technology[D]It may interfere with our conceptual thinking34.It is indicated in Paragraph3that how the Internet affects our brains________.[A]requires further academic research[B]is most studied in older adults[C]is reflected in our reading speed[D]depends on our web-surfing habits35.Neither Sparrow nor Storm would agree that________.[A]our reliance on the Internet will be costly[B]the Internet is weakening our memory[C]memory exercise is a must for our brains[D]our ability to focus declines with ageText4Teenagers are paradoxical.That’s a mild and detached way of saying something that parents often express with considerably stronger language.But the paradox is scientific as well as personal.In adolescence,helpless and dependent children who have relied on grown-ups for just about everything become independent people who can take care of themselves and help each other.At the same time, once cheerful and compliant children become rebellious teenage risk-takers.A new study published in the journal Child Development,by Eveline Crone of the University of London and colleagues,suggests that the positive and negative sides of teenagers go hand in hand. The study is part of a new wave of thinking about adolescence.For a long time,scientists and policy makers concentrated on the idea that teenagers were a problem that needed to be solved.The new work emphasizes that adolescence is a time of opportunity as well as risk.The researchers studied“prosocial”and rebellious traits in more than200children and young adults,ranging from11to28years old.The participants filled out questionnaires about how often they did things that were altruistic and positive,like sacrificing their own interests to help a friend,or rebellious and negative,like getting drunk or staying out late.Other studies have shown that rebellious behavior increases as you become a teenager and then fades away as you grow older.But the new study shows that,interestingly,the same pattern holds for prosocial behavior.Teenagers were more likely than younger children or adults to report that they did things like unselfishly help a friend.Most significantly,there was a positive correlation between prosociality and rebelliousness.The teenagers who were more rebellious were also more likely to help others.The good and bad sides of adolescence seem to develop together.Is there some common factor that underlies these apparently contradictory developments?One idea is that teenage behavior is related to what researchers call“reward sensitivity.”Decision-making always involves balancing rewards and risks,benefits and costs.“Reward sensitivity”measures how much reward it takes to outweigh risk.Teenagers are particularly sensitive to social rewards—winning the game,impressing a new friend,getting that boy to notice you.Reward sensitivity,like prosocial behavior and risk-taking, seems to go up in adolescence and then down again as we age.Somehow,when you hit30,the chance that something exciting and new will happen at that party just doesn’t seem to outweigh the effort ofgetting up off the couch.36.According to Paragraph1,children growing into adolescence tend to________.[A]develop opposite personality traits[B]see the word in an unreasonable way[C]have fond memories of their past[D]show affection for their parents37.It can be learned from Paragraph2that Crone's study________.[A]explores teenagers'social responsibilities[B]examines teenagers'emotional problems[C]provides a new insight into adolescence[D]highlights negative adolescent behavior38.What does Crone's study find about prosocial behavior?[A]It results from the wish to cooperate[B]It is cultivated through education[C]It is subject to family influence[D]It tends to peak in adolescence39.It can be learned from the last two paragraphs that teenagers________.[A]overstress their influence on others[B]care a lot about social recognition[C]become anxious about their future[D]endeavor to live a joyful life40.What is the text mainly about?[A]Why teenagers are self-contradictory.[B]Why teenagers are risk-sensitive.[C]How teenagers develop prosociality.[D]How teenagers become independent.Part BDirections:Read the following text and match each of the numbered items in the left column to its corresponding information in the right column.There are two extra choices in the right column. Mark your answers on the ANSWER SHEET.(10points)Net-zero rules set to send cost of new homes and extensions soaring New building regulations aimed at improving energy efficiency are set to increase the price of new homes,as well as those of extensions and loft conversions on existing ones.The rules,which came into effect on Wednesday in England,are part of government plans to reduce the UK's carbon emissions to net zero by2050.They set new standards for ventilation,energy efficiency and heating,and state that new residential buildings must have charging points for electric vehicles.The moves are the most significant change to building regulations in years,and industry experts say they will inevitably lead to higher prices at a time when a shortage of materials and high labour costs are already driving up bills.Brian Berry,chief executive of the Federation of Master Builders,says the measures will require new materials,testing methods,products and systems to be installed.