浙江省2018年选拔优秀高职高专毕业生进入本科学习统一考试
浙江省专升本考试简介
专升本考试简介普通高校专升本一般是指在校的专科生，在大三的时候（毕业的时候，且必须是应届生才能参加）参加由浙江省考试院统一组织的考试，选拔优秀的专科生在毕业的时候进入本科院校学习，最后颁发的学历是普通高等教育（与正式本科基本相同）。
普通专升本属普通高等毕业证书，根据我国近几年的举办普通专升本的经验，从国家、从学校、从学生本人角度看来，是一个非常理想的途径，教育部政策允许专科生毕业时再考入其他本科学校。
专科学校领导很多都很重视教育部的文件，支持专科生考入其他本科学校。
况且考上后，学生就可以享受与该本科学校学生一样的待遇，发的毕业证也和普通本科生的毕业证几乎一样，对学校和学生都是好事。
并且从近三年大学生找工作、继续深造考研、考公务员等方面来看，社会上通常会认为这种专升本含金量优于其他几种，等同于四年制本科。
考试、命题1.考试科目：考试科目分文、理科，具体为：考试科类考试科目录取类别大学语文、英语文史类文科法学类教育类艺术类理科高等数学、英语理工类经管类农学类医学类艺术体育专业经省教育考试院同意，可由招生院校组织专业加试，并在报名工作开始前完成。
专业加试合格考生才能填报相应院校、专业志愿。
各科满分均为150分。
2.命题、评卷工作由省教育考试院统一组织。
公布成绩时间为5月初。
考生如对成绩有疑问，可在成绩公布后三个工作日内，凭准考证申请查卷。
查卷只查漏评、误评，积分及统分差误，不查评卷的宽严。
3.2012年考试日期为4月15日；2013年考试日期为4月21日，上午（9﹕00—11﹕30）考高等数学、大学语文，下午（14﹕30—17﹕00）考英语。
2014年考试日期为4月20日，上午考高等数学、大学语文（9∶00～11∶30），下午考英语（14∶30～17∶00）。
2015年考试日期为4月17日，上午考高等数学、大学语文（9∶00～11∶30），下午考英语（14∶30～17∶00）。
4.考试由省教育考试院统一组织管理，各设区市招生考试机构具体组织实施，考点设在设区市。
浙江省2004年选拔优秀高职高专毕业生进入本科学习试点工作实.
浙江省2004年选拔优秀高职高专毕业生进入本科学习试点工作实施细则为有利于在更广的范围和更高的层次上提升各类优秀专科学生的学历层次和知识结构，有利于全面促进专科学校的校风、学风建设，决定今年在浙江大学、浙江工业大学、宁波大学、浙江师范大学、杭州电子工业学院、温州医学院、杭州师范学院、浙江林学院、浙江大学城市学院、浙江科技学院开展面向全省高校选拔优秀专科生进入本科学习试点工作（以下简称“普通高校专升本”）。
现特制定《实施细则》如下：二、招生对象及条件。
招生对象为浙江省各级各类全日制普通高校同专业或相近专业的应届专科毕业生（包括普通高专、高职、电大普通班的应届毕业生）。
报考者应具备下列条件：1、坚持四项基本原则、遵纪守法；2、所学专业与招生专业相同或相近；3、3月前已通过CET—3或高职高专英语应用能力A级（艺术类专业除外）；浙江省高校计算机等级考试一级；专科专业为英语专业的考生无须通过CET—3，专科专业为计算机专业的考生无须通过计算机等级考试；4、身体健康。
下列人员不能报考：在校期间受记过（含）以上处分者；当年读完专科，因各种原因不能按期正常毕业者；所学专业与招生专业非相同或相近的专科毕业生。
三、报名。
1、符合报考条件的考生，向所在学校招生办领取考生登记表，填妥后上交所在学校招生办。
所在学校招生办负责考生资格初审，填妥《考生花名册》（格式见实施意见附件三）后，将符合报考条件的考生材料，于3月16日送到浙江工业大学翔园宾馆，分别办理集体报名手续（10个招生院校均在翔园宾馆接受报名）。
报考材料如下：（1）大学期间所有课程成绩单；（2）考生身份证复印件；（3）考生登记表（格式见实施意见附件一）；（4）CET-3级考试证书或高职高专英语应用能力A级证书和计算机等级证书复印件；（5）考生近期一寸正面免冠照片2张（照片背面写上毕业学校及考生姓名），一张贴在报考登记表上，一张用于准考证；（6）报考费（同普通高校高考报考费）90元/人。
2017年浙江3+2专升本高数真题--答案解析(知乎内部资料)
10. 1 dx 解析: 方程 ey xy e 0 两边同时对 x 求导，即： ey y y xy 0 ， e
把 x 0 代入原方程，可得 y 1 ，再把 x 0 ， y 1 代入 ey y y xy 0 可得：
y
x0
1 e
，故
dy
x0
1 e
dx
11.
1
xx
(
1 x2
ln
x 3
x 1
x5
三、计算题：本题共有 8 小题，其中 16-19 小题每小题 7 分，20-
23 小题每小题 8 分，共 60 分。计算题必须写出必要的计算过程，
只写答案的不给分。
16. 解:
lim ln(1 x3 ) x0 x sin x
lim x0
x3
洛
lim
3x2
x sin x x0 1 cos x
0x
1
x
1
2 dx
2
0
x |10 2 ；所以
1 0
1 x
dx 收敛，故选项 A 错误。
1
0
1 1 x2
dx
arcsin
x
|10
2
；所以
1 0
1 dx 收敛，故选项 B 错误。 1 x2
1
1 x2
dx
(
1 x
)
|1
lim
x
1 x
1 1；所以
1
1 x2
dx 收敛，故选项 C 错误。
1 1
a
，因为在
x
1
处可导，所
以 a 2 ，联立后可得： a 2 ， b 1
即当 a 2 ， b 1时，函数 f (x) 在 x 1 处连续且可导
浙江省2012年选拔优秀高职高专毕业生进入本科学习统一考试
浙江省2012年选拔优秀高职高专毕业生进入本科学习统一考试大学语文请考生按规定用笔将所有试题的答案涂、写在答题纸上。
选择题部分注意事项：1.答题前,考生务必将自己的姓名、准考证号用黑色字迹的签字笔或钢笔填写在答题纸规定的位置上。
2.每小题选出答案后,用2B 铅笔把答题纸上对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其他答案标号。
不能答在试题卷上。
一、选择题：在每一小题的四个答案中选出一个正确的答案。
本题共有20小题,每小题1分，共20分。
1.下列加点词语解释不正确的是（）。
A.今尔出于崖涘，观于大海，乃知尔丑．丑：鄙陋，此处指水小。
B.大道之行也，与三代之英，丘未之逮．也逮：及，到。
C.故谋用是作，而兵．由此起兵：指士兵。
D.城郭沟池．以为固，礼义以为纪池：护城河。
2.下列加点词语解释不正确的是（）。
A.抑本．其成败之迹，而皆自于人欤？本：考察。
B.故方其盛也，举．天下之豪杰，莫能与之争举：提到。
C.其后用兵，则遣从事以一少牢告．庙告：祷告、祭告。
D.姜氏欲之，焉．辟害！焉：怎么，如何。
3.下列加点词语解释正确的是（）。
A.使人属．孟尝君属：隶属，臣属。
B.于是乘其车，揭其剑，过．其友过：拜访。
C.汉军罢．，弗能追罢：罢休，收兵。
D.终不能复对刀笔之吏．．．．刀笔之吏：指经常带刀带笔的官。
4.下列成语中没有错别字的是（）。
A.出奇制胜B.既往不究C.震聋发聩D.金壁辉煌5.下列表述正确的是（）。
A.请示、报告等上行公文可以不用书写主送机关B.上级领导发给下级的下行公文可以不用书写主送机关C.直接向社会公众发布的公文（如通告、公告等）可以不用书写主送机关D.所有公文都必须书写公文的主送机关6.下列《前赤壁赋》的语句中，描写箫声的是（）。
A.耳得之而为声B.飘飘乎如遗世独立C.舞幽壑之潜蛟D.寄蜉蝣于天地7.《陌上桑》中见了罗敷后“脱帽著帩头”的是（）。
A.使君B.耕者C.少年D.行者8.柳永《八声甘州》抒写的主要情感内容是（）。
2015浙江省专升本高等数学试卷和答案
浙江省 2015年选拔优秀高职高专毕业生进入本科学习统一考试高等数学请考生按规定用笔将所有试题的答案涂、写在答题纸上。
选择题部分注意事项:1.答题前,考生务必将自己的姓名、 准考证号用黑色字迹的签字笔或钢笔填写在答题纸规定的位置上。
2.每小题选出答案后，用2B 铅笔把答题纸上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
不能答在试题卷上。
一、选择题: 本大题共5小题,每小题4分,共 20分。
在每小题给出的四个选项中，只有一项是符合题目要求的。
1.当x →0x 时，f(x)是g(x)的高阶无穷小，则当x →0x 时，f(x)-g(x)是g(x)的A ．等价无穷小B ．同阶无穷小C ．高阶无穷小D ．低阶无穷小2.设f(x)在x=a 处可导，则()xx a f x a f x --+→)(lim 0等于 A. f ’(a) B.2 f ’(a) C.0 D. f ’(2a)3.设可导函数F(x)满足F ’(x)=f(x),且C 为任意常数，则A.⎰+=C x f dxx F )()(' B. ⎰+=C x F dx x f )()( C.⎰+=C x F dx x F )()( D. ⎰+=C x F dx x f )()(' 4.设直线L 1：2-31511+=-=-z y x 与L 2：⎩⎨⎧=+=32z y 1z -x ，则L 1与L 2的夹角是 A.6π B. 4π C.3π D.2π5在下列级数中，发散的是A.)1ln(1)1(11+-∑∞=-n n n B. ∑∞=-113n n n C.n n n 31)1(11∑∞=-- D . ∑∞=-113n n n非选择题部分注意事项:1.用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。
2.在答题纸上作图，可先使用2B 铅笔，确定后必须使用黑色字迹的签字笔或钢笔描黑。
二、 填空题: 本大题共10小题，每小题 4分，共40分。
2018年高考浙江卷英语真题及答案
2018年普通高等学校招生全国统一考试（浙江卷）英语第二部分阅读理解（共两节，满分35分）第一节（共10小题；每小题2.5分，满分25分）阅读下列短文，从每题所给的A、B、C和D四个选项中，选出最佳选项，并在答题纸上将该项涂黑。
AIn 1812, the year Charles Dickens was born, there were 66 novels published in Britain. People had been writing novels for a century—most experts date the first novel to Robinson Crusoe in 1719—but nobody wanted to do it professionally. The steam-powered printing press was still in its early stages; the literacy（识字） rate in England was under 50%. Many works of fiction appeared without the names of the authors, often with something like “By a lady.”Novels, for the most part, were looked upon as silly, immoral, or just plain bad.In 1870, when Dickens died, the world mourned him as itsfirst professional writer and publisher, famous and beloved, who had led an explosion in both the publication of novels and their readership and whose characters —from Oliver Twist to Tiny Tim— were held up as moral touchstones. Today Dickens’ greatness is unchallenged. Removing him from the pantheon（名人堂） of English literature would make about as much sense as the Louvre selling off the Mona Lisa.How did Dickens get to the top? For all the feelings readers attach to stories, literature is a numbers game, and the test of time is extremely difficult to pass. Some 60,000 novels were published during the Victorian age, from 1837 to1901; today a casual reader might be able to name a half-dozen of them. It’s partly true that Dickens’style of writing attracted audiencesfrom all walks of life. It’s partly that his writings rode a wave of social, political and scientific progress. But it’s also that he rewrote the culture of literature and put himself at the center. No one will ever know what mix of talent, ambition, energy and luck made Dickens such a singular writer. But as the 200th anniversary of his birthapproaches, it is possible —and important for our own culture—to understand how he made himself a lasting one. 21. Which of the following best describes British novels in the 18th century?A. They were difficult to understand.B. They were popular among the rich.C. They were seen as nearly worthless.D. They were written mostly by women.22. Dickens is compared with the Mona Lisa in the text to stress________.A. his reputation in FranceB. his interest in modern artC. his success in publicationD. his importance in literature23. What is the author’s purpose in writing the text?A. To remember a great writer.B. To introduce an English novel.C. To encourage studies on culture.D. To promote values of the Victorian age.BSteven Stein likes to follow garbage trucks. His strange habit makes sense when you consider that he’s an environmental scientist who studies how to reduce litter, including things that fall off garbage trucks as they drive down the road. What is even more interesting is that one of Stein's jobs is defending an industry behind the plastic shopping bags.Americans use more than 100 billion thin film plastic bags every year. So many end up in tree branches or along highways that a growing number of cities do not allow them at checkouts(收银台) . The bags are prohibited in some 90 cities in California, including Los Angeles. Eyeing these headwinds, plastic-bag makers are hiring scientists like Stein to make the case that their products are not as bad for the planet as most people assume.Among the bag makers' argument: many cities with bans still allow shoppers to purchase paper bags, which are easily recycled but require more energy to produce and transport. And while plastic bags may be ugly to look at,they represent a small percentage of all garbage on the ground today.z.x.xkThe industry has also taken aim at the product that has appeared as its replacement: reusable shopping bags. The stronger a reusable bag is, the longer its life and the more plastic-bag use it cancels out. However, longer-lasting reusable bags often require more energy to make. One study found that a cotton bag must be used at least 131 times to be better for the planet than plastic.Environmentalists don't dispute（质疑） these points. They hope paper bags will be banned someday too and want shoppers to use the same reusable bags for years.24. What has Steven Stein been hired to do?A. Help increase grocery sales.B. Recycle the waste material.C. Stop things falling off trucks.D. Argue for the use of plastic bags.25. What does the word “headwinds”in paragraph 2 refer to?A. Bans on plastic bags.B. Effects of city development.C. Headaches caused by garbage.D. Plastic bags hung in trees.26. What is a disadvantage of reusable bags according to plastic-bag makers?A. They are quite expensive.B. Replacing them can be difficult.C. They are less strong than plastic bags.D. Producing them requires more energy.27. What is the best title for the text?A. Plastic, Paper or NeitherB. Industry, Pollution and EnvironmentC. Recycle or Throw AwayD. Garbage Collection and Waste ControlCAs cultural symbols go, the American car is quite young.The Model T Ford was built at the Piquette Plant in Michigan a century ago, with the first rolling off the assembly line （装配线）on September 27, 1908. Only eleven cars were produced the next month. But eventually Henry Ford would build fifteen million of them.Modern America was born on the road, behind a wheel. The car shaped some of the most lasting aspects of American culture: the roadside diner, the billboard, the motel, even the hamburger. For most of the last century, the car represented what it meant to be American—going forward at high speed to find new worlds. The road novel, the road movie, these are the most typical American ideas, born of abundant petrol, cheap cars and a never-ending interstate highway system, the largest public works project in history.In 1928 Herbert Hoover imagined an America with “a chicken in every pot and a car in every garage.” Since then, this society has moved onward, never looking back, as the car transformed America from a farm-based society into an industrial power.zxx.kThe cars that drove the American Dream have helped to create a global ecological disaster. In America the demandfor oil has grown by 22 percent since 1990.The problems of excessive（过度的）energy consumption, climate change and population growth have been described in a book by the American writer Thomas L. Friedman. He fears the worst, but hopes for the best.Friedman points out that the green economy（经济）is a chance to keep American strength. “The ability to design, build and export green technologies for producing clean water, clean air and healthy and abundant food is going to be the currency of power in the new century.”28. Why is hamburger mentioned in paragraph 2?A. To explain Americans’ love for travelling by car.B. To show the influence of cars on American culture.C. To stress the popularity of fast food with Americans.D. To praise the effectiveness of America’s road system.29. What has the use of cars in America led to?A. Decline of economy.B. Environmental problems.C. A shortage of oil supply.D. A farm-based society.30. What is Friedman’s attitude towards America’s future?A. Ambiguous.B. Doubtful.C. Hopeful.D. Tolerant.第二节（共5小题；每小题2分，满分10分）根据短文内容，从短文后的选项中选出能填入空白处的最佳选项。
浙江省2014年选拔高职高专毕业生进入本科学习统一考试英语试题与答案
