2019年上海交大附中第一学期摸底考-含解析
精品解析：【全国百强校】上海市交大附中2019届高三上9月开学摸底考试数学试题(解析版)
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一、填空题.1.方程组的增广矩阵是______．【答案】【解析】试题分析：根据增广矩阵的定义可知为.考点：本小题主要考查增广矩阵的定义和应用.点评：增广矩阵就是在系数矩阵的右边添上一列，这一列是线性方程组的等号右边的值。
2.若直线的参数方程为，则直线的倾斜角是_______．【答案】【解析】【分析】根据题意，将直线的参数方程变形为普通方程为y+2（x﹣3），求出其斜率，结合直线的斜率与倾斜角的关系可得tanθ，结合θ的范围，分析可得答案．【详解】根据题意，直线l的参数方程为，则其普通方程为y+2（x﹣3），其斜率k，则有tanθ，且0°≤θ＜180°，则θ＝120°；故答案为：120°．【点睛】本题考查直线的参数方程，关键是将直线的参数方程变形为普通方程,熟记斜率与倾斜角的关系是关键，是基础题3._______．【答案】【解析】【分析】利用二项式定理系数的性质，求解分子，然后利用数列极限的运算法则求解即可．【详解】由二项式定理系数的性质可得，．故答案为：．【点睛】本题考查二项式定理系数的性质，数列的极限的运算法则的应用，考查计算能力，是基础题4.已知数列的前项的和，则当为正偶数时，______．【答案】【解析】【分析】由已知求得，当n≥2且n为正偶数时，a n＝S n﹣S n﹣1＝2n﹣[2（n﹣1）﹣1]＝2n﹣2n+3，验证a2＝3适合，由此可得当n为正偶数时的a n．【详解】由，得＝1，；当n≥2且n为正偶数时，a n＝S n﹣S n﹣1＝2n﹣[2（n﹣1）﹣1]＝2n﹣2n+3．验证＝3适合上式，∴当n为正偶数时，．故答案为：2n﹣2n+3．【点睛】本题考查数列通项公式，考查利用数列的前n项和求数列的通项公式，是中档题．5.函数是奇函数，那么______．【答案】【解析】【分析】求f（﹣x）＝，再根据f（x）为奇函数，可得出＝-整理化简即可求出a的值．【详解】由题f（﹣x）＝函数是奇函数，∴- f（﹣x）＝，即-解得2,∴故答案为-1【点睛】本题考查奇函数的定义，多项式的运算，多项式相等的充要条件，准确利用定义计算是关键，是基础题6.若函数无最值，则的取值范围是______．【答案】a或a【解析】【分析】由题意函数f（x）＝lg（x2﹣ax+2）无最值，即f（x）的值域为R，那么（0，+∞）是y＝x2﹣ax+2的值域的子集，即△≥0，可得a的取值范围．【详解】由题意，函数f（x）＝lg（x2﹣ax+2）无最值，即f（x）的值域为R，那么（0，+∞）是y＝x2﹣ax+2的值域的子集，即△≥0，∴a2﹣8≥0，则a或a；故答案为：a或a．【点睛】本题考查对数型复合函数的值域，考查对数函数的性质，明确真数无最值是突破点，准确利用二次函数的△≥0解决问题是关键，是中档题7.△的内角，，的对边分别为，，，已知△的面积为，，则______．【答案】【解析】【分析】直接利用三角形的面积公式和正弦定理求出sinBsinC的值，进一步利用三角函数关系式的变换即可求出A 的值．【详解】已知△ABC的面积为，则：S△ABC acsinB，整理得：3csinBsinA＝2a，由正弦定理得：3sinCsinBsinA＝2sinA，由于sinA≠0，故：sinBsinC，由于：6cosBcosC＝1，所以：cosBcosC，所以：cosBcosC﹣sinBsinC，所以：cos（B+C），故：cosA，A所以：A．故答案为：．【点睛】本题考查的知识要点：三角函数关系式的恒等变换，正弦定理和三角形面积公式的应用，主要考查学生的运算能力和转化能力，属于基础题型．8.设，是虚数单位，已知集合，，若，则的取值范围是________．【答案】【解析】【分析】根据复数的代数表示法及其几何意义可知集合A表示的点的轨迹是以（0，1）为圆心，半径为2的圆及内部；集合B表示圆的圆心移动到了（1，1+b）；两圆面有交点即可求解b的取值范围．【详解】由题意，集合A表示的点的轨迹是以（0，1）为圆心，半径为2的圆及内部；集合B表示点的轨迹为（1，1+b），半径为2的圆及内部∵A∩B≠∅，说明，两圆面有交点；∴．可得：，故答案：，【点睛】本题考查复数几何意义，圆与圆的位置关系，体现了数学转化思想方法，明确A.B集合的意义是关键，是中档题9.从双曲线（，）的左焦点引圆的切线，切点为，延长交双曲线右支于点，若是线段的中点，为坐标原点，则的值是____．【答案】【解析】试题分析：如图所示，设双曲线的右焦点为，连接，，，则，在中，，，所以，又是线段的中点，为中点，所以，所以即，故应填入.考点：1.双曲线的定义；2.直线与圆相切；3.数形结合的应用.10.胡涂涂同学用一颗均匀的骰子来定义递推数列，首先，他令，当时，他投一次骰子，若所得点数大于，即令，否则，令，则的概率为______（结果用最简分数表示）．【答案】【解析】【分析】胡涂涂同学掷了3轮，要使得，分两种情况讨论，再利用古典概型求的概率.【详解】胡涂涂同学掷了3轮，要使得，有两种情况，① 一轮点数为1，二轮点数为1、2、3、4、5、6，三轮点数为1；② 一轮点数为2、3、4、5、6，二轮点数为1、2，三轮点数为1；∴由古典概型得所求的概率为.故答案为：【点睛】本题主要考查排列组合的应用，考查古典概型，意在考查学生对这些知识的理解掌握水平和分析推理计算能力.11.关于的方程恰有3个实数根，，，则__________．【答案】2【解析】【分析】令f（x）＝x2+arcsin（cosx）+a，判断f（x）的奇偶性，由题意可得f（0）＝0，求得a，再由反三角函数的定义和性质，化简函数，求得f（x）＝0的解，即可得到所求和．【详解】令f（x）＝x2+arcsin（cosx）+a，可得f（﹣x）＝（﹣x）2+arcsin（cos（﹣x））+a＝f（x），则f（x）为偶函数，∵f（x）＝0有三个实数根，∴f（0）＝0，即0a＝0，故有a，关于x的方程即x2+arcsin（cosx）0，可设＝0，且2+arcsin（cos）0，2+arcsin（cos）0，由y＝x2和y arcsin（cosx），当x＞0，且0＜x＜π时，y arcsin（cosx）arcsin（sin（x））（x））＝x，则﹣π＜x＜0时，y arcsin（cosx）＝﹣x，由y＝x2和y arcsin（cosx）的图象可得：它们有三个交点，且为（0，0），（﹣1，1），（1，1），则2+2+2＝0+1+1＝2．故答案为：2．【点睛】本题考查函数与方程，函数的奇偶性，反三角函数的定义和性质，函数方程的转化思想，以及化简整理的运算能力，属于中档题．12.由无理数论引发的数字危机一直延续到19世纪，直到1872年，德国数学家戴德金从连续性的要求出发，用有理数的“分割”来定义无理数（史称戴德金分割），并把实数理论建立在严格的科学基础上，才结束了无理数被认为“无理”的时代，也结束了持续2000多年的数学史上的第一次大危机，所谓戴德金分割，是指将有理数集划分为两个非空的子集与，且满足，，中的每一个元素都小于中的每一个元素，则称为戴德金分割.试判断，对于任一戴德金分割，下列选项中，可能成立的是____．①没有最大元素，有一个最小元素；②没有最大元素，也没有最小元素；③有一个最大元素，有一个最小元素；④有一个最大元素，没有最小元素.【答案】①②④【解析】由题意依次举例对四个命题判断，从而确定答案．【详解】若M＝{x∈Q|x＜0}，N＝{x∈Q|x≥0}，则M没有最大元素，N有一个最小元素0，故①可能成立；若M＝{x∈Q|x}，N＝{x∈Q|x}；则M没有最大元素，N也没有最小元素，故②可能成立；若M＝{x∈Q|x≤0}，N＝{x∈Q|x＞0}；M有一个最大元素，N没有最小元素，故④可能成立；M有一个最大元素，N有一个最小元素不可能，因为这样就有一个有理数不存在M和N两个集合中，与M和N的并集是所有的有理数矛盾，故③不可能成立．故答案为：①②④【点睛】本题考查新定义的理解和运用，考查列举法和推理能力，对每个选项举出反例说明是关键，属于基础题．二、选择题。
上海交通大学附属中学2018-2019学年高三第一学期摸底考试
上海交通大学附属中学2018-2019学年高三第一学期摸底考试上海交通大学附属中学2018-2019学年高三第一学期摸底考试英语试卷（考试时间120分钟；满分140分）第I卷Ⅰ. VocabularyDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.(A)1-5 BD A BC ABC D 6-10 B AB CB AC CTeenagers seem more likely to give in to peer influence than adults, but that may not be because teens are less 1 of making rational decisions themselves, studies on peer pressure suggest.Research finds people are strikingly susceptible to influences teenagers, but to what degree varies widely. In a growing body of work, scientists suggest that teens are more 2 to peer pressure than adults because they get greater pleasure from behavior they experience as rewarding. They tend to find being liked by other people very pleasing.Peer influence during adolescence is normal. During that time, people experience an increase in novelty-seeking, 3 by interest in exploring a new environment. This peer influence tends to 4 around age 15 and then decline. Teens get better at setting boundaries with peers by age 18, according to Laurence Steinberg, a psychology professor at Temple University.In years pas t, people thought teens didn’t have fully 5 frontal lobes (额叶), the part of the brain critical for decision-making and other more complex cognitive tasks. But an increasing amount of research seems to show that teens are able to make decisions as well as adults when they are not overwhelmed 6 with emotions.Peer pressure is often seen as negative, and indeed it can 7 teens into unhealthy behavior like smoking or speeding. But it can also lead to 8 in more useful social behavior. If peers value doing well in school or excelling at sports, for instance, it might encourage kids to study or train harder. And both peer pressure and learning to 9 it are important developmental steps to self-reliance, experts say.Facing the influence of friends represents an important developmental step for teens on their way to becoming independent-thinking adults, scientists say.In order for kids to develop the ability to stand up to peer pressure, parents have to let their children stand up to them, too, according to Dr. Steinberg. “If you’re the kind of parent that raises your children with the ‘do it because I said so’ 10 , you’re raising a child who’s going to be more susceptible to others saying, ‘Do this,’” he says.(B)1-5 CD C A D AC 6-10 ABC BC AB B BDStudents Honor 9/11 Through VolunteeringIn the days after Sept. 11, 2001, thousands poured into Ground Zero to lend their hands in one of the largest recoveryefforts(恢复经济) in American history. Now, 12 years later, colleges are finding ways to channel（疏通）the same 1 into service projects in their own communities on September 11th."9/11 is such a(n) __2__ touchstone（试金石）for our country, I think people want to find ways to do something, and students as well," says Kevin Kruger, president of the student affairs group. "The idea of giving something back to the __3__ ties in well to（密切配合）the emotional significance of that."Though no corner of the country was untouched by the terrorist attacks, they especially rocked （晃动）New York University on 9/11. Less than two miles from Ground Zero, students__4__ the plane-on-tower impact from their dorm rooms. The university coordinated（协调）shelters and counseling（提供建议）in the days afterward.Because of this, NYU public affairs director Philip Lentz says the volunteer work the students do this week has a "special relevance（关联）." Students today __5__ at a rescue mission, wrote cards for soldiers and veterans（老兵）and made donations for the families of victims and first responders （现场目击者）on 9/11."NYU feels it has a special __6__ to offer this service opportunity to students that are here so they can give back to the community that was so devastated（毁灭）by the attacks," Lentz says.Similar deeds have been taking place in George Washington University in Washington, D.C. "For the past five years at GW, freshmen have boarded buses immediately after their official welcome __7__ in early September to head for the nation's financial capital and volunteer in __8__ that aid the environment, education, veterans and community organizations," says AmyCohen, theuniversity's director for civic engagement and public service."We hope that students will learn that community __9__ is part of how we build strong communities and a vibrant __10__ society," Cohen wrote in an e-mail to USA TODAY. "We ask students to reflect on the tragedy of 9/11 and to use this day as a way to show civic engagement and community building."Ⅰ. Reading comprehension.Section ADirections:For each blank in the following passage there are four words or phrases marked A, B, C, D. Fill in each blank with the word or phrase that best fits the context.