“All this comes at an increased cost during a time when prices are already sky high.Inevitably,consumers will have to pay more,"he says.Gareth Belsham,of surveyors Naismiths,says people who are upgrading,or extending their home,will be directly affected.“The biggest changes relate to heating and insulation,”he explains.“There are new rules concerning the amount of glazing used in extensions,and any new windows or doors must be highly insulated.”Windows and doors will have to adhere to higher standards,while there are new limits on the amount of glazing you can have to reduce unwanted heat from the sun.Thomas Goodman,of MyJobQuote,says this will bring in new restrictions for extensions.“Glazing on windows,doors and rooflights must cover no more than25%of the floor area to prevent heat loss,"he says.As the rules came into effect last Wednesday,property developers were rushing to file plans just before the deadline.Any plans submitted before that date are considered to be under the previous rules, and can go ahead as long as work starts before15June next year.Builders which have costed projects,but have not filed the paperwork,may need to go back and submit fresh estimates,says Marcus Jefford of Build Aviator.Materials prices are already up25%in the last two years.How much overall prices will increase as a result of the rule changes is not clear."Whilst admirable in their intentions,they will add to the cost of housebuilding at a time when many already feel that they are priced out of homeownership," says Jonathan Rolande of the National Association of Property Buyers.“An average extension will probably see around£3,000additional cost thanks to the new regs."John Kelly,a construction lawyer at Freeths law firm,believes prices will eventually come down.But not in the immediate future."As the marketplace adapts to the new requirements,and the technologies that support them,the scaling up of these technologies will eventually bring costs down, but in the short term,we will all have to pay the price of the necessary transition.”he says.However,the long-term effects of the changes will be more comfortable and energy-efficient homes,adds Andrew Mellor,of PRP architects.“Homeowners will probably recoup that cost over time in energy bill savings.It will obviously be very volatile at the moment,but they will have that benefit over time.”A.The rise of home prices is a temporary matter.41.Brian Berry B.Builders possibly need to submit new estimates of their projects.42.Gareth Belsham C.There will be specific limits on home extensions to prevent heatloss.43.Marcus Jefford D.The new rules will take home prices to an even higher level.44.John Kelly E.Many people feel that home prices are already beyond what theycan afford.45.Andrew Mellor F.The new rules will affect people whose home extensions includenew windows or doors.G.The rule changes will benefit homeowners eventually.Section III Translation46.Directions:Translate the following text into Chinese.Write your translation on on the ANSWER SHEET.(15points)In the late18th century,William Wordsworth became famous for his poems about nature.And he was one of the founders of a movement called Romanticism,which celebrated the wonders of the natural world.Poetry is powerful.Its energy and rhythm can capture a reader,transport them to another world and make them see things differently.Through carefully selected words and phrases,poems can be dramatic,funny,beautiful,moving and inspiring.No one knows for sure when poetry began but it has been around for thousands of years,even before people could write.It was a way to tell stories and pass down history.It is closely related to song and even when written it is usually created to be performed out loud.Poems really come to life when they are recited.This can also help with understanding them too,because the rhythm and sounds of the words become clearer.Section IV WritingPart A47.Directions：An art exhibition and a robot show are to be held on Sunday and your friend David asks you which one he should go to.Write him an email to1)make a suggestion,and2)give your reason(s)Write your answer in about100words on the ANSWER SHEETDo not use your own name in your email,use“Li Ming”instead.(10points)Part B48.Directions:Write an essay based on the chart below.In your writing,you should1)describe and interpret the chart and2)give your comments.Write your answer in about150words on the ANSWER SHEET.(15points)health literacy健康素养2011-2021我国居民健康素养水平2023年全国硕士研究生招生考试英语（二）试题参考答案与解析Section I Use of English1.B【考点】上下文和词汇识别【解析】根据上下文语意，make a nice profit在这里表示“做的很好”，其他三个选项purchase“购买”，connection“联系”，bet“打赌”,不符合上下文语意。