Part I Reading Comprehension (60 marks, 60 minutes)Section A (每小题2分)Format ⅠDirections: There are 4 passages in this part. Each passage is followed by five questions. For each of them there are four choices marked A, B, C, and D. You should decide on the best choice and blacken the corresponding letter on Answer Sheet.(40 marks)Passage OneQuestions 1 to 5 are based on the following passage:Have you ever wondered where the first doughnut(炸面圈) was made? Who thought up the idea of a fried cake with a hole in the center?No one knows for sure who made the first doughnut. Some people think that doughnuts probably began in the 1800s as Dutch “olykoeks” or “oily cakes.” In those days, a cook would not want to waste any scraps of food. Leftover pieces of bread dough(生面团) were put into hot oil and fried. Olykoeks were tasty on the outside, but soft and uncooked in the center.Some people say that the mother of a New Englandsea captain invented the first real doughnut. Her name was Elizabeth Gregory. She replaced the soft center with spices and nuts. But,Elizabeth’s son, Captain Gregory, did not like nuts. He punched out the center, and the consequence was the first hole in a doughnut.Others say the real story is that Captain Gregory had difficulty steering his ship while trying to eat doughnuts. He asked the ship’s cook to make his doughnuts with holes so he could hang them on the steering wheel! Others think that Captain Gregory saw holed cakes in Europe and brought the idea back toAmericawith him.During World War I, homesick American soldiers inEuropewere served doughnuts by the Salvation Army. These brave women volunteering for the job were called “Doughnut Girls.” They often worked in dangerous conditions near the soldiers, so the Doughnut Girls wore helmets and uniforms. The women made doughnut cutters out of a large can with a smaller can inside it to cut out the hole. They could set up a kettle of hot oil to fry the dough almost anywhere.In the 1920s, doughnut machines were invented. Doughnuts were produced faster and easier than ever before. Still, many people preferred to make their favorite doughnuts at home.1. The passage is mainly about ______.A. the popularity of doughnutsB. the history of doughnutsC. the inventors of doughnutsD. the types of doughnuts2. The first Dutch “olykoek” came into being probably because ______.A. people did not like to eat fried foodB. cooks did not like to waste leftover foodC. Dutchmen liked oil cakes very muchD. cooks liked the soft center of cakes3. What was used to replace the uncooked center to improve doughnuts?A. Scraps of food.B. Jelly filling.C. Spices and nuts.D. Leftover bread dough.4. In paragraph 3, the word “consequence” probably means ______.A. actionB. damageC. problemD. result5. What can be inferred about the Doughnut Girls during World War I?A. They worked aboard a ship.B. They worked near battlefields.C. They used untested machines.D. They used helmets to cook doughnuts.Passage TwoQuestions 6 to 10 are based on the following passage:It is a blow for the Ugly Bettys and Plain Janes — research shows that good looks lead to better pay. A study of 4,000 young men and women found that beauty boosted pay checks more than intelligence. Those judged to be the most attractive earned up to 10 percent more than their less attractive friends and colleagues. Applied to the average salary of ￡25,000 a year, the “plainness penalty (处罚)” would make a difference of ￡2,500 a year — or around ￡50 a week.It is unclear what is behind the phenomenon but it may be that beauty creates confidence. The self-confident may appear to be doing better than they are and will not hesitate about asking for a pay rise.Researcher Jason Fletcher, ofYaleUniversityin theU.S., rated the attractiveness of the 4,000 men and women. Just over half were judged average, while 7 percent were felt to be very attractive and 8 percent were judged unattractive or very unattractive. The volunteers also sat an IQ test and reported their salary. It became clear that pay scales were far from fair. For instance, a 14-point increase on the IQ score was associated with a 3 to 6 percent increase in wage. But being of above-average looks increased pay by 5 to 10 percent.For a plain person to be paid the same as a very attractive one, they would have to be 40 percent brighter, the journal Economics Letters reports.Dr Fletcher said: “The results do show that people’s looks have an impact on their wages and it can be very important.”6. What is the “plainness penalty”?A. To be paid less for being ordinarily-looking.B. To be laughed at for being ordinarily-looking.C. To be fired for being ordinarily-looking.D. To be questioned for being ordinarily-looking.7. What’s the average annual salary of a good-looking person?A. ￡2,500.B. ￡25,000.C. ￡22,500.D. ￡27,500.8. Good-looking people are paid more probably because ______.A. they look smarterB. they have higher degreesC. they are better at pleasing othersD. they are more confident9. How many people were rated as very attractive in Jason Fletcher’s study?A. About 280B. About 4,000C. About 2,000D. About 32010. Which of the following best summarizes the main idea of the passage?A. IQ is less important than appearance.B. Confidence makes people prettier.C. Good looks earn an extra penny.D. How Plain Janes get a higher salary.Passage ThreeQuestions 11 to 15 are based on the following passage:Were you constantly bored as a child? Maybe that helped you to develop your ability to be creative.Boredom can be a good thing for children, according to Dr Teresa Belton, researcher at theUniversityofEast Anglia’sSchoolofEducationand Lifelo ng Learning. After interviewing authors, artists and scientists inBritain, she’s reached the conclusion that cultural expectations that children should be constantly active could block the development of their imagination.British actress and writer Meera Syal grew up in a small mining village with few distractions. The researcher said: “Lack of things to do urged her to talk to people she wouldn’t otherwise have engaged with and try activities she wouldn’t, under other circumstances, have experienced, such as talking to elderly neighbors and learning to bake cakes.”Belton added: “Boredom made her write. Meera Syal kept a diary from a young age, filling it with observations, short stories, poems.”The researcher didn’t ignore the old saying the devil finds work for idle hands, though. Belton pointed out that young people who don’t have the interior resources to deal with boredom creatively may end up smashing up bus shelters or taking cars out for a joyride.How about watching TV and videos on the computer? The researcher believes that nothing replaces standing and staring at things and observing your surroundings.It’s the sort of thing that stimulates the imagination, she said, while the screen “tends to short circuit that process and the development of cre ative capacity”.Dr Belton concluded: “For the sake of creativity, perhaps we need to slow down and stay offline from time to time.”11. Dr Teresa Belton did her research by ______.A. studying cultural differencesB. interviewing professionalsC. keeping a diaryD. observing the surroundings12. Which of the following best describes the village where Meera Syal grew up?A. Modern and open.B. Tiny and unexciting.C. Poor and underdeveloped.D. Remote and violent.13. The expression “the devil finds work for idle hands” probably means that people are more likely to ______.A. do what they should not do if they meet devilsB. achieve nothing if they work with devilsC. do more work if they didn’t work hard when they were youngD. get involved in trouble if they have nothing to do with their time14. What is Dr Belton’s advice for youngsters?A. Observe the world around them.B. Get information online from time to time.C. Remain constantly active.D. Read as many books as possible.15. Which of the following is the best title for the passage?A. Deal with boredom wisely.B. Learn from a young age.C. Enjoy village life.D. Forget old sayings.Passage FourQuestions 16 to 20 are based on the following passage:During her junior year of high school, Candice Backu s’s teacher handed her a sheet and instructed the 17-year-old to map out her future financial life. Backus pretended to buy a car, rent an apartment, and apply for a credit card. Then, she and her classmates played the “stock market game,” investing the hy pothetical(假设的) earnings from their hypothetical jobs in the market in the fateful fall of 2008. “Our pretend investments crashed,” Backus says, still horrified. “We felt what actual shareholders were feeling.”That pain of earning and losing money is a feeling that public schools increasingly want to teach. Forty states now offer some types of financial instruction at the elementary or high-school level, including lessons in balancing checkbooks(支票本) and buying stock in math andsocial-studies classes. The interest in personal-finance classes has risen since 2007 when bank failures became a regular occurrence.Rather than teach investment strategies, these courses offer a basic approach to handling money: Don’t spend what you don’t have. Put part of your mo nthly salary into a savings account, and invest in the stock market for the long-term rather than short-term gains. For Backus, this means dividing her earnings from her part-time job at a fast-food restaurant into separate envelopes for paying bills, spen ding, and saving. “Money is so hard to make but so easy to spend,” she says one weekday after school.After Backus finished her financial classes, she opened up a savings account at her local bank and started to think more about how she and her family woul d pay for college. “She just has a better understanding of money and how it affects the world,” says her mother, Darleen. All of this talk of money can make Backus worry, she says, but luckily, she feels prepared to face it.16. The purpose of the high sch ool class’s “stock market game” is to ______.A. introduce a new courseB. encourage personal savingsC. learn about investmentD. teach credit card hazards17. Student interest in taking classes on finance has increased because of ______.A. the state of the economyB. the need for employmentC. the rate of graduationD. the desire to purchase cars18. According to the passage, taking money management courses will help young people to ______.A. get accepted by collegesB. become very wealthyC. take more vacationsD. prevent from going into debt19. After Candice Backus completed the class about money, she ______.A. is debt freeB. manages the family incomeC. will graduate earlyD. feels more competent20. The author’s attitude toward financial classes i n public schools is ______.A. positiveB. criticalC. objectiveD. worriedFormat ⅡDirections: In the following passage, some sentences have been removed. For questions 21—25, choose the most suitable one from the list A—G to fit into each of the numbered blanks. There are two extra choices, which do not fit into any of the gaps. Mark your answers on Answer Sheet.(10 marks)Now put on sunscreen(防晒霜)Some sunscreens prevent sunburn but not other types of skin damage. Make sure yours offers a broad range of protection.● 21. ______ Anything higher than SPF 50+ can tempt you to stay in the sun too long. Even if you don’t burn, your skin may be damaged. Stick to SPFs between 15 and 50+. Pick a product based on your own skin color, time outside, shade and cloud cover.● News about vitamin A. Eating vitamin A-rich vegetables is good for you, but spreading vitamin A on your skin may not be. Government data shows that cancers develop sooner on skin coated with creams with vitamin A. 22. ______● Pick a good sunscreen. EWG’s sunscreen database rates the safety and effect of about 1,400 SPF-rated products, including about 750 sunscreens for beaches and sports use. We give high ratings to brands that provide broad-range, long-lasting protection with ingredients that pose fewer health concerns when absorbed by the body.● 23. ______ Cream, because spr ays cloud the air with tiny particles that may not be safe to breathe. Reapply cream often. Sunscreen chemicals sometimes degrade in the sun, wash off or rub off on towels and clothing.● 24. ______ The FDA treats powdered sunscreens as unapproved new drug s and may take enforcement action against companies that sell them-except for small businesses, which can sell powders until December 2013.