(A)Harvard LibraryIf we compare professors and students to the host of a university, then the library of a university can be compared to the hallway. The quality of a university, 1 , is in direct proportion to that of its library. At Harvard，the library is an essential part of everybody's life. Both the quantity and the 2 of the library make study a pleasant process.Harvard Library is not only the most ancient library in the United States, but the largest university library with the largest scale. In 1638 John Harvard 3 his whole library to the then Harvard College. After 300 years of development, the library now holds 10 million books and 4 more than 100 branch libraries. In addition to the libraries owned by each school, there are some branch libraries that are 5 in some aspects. While most of the branch libraries are on Harvard campus, some are as far as in Washington, D.C., or even in Florence of Italy. Yenching Library is famous for its 6 of East Asian literature. Lamont Library is the firstlibrary in the world that is 7 for undergraduates. Widener Library is the largest library in Harvard, only second to Library of Congress.What 8 to be mentioned is the system or rather theservice of the libraries. Usually the libraries are open from 9 a.m. to 5p.m.. The main libraries are open until 10 p.m.. The libraries forundergraduates will even be open all night during the 9period. The libraries also provide with students the service of 10 reading materials for all courses. At the beginning of a semester, each teacher will give a list of books to the librarians. The librarians are 11 to find out these books and put them at the places where students can easily find them.There is no limitation for the number of books that students can borrow. As the space for thelibrary is limited, many books are 12 in suburban library. Despite this, students can go to fetch the book at the 13 library within 24 hours after they submit request for that book. Even if there is only one book to be fetched from the suburban library, the libraries on campus will send someone to do the job. This kind of 14 which put readers in the first place is rare even in Ivy League. Therefore, study at Harvard will be a(n) 15 experience.A）1-5 BCADB 6-10 ACDAB 11-15 DCABD1. A. as a result B. to some extent C. on the contrary D. at all times2. A. influence B. discipline C. quality D. prospect3. A. donated B. assigned C. adapted D. distributed4. A. contains B. composes C. involves D. includes5. A. informative B. different C. secure D. peculiar6. A. collections B. documents C. phenomena D. exhibitions7. A. unusually B. formally C. specially D. especially8. A. remains B. happens C. appears D. deserves9. A. examination B. experiment C. vacation D. graduation10. A. confirming B. preparing C. selecting D. designing11. A. desperate B. willing C. reluctant D. responsible12. A. exhibited B. reserved C. stored D. classified13. A. appointed B. accepted C. expected D. restricted14. A. performance B. service C. activity D. response15. A. fortunate B. creative C. positive D. enjoyable(B)Instead of cruising in on a hoverboard, I rode my bike to the office today. The bicycle was invented in the 19th century. Instead of taking a pill for breakfast, I had a bacon roll, cooked using gas. Science fiction has 1 to us.Making predictions is tricky, especially about the future, as physicist Niels Bohr joked. In science fiction, you can't escape that 2 though. Since its birth in the 19th century, writers have 3 imagined the things to come: devices that humankind will invent to make life easier. But in so many instances, those promises have not come to pass. The biggest 4 are in travel--jet packs, hoverboards and flying cars are yet to fill the skies. Air travel has become significantly cheaper and wide-reaching, but only using distinctly 20th-century technology: commercial aero planes are much the same as they were 50 years ago.5 is what science fiction frequently delivers, but its arrival in the real world has been unpredictable. Domestic robots with a degree of intelligence are yet to6 , though robotic vacuum cleaners are commercially available--even if they are fairly hopeless. Video calls have nowarrived--sort of--but conferencing on Skype is still dissatisfying. In mobiles, video call technology is now available, so when your dad rings to update you on his vegetable patch, he'll be able to7 your look of boredom.The truth is that we quickly 8 the astonishment of invention: our wonderment is soon replaced with the feeling of nothing new. We should ty to stay in that period of 9 . It is astonishing that the contents of every book ever written can be stored in a small box. Or that you can carry 10,000 albums on an object kept in your pocket. Or that almost all the information in the world can be accessed almost anywhere at any time. All these 10 are dependent on the emergence of the microchip and its place in computers. Yet sci-fi didn’t 11 the dominance of the computer in running our lives.But the real area where 12 far outstrips predictions is medicine. Sure, fiction would describe humans as ‘disea se-free’ but without going into detail. “Disease-fee” humans are still absent, but the progress made in 13 life is breathtaking. With relative ease, we can sequence anyone's genome (基因组), giving a read-out of our entire genetic code. This means we can find out the underlying genetic cause of thousands of diseases in minutes.Photosensitive implants now exist that can replace damaged cells in the retina (视网膜) and can thus 14 sight to the blind. While the inventions of science fiction can show great ideas we’d like to happen, nothing 15 the inventiveness of people in the real world.B）1-5 BBDAC 6-10 ACCBD 11-15 ADACD1. A. tuned B. lied C. objected D. talked2. A. opportunity B. challenge C. Imagination D. conflict3. A. hesitantly B. critically C. temporarily D. tirelessly4. A. disappointments B. advancements C. enjoyments D. experiments5. A. Modernization B. Exploration C. Automation D. Transportation6. A. materialize B. identify C. honour D. liberate7. A. imagine B. feel C. see D. ignore8. A. arouse B. discover C. forget D. evaluate9. A. frustration B. amazement C. boredom D. limitation10. A. modes B. worries C. potentials D. actions11. A. predict B. overlook C. motivate D. prevent12. A. quality B. obstacle C. passion D. reality13. A. maintaining B. creating C. researching D. encountering14. A. show B. lend C. restore D. label15. A. guarantees B. overestimates C. releases D. OutperformsSection BDirections:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)In his book The Tipping Point Canadian author Malcolm Gladwell explains how a trend can take many forms. It can be a general change in social behaviour, an idea or a fashion. However, why do some trends catch on and others not? What makes one particular brand of training shoe suddenly become the must-have product? How do people find out about trends and what makes people want to buy into them? Is it simply a question of keeping up with other people?In his new work, Gladwell explores the moment when something becomes common and how products, ideas messages and forms of behaviour spread. He looks at the reasons why trends are similar in the way they develop to outbreaks of disease, or medical epidemics.Epidemics, like trends, start in a very small way, maybe from a single person with a virus, then spread very quickly until they take over the population and appear to be everywhere. Eventually, they will slowdown gradually or die out suddenly. Gladwell shows how these changes happen not gradually but at one dramatic moment.Gladwell identifies three types of people who are influential in the development of these kinds of social epidemics.Connectors are people in a community who have wide social circles. They know a lot of people and like to introduce people to catch other. The people they know also tend to come from a variety of social, cultural professional and economic circles.Mavens are people with a lot of knowledge or experts in a particular field. They wish to pass on their knowledge to others. Mavens collect and gather information so are the first to pick up on new trends.Salesmen are people with charisma and powerful negotiation skills. They have a soft influence over people rather than actual power. This means they are influential because people want to imitate them.Overall, Gladwell's book is a thought-provoking read for anyone interested in the origins oftrends. What's more, he writes in a clear style so even the most difficult ideas are easy to understand.71.According to Gladwell, which of the following is asimilarity between trends and epidemics?A. Both of them start from nowhereB. Both of them die out in a short timeC. Both of them become popular overnightD. Both of them change he way people think72. What can be concluded from the passage about The Tipping Point?A. It is the writers first book to touch on social phenomenaB. It is intended to introduce the trends that once took overC. It deals with the ideas that most people identify withD. It explores How a trend originates and spreads73. The passage is most likely to beA. an adver sementB. a reviewC. a news reportD. a feature story74. Salesmen work in the development of trends by means ofA people intention to follow themB the way they gather informationD. their influence on the trendsC. their professional knowledge（B）(*Please purchase a ticket before boarding the coach75. On December 25th, 2014, the first coach from, Heathrow Terminal I to Reading departs at____.A.7:15B.7:00C.6:50D.6:3576. If you are to reach Terminal 2 of the Heathrow Airport before 10: 00 a.m., you need to get to Reading Station not later than____.A $. 