2020年全国硕士研究生招生考试经济类专业学位联考综合能力试题一、逻辑推理：第1~20小题，每小题2分，共40分。

下列每题给出的A、B、C、D、E五个选项中，只有一项是符合试题要求的。

1、“群众是真正的英雄，我是群众，所以我是真正的英雄。

”这个推理中的逻辑错误，与下列哪项中出现的最为类似?A、作案者都有作案时间，王某有作案时间，所以王某一定是作案者。

B、各级干部都要遵纪守法，我不是干部，所以我不要遵纪守法。

C、世间万物中，人是第一个可宝贵的。

我是人，所以我是世间万物中第一个可宝贵的。

D、公民都要遵守法律，你没有遵守法律，所以你不是公民。

E、想当翻译就要学外语，我又不想当翻译，何必费力学外语。

2、那些认为动物园的安全措施已十分齐备的人，面对下面的新闻应当清醒了。

昨天，一对年轻父母不慎使自己的小孩落如假山里被群猴抓伤，幸好管理人员及时赶到，驱散群猴，将小孩送入医院抢救，才没有酿成严重后果。

因此，需要进一步检查动物园的安全措施。

以下哪项是对上述论证方法的恰当概括?A、从一个特定事件得出一个普遍结论。

B、用个人而非逻辑的理由进行批评。

C、将一个普遍的原理适用于一个特定的事例。

D、混淆了某一事件所发生的原因。

E、对相似但意义不同的术语的混淆。

3、某公司的销售部有五名工作人员，其中有两名本科专业是市场营销，两名本科专业是计算机，有一名本科专业是物理学。

又知道五人中有两名女士，她们的本科专业背景不同。

根据上文所述，以下哪项论断最可能得出?A、该销售部有两名男士是来自不同本科专业的。

B、该销售部的一名女士一定是计算机本科专业毕业的。

C、该销售部三名男士来自不同的本科专业，女士也来自不同本科专业。

D、该销售部至多有一名男士是市场营销专业毕业的。

E、该销售部本科专业为物理学的一定是男士，不是女士。

4、免疫研究室的钟教授说:“生命科学院从前的研究生那种勤奋精神越来越不多见了，因为我发现目前在我的研究生中，起早摸黑做实验的人越来越少了。

級 法律學系碩士班E組時間90 分鐘科 目 行政法 本科總分100 分一、A公立學校教師B因涉及於大學指定科目考試主導策劃學生舞弊事件，經A學校教師評審委員會召開會議，以其行為不檢有損師道，遂依教師法第14條第1項第6款之規定，決議通過B不予續聘案。

A 於報經主管教育行政機關核准後，發函通知B該不予續聘決定。

B不服，於法定期間內提起訴願。

問：訴願管轄機關應否受理其訴願？（25%）參考法條：教師法第14條第1項：「教師聘任後，除有下列各款之一者外，不得解聘、停聘或不續聘：一、……。

六、行為不檢有損師道，經有關機關查證屬實。

…」二、A應公務人員特種考試第2次警察人員考試4等考試行政警察人員類科及格錄取，經內政部警政署分配至B警察局占缺實施實務訓練，並訓練期滿成績及格。

嗣B於辦理擬任警察官人員查核得知A為大陸地區人民，自其在臺灣地區初設戶籍登記，計至實務訓練期滿之次日，在臺灣地區設有戶籍未滿10年，依警察人員人事條例第10條之1 第1 項第7 款及臺灣地區與大陸地區人民關係條例第21條第1 項規定不得擔任公務人員。