● 25. ______ Wear sunscreen. In 2009, nearly twice as many American men died from skin cancers as women. Surveys show that 34 percent of men wear sunscreens, compared to 78 percent of women.● Got your vitamin D? Many people don’t get enough vitamin D, a hormone manufactured by the skin in the presence of sunlight. Your doctor can test your level and recommend supplements if you are low in this vital nutrient.A. No powder!B. Avoid midday sun.C. Message for men:D. Cream or spray?E. Don’t fall for high SPF labels.F. Take special precautions with infants and children.G. Avoid any sun product whose label says vitamin A.Section B (每小题1分)Directions: In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passage through carefully before making your choices. Please blacken the corresponding letter for each item on Answer Sheet. You may not use any of the words in the bank more than once.(10 marks)A survey of English schoolchildren shows boys and girls are worrying about the way they look. The 26 found that over half of male schoolchildren lacked confidence because of their body27 . The figure for girls was slightly 28 , at 59 percent. Researchers questioned 693 teachers about how their students 29 about their bodies. All the children had taken lessons on body image and self-esteem. Teachers said many children were very 30 if others said bad things about their appearances. Around 55 percent of teachers reported that girls were extremely sensitive to comment 31 their looks; the figure for boys being easily hurt by teasing(取笑) was 27 percent.Teachers gave a number of 32 why children as young as four years old were stressing out about their shapes. Over 90 percent of teachers 33 the Internet and television. Children see images of “perfect” bodies every day and they feel they have to look that way too. Many children are on diets to make themselves 34 to the opposite sex. One elementary school teacher said: “I work with four to five-year-olds and some say things like, ‘I can’t eat cheese, it will make me35 ’ ”. A teachers’ spokeswoman warned that children trying to look like “celebrities in the media only lead to misery”.A. about F. fat K. questionsB. attractive G. felt L. reasonsC. blame H. for M. shapeD. complete I.higher N. studyE. discover J. lazy O. upsetPart ⅡIntegrated Testing (30 marks, 30 minutes)Section A Cloze (每小题1分)Directions: There are 20 blanks in the following passage. For each blank there are four choices marked A, B, C and D. You should choose the ONE that best fits into the passage. Then blacken the corresponding letter on Answer Sheet.(20 marks)To stay economically competitive on a global scale, the United States needs 8 million more college graduates 36 2020. That may sound impossible, 37 according to Education at a Glance 2013, the 38 international report on the state of education 39 Tuesday by the Organization for Economic Cooperation and Development (OECD), the 40 is still the world leader in producing college graduates. 41 , OECD data 42 that almost half of the world’s university graduates come from three countries—theUnited States,ChinaandJapan.43 the 34 OECD countries, 44 26 percent of the total 255 million college-educated 45 between the ages of 25 and 64 come from theUnited States.Chinacomes in a distant second at 12.1 percent andJapanis a 46 third at 11.4 percent.Global prosperity(繁荣) won’t increase if only three nations 47 higher education output, so it’s exciting to see that the number of students 48 to college increased 25 percent across all OECD countries 49 1995 and 2012. If that 50 continues, 59 percent of young adults in those countries will go on to college, 51 19 percent will enter vocational programs over their lifetimes.The number of students who actually graduate 52 college has increased as well. In 2012, an average of 39 percent of students in OECD nations 53 college, up from 20 percent in 1995. Since college dropouts 54 theU.S.economy billions of dollars every year, an international increase in graduation 55 is good news for the entire planet.36. A. at B. sinceC. fromD. by37. A. if B. soC. butD. for38. A. annual B. averageC. advancedD. available39. A. recovered B. releasedC. recommendedD. required40. A. university B. organizationC. nationD. continent41. A. However B. OtherwiseC. In factD. By the way42. A. appeals B. exposesC. emergesD. shows43. A. Above B. AmongC. BeyondD. Beneath44. A. nearly B. reallyC. rarelyD. necessarily45. A. objects B. individualsC. subjectsD. targets46. A. close B. counterC. furtherD. forward47. A. demonstrate B. occupyC. dominateD. reach48. A. confronting B. encounteringC. longingD. heading49. A. including B. betweenC. excludingD. toward50. A. trend B. currencyC. directionD. distinction51. A. so B. whileC. beforeD. because52. A. for B. againstC. fromD. in53. A. tried B. huntedC. leftD. completed54. A. give B. costC. bringD. plan55. A. fee B. benefitsC. ratesD. advantages非选择题部分注意事项：用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。
浙江省2020 年选拔优秀高职高专毕业生进入本科学习统一考试高等数学2
x
2n
，收敛域为：
x
0,4
四、综合题： 本大题共 3 小题， 每小题 10 分， 共 30 分。
24.解:设
f
(x)
tan x
x
，
x (0, ) ，所以 2
f
( x)
x sec2
x tan x2
x
x cos2
x x2
sin x cos x
x
sin x cos x2 cos2 x
x
x 1 sin 2
23.解:因 ln(1 x) (1)n1 xn ，收敛域为： ( 1,1] ，所以 ln x ln[2 (x 2)]
n1
n
ln2(1
x2 2)
ln2 ln(1
x 2) 2
ln2
n1
(1)n1 n
x 2n 2
，收敛域为：
1
x
2
2
1，
所以
ln
x
ln
2
n1
(1)n1 n 2n
e
e
e
e
【图 1】
13. y Cex （ C 为任意常数）解析:由微分方程 y y 0 ，可知 y y ，即 dy y ，
dx
所以可分离变量后得： dy dx ，两边同时积分，得： dy dx ，所以 ln y x A ，
y
y
y exA ex eA ，因此 y eA ex Cex ，其中 C e A ，所以通解为： y Cex ，
2
当
n
0
，
n
1，且
n
Z
时，极限为：
lim
xn
f
(x)
lim
2013-2019历年浙江专升本高等数学真题及解析
出的四个选项中，只有一项是符合题目要求的）
1.设 f (x) sin(cos 2x), x R ，则此函数是（ ）
（A）有界函数 【答案】（A）。
（B）奇函数
（C）偶函数
（D）周期函数
【解析】由于1 sin(cos 2x) 1 ，故 f (x) 为有界函数，显然容易验证 f (x) 不是奇偶函数
【解析】对 y P(x) y Q(x) y 2 两边同时除以 y2 可得 y2 y P(x) y1 Q(x) ，令
z y1 ，原微分方程可化为一阶线性微分方程 z P(x)z Q(x) 进行求解，即 z P(x)z Q(x) ，由一阶微分线性方程的求解公式可求得
z e P(x)dx[
【解析】要使得 sin x 有意义，则 sin x 0 ，故 x [2kπ, (2k 1)π],k Z 。
8.已知 f (1) 1 ， lim f (1 x) f (1 x)
。
x0
x
【答案】 2 。
【解析】将极限转化成导数的定义式
lim f (1 x) f (1 x) lim f (1 x) f (1) f (1) f (1 x)
非选择题部分
注意事项：
1.用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。 2.在答题纸上作图，可先使用 2B 铅笔，确定后必须使用黑色字迹的签字笔或钢笔描黑。 二．填空题（本大题共 10 小题，每小题 4 分，共 40 分）
6.极限 lim x ln sin(x2)
。
x0
【答案】 0 。
16.设
f
(x)
ex
sin
2018年浙江省专升本真题
浙江省2018年选拔优秀高职高专毕业生进入本科学习统一考试英语请考生按规定用笔将所有试题的答案涂、写在答题纸上。
选择题部分注意事项：1.答题前,考生务必将自己的姓名、准考证号用黑色字迹的签字笔或钢笔填写在答题纸规定的位置上。
2.每小题选出答案后,用2B铅笔把答题纸上对应题目的答案标号涂黑。
如需改动,用橡皮擦干净后,再选涂其他答案标号。
不能答在试题卷上。
Part I Reading Comprehension(60marks,60minutes)Section A(50marks:2marks for each item)Format IDirections:There are4passages 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 AnswerSheet1.Passage OneQuestion1to5are based on the following passage:A U.N.report says water is in demand around the world as temperatures on Earth’s surface rise and demand grows along with populations.The report was released this week at the World Water Forum in Brasilia.The conference has been described as the world’s largest water-related event.Federal District Governor Rodrigo Rollemberg spoke at a panel discussion on Tuesday at the forum.He described water shortages as a worldwide problem.The public water supply has less water because of low rainfall as well as fast and disorderly growth in Brasilia,which is part of the Federal District,Rollemberg said.In January2016,after three years of little rain,district officials began limiting how much water people could use.The governments of the Federal District and the nearby state of Goias also gave$166million to develop water infrastructure(基础设施).Demand around the world is expected to increase by nearly one-third by2050.By then,5billion people could be left with poor access to water,the U.N.warned in its2018World Water Development Report.To avoid such a crisis,U.N.officials called for“nature-based solutions”that use or copy natural processes that should be used to increase water availability.They said solutions could include changing farming methods so fields keep more moisture and nutrients, collecting rainwater,and protecting wetlands.The officials also proposed reestablishing floodplains and said that plants could be grown on housetops.Such proposals will become more important as water industries grow.1.Who talked about water shortages in Brasilia at a panel discussion?A.A journalist.B.A U.N.official.C.A Federal District official.D.An official from the state of Goias.2.What is among the reasons for less public water supply in Brasilia?A.Waste of rainwater.B.Insufficient rainfall.C.Growing plants on the roofs.D.Development in infrastructure.3.What did the Federal District government do to deal with water shortages?A.They controlled population.B.They limited water consumption.C.They invested in artificial rainmaking.D.They suggested“nature-based solutions”.4.What is NOT a“nature-based solution”?A.Gathering rainwater.B.Preserving wetlands.C.Sustaining water in soil.D.Building houses on floodplains.5.What is the main idea of this passage?A.Brasilia is facing the problem of water shortages.B.The world has found a solution to water shortages.C.The world is facing the problem of water shortages.D.A report was released at the World Water Forum in Brasilia.Passage TwoQuestions6to10are based on the following passage:The Queen has only given one interview while a sovereign(君主).Her true personality remains elusive to the public.However,one thing is clear:Queen Elizabeth is an introvert. Introverts prefer quiet environments and feel energized from spending time alone or with people they know well.They aren’t necessarily shy,but they do tend to be more reserved and guarded with strangers.Fellow introverts will appreciate how draining an average day for Her Majesty must be.Fortunately,the Queen has some tricks to make public engagements easier.Just like uscommoners rely on friends to save us from awkward situations or boring conversations,she subtly signals to her staff when she wants an intervention.If she places her handbag on the table,it indicates that she wants the event to end in the next five minutes.For more urgent situations, putting her bag on the floor shows that she wants her lady-in-waiting to rescue her immediately.Most comfortable in the countryside,the Queen has a well-known passion for horses and dogs.There is a scene in the hit Netflix show The Crown which reveals a fascinating side of the monarch.While giving Jackie Kennedy a personal tour of Buckingham Palace,the two women find themselves bonding over their respective positions as introverted women who have found themselves in the limelight.Surrounded by the Queen’s beloved corgis,both women admit they are happiest around animals and that their extroverted sisters would have been much better suited to their public roles.6.The underlined word“draining”(paragraph1)is the closest in meaning to“”.A.frustratingB.exhaustingC.demandingD.aspiring7.To be rescued immediately in a public engagement,the Queen would.A.end the event within five minutesB.place he handbag on the tableC.wave to her lady-in-waitingD.put her bag on the floor8.In the last paragraph,the underlined expression“the two women find themselves bonding over their respective positions”means that the two ladies.A.admire each otherB.help each other in publicC.grow closer to each otherD.show respect for each other9.Queen Elizabeth and Jackie Kennedy share the following traits or facts EXCEPT that.A.both have sistersB.both love animalsC.both enjoy being in publicD.both are introverted women10.The author’s attitude can be described as.A.neutralB.criticalC.pessimisticD.subjective Passage ThreeQuestions11to15are based on the following passage:Back when Disney products were to be watched,not experienced,Walt Disney had a vision: a theme park that felt like stepping into a magical new place.Now,we can finally witness Walt’s first dream.Before construction could start,Walt needed funding.He and his friend Herb Ryman put their heads together and mapped out their dream for the Disneyland that was still just a figment of their imaginations.In just one frenzied1953weekend,their idea came to life on paper—and you’ll notice both subtle differences from and remarkable similarities to the modern Anaheim, California,park.Like today,visitors would have entered the park into a Main Street USA-type area.The tunnels aren't as wide as they were imagined more than60years ago,but park-goers are still greeted with a train passing overhead as they make their way toward the magic.