30am B.8:45am C.9:00a,m. D.9:15a.m77. The information leaflet is produced by____.A. ReadingB. IntercityC. Railair LinkD. Heathrow Airport(C)As students are discussing their favorite colleges, there’s one characterist ic they can’t control their race. That’s one reason voters, courts and politicians in six states have outlawed racial preferences in college admissions, while other colleges, fearful-of lawsuits, play down their affirmative action efforts these days. But make no mistake race still matters. How much depends on the school and the state.In: Texas, public universities have managed to reduce the effect of racial-preference bans by automatically admitting the top 10% of the graduating class of every high school, including those schools where most students are minorities. But Rice University in Houston, private and highly selective, has had to reinvent its admissions strategies to maintain the schools minority enrollment. Each February, 80 to 90 black, Hispanic(西班牙裔) and Native American kids visit Rice on an expenses-paid trip. Rice urges headmasters from high schools with large minority populations to recommend qualified students. And in the fall, Rice sends two recruiters on the road to find minority applicants; each recruiter visits about 80 mainly black or Hispanichigh schools. Two weeks ago, Rice recruiter Tamara Siler dropped in on Westlake High in Atlanta, where 99% of the 1296 students are black. Siler went hearing literature and advice, and though only two kids showed up, she said: "Tm pleased I got two."Rice has also turned to some almost comical end-runs around the spirit of the law. The university used to award a yearly scholarship to a Mexican-American student; now it goes to a student who speaks Spanish really well. Admissions officers no longer know an applicant’s race. But a new essay question asks about each student "background" and "cultural traditions". When Rice officials read applications, they look for "diverse life experiences and what they awkwardly call "overcome students", who have triumphed over hardship.Last spring, admissions readers came across a student whose SAT score was lower than 1,200 and who did not rank in the top 10% of her class. Numerically speaking, she was far behind most accepted applicants: But her essay and recommendations indicated a strong interest in civil rights and personal experience with racial discrimination. She was admitted. All the newspapers say affirmative action is done, “says an experienced adviser at a large New York City high school. But nothing has changed. I have a(minority)kid at Yale with an SAT score in the high 900s.78. What does the word outlaw"(in Para. 1)most probably mean?A. supportB. consider D. hateC. ban79. What can we infer from the passage about affirmative action?A. It guarantees students, of different races to be admittedequally.B It discriminates against minority students in college admissions.C. It gives preference to minority students in college admissions.D. It is popular with American colleges but not with the American public80. Why does Rice University send two recruiters to find minority applicants?A. Rice has a large minority populationB: Rice wants to maintain its minority enrollmentC Minority students do not favor Rice very muchD. Minority students have better school performance81. Which of the following might be the best title of the passage?A: Here Comes Equality at LastB. Yes. Your Race Still MattersC. Well Done. Affirmative ActionD. Minorities Are Still a Minority in Universities(D)Direction: Read the following passage. Fill in each blank with a proper sentence given in the box.Sleep in a BoxHaving a newborn can be discouraging and troublesome. What do you need to buy? How will you get the baby to sleep? And how will you pay for everything? Could the answers to these worries lie in a “baby box"?The baby box has taken the world by storm, but what is it? Well, it originated in Finland in thel930s as a kind of basic items for parents-to-be. The box, provided by the government, contains supplies, such as bibs, nappies, and teething toys. It also comes with a small mattress, which is placed in the bottom of the box to create the baby’s first small bed. Now, the idea of putting a child to sleep inbox may shock some. 82_______ the box has been a huge success and is said to be one of the main reasons why the death rate of infants in Finland is so low.A few years ago, stories of the Finnish baby box went relating to viruses. Other countries around the world have since caught onto the idea and adapted it to suit local needs. For example, in South Africa, the box is made of plastic and can be used as a bath rather than a bed. A(83* The version tested in India includes other appropriate supplies, such as a mosquito het to protect babies from malaria(疟疾).In Canada, additions to the baby box include a bed-side assistance booklet “to help fathers connect with their babies, Written in the style of a car-repair manual, the booklet offers first-time dads helpful advice on matters such as how to burp(使打嗝)their child. 84________ I wanted to make that moment available to all parents,” said Morris, a father of a two-month baby boy.85_________ Many believe governments should focus on providing parents with adequate maternity and paternity Leaves(父母产假) and improving health care andeducation．Good things cone in small packages, though, and for such a simple idea the baby box really does do a lot of things!第II卷Ⅰ.GrammarDirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)E-cigarettes, widely prompted as an alternative (1)_____to smoking, are actually attractingyoung people who might not otherwise (2)_____(smoke) tobacco products, a new US study suggested Monday.E-cigarettes (3)_____(think) by some to be responsible for a decline in American youth cigarette smoking, but researchers from the University of California, San Francisco (UCSF) indicated the reality is the opposite.The USCF researchers concluded that many kids who went on (4)_____(smoke) regular cigarettes may not have used nicotine(尼古丁) at all if e-cigarettes did not exist. "We didn't find any evidence that e-cigarettes are causing youth smoking to decline," said lead author Lauren Dutra of the UCSF.(5)_____ some of the kids using e-cigarettes were also smoking cigarettes, we found that kids who were at low risk of starting nicotine with cigarettes were using e-cigarettes," Dutra said. "Recent declines in youth smoking are likely (6)_____ tobacco control efforts, not to e-cigarettes."The findings, published in U.S. journal Pediatrics, built on a growing body of evidence that adolescents who start with e-cigarettes are (7)_____(likely) to subsequently smoke traditional cigarettes.They found that cigarette smoking among U.S. adolescents declined during that decade, but did not decline faster (8)_____ the advent of e-cigarettes in the U.S. between 2007 and 2009."E-cigarettes are encouraging -- not discouraging -- youth to smoke and to consume nicotine, and (9)_____(expend) the tobacco market," said senior author Stanton Glantz, UCSF professor of medicine and director of the UCSF Center for Tobacco Control Research and Education.In August 2016, the U.S. Food and Drug Administration restricted e-cigarette purchases to adults ages 18 and older. The FDA will also require a warning label on e-cigarettes, starting August 2018, regarding the addictive nature of nicotine. However, the FDA's (10)_____(rule) does not regulate advertising or flavors, and e-cigarettes continue to be sold in flavors that appeal to youth, the UCSF researchers said.(B)There seems never (11)______(be) a civilization without toys, but when and how they developed is unknown. They probably came about just to give children something to do.In the ancient world, (12)______is today, most boys played with some kinds of toys and most girls with another. In societies (13)______ social roles are rigidly determined, boys pattern their play after the activities of their fathers and girls are (14)______ the tasks of their mothers. This is true because boys and girls are being prepared, even in play, (15)______(step) into the roles and responsibilities of the adult world.What is remarkable about the history of toys is not so much (16)______ they changed over the centuries but how much they(17)______(remain) the same.The changes have been mostly in terms of craftsmanship, mechanics, and technology. It is the universality of toys with regard to their development in all parts of the world and (18)______ persistence to the present that is amazing. In Egypt, America, China, Japan and among the Arctic people, generally the same kinds of toys (19)______(appear). Variations depended on local customs and ways of life (20)______ toys imitate their surroundings. Nearly every civilization had dolls, little weapons, toy soldiers, tiny animals and vehicles.(C)In a shocking turn of events, the Academy Award for Best Picture was mistakenly awarded to "La La Land," (21)______ cast(剧组演员) and crew took the stage and began giving speeches－until a moment later the producers realized actually the award (22)_______(me an) for "Moonlight”.Presenter Warren Beatty explained afterwards that he was handed the wrong envelope, which contained the winner for best actress Emma Stone (23)______(star) in " La la land” After staring at the card for several moments, in (24)______ appeared to be an attempt to build suspense, his co-presenter Faye Dunaway announced that “La La Land" had won best picture.Realizing the mistake, representatives of Price Waterhouse Coopers raced onstage to stop the acceptance speeches from the "La La Lan d” team, and called the "Moonlight" cast and crew to the stage. Barry Jenkins’ "Moonlight" had actually won best picture in a historic Oscar upset."La La land" came in with 14 nominations, a record that tied (25)_____with “Titanic” and “All About Eve”. Ba rry Jenkins tender, coming-of-age drama, made for just $1.5 million, is an unusually small Oscar winner. "Even in my wildest dreams thiscannot be true, " said the astonished Jenkins once he reached the stage.Host Jimmy Kimmel had come forward(26)______(inform) the cast that "Moonlight" had indeed won, showing the inside of the envelope(27)_______ proof. And Producer Jordan Horwitz then graciously passed his statue to the "Moonlight" producers.Barry Jenkins, the writer-director of "Moonlight" and Tare Alvin McCraney, whose play it was based on, won for(28)_______(adapt) screenplay. “For all you people out there (29)_______feel like there isn’t a mirror out there for you, the academy has your back, the ACLU has your back and for the next four years we will not leave you alone, we will not forget you, " said Jenkins.Backstage, Oscar winner Emma Stone said, "I think everyone’s in a state of confusion still. Later the actress, who pledged her deep love of "Moonlight" added, "Is that(30)______(crazy)Oscar moment of all time? Cool!Ⅰ.Translation1．你是否具备了成为一名演员的必要素质？(take)2．不可否认的是均衡的饮食是保持健康的关键之一。