B乃發函通知A其依法不得任用為警察官辦理派代送審，並請自該書函送達之次日起離職。

A不服，提起復審，經公務人員保障暨培訓委員會以原告於實務訓練期滿後，未經B依法派代為公務人員，非屬公務人員保障法第3 條所定公務人員或同法第102 條第 5 款所定應各種公務人員考試錄取占法定機關、公立學校編制缺參加學習或訓練之人員，不得適用或準用該法提起復審以資救濟為由，決定不受理。

A不服，向台北高等行政法院提起行政訴訟，請求撤銷復審決定。

問：台北高等行政法院應如何裁判？（25%）參考法條：公務人員保障法第3條：「本法所稱公務人員，係指法定機關依法任用之有給專任人員及公立學校編制內依法任用之職員。

前項公務人員不包括政務人員及民選公職人員。

」級 法律學系碩士班E組時間90 分鐘科 目 行政法 本科總分100 分公務人員保障法第102條：「下列人員準用本法之規定：一、……。

2022年全国硕士研究生招生考试管理类专业学位联考综合能力试题⼀ . 问题求解：第1-15小题，每小题3分，共45分。

下列每题给出的A 、B 、C 、D 、E五个选项中，只有⼀项是符合试题要求的。

1. 一项工程施工3天后，因故障停工2天，之后工程队工作效率提高，仍能按原计划完成，则原计划工期为A.9天B.10天C.12天D.15天E.18天2. 某商品的成本利润率为，若其成本降低而售价不变，则利润率为A.B.C.D.E.3. 设，为实数，则的最小值为A.1B.C.2D.E.34. 如图，是等腰直角三角形，以为圆心的圆弧交于，交于，交的延长线于，若曲边三角形与的面积相等，则A.B.C.D.E.5. 如图，已知相邻的圆都相切，从这6个图中随机取2个，这2个圆不相切的概率为A.B.C.D.E.6. 如图，在棱长为2的正方体中，，是顶点，，是所在棱的中点，则四边形的面积为A.B.C.D.E.7. 桌上放有8只杯子，将其中的3只杯子翻转(杯口朝上与朝下互换)作为一次操作，8只杯口朝上的杯子经次操作后，杯口全部朝下，则的最小值为A.3B.4C.5D.6E.88. 某公司有甲、乙、丙三个部门，若从甲部门调26人到丙部门，则丙部门是甲部门人数的6倍；若从乙部门调5人到丙部门，则丙部门的人数与乙部门人数相等。

甲，乙两部门之差除以5的余数为A.0B.1C.2D.3E.49. 在直角中，为斜边的中点，以为直径的圆交于点，若的面积为8，则的面积为A.1B.2C.3D.4E.610. 一个自然数的各位数字都是105的质因数，且每个质因数最多出现一次，这样的自然数有( )个。

A.6B.9C.12D.15E.2711. 购买A玩具和B玩具各1件需花费1.4元，购买200件A玩具和150件B玩具需花费250元，则A玩具的单价为A.0.5元B.0.6元C.0.7元D.0.8元E.0.9元12. 甲、乙两支足球队进行比赛，比分为，且在比赛过程中乙队没有领先过，则不同的进球顺序有A.6种B.8种C.9种D.10种E.12种13. 4名男生和2名女生随机站成一排，女生既不在两端也不相邻的概率为A.B.C.D.E.14. 已知A，B两地相距，甲，乙，丙三车的速度分别为，，，甲、乙两车从A地出发去B地，丙车从B地出发去A地，三车同时出发。