(Even with a modern Disneyland map,it's tough to find these secret Disney park spots you never knew existed.) Walt always hoped for a castle as a focal point of the park,but its real-life iteration changed from his initial dream.The first palace was a sprawling fortress,hiding a massive carousel(旋转木马)beyond its walls.Now,Sleeping Beauty Castle has more intricate spires,and King Arthur Carrousel takes its spins in Fantasyland,behind the palace.Walt’s vision for the Mark Twain steamboat circling around Tom Sawyer Island and its Pirate’s Lair(巢穴)hasn’t changed much,though at that point it was called Frontier Country instead of Frontierland.That wasn't the only name change,though.World of Tomorrow turned into Tomorrowland—and eventually lost its rocket.Astronauts walked on the moon14years after the park was built,making the Rocket to the Moon seem out-of-date.Meanwhile,True-Life Adventureland lost its first word,while most of the areas took on totally different themes.11.What was Walt Disney’s first dream?A.To build a theme parkB.To draw a map on paper.C.To travel in a magical place.D.To design a series of products.12.Before construction started,Walt Disney did the following things EXCEPT.A.getting fundingB.planning the parkC.drawing the park on paperD.daydreaming with a friend13.Which of the following park spots has not changed much since Walt’s vision came to life on paper?A.A Main Street area.B.World of Tomorrow.C.Sleeping Beauty Castle.D.True-Life Adventureland.14.How many name changes have been mentioned in this passage?A.One.B.TwoC.Three.D.Four.15.What is the theme of this passage?A.A tour in Disneyland.B.Walt Disney’s life story.C.The future of Disneyland.D.Walt Disney’s first dream.Passage ThreeQuestions16to20are based on the following passage:You’ve made it.You managed to navigate your way through the world’s largest airport without robot assistance;you breezed through security because you didn’t pack any items that get you flagged by the TSA;and you successfully boarded the plane.Now you’re comfortable in your seat in the(kind of incredibly germ-ridden)cabin,and there’s even a little bit of elbow room,asthe flight isn’t fully booked for once.With the hassle behind you,you settle in with your neck pillow,pop some Kenny G on your iPod,and get ready to spend quality time sleeping on a plane. And you’re about to make a huge mistake that will put your health at risk,as reported by Travel+ Leisure.It’s not because of the Kenny G.It’s the shuteye part.According to MedlinePlus,falling asleep during landing or takeoff could cause serious damage to your ears.It all has to do with the rapid changes in air pressure in the cabin.If you’re awake,a natural response to alleviate pressure on your eardrums during takeoff and landing is to'pop'them,to maintain a pressure equilibrium.If you’re sleeping on a plane,you can’t actively work to relax those muscles and release the tension,so you can become susceptible to dizziness,ear infections,eardrum damage,hearing loss and nose bleeds.‘A quick change in altitude affects the air pressure in the ear,’says Angel Chalmers,a British pharmacist,via Express.'This leads to a vacuum in the Eustachian tubes(咽鼓管)which makes the ears feel blocked and sound dull.'Keep those Eustachian tubes clear and keep those eyes open for at least another few minutes. Crack open that book you just bought in the terminal.After all,there are some major perks to buying your reading material at the airport.16.The underlined sentence“You’ve made it.”(Paragraph1)means that you have managed.A.to board the planeB.to get a bit of elbow roomC.to get ready to sleep after boardingD.to make yourself comfortable after boarding17.What would damage your health when the plane takes off or lands?ing a neck pillow.B.Shutting your eyes.C.Listening to music.D.Falling asleep.18.The underlined word“alleviate”(Paragraph2)is the closest in meaning to“”.A.increaseB.reduceC.maintainD.escape19.Having a vacuum in the Eustachian tubes during takeoff and landing could cause unpleasant symptoms to the following body parts EXCEPT.A.the throatB.the noseC.the earsD.the head20.The author suggests that you read a book during the plane taking off and landing.A.to amuse yourselfB.to stay awakeC.to keep your ears clearD.to make yourself comfortableFormat IIDirections:In the following passage,some sentences have been removed.For questions21to25, choose the most suitable sentence from choices A to G to fit into each of the numbered blanks. There are two extra choices,which do not fit into and of the blanks.You should decide on the bestchoice and blacken the corresponding letter on The Answer Sheet.(10points)Whether it’s a hotel stay,shopping or dining ont,a vacation to Paris can be a pricey proposition.But there are plenty of ways to stretch your dollar in the City of Lights and have a high-end getaway.Barkley Hickcox,a Paris specialist and an owner of Local Foreigner,a travel consultancy, has a few tips to help travelers make the most of their Parisian getaway.21..The ideal time to visit Paris is between November and April,when hotel prices are at their lowest.Some high-end properties offer even further discounts if you a stay several months in advance.22..Families traveling to Paris should consider staying in a high-end apartment instead of a hotel, Ms.Hickcox said.“An apartment is less expensive than booking multiple rooms at a five-star hotel,and since you have a kitchen,you can save on food costs by eating in occasionally,“she said.23..Paris is known for fine cuisine,but rather than dining at one of the city’s renowned restaurants at dinnertime,go for lunch,when the tab will be much lower and the cuisine just as good.“You’ll find lots of great eateries where you can have dinner with wine for35to50euros a person,”she said.24..Ms.Hickcox’s favorite way to explore Paris is on foot.“You can fully appreciate the city’s beauty by walking,and it’s designed for walkers because there are walking paths and sidewalks everywhere,”she said.For longer distances,she suggested using the city’s bike share system,Velib.A weeklong pass costs15euros,and there are stations everywhere.There is another choice if you are not so much fond of biking.25.,Paris’subway system.It’s convenient,and you can buy daily and weekly passes.A.Dine outB.Eat smartC.Try the MetroD.Stay in a hotelE.Ditch taxis and carsF.Travel at the right timeG.Choose the right accommodationsSection B Banked Cloze(每小题1分，共10分)Directions:In this section,there is a passage with ten blanks.You are required to select one word for each blank from a list of choices given in a word bank following the passage.Read the passage through carefully before making your choices.Please blacken the corresponding letter for each choice on The Answer Sheet.You may not use any of the words in the word bank more than once. (10points)I knew this woman who was afraid to tell people what she wanted.She didn’t know__26__ to say no.Instead,she got herself tangled in a web of obligations,anxiety,and white lies.She was __27__.__28__recently,I decided I’d had enough.As an experiment,I began__29__up for myself, even at the risk of alienating(疏远)everyone and having__30__entire life come crashing down around me.That didn’t happen.Here’s what did:I stopped making petty excuses.Saying“no”is so much easier.If someone asks me to do something I have zero interest __31__,I’m polite but honest.The phrase.”I’m sorry,I don’t think that’s really__32__me,“slips out my mouth faster than some lame excuse.My friends and family didn’t mind.__33__I stopped people-pleasing,no one cared.A good friend asked me to go for coffee at5PM.I was__34__to hit the gym.I said,“Sorry,I’ve got things I want to do tonight.”She said,“That’s fine.Maybe another time.”Learning how to say“no”has added several extra hours to my days,days__35__my weeks, and what feels like months to my years.Saying“no”has set me free.A.facingB.toC.herD.inE.forF.whatG.standingH.AndI.myJ.ButK.meL.WhenM.onN.planningO.howPart II Integrated Testing(30points,30minutes)Section A Cloze(每小题1分，共20分)Directions:There are20blanks in the following passage.For each blank there are four choices marked A,B,C and D.You should choose the ONE that best fits into the passage.Then blacken the corresponding letter on The Answer Sheet.(20points)Brazilian Zarela Mosquera moved to the United States as a teenager.The adjustment to a new place was__36__.Mosquera says she became a bratty(顽皮的)teenager,as a result.But it was not just the__37__that affected her behavior.Mosquera says there was another major stress in herlife at that time:She was the only member of her__38__who spoke English.“Being in a country with my family that doesn’t speak Spanish and my parents don’t really speak__39__,my parents were trying to give me all these responsibilities.”Along with Spanish and English,Mosquera also speaks Portuguese.But there was another universal language she learned to love as a child:art.Zarela Mosquera connected with drawing and painting while in school.__40__she mostly dismissed art as a path to a career.She says her Dad__41__always say,“Think about the __42__.”Mosquera did not think he would support the study of__43__once she went to college.But,to her__44__,it was her parents who suggested just that.They urged her to__45__ to technical and liberal arts schools.“One of them was Rhode Island School of Design,which was like my__46__choice.”RISD,as it is called,__47__Mosquera as well.She enrolled in industrial design.“It’s basically to design__48__and services.I could be doing something technical or something more__49__to problem solving.Whether it’s__50__out a better way to filter water or developing a type of specific shelter__51__refugees for example.”Mosquera says the course of study was__52__including metal working,woodworking and model making.She says in one class she just drew cubes for an entire month,which led her to a__53__:“Wow!Do I really want to do this?”But,she says,she__54__the cube study.And, then she began__55__on more interesting projects.Mosquera is now a design strategist for Marshall Moya Design,an architecture and interior design company in Washington,D.C.36.A.successful B.important C.necessary D.difficult37.A.age B.growth C.adjustment cation38.A.family B.peers C.friends D.class39.A.Spanish B.English C.Portuguese D.French40.A.So B.Moreover C.And D.But41.A.could B.should C.would D.might42.A.time B.past C.present D.futurenguage B.art C.technology D.design44.A.disappointment B.surprise C.annoyance D.dissatisfaction45.A.apply B.cater C.adapt D.move46.A.top B.moral C.natural D.popular47.A.failed B.rejected C.chose D.urged48.A.machines B.shelters C.filters D.products49.A.adjusted B.related C.affiliated D.exposed50.A.figuring B.wiping C.filling D.ruling51.A.with B.for C.on D.in52.A.easy B.pleasant C.tough D.smooth53.A.question B.problem C.door D.road54.A.undertook B.funded C.started D.survived55.A.putting B.relying C.working D.counting非选择题部分注意事项：用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。
2015年浙江省普通高校“专升本”联考《高等数学(一)》试卷【附答案】
1 dx
12. 1 e x
已知级数
1
2
，则级数
1 的和为
13.
n2
n 1
6
n1（2n - 1）2
14.函数 lnx 在 x=1 处的幂级数展开式为
15.直线 x 2 y - 3 z与平面x 2y 2z 5的交点坐标是
3
-2
三、计算题：本题共有 8 小题，其中 16-19 小题每小题 7 分，20-23 小题每小题 8 分，共 60 分。计算题必须写出必要的计算过程， 只 写答案的不给分。
8. （0，1）
9. 2
2
- 2-xln2
10.
dx 1 2-x
11.
1 2x2源自 3,x01 2x2
3,x
0
12 x-ln(1+e x )+c
13. 2
8
14.
(1)n(x 1)n 1 ,x (0,2]
n 0
n 1
15. （1，1，1）
四、计算题：本题共有 8 小题，其中 16-19 小题每小题 7 分，20-23
小题每小题 8 分，共 60 分。计算题必须写出必要的计算过程，
只写答案的不给分。
16.