上海交通大学附属中学2018-2019学年度第一学期高一物理摸底试卷
上海交通大学附属中学2018-2019学年度第一学期高一物理摸底试卷（满分100分，60分钟完成。
答案请写在答题纸上）一、单项选择题（40分）（本大题共12小题。
第1题到系题导小题】分，第9题到第121.2014年在微罗斯举力的第22届冬季节奥运会比赛项目中，冰高运时员需要运用多种旋转技术推出冰壶，冰球运动员需要用力得冰球打人对方大门，如道速滑送动员在弯通处要控制好身体的倾斜程度：自由式滑雪空中技巧运动员在高空中需要做出各种高难度翻转。
在这些项目中可以看做质点的是（）A.冰壶比赛中运动的冰壶B.冰球比赛中运对的冰球C.短道速滑中的运动员D.高空翻腾技巧运动中的运动员2.磁带录放机可高速、低速播放正常录制的声音，当它在低速播放时，最有可能听不到的声音是正常录制是（）A.须率较低的声音B.频率较高的声音C.振动较弱的声音D.振动较强的声音3.一小球的s-t图如图所示，从图像可知小球在做（）A.匀速直线运动B.速率不变的来回运动C.小球运动方向是不变的D.小球运动的方向和速率是变化的4.在图所示的内燃机工作的一个循环中，其四个冲程的顺序应当是（）A.乙丁甲两B.乙甲丁丙C.丙甲丁乙D.丙丁甲乙5.用如图所示的实验装置，可以研究( )A.电磁铁的磁性强弱与电流大小的关系D.电磁感应现象及感应电流产生的条件C.通电导体在磁场中受到磁场力的作用D.通电导体所受磁场力方向与电流方向的关系6.把正在熔化的冰和正在凝固的水放入同一保温瓶中（）。
A.冰继续熔化B.水继续凝固C.冰的温度上升，水的温度下降D.瓶内的温度一定不会变化7.A、B.C三种物质的质量与体积的关系如图所示，由图可知（）.A.p A>p B>P C且P C>p水B.p A>p B>P C且p A>p水C.p A<p B<P C且P C>p水D.p A<p B<P C且p A>p水8.如图所示，同一金属块先后段入a.b，c三个杯子中，a.c杯内盛有酒精，易杯内感盛有水金属块受到的浮力分别用Fa，Fb，Fc表示，则（）A.Fa>Fb>FcB.Fb>Fc>FaC.Fc>Fb>FaD.Fb>Fa>Fc9、有甲，乙，丙三杯水，甲杯中水的质量是丙杯中水的质量的3倍，乙杯中水的质量是丙杯中水的质量的2倍，甲，乙，丙三杯水的温度分别是T1，T2，T3，且T1>T2>T3，弱把三杯水混合，不计热量损失，则混合后水的温度是（）A.T1+T2+T3B. T1+2T2+3T33 3C. T1+2T2+3T3D. 3T1+2T2+T36 6三、实验题（10分）（本大题共1小题）1.小明同学阅读课外资料时，发现一“220V 100W”白炽灯泡的电流I和电压U关系的图象如图（a）所示。
2018-2019学年上海市交大附中高二上学期9月摸底考试数学试题(解析版)
2018-2019学年上海市交大附中高二上学期9月摸底考试数学试题一、单选题1．若平面向量()1,a x =和()23,b x x =+-互相平行，其中x ∈R ，则a b -=（ ）A. B.2或 C.2-或0D.2或10【答案】B【解析】先根据向量平行得方程解得x ，再根据向量模的坐标表示得结果. 【详解】因为向量()1,a x =和()23,b x x =+-互相平行，所以()1(23)02x x x x x ⋅-=+⇒==-或，因为(22,2),a b x x -=--则(2,0)2a b -=-=或(2,-4)a b -== B.【点睛】本题考查向量平行、向量模的坐标表示，考查基本求解能力.2．已知ABC ∆两内角A 、B 的对边边长分别为a ，b ，则“A B =”是“cos cos a A b B =”（ ）． A.充分非必要条件 B.必要非充分条件 C.充要条件 D.既非充分也非必要条件【答案】A【解析】当A B =时，易得cos cos a A b B =，反过来，cos cos a A b B =时，根据正弦定理和两角和的正弦公式变形为sin 2sin 2A B =，再判断是否能推出A B =. 【详解】cos cos sin cos sin cos sin 2sin 2a A b B A A B B A B =⇒=⇒=，则A B =或2A B π+=，故“A B =”是“cos cos a A b B =”充分非必要条件.故选：A. 【点睛】本题考查判断命题的充分非必要条件，意在考查充分必要条件的判断方法，以及三角函数恒等变形，属于基础题型.3．函数()321f x ax a =-+，若存在()01,1x ∈-，使()00f x =，那么（ ）A.115a -<< B.1a <-C.1a <-或15a >D.15a <【答案】C【解析】根据零点存在定理列不等式，解得结果，即得选项. 【详解】由题意得()11(1)05f f a -⇒或1a <-，选C 【点睛】本题考查零点存在定理应用，考查基本求解能力.4．定义域为[],a b 的函数()y f x =图像的两个端点为,A B ，向量()1ON OA OB λλ=+-，(),M x y 是()f x 图像上任意一点，其中()1x a b λλ=+-，[]0,1λ∈。
2018-2019学年交大附中高三英语摸底考 上海市 英语试卷及答案
上海交通大学附属中学2018-2019学年第一学期高三英语摸底考试卷命题：廖智敏审核：朱雪艳II.Grammar and VocabularySection ADirections: After reading the passages below, fill in the blanks to make the passages coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)Space is a dangerous place, not only because of meteors but also because of rays from the sun and other stars. The atmosphere again acts (1)__________our protective blanket on earth. Light gets through, and this is essential for plants (2) __________ (make) the food which we eat. Heat, too, makes our environment endurable. Various kinds of rays come through the air from outer space, but enormous quantities of radiation from the sun (3) __________ (screen) off. As soon as men leave the atmosphere they are exposed to this radiation but their spacesuits or the walls of their spacecraft, (4)__________they are inside, do prevent a lot of radiation damage.Radiation is (5) __________ (great) known danger to explorers in space. The unit of radiation is called "rem". Scientists have reason to think that a man can put up with far more radiation than 0.1 rem without (6) __________ (damage); the figure of 60 rems has been agreed on. The trouble is (7) __________it is extremely difficult to be sure about radiation damage - a person may feel perfectly well, but the cells of his or her sex organs may be damaged, and this will no be discovered (8)the birth of deformed children or even grandchildren. Missions of the Apollo flights have had to cross belts of high amount of rems. So far, no dangerous amounts of radiation have been reported, but the Apollo missions have been quite short. We simply do not know yet (9) __________men are going to get on when they spend weeks and months outside the protection of the atmosphere, working in a space laboratory. Drugs might help to decrease the damage (10) __________ (do) by radiation, but no really effective ones have been found so far.(B)Before I went to the British Koi Keepers’ Annual Show, I didn’t understand(1)______ people could take fish so seriously. However, the more I learned about koi, the more interested I became. As one expert told me, “Collecting koi is far more addictive than you might think. They’re as beautiful as butterflies and very calmi ng to watch.” Freddie Mercury, the lead singer of Queen, would have agreed----the pool in his specially built Japanese garden was home to 89 koi, (2) __________ cost up to £10,000 each.At the show I met koi euthusiast Jean Kelly. “Koi are getting more and more expensive,” she told me. “One recently sold for £250,000.” I was shocked-----that’s almost as much as I paid for my house. “Well, that was a record,” (3) __________ (admit) Jean. “The normal price is nowhere near as high as that.”Nevertheless, serious collectors can pay up to ￡15,000 for a fully (4)_______ (grow) koi, which is nearly as expensive as a new luxurious car, and the bigger they are, the more they cost. The cheapest I (5)________ find was ￡75 each, but they were only about twice as big as my goldfish. Jean wasn’t impressed by one of the koi on sale either. “Actually, these koi aren’t any nicer than (6)_______,” She commented. “(7)_______ they are slightly bigger than the ones I’ve got, I paid considerable less than this.”I wasn’t quite as enthusiastic as Jean, but I did consider (8)________ (buy) one. Then I remember that all but 5 of Freddie Mercury’s koi died when someone accidentally turned off the electricity supply to their pool. Jean assured me that with all the new equipment available the survival rate was getting better and better, and that looking (9)______ koi was no harder than taking care of any other pet. However, in the end of I decided to stick with my goldfish. They’re not nearly as beautiful as koi—but they’re a great deal c heaper (10)______(replace)!Section BDirections: Complete the following passage by using the words in the box. Each word can only beThe Beadles sang that money can't buy you love. But what about happiness? Research (41)______ shows that the more money people have, the more likely they are to report being satisfied with their lifes.And that makes sense: money buys you things that make life easier and more satisfying; the easier your life, the happier you tend to be. That relationship isn’t entirely linear, since there's a(n) (42)______to how much money can please you; the happiness benefit of an increasing income is especially powerful among people who don’t have much money to start with, and (43) ______as wealth increases. But studies also reveal that as (44) ______income levels have risen over time in the U.S. and European nations. For example---residents of those countries have not reported being any happier than people were 30 or 40 year ago. It's a paradox that while income and happiness may be (45) ______within a population at any given moment, overall economic growth does not appear to corresponded to a boost in national satisfaction over time.To understand why, researchers at the University of Warwick and Cardiff University decided to break down how individual people evaluate their income. What does wealth mean to people? Previous work has suggested that people tend to value their own wealth more-and are happier-when it compares (46) ______to everyone else's. The so-called reference-income hypothesis holds that it is not simply how much money you make that (47) ______to satisfaction, but how much more money make than, say, the national average. The higher your salary than the norm, the happier you tend to be.But the reference-income hypothesis is rather (48) ______. The researchers wondered whether there was a more concrete way to capture how people valued their income. They (49) ______that people tended to make specific comparisons of personal wealth, not only with the average income of the larger population, but with the individual incomes of their neighbors, colleagues from college. And the higher their rank, the greater their sense of happiness and self-worth would (50) ______ be. "For example, people might care about whether they are the second most highly paid person or the eighth most highly paid person, in their comparison set.” write the author, Chris Boyce, a psychologist at the University of Warwick.III.Reading ComprehensionSection ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that best fits the context.The beauty, majesty and timelessness of a primary rainforest are incredible. It is impossibleto 51._______ on film, to describe in words, or to explain to those who have never had the awe-inspiring experience of standing in the heart of a primary rainforest.Rainforests have 52.