2023 考研数学二真题及解析一、选择题：1~10 小题，每小题 5 分，共 50 分.在每小题给出的四个选项中，只有一个选项是最符合题目要求的，请将所选项前的字母填在答题纸指定位置上.1．曲线1ln e 1y x x=+ −的斜渐近线方程为（ ）. （A ）ey x =+（B ）1ey x =+（C ）yx = （D ）1ey x =−【答案】（B ）【解析】方法1. 1ln e 11limlim x x y k x x →∞→∞=+==− ()()11lim lim ln e 1lim ln e ln 111e 1x x x b y x x x x x →∞→∞→∞=−=+−=++− −−()11lim e 1ex xx →∞=−故曲线的斜渐近线方程为1ey x =+．故选（B ） 方法2. ()()11ln e 11ln 1e 1e 1y x x x x=+=++−−()11ln 1e 1e x x x x α =++=++ −，其中lim 0x α→∞=，故1e y x =+为曲线的斜渐近线. 【评注】由()11lim ln 1e 1e x x x →∞+= − ，知()11ln 1e 1ex x α +=+ − 【评注】1.由()11lim ln 1e 1e x x x →∞ += − ，知()11ln 1e 1e x x α +=+ −2.本题属于常规题：《基础班》《强化班》的例子不再对应列举，《答题模版班》思维定势19【例13】2.函数() 0,()1cos ,0.x f x x x x ≤=+>的一个原函数是( )(A) ), 0,()(1)cos sin ,0.x x F x x x x x −≤= +−>(B))1, 0,()(1)cos sin ,0.x x F x x x x x +≤= +−>(C) ), 0,()(1)sin cos ,0.x x F x x x x x −≤= ++>(D))1, 0,()(1)sin cos ,0.x x F x x x x x +≤= ++>【答案】 (D) .【分析】本题主要考查原函数的概念,分段函数不定积分的求法以及函数可导与连续的关系.【详解】由于当0x <时，)1()lnF xx x C ==++∫当0x >时，()()2()1cos d 1sin cos F x x x x x x x C =+=+++∫ 由于()F x 在0x =处可导性，故()F x 在0x =处必连续 因此，有00lim ()lim ()x x F x F x −+→→=，即 121C C =+.取20C =得)1, 0,()(1)sin cos ,0.x x F x x x x x −+≤= ++> 应选(D) .【评注】此题考查分段函数的不定积分，属于常规题，与2016年真题的完全类似，在《真题精讲班》系统讲解过. 原题为已知函数2(1),1,()ln ,1.x x f x x x −< = ≥ 则()f x 的一个原函数是( )(A) 2(1),1,()(ln 1), 1.x x F x x x x −<=−≥ (B) 2(1),1,()(ln 1)1, 1.x x F x x x x −<= +−≥ (C) 2(1),1,()(ln 1)1, 1.x x F x x x x −<=++≥ (D) 2(1),1,()(ln 1)1, 1.x x F x x x x −<= −+≥3.设数列{}{},n n x y 满足211111,sin ,2n n n n x y x x y y ++====()1,2,n = ，则当n →∞时（ ） （A ）n x 是n y 的高阶无穷小（B ）n y 是n x 的高阶无穷小（C ）n x 是n y 的等阶无穷小 （D ）n x 是n y 的同阶但不等价无穷小 【答案】（B ）【解析】由2111,,2n n y y y +==知2112nn y + =，则有112n n y y +< 利用12sin n n n x x x π+=>，则1112n nx x π+<故21111111224444n n nn nn n n n n y y y y y x x x x x πππππ+−+− ≤=≤≤≤= 于是1110lim lim 04nn n n n y x +→∞→∞+ ≤≤= ，由夹逼准则lim 0nn ny x →∞=，选（B ） 【评注】本题属于今年难度较大的题，涉及到两个递推数列确定的无穷小的比较，涉及到不等式的放缩，有一定的综合性.4．若微分方程0y ay by ′′′++=的解在(,)−∞+∞上有界，则（ ）（A ）00a b <>， （B ）00a b >>， （C ）00a b =>， （D ）00a b =<， 【答案】（C ）【解析】特征方程为20r ar b ++=，解得1,2r =．