解： f(x
1 )
x
1 x2 1
x2
1
x
1 x
2
,令 x
2
1 x
t ,则 f(t)= 1
t2 2
由于函数的对应法则与自变量选取的无关性，则 f(x)= 1 。
x2 2
1
17．解：原式= lim x
x2
1 1
ax
b
2，则a和b的值为
8. 函数F(x )
2018年高考真题—— (浙江卷) +word版含解析
2018年普通高等学校招生全国统一考试 (浙江卷)数 学注意事项：1．答题前，先将自己的姓名、准考证号填写在试题卷和答题卡上，并将准考证号条形码粘贴在答题卡上的指定位置。
2．选择题的作答：每小题选出答案后，用2B 铅笔把答题卡上对应题目的答案标号涂黑，写在试题卷、草稿纸和答题卡上的非答题区域均无效。
3．非选择题的作答：用签字笔直接答在答题卡上对应的答题区域内。
写在试题卷、草稿纸和答题卡上的非答题区域均无效。
4．考试结束后，请将本试题卷和答题卡一并上交。
一、选择题(本大题共10小题，每小题4分，共40分)1. 已知全集U ={1，2，3，4，5}，A ={1，3}，则C U A =( )A . ∅B . {1，3}C . {2，4，5}D . {1，2，3，4，5}2. 双曲线−y 2=1的焦点坐标是( )A . (−，0)，(，0)B . (−2，0)，(2，0)C . (0，−)，(0，)D . (0，−2)，(0，2)3. 某几何体的三视图如图所示(单位：cm )，则该几何体的体积(单位：cm 3)是( )A . 2B . 4C . 6 D. 8俯视图正视图4. 复数(i 为虚数单位)的共轭复数是( )A . 1+iB . 1−iC . −1+iD . −1−i5. 函数y =sin 2x 的图象可能是()D C B A6. 已知平面α，直线m ，n 满足m ⊄α，n ⊂α，则“m ∥n ”是“m ∥α”的( ) A . 充分不必要条件 B . 必要不充分条件 C . 充分必要条件 D . 既不充分也不必要条件7. 设0<p <1则当p 在(0，1)内增大时( ) A . D (ξ)减小 B . D (ξ)增大 C . D (ξ)先减小后增大 D . D (ξ)先增大后减小 8. 已知四棱锥S −ABCD 的底面是正方形，侧棱长均相等，E 是线段AB 上的点(不含端点)，设SE 与BC 所成的角为θ1，SE 与平面ABCD 所成的角为θ2，二面角S −AB −C 的平面角为θ3，则( ) A . θ1≤θ2≤θ3 B . θ3≤θ2≤θ1 C . θ1≤θ3≤θ2D . θ2≤θ3≤θ1 9. 已知a ，b ，e 是平面向量，e 是单位向量，若非零向量a 与e 的夹角为，向量b 满足b 2−4e •b +3=0，则|a −b |的最小值是( ) A . −1 B . +1 C . 2 D . 2− 10. 已知a 1，a 2，a 3，a 4成等比数列，且a 1+a 2+a 3+a 4=ln (a 1+a 2+a 3)，若a 1>1，则( ) A . a 1<a 3，a 2<a 4 B . a 1>a 3，a 2<a 4 C . a 1<a 3，a 2>a 4 D . a 1>a 3，a 2>a 4 二、填空题(本大题共7小题，多空题每题6分，单空题每题4分，共36分) 11. 我国古代数学著作《张邱建算经》中记载百鸡问题：“今有鸡翁一，值钱五；鸡母一，值钱三；鸡雏三，值钱一，凡百钱，买鸡百只，问鸡翁、母、雏各几何？”设鸡翁、鸡母，鸡雏个数分别为x ，y ，z ，则，当z =81时，x =__________________________，y =___________________________ 12. 若x ，y 满足约束条件，则z =x +3y 的最小值是________________________，最大值是_____________________ 13. 在△ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，若a =，b =2，A =60°，则sinB =_________________，此卷只装订不密封 班级姓名准考证号考场号座位号c=___________________14.二项式(+)8的展开式的常数项是_________________________15.已知λ∈R，函数f(x)=，当λ=2时，不等式f(x)<0的解集是_____________________，若函数f(x)恰有2个零点，则λ的取值范围是________________________16.从1，3，5，7，9中任取2个数字，从0，2，4，6中任取2个数字，一共可以组成______________________个没有重复数字的四位数(用数字作答)17.已知点P(0，1)，椭圆+y2=m(m>1)上两点A，B 满足=2，则当m=____________________时，点B横坐标的绝对值最大三、解答题(本大题共5小题，共74分)18.(14分)已知角α的顶点与原点O重合，始边与x轴的非负半轴重合，它的终边过点P (−，−)(1)求sin(α+π)的值(2)若角β满足sin(α+β)=，求c osβ的值19.(15分)如图，已知多面体ABCA1B1C1，A1A，B1B，C1C均垂直于平面ABC，∠ABC=120°，A1A=4，C1C=1，AB=BC=B1B=2(1)证明：AB1⊥平面A1B1C1(2)求直线AC1与平面ABB1所成的角的正弦值C1B1A1CA20.(15分)已知等比数列{a n}的公比q>1，且a3+a4+a5=28，a4+2是a3，a5的等差中项，数列{b n}满足b1=1，数列{(b n+1−b n)a n}的前n项和为2n2+n(1)求q的值(2)求数列{b n}的通项公式21.(15分)如图，已知点P是y轴左侧(不含y轴)一点，抛物线C：y2=4x上存在不同的两点A，B满足PA，PB的中点均在C上(1)设AB中点为M，证明：PM垂直于y轴(2)若P是半椭圆x2+=1(x<0)上的动点，求△PAB面积的取值范围22.(15分)已知函数f(x )=−lnx(1)若f(x)在x=x1，x2(x1≠x2)处导数相等，证明：f(x1)+f(x2)>8−8ln2(2)若a≤3−4ln2，证明：对于任意k>0，直线y=kx+a与曲线y=f(x)有唯一公共点2018年普通高等学校招生全国统一考试 (浙江卷) 数 学 答 案1.答案：C解答： 由题意知U C A ={2,4,5}.2.答案：B解答：∵2314c =+=，∴双曲线2213xy -=的焦点坐标是(2,0)-，(2,0).3.答案：C解答：该几何体的立体图形为四棱柱，(12)2262V +⨯=⨯=.4.答案：B解答：22(1)11(1)(1)i z i i i i +===+--+，∴1z i =-.5.答案：D解答：令||()2sin 2x y f x x ==，||||()2sin(2)2sin 2()x x f x x x f x --=-=-=-，所以()f x 为奇函数①；当(0,)x p Î时，||20x >，sin 2x 可正可负，所以()f x 可正可负②.由①②可知，选D.6.答案：A解答：若“//m n ”，平面外一条直线与平面内一条直线平行，可得线面平行，所以“//m α”；当“//m α”时，m 不一定与n 平行，所以“//m n ”是“//m α”的充分不必要条件.7.答案：D解答：111()0122222ppE p x -=???+，22211113()()()()222222p p D p p p x -=?+?+?22111()422p p p =-++=--+， 所以当p 在(0,1)内增大时，()D x 先增大后减小，故选D. 8.答案：D 解答： 作SO 垂直于平面ABCD ，垂足为O ，取AB 的中点M ，连接SM .过O 作ON 垂直于直线SM ，可知2SEO θ=∠，3SMO θ=∠，过SO 固定下的二面角与线面角关系，得32θθ≥. 易知，3θ也为BC 与平面SAB 的线面角，即OM 与平面SAB 的线面角， 根据最小角定理，OM 与直线SE 所成的线线角13θθ≥， 所以231θθθ≤≤. 9.答案：A 解答： 设(1,0)e = ，(,)b x y = ， 则222430430b e b x y x -⋅+=⇒+-+= 22(2)1x y ⇒-+= 如图所示，a OA = ，b OB = ，（其中A 为射线OA 上动点，B 为圆C 上动点，3AOx π∠=.）∴min 11a b CD -=-= .（其中CD OA ⊥.）10.答案：B解答：∵ln 1x x ≤-，∴1234123123ln()1a a a a a a a a a a +++=++≤++-，得41a ≤-，即311a q ≤-，∴0q <.若1q ≤-，则212341(1)(1)0a a a a a q q +++=++≤，212311(1)1a a a a q q a ++=++≥>，矛盾.∴10q -<<，则2131(1)0a a a q -=->，2241(1)0a a a q q -=-<.∴13a a >，24a a <.11.答案：8 11解答：当81z =时，有811005327100x y x y ì++=ïïíï++=ïî，解得811x y ì=ïïíï=ïî.12.答案：2- 8解答：不等式组所表示的平面区域如图所示，当42x yì=ïïíï=-ïî时，3z x y =+取最小值，最小值为2-；当22x y ì=ïïíï=ïî时，3z x y =+取最大值，最大值为8.13.答案：73解答： 由正弦定理sin sin a b A B =2sin B =，所以sin 7B =由余弦定理，222cos 2b c a A bc +-=，得214724c c +-=，所以3c =. 14.答案：7 解答： 通项1813181()()2r r r r T C x x --+=843381()2r r r C x -=. 84033r -=，∴2r =.∴常数项为2281187()7242C ⨯⋅=⨯=. 15.答案：(1,4) (1,3](4,)⋃+∞ 解答： ∵2λ=，∴24,2()43,2x x f x x x x -≥⎧=⎨-+<⎩. 当2x ≥时，40x -<得24x ≤<. 当2x <时，2430x x -+<，解得12x <<. 综上不等式的解集为14x <<. 当243y x x =-+有2个零点时，4λ>. 当243y x x =-+有1个零点时，4y x =-有1个零点，13λ<≤. ∴13λ<≤或4λ>. 16.答案：1260 解答： 224121353435337205401260C C A C C C A +=+=. 17.答案：5 解答：方法一：设11(,)A x y ，22(,)B x y ，当直线斜率不存在时，9m =，20x =.当直线斜率存在时，设AB 为1y kx =+.联立2241x y m y kx ⎧+=⎪⎨⎪=+⎩得22(41)8440k x kx m +++-=，20410mk m ∆>⇒+->，122841kx x k +=-+，1224441mx x k -=+.∵2AP PB = ，∴122x x =-，解得121641kx k -=+，22841kx k =+. ∴228821414k x k k k==≤++（当且仅当12k =时取“=”）.122216884141k k x x k k -=⋅=-++，122442241mx x m k -==-+，得5m =，∴当5m =时，点B 横坐标最大.方法二：设11(,)A x y ，22(,)B x y ，则11(,1)AP x y =-- ，22(,1)PB x y =-，∵2AP PB = ，∴1212232x x y y =-⎧⎨=-⎩， ∴22222222(2)(32)(1)4(2)4x y m x y m ⎧-+-=⎪⎪⎨⎪+=⎪⎩，由(1)(2)得234m y +=.(3)将(3)代入(2)，得222(5)164m x --+=，∴2x =，∴当5m =时，2x 取最大值.18.答案：（1）45；（2）5665-或1665. 解答： （1）445sin()sin 15απα-+=-=-=. （2）∵()βαβα=+-，∴cos cos[()]βαβα=+-， ∵5sin()13αβ+=，∴12cos()13αβ+=±， 又∵4sin 5α=-，且α终边在第三象限，∴3cos 5α=-. ①当12cos()13αβ+=时， cos cos()cos sin()sin βαβααβα=+++ 12354362056()()1351356565--=⨯-+⨯-==-. ②当12cos()13αβ+=-时， cos cos()cos sin()sin βαβααβα=+++ 1235416()()()13513565=-⨯-+⨯-=. 19.答案： （1）略； （2解答： （1）∵12AB B B ==，且1B B ⊥平面ABC ， ∴1B B AB ⊥，∴1AB =.同理，1AC ===过点1C 作1B B 的垂线段交1B B 于点G ，则12C G BC ==且11B G =，∴11B C =. 在11AB C ∆中，2221111AB B C AC +=， ∴111AB B C ⊥，①过点1B 作1A A 的垂线段交1A A 于点H .则12B H AB ==，12A H =，∴11A B =.在11A B A ∆中，2221111AA AB A B =+，∴111AB A B ⊥，②综合①②，∵11111A B B C B ⋂=，11A B ⊂平面111A B C ，11B C ⊂平面111A B C ，∴1AB ⊥平面111A B C .（2）过点B 作AB 的垂线段交AC 于点I ，以B 为原点，以AB 所在直线为x 轴，以BI 所在直线为y 轴，以1B B 所在直线为z 轴，建立空间直角坐标系B xyz -.则(0,0,0)B ，(2,0,0)A -，1(0,0,2)B，1(1C ，设平面1ABB 的一个法向量(,,)n a b c =，则1020200n AB a c n BB ⎧⋅==⎧⎪⇒⎨⎨=⋅=⎩⎪⎩，令1b =，则(0,1,0)n = ，又∵1AC =，1cos ,13n AC <>==.由图形可知，直线1AC 与平面1ABB 所成角为锐角，设1AC 与平面1ABB 夹角为α.∴sin 13α=. 20.答案： （1）2q =； （2）243152n n n b -+=-. 解答： （1）由题可得34528a a a ++=，4352(2)a a a +=+，联立两式可得48a =. 所以34518(1)28a a a q q ++=++=，可得2q =（另一根112<，舍去）. （2）由题可得2n ≥时，221()2[2(1)(1)]41n n n b b a n n n n n +-=+--+-=-， 当1n =时，211()213b b a -=+=也满足上式，所以1()41n n n b b a n +-=-，n N +∈, 而由（1）可得41822n n n a --=⋅=，所以1141412n n n n n n b b a +----==， 所以121321()()()n n n b b b b b b b b --=-+-++- 01223711452222n n --=++++ ， 错位相减得1243142n n n b b -+-=-， 所以243152n n n b -+=-. 21.答案： （1）略； （2）. 解答： （1）设00(,)P x y ，211(,)4y A y ，222(,)4y B y ， 则PA 中点为20011(,)282x y y y ++，由AP 中点在抛物线上，可得220101()4()228y y x y +=+，化简得2210100280y y y x y -+-=，显然21y y ≠， 且对2y 也有2220200280y y y x y -+-=， 所以12,y y 是二次方程22000280y y y x y -+-=的两不等实根，所以1202y y y +=，1202M P y y y y y +===，即PM 垂直于x 轴.（2）121()(||||)2M P M M S x x y y y y =--+-0121()||2M x x y y =--，由（1）可得1202y y y +=，212008y y x y =-，2220000012(2)4(8)8(4)0()y x y y x y y ∆=--=->≠，此时00(,)P x y 在半椭圆221(0)4y x x +=<上，∴2220000008(4)8[4(1)4]32(1)y x x x x x ∆=-=--=--，∵010x -≤<，∴0∆>，∴12||y y -===2222220000121212000042(8)6(44)()2||38888M P y x y x y y y y y y x x x x x x ---++--=-=-=-=-2003(1)x x =--，所以23012001()||2M S x x y y x x =--=--=，t =，所以3S =∈，即PAB ∆的面积的取值范围是4.22.答案：（1）略；（2）略.解答：（1）1()f x x '=-，不妨设12()()f x f x t ''==，即12,x x1t x -=的两根，2102xtx -+=的根， 所以1404t ∆=->，得1016t <<12t =1t =，12122111()()ln ln 2ln 22f x f x x x t t t t +=-=-=+， 令1()2ln 2g t t t =+，222141()022t g t t t t -'=-=<，∴()g t 在1(0,)16上单调递减. 所以1()()88ln 216g t g >=-，即12()()88ln 2f x f x +>-. （2）设()()()ln h x kx a f x kx x a =+-=+， 则当x 充分小时()0h x <，充分大时()0h x >，所以()h x 至少有一个零点，则2111())164h x k k x '=+=-+-， ①116k ≥，则()0h x '≥，()h x 递增，()h x 有唯一零点， ②1016k <<，则令211())0416h x k '=+-=，得()h x 有两个极值点1212,()x x x x <，14>，∴1016x <<. 可知()h x 在1(0,)x 递增，12(,)x x 递减，2(,)x +∞递增，∴1111111()ln )ln h x kx x a x x a x =+=+11ln x a =++，又1111()h x x '=+=， ∴1()h x 在(0,16)上单调递增， ∴1()(16)ln163ln16334ln 20h x h a <=-+≤-+-=， ∴()h x 有唯一零点， 综上可知，0k >时，y kx a =+与()y f x =有唯一公共点.。
2016年浙江3+2专升本高数真题--答案解析(知乎内部资料)
1 (1 x)2
，
1 (1 x)2
11
x
(1)n n0
xn
n0
(1)n nxn1
，所以
f
(x)
1 (1 x)2
(1)nnxn1 (1)n1nxn1 (1)n1nxn1 ，收敛域为： x
n0
n0
n1
1,1
四、综合题： 本大题共 3 小题， 每小题 10 分， 共 30 分。
lim ln(1 x)
x0
x
1 ，因为
f ' (0)
f ' (0) ，所以
f '(0) 1
所以
f
'(x)
1 (2x 1)2
,
x
0
1
1
x
,
x
0
18.