______ over millions of years to turn into the incredible complex environment they are today. Rainforests represent a store of living and 53._______ renewable natural resources that for eons, by virtue of their richness in both animal and plant species, have 54. _______ a wealth of resources for the survival and well-being of mankind. These resources have included basic food supplies, clothing, shelter, fuel, species, industrial raw material, and medicine for all those who have lived in the majesty of the forest. 55._______ the inner dynamics of a tropical rainforest is an intricate and fragile system. Everything is so 56. _______ that upsetting one part can lead to unknown damage or even destruction of the whole. Sadly, it has taken only a century of human intervention to destroy what nature designed to 57._______ forever.The scale of human 58._______ on ecosystems everywhere has increased in the last few decades. Since 1980 the global economy has tripled in size and the world population has increased by 30 percent. Consumption of everything on the planet has risen -- at a cost to our 59._______. in 2001, the World Resources Institute estimated that the demand for rice, wheat and corn is expected to grow by 40% by 2020, increasing irrigation water demands by 50% or more. The further reported that the demand for wood could double by the year 2050, 60._______ it is still the tropical forests of the world that supply the bulk of the world’s demand for wood.In 1950, about 15 percent of the Earth’s land surface was covered by rainforest. Today, more than half has already gone up in 61._______. in fewer than fifty years, more than half of the worlds tropical rainforests have fallen 62._______ to fire and the chainsaw, and the rate of destruction is still accelerating. Unbelievably, more that 200,000 acres of rainforest are burned every day. That is more that 150 acres lost every minute of every day, and 78 million acres lost every year! More than 20 percent of the Amazon rainforest is already gone, and much more is vanishing at a rate of 20,000 square miles a year. If nothing is done to curb this 63._______, the entire Amazon could well be gone within fifty years.Massive 64._______ brings with it may ugly consequences--air and water pollution, soil erosion, malaria epidemics, the release of carbon dioxide into the atmosphere and the 65._______ of biodiversity through extinction of plants and animals. Fewer rainforests mean less rain, less oxygen for us to breathe, and an increased threat from global warming.51.A.present B.capture C.claim D.prove52.A. changed B.evolved C.expanded D.existed53.A. energizing B.healing C.isolating D.breathing54.A. contributed B.stored C.reduced D.affected55.A. However B.Furthermore C.Therefore D.Otherwise56.A. active B.sensitive C.interdependent D.delicate57.A. restore B.support C.revive st58.A. pressure B.power C.concern D.strength59.A.existence B.ecosystem C.planet D.survival60.A.unfortunately B.consequently C.naturally D.similarly61.A.store B.food C.smoke D.wealth62.A. subject B.down C.apart D.victim63.A.trend B.practice C.decrease D.attitude64.A.destruction B.industrialization C.modernization D.deforestation65.A. appearance B.explosion C.loss D.increase Section BDirection：Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)The definition of the standard kilogram is almost fundamentally wrong. Getting the definition right is a challenge that has tried the patience and intelligence of scientists for decades.Scientists use just seven basic units to define all the other quantities we use — quantities such as speed or electric power. All of those basic units except the kilogram are themselves defined according to natural properties that are beyond human control.For example, the standard second (time) is defined as a specific number of vibration of a type of radiation sent out by atoms of a special metal. The standard metre (length), in turn, is defined as the length of the path light travels during a specific fraction of a second.Not so the kilogram. This orphan of the basic unit family is simply the mass of a small platinum-iridium alloy cylinder（铂—铱合金筒）locked away in a container maintained by the International Bureau of Weights & Measures in Sevres, France.Embarrassingly, the last time the copies were brought to Sevres for a checkup in the 1980s, officials found that some copies had gained about 20 parts per billion in weight compared to the master cylinder since the previous checkup in the 1940s. This implies that the master cylinder itself may be an inconstant standard.No one kno ws what causes the weight changes. But the uncertainty can’t be tolerated when precision(精密度) in research and some manufacturing now demands accuracy to a few parts per billion.Several efforts in several different countries are under way to redefine the kilogram in terms of basic physical quantities such as counting the actual number of atoms of a specific substance in a kilogram or the electromagnetic force that balances a kilogram mass against gravity.A project of the latter type at the laboratories in Gaithersburg, Md., hopes eventually to define mass by means of electrical units. So far, none of these redefinition projects has borne fruit. They require the very accuracy of measurement and control of experimental conditions. The slightest pollution, tiny vibration, or other influence -- even changes in weather -- can ruin results. You’ve got to hand it to scientists who are willing to devote many years to such painstaking but extremely important research.66.Which of the following best paraphrases the s entence “Not so kilogram” in paragragh 4? A．The kilogram is not as accurate as the standard second.B．The kilogram is not universally accepted in the world.C．The kilogram is not defined in terms of natural properties.D．The kilogram is not well defined as time and length.67.Which of the following can NOT be concluded from the passage?A．Experiments are being carried out to redefine the kilogram.B．The uncertainty in the standard kilogram can seriously affect some research.C．The redefining of the standard kilogram is quite complicatedD．Scientists will achieve success in redefining the kilogram in the near future68.According to the passage, to define the weight of mass in terms of electrical units ________.A．is one of the best methods to redefine the kilogram.B．has been accepted as the only possible redefinition projectC．is not as simple as what people can understandD．has been considered by some scientists as a better approach69.We can know form the passage that the redefinition of the kilogram is ________.A．more important in keeping market honesty.B．worth years of scientists’ painstaking research.C．the urgent requirement of business and manufacturing.D．bring about important and fruitful results.（B）Stewart Island Ferry ServicesWhile most visitors spend at least one night on Stewart Island, it is also readily accessible by ferry as a day excursion from Invercargill and Bluff.Experience Foveaux Strait in comfort and style on board our express catamarans. During the one-hour crossing between Bluff and Stewart Island keep a lookout for wildlife, especially seabirds. Watching mollymawks (albatross) soaring behind the ferry is a fantastic sight.Interesting landmarks commonly seen include Dog Island Lighthouse, Ruapuke Island, Titi Islands and Mt Anglem - Stewart Island’s highest point.Free tea and coffee on boardInterpretation handouts are available (English only).Wheelchair access availablePersonal baggage is carried free on the ferries - max. two bags per person (one stowed and one small carry-on). Additional baggage is by prior arrangement.“20% Multi-Purchase REWARD” on Return Ferry ServicesBuy 2 or more different excursions and SA VE 20% off all lower priced!Kids Go FREE on selected departures during NZ School Holidays!Kids Go FREE for travel 20 April - 5 May 2013.70.If leaving a car at Bluff, a traveler had better_________.A．refer to the handouts first B．use wheelchair accessC．make a reservation D．park it 30 minutes before departure time71.John, who went to Stewart Island on Dec. 28th, got to the ferry dock at 7:55am. When did he most probably leave Bluff?A．At 8:00a.m..B．At 9:30a.m..C．At 11:00a.m..D．At 3:00p.m..72.Which of the following is false about the ferry services?A．Tea and coffee are free for passengers.B．Children go free for travel for about 15 days.C．Travelers are sure to see some seabirds during the crossing.D．Passengers have to pay extra cost for extra pieces of luggage.