记24a b ∆=−当0∆>时，方程的通解为1212()e e r x r x yx c c ⋅⋅=+，当12,c c 不全为零时()y x 在(,)−∞+∞上无界.当12,c c 不全为零时()y x 在(,)−∞+∞上无界.当0∆=时，1202ar r −=<=，方程的通解为1112()e e r x r x yx c c x =+，当12,c c 不全为零时()y x 在(,)−∞+∞上无界.当0∆<时，1,22a r i β=−±,方程的通解为()212()e cos sin ax y x c x c x ββ−=+．只有当0a =，且240a b ∆=−<，即0b >时，lim ()lim ()0x x y x y x →+∞→−∞==，此时方程的解在(,)−∞+∞上有界. 故选（C ）【评注】此题关于x →+∞方向的讨论，在《基础班》习题课上讲解过，见《基础班》习题课第八讲《常微分方程》第15题.5.设()y f x =由2,sin ,x t t y t t =+=确定，则（ ） （A ）()f x 连续，(0)f ′不存在 （B ）(0)f ′存在，()f x ′在0x =不连续 （C ）()f x ′连续，(0)f ′′不存在 （D ）(0)f ′′存在，()f x ′′在0x =不连续 【答案】（C ） 【解析】0t ≥时3,sin ,x t y t t == ，即有sin 33x xy =.0t <时,sin ,x t y t t = =−，即有sin y x x =−.sin ,033sin ,0x x x y x x x ≥= −< ,显然有()f x 在0x =不连续，且(0)0f = 0x >时，sin cos 33(3)9x x x xf x =+′；0x <时，sin ()cos x f x x x ′=−−， 利用导数定义可得()0sin 0330lim 0x x xf x ++→−′==，()0sin 0lim 0x x x f x+−→−′==，即得(0)0f ′= 易验证()0lim ()lim ()00x x f x f x f +−→→′′===，即()f x ′在0x =连续()01sin cos 233930lim 9x x x xf x ++→+′′=，()0sin cos 0lim 2x x x x f x+−→−−′′==−，故(0)f ′′不存在 ，选（C ） 【评注】此题考查参数方程确定的分段函数，只要在参数方程中去掉绝对值的过程，就成了我们常规的分段函数求导的问题，无论是《基础班》第二讲例24，《强化班》第二讲例17. 6.若函数()()121d ln f x x x αα+∞+=∫在0αα=处取得最小值，则0α=（ ）（A ）()1ln ln 2−（B ）()ln ln 2−（C ）1ln 2−（D ）ln 2【答案】（A ）【解析】反常积分的判别规律知11α+>，即0α>时反常积分()121d ln x x x α+∞+∫收敛此时()()()212111d ln ln f x x x x αααα+∞+∞+==−∫()11ln 2αα=令()()()2111ln ln 2ln 2ln 2f ααααα′=−−()2111ln ln 20ln 2ααα =−+= 得唯一驻点()1ln ln 2α=−，故选（A ）【评注】此题是属于由反常积分确定的函数求最值的问题，积分本身不难，积分结果再求导，找驻点得结果.难度不大，只要基本计算能力过关，可轻松应对.《基础班》《强化班》相应问题得组合而已. 7.设函数()()2e xf x xa =+，若()f x 没有极值点，但曲线()f x 有拐点，则a 的取值范围是（ ）（A ）[)0,1（B ）[)1,+∞ （C ）[)1,2 （D ）[)2,+∞【答案】（C ）【解析】()()2e xf x xa =+，()()22e x f x xa x ′=++，()()242e x f x xa x ′′=+++由()()211e x f x x a ′=++−，知10a −≥时，()0f x ′≥，此时()f x 无极值点.由()()222e x f x x a ′′=++−，知20a −<时，()f x ′′在2x =±的左右两侧变号，依题意有[)1,2a ∈，选（C ）【评注】本题考查了极值点、拐点的必要条件与判定，题目本身是常规的，分开对这两个考点出题，在《基础班》和《强化班》都讲过，但这种问法有些学生可能会觉得很别扭.8．