解:
f (x)
7x 6 x2 3x 2
7x 6 (x 1)(x 2)
8 x2
1 ，定义域为： x 1
x x 1且x 2
，
(1,2)
f (x)
0
f (x)
凸
拐点
凹
凸
凹区间： (0,1) ， (2,) ；凸区间： (,0) ， (1,2) ，拐点： (0,3)
(2,)
凹
19.
解:
该方程为欧拉方程：令
x
et
，则
dy dx
dy dt
dx dt
et
dy dt
，
d2y dx2
d (dy) dt dx
dx
dt
et dy dt
1
6. 1
解析: 方法一： lim
x
1
2015年专升本高数真题答案解析(浙江)
浙江省2015年选拔优秀高职高专毕业生进入本科学习统一考试高等数学参考答案选择题部分一、选择题:本大题共5小题,每小题4分,共20分。
题号12345答案BBBCD1.B 解析:根据题意，0)()(lim0=→x g x f x x ，0)(lim 0=→x f x x ，0)(lim 0=→x g x x ，所以)()()(lim0x g x g x f x x -→11)()(lim 0-=-=→x g x f x x ，故当0x x →时，)()(x g x f -是)(x g 的同阶无穷小，所以选项B 正确。
2.B 解析:根据题意，)(a f '存在，+-+=--+→→x a f x a f x x a f x a f x x )()(lim )()(lim00)(2)()(lim 0a f xx a f a f x '=--→，所以选项B 正确。
3.B 解析:由)()(x f x F ='可知，)(x F 是)(x f 的一个原函数，即：C x F dx x f +=⎰)()(，可见选项B 正确。
4.C 解析:直线1L 方程的方向向量为：)2,1,1(1-=→s ，直线2L 方程的方向向量为：→→→⨯=211n n s →→→→→→→→→+-=+---=-=k j i k j i kj i 2100120112110210101，所以1L 与2L 的夹角可由公式得到：21cos 2121=⋅⋅=→→→→s s s s θ，所以3πθ=，可见选项C 正确。
5.D 解析:A 选项：根据莱布尼茨判别法，可知级数是收敛的，但是通项加绝对值后得到正项级数∑∞=+1)1ln(1n n ，由于)1ln(11+<n n ，根据小散证大散，推得∑∞=+1)1ln(1n n 是发散的，因此级数)1ln(1)1(11+-∑∞=-n n n 为条件收敛。
B 选项：根据比值判别法，131331lim1<=+-∞→n n n n n ，可知级数是收敛的。
2018年普通高等学校招生全国统一考试英语试题(浙江卷,含解析)
高考衣食住用行衣：高考前这段时间，提醒同学们出门一定要看天气，否则淋雨感冒，就会影响考场发挥。
穿着自己习惯的衣服，可以让人在紧张时产生亲切感和安全感，并能有效防止不良情绪产生。
食：清淡的饮食最适合考试，切忌吃太油腻或者刺激性强的食物。
如果可能的话，每天吃一两个水果，补充维生素。
另外，进考场前一定要少喝水！住：考前休息很重要。
好好休息并不意味着很早就要上床睡觉，根据以往考生的经验，太早上床反而容易失眠。
考前按照你平时习惯的时间上床休息就可以了，但最迟不要超过十点半。
用：出门考试之前，一定要检查文具包。
看看答题的工具是否准备齐全，应该带的证件是否都在，不要到了考场才想起来有什么工具没带，或者什么工具用着不顺手。
行：看考场的时候同学们要多留心，要仔细了解自己住的地方到考场可以坐哪些路线的公交车？有几种方式可以到达？大概要花多长时间？去考场的路上有没有修路堵车的情况？考试当天，应该保证至少提前20分钟到达考场。
2018年普通高等学校招生全国统一考试英语试题（浙江卷）选择题部分第一部分听力做题时，先将答案标在试卷上。
录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题纸上。
第一节听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. What will James do tomorrow?A. Watch a TV program.B. Give a talk.C. Write a report.【答案】B2. What can we say about the woman?A. She’s generous.B. She’s curious.C. She’s helpful.【答案】C3. When does the train leave?A. At 6:30.B. At 8:30.C. At 10:30.【答案】C4. How does the woman go to work?A. By car.B. On foot.C. By bike.【答案】B5. What is the probable relationship between the speakers?A. Classmates.B. Teacher and student.C. Doctor and patient.【答案】A第二节听下面5段对话或独白。
2018年浙江专升本---英语考试真题卷
浙江省2018年选拔优秀高职高专毕业生进入本科学习统一考试英语请考生按规定用笔将所有试题的答案涂、写在答题纸上选择题部分注意事项：1.答题前，考生务必将自己的姓名、准考证号用黑色字迹的签字笔或钢笔写在答题卷规定的位置上。
2.每小题选出答案后，用2B铅笔把答题纸上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其他答案标号，不能答在试题卷上。
Part I Reading Comprehension(60marks,60minutes)Section A Passage Reading(50marks:2marks for each item)Format IDirections:There are4passages 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 Answer Sheet1.Passage OneQuestions1to5are based on the following passage:A U.N.report says water is in demand around the world as temperatures on Earth’s surface rise and demand grows along with populations.The report was released this week at the World Water Forum in Brasilia.The conference has been described as the world’s largest water-related event.Federal District Governor Rodrigo Rollemberg spoke at a panel discussion on Tuesday at the forum. He described water shortages as a worldwide problem.“Here in Brasilia,it is no different,”he added.The public water supply has less water because of low rainfall as well as fast and disorderly growth in Brasilia,which is part of the Federal District,Rollemberg said.In January2016,after three years of little rain,district officials began limiting how much water people could use.The governments of the Federal District and the nearby state of Goias also gave$166million to develop water infrastructure（基础设施）.Demand around the world is expected to increase by nearly one-third by2050.By then,5billionpeople could be left with poor access to water,the U.N.warned in its2018World Water Development Report.To avoid such a crisis,U.N.officials called for“nature-based solutions”that use or copy natural processes that should be used to increase water availability.They said solutions could include changing farming methods so fields keep more moisture and nutrients,collecting rainwater,and protecting wetlands.The officials also proposed reestablishing floodplains and said that plants could be grown on housetops.Such proposals will become more important as water industries grow.1.Who talked about water shortages in Brasilia at a panel discussion?A.A journalistB.A.U.N.officialC.A Federal District officialD.An official from the state of Goias.2.What is among the reasons for less public water supply Brasilia?A.Waste of rainwaterB.Insufficient rainfallC.Growing plants on the roofsD.Development in infrastructure3.What did the Federal District government do to deal with water shortages?A.They controlled populationB.They limited water consumptionC.They invested in artificial rainmakingD.They suggested"nature-based solutions”4.What is not a"nature-based solution"?A.Gathering rainwater B,Preserving wetlandsC.Sustaining water in soilD.Building houses on floodplain.5.What is the main idea of this passage?A.Brasilia is facing the problem of water shortagesB.The world has found a solution to water shortagesC.The world is facing the problem of water shortagesD.A report was released at the World Water Forum in Brasilia.Passage TwoQuestions6to10are based on the following passage:The Queen has only given one interview while a sovereign（君主）.Her true personality remains elusive to the public.However,one thing is clear:Queen Elizabeth is an introvert.Introverts prefer quiet environments and feel energized from spending time alone or with people they know well.They aren’t necessarily shy,but they do tend to be more reserved and guarded with strangers.Fellow introverts willappreciate how draining an average day for Her Majesty must be.Fortunately,the Queen has some tricks to make public engagements easier.Just like us commoners rely on friends to save us from awkward situations or boring conversations,she subtly signals to her staff when she wants an intervention（介入）.If she places her handbag on the table,it indicates that she wants the event to end in the next five minutes.For more urgent situations,putting her bag on the floor shows that she wants her lady-in-waiting to rescue her immediately.Most comfortable in the countryside,the Queen has a well-known passion for horses and dogs. There is a scene in the hit Netflix show The Crown which reveals a fascinating side of the monarch. While giving Jackie Kennedy a personal tour of Buckingham Palace,the two women find themselves bonding over their respective positions as introverted women who have found themselves in the limelight.Surrounded by the Queen’s beloved corgis,both women admit they are happiest around animals and that their extroverted sisters would have been much better suited to their public roles.6.The underlined word“draining”(Paragraph1)is the closest in meaning to________.A.frustratingB.exhaustingC.demandingD.aspiring7.To be rescued immediately in a public engagement,the Queen would__________.A.end the event within five minutesB.place her handbag on the tableC.wave to her lady-in-waitingD.put her bag on the floor8.In the last paragraph,the underlined expression“the two women find themselves bonding over their respective positions”means that the two ladies__________.A.admire each otherB.help each other in publicC.grow closer to each otherD.show respect for each other9.Queen Elizabeth and Jackie Kennedy share the following traits or facts EXCEPT that________.A.both have sisterB.both love animalsC.both enjoy being in publicD.both are introverted other10.The author’s attitude can be described as___________.A.neutralB.criticalC.pessimisticD.subjectivePassage ThreeQuestions11to15are based on the following passageBack when Disney products were to be watched,not experienced,Walt Disney had a vision:theme park that felt like stepping into a magical new place.Now,we can finally witness Walt’s first dream. Before construction could start,Walt needed funding.He and his friend Ryman put their heads together and mapped out their dream for the Disneyland.In just one frenzied1953weekends,their idea came to life on paper—you’ll notice both subtle differences and remarkable similarities to the modern Anaheim California park.Like today,visitors would have entered the park into a street USA-type area.The tunnels aren’t as wide as they were imagined more than60years ago,but park-goers are still greeted with a train passing overhead as they make their way to word the magic.(Even with a modern Disneyland map,it’s tough to find these secret Disney park spots you never knew existed.)Walt always hoped a castle as a focal point of the park,but its real-life copy changed from his initial dream.The first palace was a sprawling fortress,hiding a massive carrousel（旋转木马）beyond its walls.Now,Sleeping Beauty Castle has more intricate towers,and King Arthur Carrousel takes its spins in Fantasy land,behind the palace.Walt’s vision for the Mark Twain steamboat circling around Tom Sawyer Island and its Pirate’s Lair （窠臼）hasn’t changed much,though at that point it was called Frontier Country instead Frontier land. That wasn’t the only name change,though.World of Tomorrow turned into Tomorrow land—and eventually lost its rocket.Astronauts walked on the moon14years after the par was built,making the Rocket to the Moon seem out-of-date.Meanwhile,True-Life Adventure land lost its first word,while most of the areas took on totally different themes.11.What was Walt Disney’s first dream?.A.To build a theme parkB.To draw a map on paperC.To travel in a magical placeD.To design a series of products12.Before construction started,Walt Disney did the following things EXCEPT.A.getting fundingB.planning the parkC.drawing the park on paperD.daydreaming with a Friend13.Which of the following park spots has not changed much since Walt’s vision came to life on paper?.A.A Main Street areaB.World of TomorrowC.Sleeping Beauty CastleD.True-Life Adventureland14.How many name changes have been mentioned in this passage?.A.OneB.TwoC.ThreeD.Four15.What is the theme of this passage?.A.A tour in DisneylandB.Walt Disney’s life storyC.The future of DisneylandD.Walt Disney’s First dreamPassage fourQuestions16to20are based on the following passageYou’ve made it.You managed to navigate your way through the world’s largest airport you breezed through security and you successfully boarded the plane.Now you’re comfortable in your seat in the cabin,and there’s even a little bit of elbow room,as the flight isn’t fully booked for once.With the hassle behind you,you settle in with your neck pillow,pop some Kenny G on your iPod,and get ready to spend quality time sleeping on a plane.And you’re about to make a huge mistake that will put your health at risk,as reported by Travel+Leisure.It’s not because of the Kenny G.It’s the shuteye part.According to Medline Plus,falling asleep during landing or takeoff could cause serious damage to your ears.It all has to do with the rapid changes in air pressure in the cabin.If you’re awake,a natural response to alleviate pressure on your eardrums during takeoff and landing is to“pop”them,to maintain a pressure equilibrium.If you’re sleeping on a plane,you can’t actively work to relax those muscles and release the tension,so you can become susceptible to dizziness,ear infections,eardrum damage,hearing loss and nose bleeds.