（C）Like every dog, every disease now seems to have its day. World Tuberculosis (infections disease in which growths appear on the lungs) Day is on Saturday March 24th.Tuberculosis was once terribly fashionable. Dying of "consumption" seems to have been a favorite activity of garret-dwelling 19th-century artists, h has, however, been neglected of late. Researchers in the field never tire of pointing out that TB kills a lot of people. According to figures released earlier this week by the World Health Organization, 1.6 million people died of the disease in 2005, compared with about 3m for AIDS and l m for malaria. But it receives only a fraction of the research budget devoted to AIDS. America’s National Institutes of Health, for example, spends 20 times as much on AIDS as on TB. Nevertheless, everyone seems to getting in on the TB-day act this year.The Global Fund an international organization responsible fur fighting all three diseases but best known for its work on AIDS, has used the occasion to trumpet its tuberculosis projects. The fund claims that its anti-TB activities since it opened for business in 2002 have saved the lives of over 1m people. The World Health Organization has issued a report that contains some good news. Although the number of TB cases is still rising, the rate of illness seems to have stabilized; the caseload, in other words, is growing only because the population itself is going up.Even drug companies are involved. In the run-up to the day itself, Eli Lilly announced a $ 50m boost to its MDRTB Global Partnership. MDR stands for multi-drug resistance, and it is one of the reasons why TB is back in the limelight. Careless treatment has caused drug-resistant strains to evolve all over the world. The course of drugs needed to clear the disease completely takes six mouths, anti persuading people lo stay that course once their symptoms have gone is hard. Unfortunately, those infected with MDR have to be treated with less effective, more poisonous and more costly drugs. Naturally, these provoke still more. non-compliance and thus still more evolution.The other reason TB is back is its relationship to AIDS. The (global Fund’s joint responsibility for the diseases is no coincidence. AIDS does not kill directly. Rather, HIV, the virus that causes it, weakens the body’s immune system and exposes the sufferer to secondary infections. Of these, TB is one of the most serious. It kills 200 000 AIDS patients a year. However, some anti-TB drugs interfere with the effect of some anti-HIV drugs. Conversely, in about 20% of cases where a patient has both diseases, anti-HIV drugs make the tuberculosis worse. The upshot is that 125 years after human beings worked out what caused TB, it is still a serious threat.73.The first sentence “Like every dog, every disease now seems to have its day.”means_______.A.every dog enjoys good luck or success sooner or laterB.human beings can deal with problems caused by diseaseC.Tuberculosis becomes a serious infection diseaseD.people attach importance to Tuberculosis recently74.By referring to AIDS in Paragraph 2,the author intends to show________.A.the US government is reluctant to spend millions of dollars on TuberculosisB.the death rate of AIDS is higher than that of TuberculosisC.the officials didn’t pay much attention to the research of Tuberculosis in the pastpared with AIDS,Tuberculosis can be cured effectively75.Which of the following is best defines the word “upshot”(Line 6, Para 5)?A.OutcomeB.UpholdC.AchievementD.Project76.Which of the following proverbs is closest in meaning to the message the passage tries to convey?A.Forgive and forgetB.Forgotten,but not goneC.When the wound is healed,the pain is forgottenD.Every dog is brave at his own doorSection CDirections: Read the following passage and choose the most suitable statement from A-F for eachAdolescents refer to boys and girls at high-school level--more specifically the second,third and forth years of high schools.In dealing with students at this level,we must bear in mind that to some degree they are at the difficult stage,generally called adolescence.Students at this level are likely to be confused mentally. They usually find it hard to concentrate on what they intend to do and often have romantic dreams._________77_______ They lack frankness and are usually very easily affected by their own emotions but hate to admit it. They are driven either by greater ambition,probably beyond their capability,or by extreme laziness caused by the fear of not succeeding or achieving objectives._________78_________.They are willing to work,but they hate to work without obtaining the result they think they should obtain.Regarding school issues,although they seldom say so,they really want to be consulted and given an opportunity to direct their own affairs,but they need a good amount of guidance.They seldom admit that they need this guidance and they frequently rebel against it. But if it its intelligently offered they accept it with enthusiasm.As to personal beliefs,most of adolescents are trying to form political ideals and they have a tendency to be sometimes extremely idealistic,and at other times conventional,blindly accepting what their fathers and grandfathers believed in._______79________.On the one hand they are too modest and on the other hand unreasonably boastful.They tend to be influenced more by a strong character than by great intelligence.__________80_________.Having a better understanding of the characteristics and needs of young people at this age is a task that falls both on educators and other people involved.It may also help the young go through this difficult and critical stage of life in a more constructive manner.IV.Summary WritingDirections: Read the following passage. Summarize the main idea and the main point(s) of the passage in no more than 60 words. Use your own words as far as possible.When I was quite young, my father had one of the first telephones in our neighborhood. I remember well the polished wooden case fastened to the wall on the lower stair landing. But my first personal experience with this genie-the-receiver came one day while my mother was visiting a neighbor. Amusing myself at the tool bench in the basement, I hurt my finger with a hammer. The pain was terrible, but there didn’t seem to be much use crying, because there was no one home to offer sympathy, I walked around the house, and finally arrived at the stairway. The telephone! Quickly I ran for the footstool and dragged it to the landing. Climbing up, I unhooked the receiver and held it to my ear, “Information Please,” I said the mouthpiece just above my head.A click or two and a small clear voice spoke into my ear, “Information.”“I hurt my finger…” I cried into the telephone.. Th e tears came readily enough now that I had an audience.“Isn’t your mother home?” came the question.“Nobody’s home but me.” I sobbed.“Are you bleeding?”“No,” I replied. “I hit my finger with the hammer and it hurts.”“Can you open your icebox?” she asked. I said I could. “Then chip off a little piece of ice and hold it to your finger. That will stop the hurt，Be careful when you use the icepick(冰锥).” she said，“And don’t cry. You’ll be all right.”After that I called Information Please for everything. I asked her for help with my geography,and she told me where Philadelphia was, and the Orinoco, the romantic river that I was going to explore when I grow up. She helped me with my arithmetic, and she told that my pet chipmunk —I had caught him in the park just the day before—would eat fruit and nuts.________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ ________ 60V.Translation:81.正是那位作家对他说的一番话激起了他投身于写作。
上海交通大学附属中学2018-2019学年第一学期高三英语摸底考试卷
上海交通⼤学附属中学2018-2019学年第⼀学期⾼三英语摸底考试卷上海交通⼤学附属中学2018-2019学年第⼀学期⾼三英语摸底考试卷II.Grammar and VocabularySection ADirections:After reading the passages below,fill in the blanks to make the passages coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form ofthe given word;for the other blanks,use one word that best fits each blank.(A)Space is a dangerous place,not only because of meteors but also because of rays from the sun and other stars.The atmosphere again acts(1)__________our protective blanket on earth.Light gets through,and this is essential forplants(2)__________(make)the food which we eat.Heat,too, makes our environment endurable.Various kinds of rays come through the air from outer space,but enormous quantities of radiation from the sun(3)__________(screen)off.As soon as men leavethe atmosphere they are exposed to this radiation but their spacesuits or the walls of their spacecraft, (4)__________they are inside,do prevent a lot of radiation damage.Radiation is(5)__________(great)known danger to explorers in space.The unit of radiationis called"rem".Scientists have reason to think that a man can put up with far more radiation than0.1rem without(6)__________(damage);the figure of60rems has been agreed on.The troubleis(7)__________it is extremely difficult to be sure about radiation damage-a person may feel perfectly well,but the cells of his or her sex organs may be damaged,and this will no be discovered (8)the birth of deformed children or even grandchildren.Missions of the Apollo flights have had to cross belts of high amount of rems.So far,no dangerous amounts of radiation have been reported,but the Apollo missions have been quite short.We simply do not know yet(9) __________men are going to get on when they spend weeks and months outside the protection ofthe atmosphere,working in a space laboratory.Drugs might help to decrease the damage(10) __________(do)by radiation,but no really effective ones have been found so far.(B)Before I went to the British Koi Keepers’Annual Show,I didn’t understand(1)______ people could take fish soseriously.However,the more I learned about koi,the more interested I became.As one expert told me,“Collecting koi is far more addictive than you might think.They’reas beautiful as butterflies and very calming to watch.”Freddie Mercury,the lead singer of Queen, would have agreed----the pool in his specially built Japanese garden was home to89koi,(2) __________cost up to￡10,000each.At the show I met koi euthusiast Jean Kelly.“Koi are getting more and more expensive,”shetold me.“One recently sold for￡250,000.”I was shocked-----that’s almost as much as I paid for my house.