设A,B 分别为n 阶可逆矩阵，E 是n 阶单位矩阵，*M 为M 的伴随矩阵，则AE OB 为（ ） （A ）*****−A B B A O A B （B ）****− A B A B O B A（C ）****−B A B A O A B （D ）**** −B A A B O A B 【答案】（D ）【解析】由分块矩阵求逆与行列式的公式，结合1∗−=A A A 得11111∗−−−−− − ==A E A E A E E A A AB B O B O B O B O B ∗∗∗∗−=B O A A A B B ，选（D ） 【评注】这钟类型的题在02年，09年均考过完全类似的题，《基础班》第二讲也讲过，原题为【例1】设,A B ∗∗分别为n 阶可逆矩阵,A B 对应的伴随矩阵，∗∗=A O C O B9.二次型()()()222123121323(,,)4f x x x x x x x x x =+++−−的规范形为（ ）. （A ）2212y y +（B ）2212y y −（C ）222123y y y −−（D ）222123y y y +−【答案】（B ） 【详解】因为123(,,)f x x x 222123121323233228x x x x x x x x x =−−+++方法1.二次型的矩阵为 211134143=− −A , 由()()211134730143λλλλλλλ−−−−=−+−=+−=−−+E A ，得特征值为0,7,3−，故选（B ）方法2.()222123123121323,,233228f x x x x x x x x x x x x =−−+++()()()22232322211232323233842x x x x x x x x x x x x ++=+++−−−+222222322332323126616222x x x x x x x x x x x +++++−=+− ()22231237222x x x x x + =+−− 故所求规范形为()2212312,,f x x x y y =−，故选（B ）【评注】本题考查二次型的规范形，与考查正负惯性指数是同一类题，在《基础班》《强化班》均讲过. 《解题模板班》类似例题为【11】设123123(,,),(,,)T T a a a b b b αβ==，,αβ线性无关，则二次型 123112233112233(,,)()()f x x x a x a x a x b x b x b x =++++的规范型为( )． (A)21y (B)2212y y + (C) 2212y y − (D) 222123y y y ++10．已知向量12121,,1222150390,1====ααββ，若γ既可由12,αα表示，也由与12,ββ表示，则=γ（ ）.（A ）334k （B ）3510k（C ）112k − （D ）158k【答案】（D ） 【解析】由题意可设11212212x y x y +==+γααββ，只需求出21,x x 即可 即解方程组112112220x y y x +−−=ααββ()121212211003,,2150010131910011,−−−−=−→− −−ααββ 得()()2211,,1,3,,1,1TTx k x y y =−−，k 为任意常数11221212133215318x k k k k k x+=−+=−+=−=γαααα，故选（D ）【评注】1.此题与《强化班》讲义第三讲练习第12题完全类似，原题为【12】(1)设21,αα，21,ββ均是三维列向量，且21,αα线性无关, 21,ββ线性无关，证明存在非零向量ξ，使得ξ既可由21,αα线性表出，又可由21,ββ线性表出．(2)当 =4311α，=5522α：1231β = − ，2343β−=−时，求所有既可由21,αα线性表出， 又可21,ββ线性表出的向量。

硕士研究生招生考试试题
考试科目: 设计图学 满分：150分 考试时间：180分钟
一、 完成下列五边形的水平投影和正面投影。

（15分）
O
X
t ’
15分）
三、在指定位置将A向视图画成半剖视图，并补画出全剖的左视图（剖切面通过B-B位
置）（20分）
四、标注尺寸,数值直接从图中量取，取整数。

（15分）
五、给定平面△ABC，试过定点S 作平面的法线，并求出垂足K。

（15分）
O X
六、画出指定的断面图,键槽深度和宽度都是3mm,C-C剖面处两平面之间的距离为10mm。

(20分)
7、已知圆柱半径50mm，高35mm，请用量点法绘制出圆柱一点透视图。

（10分）
8、已知图形俯视和正视图，绘制图形的透视图。

（15分）
9、根据已知条件，用量点法作出小柜的成角透视图。

（25分）。