“A quick change in altitude affects the air pressure in the ear,”says Angel Chalmers,a British pharmacist,via Express.“This leads to a vacuum in the Eustachian tubes（咽鼓管）which makes the ears feel blocked and sound dull.”Keep those Eustachian tubes clear and keep those eyes open for at least another few minutes.Crack open that book you just bought in the terminal.After all,there are some major perks to buying your reading material at the airport.16.The underlined sentence“you’ve made it.”(Paragraph1)means that you have managed.A.to board the planeB.to get a bit of elbow roomC.to get ready to sleep after boardingD.to make yourself comfortable after boarding17.What would damage your health when the plane lakes off or lands?ing a neck pillow.B.Shutting your eyesC.Listening to musicD.Falling asleep.18.The underlined word“alleviate”(Paragraph2)is the closest in meaning to.A.increaseB.reduceC.maintainD.escape19.Having a vacuum in the Eustachian tubes during takeoff and landing could cause unpleasant symptoms to the following body parts EXCEPT.A.the throatB.the noseC.the earsD.the head20.The author suggests that you read a book during the plane taking off and landing.A.to amuse yourselfB.to stay awakeC.to keep your ears clearD.to make yourself comfortableFormat IIDirections:In the following passage,some sentences have been removed.For questions21to25choose the most suitable sentence from choices A to G lo it into each of he numbered blanks.There are two extra choices,which do not fit into any of the blanks.You should decide o the best Choice and blacken the corresponding letter on The Answer Sheet.(10points)Whether it’s a hotel stay,shopping or dining out,a vacation to Paris can be a pricey proposition. But there are plenty of ways to stretch your dollar in the City of Lights and have a high-end getaway Barkley Hickcox,a Paris specialist and an owner of Local Foreigner,a travel consultancy,has a few tips to help travelers make the most of their Parisian getaway.21..The ideal time to visit Paris is between November and April,when hold prices are their lowest. Some high-end properties offer even further discounts if you book a stay several months in advance.22..Families traveling to Paris should consider stay in high-end apartment instead of a hotel,Ms. Hickcox said,“An apartment is less expensive than booking multiple rooms at a five-star hotel,and since you have a kitchen,you can save money on food costs by eating in occasionally,”she said.23..Paris is known for fine cuisine,but rather than dining at one of the city’s renowned restaurants atdinnertime,go for lunch,when the tab will be much lower and the cuisine just as good.“you’ll find lots of great eateries where you can have dinner with wine for35to50euros a person,”she said.24..Ms.Hickcox’s favorite way to explore Paris is on foot.“You can fully appreciate the city’s beauty by walking,and it’s designed for walkers because there are walking paths and sidewalks everywhere.”she said.For longer distances,she suggested using the city’s bike share system,Velib.A week-long pass costs15euros,and there are stations everywhere.There is another choice if you are not so much fond of biking.25..Paris’subway system.It’s convenient,and you can buy daily and weekly passes.A.Dine out.B.Eat smart.C.Try the Metro.D.Stay in a hotel.E.Give up taxis and cars.F.Travel at the right time.G.Choose the right accommodations.Section B Bank Cloze(每小题1分,共10分)Directions:In this section,there is a passage with ten blanks.You are required to select one word for each blank from a list of'choices given in a word bank following the passage.Read the passage through carefully before making your choices.Please blacken the corresponding letter for each choice on The Answer Sheet.You may not use any of the words in the word bank more than once(10points)I knew this woman who was afraid to tell people what she wanted.She didn’t know26to say no.Instead,she got herself tangled in a web of obligations,anxiety,and white lies.She was27.28recently,I decided I’d had enough.As an experiment,I began29up for myself, even at the risk of alienating（疏远）everyone and having30entire life come crashing down around me.That didn’t happen.Here’s what I did:I stopped making petty excuses.Saying“no”is so much easier.If someone asks me to do somethings I have zero interest31,I’m polite but honest.The phrase“I’m sorry,I don’t think that’s really32me,”slips out my mouth faster than some lame excuse.My friends and family didn’t mind.33I stopped pleasing people,no one cared.A good friend asked me to go for coffee at5P.M.I was34to hit the gym.I said,“Sorry,I’ve got things I want to do tonight.”She said,“That’s fine.Maybe another time.”Learning how to say“no”has added several extra hours to my days,days35my weeks,and what feels like months to my years.Saying“no”has set me free.A.facing F.what K.meB.to G.standing L.whenC.her H.and M.onD.in I.my N.planningE.fir J.But O.howPart II Integrated Testing(30points,30minutes)Section A Cloze(每小题1分,共20分)Directions:There are20blanks in the following passage.For each blank there are four choices marked A,B,C and D.You should choose the ONE that best fits into the passage.Then blacken the corresponding letter on The Answer Sheet.(20points)Brazilian Zarela Mosquera moved to the United States as a teenager.The adjustment to a new place was36.Mosquera says she became a bratty（顽皮的）teenager,as a result.But it was not just the37that affected her behavior.Mosquera says there was another major stress in her life at that time.She was the only member of her38who spoke English.“Being in a country with my family that doesn’t speak Spanish and my parents don’t really speak 39,my parents were trying to give me all these responsibilities.”Along with Spanish and English, Mosquera also speaks Portuguese.But there was another universal language she learned to love as a child:art.Zarela Mosquera connected with drawing and painting while in school.40she mostly dismissed art as a path to a career.She says her dad41always say,“Think about the42.”Mosquera did not think he would support the study of43once she went to college.But to her44,it was her parents who suggested just that.They urged her to45to technical and liberal arts schools.“One of them was Rhode island School of Design,which was like my46choice.”RISD,as it is called,47Mosquera as well.She enrolled in industrial design.“It’s basically to design48and services.I could be doing something more technical or something more 49to problem solving.Whether it’s50out a better way to filter water or developing a type of specific shelter51refugees for example.”Mosquera says the course of study was52including me at working,woodworking and model making.She says in one class she just drew cubes for an entire month,which led her to a 53,“Wow!Do I really want to do this?”But,she says,she54the cube study.And,then she began55on more interesting projects.”Mosqurera is now a design strategist for Manhall Moya Design,an architecture and interior design company in Washington,D.C36.A.successful B.important C.necessary D.difficult37.A.age B.growth C.adjustment cation38.A.family B.peers C.friends D.class39.A.Spanish B.English C.Portuguese D.French40.A.So B.Moreover C.And D.But41.A.could B.should C.would D.might42.A.time B.past C.present D.futurenguage B.art C.technology D.design44.A.disappointment B.surprise C.annoyance D.dissatisfaction45.A.apply B.cater C.adapt D.move46.A.top B.moral C.natural D.popular47.A.failed B.rejected C.chose D.urged48.A.machines B.shelters C.filters D.products49.A.adjusted B.related C.affiliated D.exposed50.A.figuring B.wiping C.filling D.ruling51.A.with B.for C.on D.in52.A.easy B.pleasant C.tough D.smooth53.A.question B.problem C.door D.road54.A.undertook B.funded C.started D.survived55.A.putting B.funded C.working D.counting非选择题部分注意事项:用黑色字迹的签字笔或钢笔将答案写在答题纸无,不能答在试题卷Section B Short Answer Questions(每小题3分,共10分)Directions:In this part there is a short passage followed by five questions or incomplete statements. Read the passage carefully.Then answer the questions or complete the statements with no more than10 words.Please write your answers ou The Answer Sheet.(10points)Researchers in Japan and Australia say they have made progress in developing blood test that could one day help doctors identify who might get Alzheimer’s disease.The scientists said the test can recognize a protein known as amyloid（淀粉状朊）beta,which other studies have linked to Alzheimer’s. They said it was correct more than90percent of the time in a study involving over370people.The findings were published in the journal Nature.Alzheimer’s disease is the most common form of demenna（痴呆）.Experts believe dementia affects close to50million people worldwide.By the year2050,it is expected to affect more than131 million people.Those numbers come from Alzheimer’s Disease International,a non-profit group. Currently,doctors have two ways to identify a buildup of amyloid beta in the brain.One is brain scan or brain imaging;the other is a spinal tap（脊椎抽液）.But both tests are invasive,costly and may only show results when the disease has already started to progress.There is no treatment that can slow the progression of Alzheimer’s.Current drugs can only case some of the effects of the disease.Having a simple,low-cost blood test could make it easier for drug companies to find enough people who are at risk of developing Alzheimer's to test new medicines,said Katsuhiko Yanagisawa.He was one of the leaders of the study.He works at the Japanese National Center for Geriatrics and GerontologyAlzheimer’s disease is thought to start developing years before patients have any signs of memory loss.Experts say an important factor in finding an effective treatment will be the ability to recognize signs of the disease early.