“Well,that was a record,”(3)__________(admit)Jean.“The normal price is nowhere nearas high as that.”Nevertheless,serious collectors can pay up to￡15,000for a fully(4)_______(grow)koi, which is nearly as expensive as a new luxurious car,and the bigger they are,the more they cost.The cheapest I(5)________find was￡75each,but they were only about twice as big as my goldfish. Jean wasn’t impressed by one of the koi on sale either.“Actually,these koi aren’t any nicer than(6)_______,”She commented.“(7)_______they are slightly bigger than the ones I’ve got,I paid considerable less than this.”I wasn’t quite as enthusiastic as Jean,but I did consider(8)________(buy)one.Then I remember that all but5of Freddie Mercury’s koi died when someone accidentally turned off the electricity supply to their pool.Jean assured me that with all the new equipment available the survival rate was getting better and better,and that looking(9)______koi was no harder than taking care of any other pet.However,in the end of I decided to stick with my goldfish.They’re not nearly as beautiful as koi—but they’re a great deal cheaper(10)______(replace)!Section BDirections:Complete the following passage by using the words in the box.Each word can only be used once.Note that there is one word more than you need.A.associatedB.likelyC.decreasesD.abstractE.limitF.funG.contributesH.consistentlyI.favorablyJ.reasonedK.averageThe Beadles sang that money can't buy you love.But what about happiness?Research(41)______shows that the more money people have,the more likely they are to report being satisfiedwith their lifes.And that makes sense:money buys you things that make life easier and more satisfying;the easier your life,the happier you tend to be.That relationship isn’t entirely linear,since there's a(n) (42)______to how much money can please you;the happiness benefit of an increasing income is especially powerful among people who don’t have much money to start with,and(43)______as wealth increases.But studies also reveal that as(44)______income levels have risen over time inthe U.S.and European nations.For example---residents of those countries have not reported beingany happier than people were30or40year ago.It's a paradox that while income and happiness may be(45)______within a population at any given moment,overall economic growth does not appearto corresponded to a boost in national satisfaction over time.To understand why,researchers at the University of Warwick and Cardiff University decidedto break down how individual people evaluate their income.What does wealth mean to people? Previous work has suggested that people tend to value their own wealth more-and are happier-whenit compares(46)______to everyone else's.The so-called reference-income hypothesis holds that itis not simply how much money you make that(47)______to satisfaction,but how much more money make than,say,the national average.The higher your salary than the norm,the happier you tend to be.But the reference-income hypothesis is rather(48)______.The researchers wondered whether there was a more concrete way to capture how people valued their income.They(49)______that people tended to make specific comparisons of personal wealth,not only with the average incomeof the larger population,but with the individual incomes of their neighbors,colleagues from college. And the higher their rank,the greater their sense of happiness and self-worth would(50)______ be."For example,people might care about whether they are the second most highly paid person orthe eighth most highly paid person,in their comparison set.”write the author,Chris Boyce,a psychologist at the University of Warwick.III.Reading ComprehensionSection ADirections:For each blank in the following passage there are four words or phrases marked A,B,C and D.Fill in each blank with the word or phrase that best fits the context.The beauty,majesty and timelessness of a primary rainforest are incredible.It is impossibleto51._______on film,to describe in words,or to explain to those who have never had the awe-inspiring experience of standing in the heart of a primary rainforest.Rainforests have52.______over millions of years to turn into the incredible complex environment they are today.Rainforests represent a store of living and53._______renewable natural resources that for eons,by virtue of their richness in both animal and plant species,have54._______a wealth of resources for the survival and well-being of mankind.These resources have included basic food supplies,clothing,shelter,fuel,species,industrial raw material,and medicine for all those who have lived in the majesty of the forest.55._______the inner dynamics of a tropical rainforest is an intricate and fragile system.Everything is so56._______that upsetting one part can lead to unknown damage or even destruction of the whole.Sadly,it has taken only a century of human intervention to destroy what nature designed to57._______forever.The scale of human58._______on ecosystems everywhere has increased in the last few decades.Since1980the global economy has tripled in size and the world population has increasedby30percent.Consumption of everything on the planet has risen--at a cost to our59._______.in 2001,the World Resources Institute estimated that the demand for rice,wheat and corn is expectedto grow by40%by2020,increasing irrigation water demands by50%or more.The further reported that the demand for wood could double by the year2050,60._______it is still the tropical forestsof the world that supply the bulk of the world’s demand for wood.In1950,about15percent of the Earth’s land surface was covered by rainforest.Today,morethan half has already gone up in61._______.in fewer than fifty years,more than half of the worlds tropical rainforests have fallen62._______to fire and the chainsaw,and the rate of destruction isstill accelerating.Unbelievably,more that200,000acres of rainforest are burned every day.That is more that150acres lost every minute of every day,and78million acres lost every year!More than20percent of the Amazon rainforest is already gone,and much more is vanishing at a rate of20,000 square miles a year.If nothing is done to curb this63._______,the entire Amazon could well begone within fifty years.Massive64._______brings with it may ugly consequences--air and water pollution,soil erosion,malaria epidemics,the release of carbon dioxide into the atmosphere and the65._______of biodiversity through extinction of plants and animals.Fewer rainforests mean less rain,less oxygen for us to breathe,and an increased threat from global warming.51.A.present B.capture C.claim D.prove52.A.changed B.evolved C.expanded D.existed53.A.energizing B.healing C.isolating D.breathing54.A.contributed B.stored C.reduced D.affected55.A.However B.Furthermore C.Therefore D.Otherwise56.A.active B.sensitive C.interdependent D.delicate57.A.restore B.support C.revive /doc/02b93573a4e9856a561252d380eb6294dd88228b.html st58.A.pressure B.power C.concern D.strength59.A.existence B.ecosystem C.planet D.survival60.A.unfortunately B.consequently C.naturally D.similarly61.A.store B.food C.smoke D.wealth62.A.subject B.down C.apart D.victim63.A.trend B.practice C.decrease D.attitude64.A.destruction B.industrialization C.modernization D.deforestation65.A.appearance B.explosion C.loss D.increase Section BDirection：Read the following three passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)The definition of the standard kilogram is almost fundamentally wrong.Getting the definition right is a challenge that has tried the patience and intelligence of scientists for decades.Scientists use just seven basic units to define all the other quantities we use—quantities suchas speed or electric power.All of those basic units except the kilogram are themselves defined according to natural properties that are beyond human control.For example,the standard second(time)is defined as a specific number of vibration of a typeof radiation sent out by atoms of a special metal.The standard metre(length),in turn,is defined asthe length of the path light travels during a specific fraction of a second.Not so the kilogram.This orphan of the basic unit family is simply the mass of a small platinum-iridium alloy cylinder（铂—铱合⾦筒）locked away in a container maintained by the International Bureau of Weights&Measures in Sevres,France. Embarrassingly,the last time the copies were brought to Sevres for a checkup in the1980s, officials found that some copies had gained about20parts per billion in weight compared to the master cylinder since the previous checkup in the1940s.This implies that the master cylinder itself may be an inconstant standard.No one knows what causes the weight changes.But the uncertainty can’t be tolerated when precision(精密度)in research and some manufacturing now demands accuracy to a few parts per billion.Several efforts in several different countries are under way to redefine the kilogram in terms of basic physical quantities such as counting the actual number of atoms of a specific substance in a kilogram or the electromagnetic force that balances a kilogram mass against gravity.A project of the latter type at the laboratories in Gaithersburg,Md.,hopes eventually to define mass by means of electrical units.So far,none of these redefinition projects has borne fruit.They require the very accuracy of measurement and control of experimental conditions.The slightest pollution,tiny vibration,or other influence--even changes in weather--can ruin results.Y ou’vegot to hand it to scientists who are willing to devote many years to such painstaking but extremely important research.66.Which of the following best paraphrases the sentence“Not so kilogram”in paragragh4?A．