“You have got to walk before you run,”said Colin Masters,a co-leader of the study and a professor at the University of Melbourne in Australia.“You have to learn to diagnose the disease directly before you can hope to see the effect of therapeutic intervention.And that’s where thereal value in this test will come.”Masters added.56.This passage reports the development of a__________test to diagnose Alzheimer's disease57.One advantage of the present test is that it costs___________than the previous tests.58.All the three tests identify Alzheimer’s disease by detecting a protein named____________.59.Can doctors cure or slow down the progression of Alzheimer’s disease today?60.Alzheimer’s disease may have already started before patients have any signs of memory.Part III Translation(30points,30minutes)(每小题3分,共30分)Section A Chinese-English translationDirections:Complete the sentences by translating into English the Chinese expressions given in the brackets.Please write your translation on The Answer Sheet.(15points)61.（起源于汉朝）,shadow-play（皮影戏）became popular among ordinary people in Tang dynasty.62.Trade between West and East moved through Central Asia along the fame silk Road,bringing(发展与繁荣).63.The Grand Canal flows southwards（纵贯四省）of Hebei,Shandong,Jiangsu and Zhejiang.64.BYD is now famous for its"plugin electric hybrid cays,which，（名称所示），can be recharged by plugging them into electricity sockets.65.If you are to study for_______________________（学士学位）,you have to take standardized examinations on a couple of subjects.Section B English-Chinese TranslationDirections:Translate into Chinese the underline sentences in the following passage.Please write your translation on The Answer Sheet.(15points)When asked how far engineers had done towards creating artificial intelligence(AI),Stephen W. Hawking replied:66.Once humans develop artificial intelligence,it would take off on its own.It will redesign itself at an ever increasing rate.Humans,who are limited by slow biological evolution,couldn't compete with them.We would be replaced.”11In my view,the late Cambridge professor is wrong because there are strong grounds for believing that computers will never copy all human cognitive abilities.67.AI has historically failed to copy human mentality,and it will continue to fail.Three fundamental problems explain why.First,computers lack true understanding.A US philosopher John Searle proposes how a computer program can appear to understand Chinese stories by responding to questions,but fail to truly understand anything of the interaction.Second,computers lack consciousness.Some researchers hold68. if a robot experiences a conscious sensation as it interacts with the world,consciousness will exist in everything everywhere：in the cup of tea I am drinking,in the seat that I am sitting on.But does everything in this world have souls or minds?If we reject this idea,we must reject machine consciousnessLastly,computers lack mathematical insight.Can the human mind be completely realized by mere computationsmy role as an Al expert on the International Committee for Robot Arms Control.I am particularly concerned by the potential development of robotic weapons systems.69.These systems can engage themselves in military action without human instruction.This is because current AI is not similar to human intelligence.When fighting against each other,poorly designed autonomous systems have the potential to make the situations worse rapidly.Such systems can exhibit true artificial stupidity.It is possible to agree that70.AI may pose an existential threat to humanity,but it will never become more intelligent than us.66.___________________________________________________________________________________________________________________________________________________________ 67.___________________________________________________________________________________________________________________________________________________________ 68.___________________________________________________________________________________________________________________________________________________________ 69.___________________________________________________________________________________________________________________________________________________________ 70.___________________________________________________________________________________________________________________________________________________________12Part IV Writing(30points,30minutes)(每小题30分,共30分)Directions:For this part,you are allowed30minutes to write a composition on the topic Population Transformation in China.You should write about120words following the Chinese outline given below, taking the information available in the following table us evidence.Please write your composition on The Answer Sheet.(30points)Population Transformation in ChinaMajor indexes Year of transition TrendPopulation below151975decrease Population of labor between2015decrease15and64Population above651975increase(1)简述表格内容,概括中国人口变化。
浙江省教育厅办公室关于调整我省普通专升本、“2+2”选拔考试管理职责的通知
浙江省教育厅办公室关于调整我省普通专升本、
“2+2”选拔考试管理职责的通知
文章属性
•【制定机关】浙江省教育厅办公室
•【公布日期】2009.11.17
•【字号】浙教办高教〔2009〕154号
•【施行日期】2009.11.17
•【效力等级】地方规范性文件
•【时效性】现行有效
•【主题分类】教育
正文
浙江省教育厅办公室关于调整我省普通专升本、“2+2”选拔
考试管理职责的通知
浙教办高教〔2009〕154号
各有关高校：
为充分发挥专门考试机构的作用，促进考试管理工作的规范化、科学化，经研究，决定自2010年起，我省选拔优秀高职高专毕业生进入本科学习（即普通专升本考试）和选拔优秀二年级本科生转入部分高校重点专业学习（即“2+2”选拔考试）的所有考试管理工作由浙江省教育考试院统一管理组织。
调整后，省教育厅高教处不再负责上述两项考试相关的工作。
请各高校与省考试院加强工作衔接，互相配合继续认真负责地做好普通专升本考试和“2+2”选拔考试的各项工作。
二○○九年十一月十七日。
(招聘面试)浙江省年选拔优秀应届高职高专毕业生进入本科学习试点工作实施
（招聘面试）浙江省年选拔优秀应届高职高专毕业生进入本科学习试点工作实施关于做好2010年“专升本”考试报名工作的通知各学院：浙江省2010年选拔优秀应届高职高专毕业生进入本科学习的工作（以下简称“专升本”）即将开始。
根据《浙江省教育考试院关于做好2010年选拔优秀高职高专毕业生进入本科学习工作的通知》文件精神，结合我校实际，现将有关做好2010年“专升本”考试报名工作的具体事项通知如下：1、“专升本”的选拔院校、专业、计划、考试科目、收费标准、选拔对象及报考条件、考试时间及加分原则、选拔院校联系办法等具体要求和情况，请参见附件《浙江省2010年选拔优秀应届高职高专毕业生进入本科学习试点工作实施细则》且执行。
2、报名时间：2010年3月20日至24日网上报名；3月26日至28日现场确认。
3、报名程序：⑴各学院向所有毕业班学生宣传、介绍2010年“专升本”的有关政策和要求。
⑵学生于3月20日至24日期间登陆浙江教育考试网（/gb/gxjx/index.html 附件：浙江省2010年选拔优秀应届高职高专毕业生进入本科学习试点工作实施细则我省2010年继续开展面向全省高校选拔优秀应届高职高专毕业生进入本科学习试点工作（以下简称“普通高校专升本”）。
根据教育部关于高等学校招生考试的有关规定，以及“公开、公平、公正”的招生考试原则，特制定本实施细则。
壹、选拔计划1.各招生院校分专业招生计划如下表：2.普通高校专升本选拔招生计划列入各校本年度总体招生计划，所需经费列入学校预算，省属高校按学生人数增加财政拨款。
如遇合格生源不足，可将剩余计划转入高考统壹招生。
二、报名1.报考条件：浙江省各级各类全日制普通高校同专业或相近专业的应届专科毕业生，符合下列条件者均可报考：（1）坚持四项基本原则、遵纪守法；（2）所学专业和选拔专业相同或相近；（3）已通过CET－3级或高职高专英语应用能力A级（艺术、体育类专业除外）及之上考试；专科专业为英语专业的考生无须通过CET－3级考试；（4）身体健康，符合专业报考要求；（5）于校期间未受记过（含）之上处分，且没有考试作弊记录者。
2018年专升本高数真题答案解析(浙江)
浙江省2018年选拔优秀高职高专毕业生进入本科学习统一考试高等数学参考答案选择题部分一、选择题:本大题共5小题,每小题4分,共20分。
题号12345答案CCABC1.C 解析:)0(0lim )(lim 0f x x f x x ===--→→，1sin lim )(lim 0==++→→xxx f x x ，所以0=x 是)(x f 的跳跃间断点，选项C 正确。
2.C 解析:02sin lim 2sin cos cos lim cos sin lim 0020==+-=-→→→xx x x x x x x x x x x x ，所以选项C 正确。
3.A 解析:因为函数)(x f 二阶可导，且0)(lim=-→x x x f x x ，所以0)()(lim 00==→x f x f x x ，故0)()()(lim )(lim000000='=--=-→→x f x x x f x f x x x f x x x x ，又因为0)(0<''x f ，所以由极值的第二充分条件可知，函数)(x f 在0x x =处取得极大值，因此选项A 正确。
4.B 解析:；⎰-=xxx f x f dx x f dx d 2)()2(2)(，故选项B 错误；由零点定理可知选项C 正确；由定积分性质中的估值定理可知选项D 正确。
5.C 解析:选项A ：交错级数，通项极限为：011lim =+∞→n n ，且n n u u <+1，所以由莱布尼茨审敛法，该级数收敛，但是加上绝对值后，级数∑∞=+111n n 发散，所以选项A为条件收敛。
选项B ：交错级数，通项极限为：0)1ln(1lim=+∞→n n ，且n n u u <+1所以由莱布尼茨审敛法，该级数收敛，但是加上绝对值后，因为nn 1)1ln(1>+，由小散证大散，级数∑∞=+1)1ln(1n n 发散，所以选项B 为条件收敛。
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
浙江省2018年选拔优秀高职高专毕业生进入本科学习统一考试
高等数学
请考生按规定用笔将所有试题的答案涂、写在答题纸上。
选择题部分
注意事项:
1.答题前,考生务必将自己的姓名、 准考证号用黑色字迹的签字笔或钢笔填写在答题纸规定的位置上。
2.每小题选出答案后，用2B 铅笔把答题纸上对应题目的答案标号涂黑，如需改动，用橡皮擦干净后，再选涂其它答案标号。
不能答在试题卷上。
一、选择题（每个小题给出的选项中，只有一项符合要求：本题共有5个小题，每小题4分，共20分）
一、选择题：本大题共5小题，每小题4分，共20分。
1、设⎪⎩⎪
⎨⎧≤>=00,,sin )(x x x
x x x f ，则)(x f 在)1,1(-内（ ）
A 、有可去间断点
B 、连续点
C 、有跳跃间断点
D 、有第二间断点
2、当0→x 时，x x x cos sin -是2
x 的（ ）无穷小 A 、低阶
B 、等阶
C 、同阶
D 、高阶
3、设)(x f 二阶可导，在0x x =处0)(0<''x f ，0)
(lim 0
=-→x x x f x x ，则)(x f 在0x x =处（ ） A 、取得极小值
B 、取得极大值
C 、不是极值
D 、()
)(0,0x f x 是拐点
4、已知)(x f 在[]b a ,上连续，则下列说法不正确的是（ ） A 、已知⎰
=b
a
dx x f 0)(2，则在[]b a ,上，0)(=x f
B 、
⎰-=x
x x f x f dt t f dx
d 2)()2()(，其中[]b a x x ,2,∈ C 、0)()(<⋅b f a f ，则()b a ,内有ξ使得0)(=ξf
D 、)(x f y =在[]b a ,上有最大值M 和最小值m ，则⎰
-≤≤-b
a
a b M dx x f a b m )()()(
5、下列级数绝对收敛的是（ ）
A 、∑∞
=-+-111)1(n n n B 、∑∞=-+-11)1ln()1(n n n C 、∑∞=+139
cos n n n D 、∑∞
=11
n n
非选择题部分
注意事项:
1.用黑色字迹的签字笔或钢笔将答案写在答题纸上，不能答在试题卷上。
2.在答题纸上作图，可先使用2B 铅笔，确定后必须使用黑色字迹的签字笔或钢笔描黑。
二．填空题: 本大题共10小题，每小题 4分，共40分。
6、=+→x
x x a 10
)sin 1(lim
7、3sin )
23()3(lim 0=--→x
x f f x ，则=')3(f
8、若常数b a ,使得5)(cos sin lim 20=--→b x a
e x
x x ，则=b
9、设⎩⎨
⎧-=+=t
t y t x arctan )1ln(，则
==1
t dx dy
10、)(x f y =是012
2
=--y x 所确定的隐函数，则=22dx
y
d
11、求2
1x
x
y +=
的单增区间是 12、求已知
⎰
+=C e dx x f x 2
)(，则=⋅∑==∞→)(1lim 1
0n k
f n
n k n
13、
=⎰
+∞
dx x x e
2
)(ln 1
14、由2
x y =：2,1==x y 围成的图形面积为
15、常系数齐次线性微分方程02=+'-''y y y 的通解为
三、计算题：本题共有8小题，其中16-19 小题每小题7分，20-23 小题每小题8分，共
60分。
计算题必须写出必要的计算过程， 只写答案的不给分。
16、求)
sin 1ln(lim 0x e e x
x x +--→
17、设x
x x y )sin 1()(+=，求)(x y 在π=x 处的微分. 18、求⎰
-π
50
2cos 1dx x
19、求dx x ⎰
arctan 20、dx x x
x x
x ⎰
++-1
1
-4
1cos 45）（
21、已知⎩⎨⎧>+≤+=0
),1ln(0
,2)(x ax x b x x f 在0=x 处可导，求b a ,
22、求过点)1,2,1(-A 且平行于0732=-+-z y x 又与直线⎪⎩
⎪
⎨⎧=+=-=t z t y t x 231相交的直线方程。
23、讨论1323
1)(23
++-=x x x x f 极值和拐点.
四、综合题（本大题共3大题，每小题10分，共30分）
24、利用
n n n x x ∑∞
=-=+0
)1(11
， （1）将函数)1ln(x +展开成x 的幂级数 （2）将函数)3ln(x +展开成2-x 的幂级数
25、)(x f 在[)∞+，1上导函数连续，0)(>x f ，已知曲线)(x f 与直线)1(,1>==t t x x 及x
轴所围成的曲边梯形绕x 轴所围成的旋转体体积是该曲边梯形的t π倍，求)(x f
26、)(x f 在[]b a ,连续且二阶可导，过点）（)(,a f a 和）（)(,b f b 的直线与曲线y ＝f （x ）交于
，证明：
（1）存在)()(21ξξf f '=' 在),(b a 存在0)(=''ξf。