The kilogram is not as accurate as the standard second.B．The kilogram is not universally accepted in the world.C．The kilogram is not defined in terms of natural properties.D．The kilogram is not well defined as time and length.67.Which of the following can NOT be concluded from the passage?A．Experiments are being carried out to redefine the kilogram.B．The uncertainty in the standard kilogram can seriously affect some research.C．The redefining of the standard kilogram is quite complicatedD．Scientists will achieve success in redefining the kilogram in the near future68.According to the passage,to define the weight of mass in terms of electrical units________.A．is one of the best methods to redefine the kilogram.B．has been accepted as the only possible redefinition projectC．is not as simple as what people can understandD．has been considered by some scientists as a better approach69.We can know form the passage that the redefinition of the kilogram is________.A．more important in keeping market honesty.B．worth years of scientists’painstaking research.C．the urgent requirement of business and manufacturing.D．bring about important and fruitful results.（B）Stewart Island Ferry ServicesWhile most visitors spend at least one night on Stewart Island,it is also readily accessible by ferry as a day excursion from Invercargill and Bluff.Experience Foveaux Strait in comfort and style on board our express catamarans.During the one-hour crossing between Bluff and Stewart Island keep a lookout for wildlife,especially seabirds. Watching mollymawks(albatross)soaring behind the ferry is a fantastic sight.Interesting landmarks commonly seen include Dog Island Lighthouse,Ruapuke Island,Titi Islands and Mt Anglem-Stewart Island’s highest point.Free tea and coffee on boardInterpretation handouts are available(English only).Wheelchair access availablePersonal baggage is carried free on the ferries-max.two bags per person(one stowed and one small carry-on).Additional baggage is by prior arrangement.V ehicle parking available at Bluff(extra cost-reservations recommended)“20% Multi - Purchase REW ARD”on Return Ferry ServicesBuy2or more different excursions and SA VE20%off all lower priced!Kids Go FREE on selected departures during NZ School Holidays!Kids Go FREE for travel20April-5May2013.70.If leaving a car at Bluff,a traveler had better_________.A．refer to the handouts first B．use wheelchair accessC．make a reservation D．park it30minutes before departure time71.John,who went to Stewart Island on Dec.28th,got to the ferry dock at7:55am.When did he most probably leave Bluff? A．At8:00a.m..B．At9:30a.m..C．At11:00a.m..D．At3:00p.m..72.Which of the following is false about the ferry services?A．Tea and coffee are free for passengers.B．Children go free for travel for about15days.C．Travelers are sure to see some seabirds during the crossing.D．Passengers have to pay extra cost for extra pieces of luggage.（C）Like every dog,every disease now seems to have its day.World Tuberculosis(infections disease in which growths appear on the lungs)Day is on Saturday March24th.Tuberculosis was once terribly fashionable.Dying of"consumption"seems to have been a favorite activity of garret-dwelling19th-century artists,h has,however,been neglected of late. Researchers in the field never tire of pointing out that TB kills a lot of people.According to figures released earlier this week by the World Health Organization,1.6million people died of the diseasein2005,compared with about3m for AIDS and l m for malaria.But it receives only a fraction ofthe research budget devoted to AIDS.America’s National Institutes of Health,for example,spends20times as much on AIDS as on TB.Nevertheless,everyone seems to getting in on the TB-day actthis year.The Global Fund an international organization responsible fur fighting all three diseases but best known for its work on AIDS,has used the occasion to trumpet its tuberculosis projects.Thefund claims that its anti-TB activities since it opened for business in2002have saved the lives ofover1m people.The W orld Health Organization has issued a report that contains some good news. Although the number of TB cases is still rising,the rate of illness seems to have stabilized;the caseload,in other words,is growing only because the population itself is going up.Even drug companies are involved.In the run-up to the day itself,Eli Lilly announced a$50m boost to its MDRTB Global Partnership.MDR stands for multi-drug resistance,and it is one of the reasons why TB is back in the limelight.Careless treatment has caused drug-resistant strains to evolve all over the world.The course of drugs needed to clear the disease completely takes six mouths,anti persuading people lo stay that course once their symptoms have gone is hard. Unfortunately,those infected with MDR have to be treated with less effective,more poisonous and more costlydrugs.Naturally,these provoke still more.non-compliance and thus still more evolution.The other reason TB is back is its relationship to AIDS.The(global Fund’s joint responsibility for the diseases is no coincidence.AIDS does not kill directly.Rather,HIV,the virus that causes it, weakens the body’s immune system and exposes the sufferer to secondary infections.Of these,TBis one of the most serious.It kills200000AIDS patients a year.However,some anti-TB drugs interfere with the effect of some anti-HIV drugs.Conversely,in about20%of cases where a patienthas both diseases,anti-HIV drugs make the tuberculosis worse.The upshot is that125years after human beings worked out what caused TB,it is still a serious threat.73.The first sentence“Like every dog,every disease now seems to have its day.”means_______.。
2019届上海市交大附中高三上9月开学摸底考试数学试题(解析版)
2019届上海市交大附中高三上9月开学摸底考试数学试题一、单选题1．已知集合，则下列选项正确的是（）A．B．C．D．【答案】B【解析】根据元素与集合的关系，用∈，集合与集合的关系，用⊆，可知B正确. 2．在空间直角坐标系中，若点在第Ⅵ卦限，则与点关于轴对称的点在（）A．第Ⅰ卦限B．第Ⅲ卦限C．第Ⅴ卦限D．第Ⅶ卦限【答案】A【解析】根据点P的卦限得坐标x，y，z的符号，再得对称点的坐标的符号，从而可得对称点的卦限．【详解】因为点P（x，y，z）在第Ⅵ卦限，所以x＜0，y＞0，z＜0，点P关于y轴的对称点为（﹣x，y，﹣z），在第Ⅰ卦限．故选：A．【点睛】本题考查了空间向量运算的坐标表示，熟记每个卦限的坐标符号是解决问题的关键，属基础题．3．设，，为实数，则实数“”是“方程表示的曲线为双曲线”的（）A．充分非必要条件B．必要非充分条件C．充要条件D．非充分非必要条件【答案】D【解析】首先求出方程Ax2+By2＝C表示的曲线为双曲线的充要条件，然后根据充分条件，必要条件的定义来判断．【详解】∵方程Ax2+By2＝C表示的曲线为双曲线，∴，∴AB＜0且C≠0；∵ABC＜0推不出AB＜0且C≠0，AB＜0且C≠0推不出ABC＜0；∴实数“ABC＜0”是“方程Ax2+By2＝C表示的曲线为双曲线”的非充分非必要条件．故选：D．【点睛】本题主要考查充分条件和必要条件的判断，熟记双曲线的方程的特点，根据充分条件和必要条件的定义是解决本题的关键，是基础题4．已知、、、是同一平面上不共线的四点，若存在一组正实数、、，使得，则三个角、、（）A．都是钝角B．至少有两个钝角C．恰有两个钝角D．至多有两个钝角【答案】B【解析】根据，移项得，两边同时点乘，得•0，再根据正实数，和向量数量积的定义即可确定∠BOC、∠COA至少有一个为钝角，同理可证明∠AOB、∠BOC至少有一个为钝角，∠AOB、∠COA至少有一个为钝角，从而得到结论．【详解】∵λ1λ2λ3，∴，两边同时点乘，得•，即||•||cos∠COA+cos∠BOC＝﹣0，∴∠BOC、∠COA至少有一个为钝角，同理∠AOB、∠BOC至少有一个为钝角，∠AOB、∠COA至少有一个为钝角，因此∠AOB、∠BOC、∠COA至少有两个钝角．故选：D．【点睛】本题考查数量积，考查向量的夹角，以及数量积的定义式，同时考查学生灵活应用知识分析解决问题的能力和计算能力,是中档题二、解答题5．如图所示，三棱柱的侧面是圆柱的轴截面，是圆柱底面圆周上不与、重合的一个点.（1）若圆柱的轴截面是正方形，当点是弧的中点时，求异面直线与所成角的大小（结果用反三角函数值表示）；（2）当点是弧的中点时，求四棱锥与圆柱的体积比.【答案】（1）（2）【解析】（1）连接，则，直线与的所成角等于直线与所成角，在△中，利用余弦定理求，即可求解（2）分别求和，再求比值即可【详解】（1）连接，则，直线与的所成角等于直线与所成角，设圆柱的底面半径为，即，，在△中，，又所以直线与所成角的大小等于.（2）设圆柱的底面半径为，母线长度为，当点是弧的中点时，，且平面，，，∴.【点睛】本题主要考查异面直线所成角，圆柱和棱锥的体积等基础知识，考查空间想象能力、运算求解能力、推理论证能力，考查数形结合思想、化归与转化思想，属于中档题．6．（1）已知是定义在上的奇函数，求实数、的值；（2）已知是定义在上的函数，求实数的取值范围.【答案】（1），；（2）【解析】（1）根据题意，由奇函数的性质可得f（0）＝lg lgb＝0，解可得b，又由f（x）+f（﹣x）＝0，可得a的值，即可得答案．（2）根据题意，分析可得不等式ax＞0在R上恒成立；即ax恒成立，转化为两个函数y=和y=ax，先求相切的临界情况，再由不等关系，即可得答案．【详解】（1）是定义在R上的奇函数，则有f（0）＝lg lgb＝0，则b，且f（x）+f（﹣x）＝lg（ax）+lg（ax）﹣2lg lg[（x2+2）﹣a2x2]﹣lg2＝lg[（1﹣a2）x2+2）]﹣lg2＝0，即（1﹣a2）x2＝0恒成立；可得：a＝±1；故a＝±1，b；（2）若f（x）＝lg（ax）﹣lgb为定义在R上的函数，则ax＞0在R上恒成立；即ax恒成立，令y=此函数为焦点在y轴上的双曲线的上支，令y=ax,当y=ax与y=相切时，两式联立消去y,得,，故ax恒成立时，﹣1<a<1即a的取值范围为（-1，1）．【点睛】本题考查函数奇偶性的性质以及应用，对数函数的运算性质，函数值域，不等式恒成立，数形结合思想，第（2）转化为两个函数交点问题是关键，属于中档题．7．某工厂在生产产品时需要用到长度为的型和长度为的型两种钢管.工厂利用长度为的钢管原材料，裁剪成若干型和型钢管，假设裁剪时损耗忽略不计，裁剪后所剩废料与原材料的百分比称为废料率.（1）要使裁剪的废料率小于，共有几种方案剪裁？请写出每种方案中分别被裁剪型钢管和型钢管的根数；（2）假设一根型钢管和一根型钢管能成为一套毛胚，假定只能按（1）中的那些方案裁剪，若工厂需要生产套毛胚，则至少需要采购多少根长度为的钢管原材料？最终的废料率为多少？【答案】（1）见解析（2）见解析【解析】（1）设每根原材料可裁剪a根A型和b根B型钢管，则，再由废料率小于得故即可设计方案，（2）设用方案一裁剪x根原材料，用方案二裁剪y根原材料，共裁剪得z套毛胚，则z＝2x+4y，由得即可求出答案．【详解】（1）设每根原料可裁剪成根型钢管和型钢管，则即根据题意，废料率为故满足条件的a与b的值为方案一：废料率为；则可裁剪成2根A 型钢管和5根B型钢管.方案二：废料率为.则可裁剪成4根A型钢管和2根B型钢管.（2）设用方案一裁剪根原材料，用方案二裁剪根原材料，共裁剪得套毛坯，则,即，故由题，所以所以至少采购100根长度为4000mm的钢管原材料，其中方案一裁剪40根，方案二裁剪60根，废料率为.【点睛】本题考查了函数在实际生活中的应用，考查了分析问题，解决问题的能力，准确计算不等式组的解是关键，属于中档题．8．在平面上，给定非零向量，对任意向量，定义.（1）若，，求；（2）若，证明：若位置向量的终点在直线上，则位置向量的终点也在一条直线上；（3）已知存在单位向量，当位置向量的终点在抛物线：上时，位置向量终点总在抛物线：上，曲线和关于直线对称，问直线与向量满足什么关系？【答案】（1）（2）见证明（3）直线与向量垂直【解析】（1）根据题意，算出7，10，代入的表达式并化简整理，即可得到（，）；（2）设（x'，y'），终点在直线Ax+By+C＝0上，由题中的表达式解出（x，y）满足的关系式，从而得到点（，）在直线Ax+By+C＝0上，化简整理得到直线（3A+4B）x+（4A﹣3B）y﹣5C＝0，说明向量的终点也在一条直线上；（3）设，则，取，解出关于和t的坐标形式，结合的终点在抛物线x2＝y上且终点在抛物线y2＝x上，建立关于和t的方程，化简整理得到±（，）．再由曲线C和C′关于直线l：y ＝x对称，算出l的方向向量满足•0，从而得到直线l与向量垂直．【详解】（1）根据题意，7，10，∴.（2）设，，则，∴于是故，从而w，由于、不全为零，所以，也不全为零.于是的终点在直线上.（3）设，则，对任意实数，取，则，∵的终点在曲线上，∴.①由于为任意实数，比较①式两边的系数得，，，从而，，∴.对曲线中任意点，可知落在曲线上，反之亦然，故曲线：与曲线：关于直线：对称，的方向向量，∵，∴，即直线与向量垂直.【点睛】本题考查向量的坐标运算，相关点法求轨迹，着重考查了向量的数量积运算、向量的坐标运算和曲线与方程的讨论等知识，属于中档题．9．设函数，，，若对任意成立，且数列满足：，.（1）求函数的解析式；（2）求证：；（3）求证：.【答案】（1）；（2）（证明略）；（3）（证明略）【解析】（1）由题令，解x=-1,所以-4≤f(-1)≤-4,则f(-1)=-4，得a=b-4，进而得对任意成立，由判别式整理解得b=2,即可得a=-2,则f(x)可求；（2）由得，进而，累乘得（3）由（2）得，累加得，再由证明数列递增，得则证得；欲证，即证,则需证，由，放缩归纳得，再证明即可【详解】（1）由题对任意成立，令，解x=-1,所以-4≤f(-1)≤-4,则f(-1)=-4又，则f(-1)=a-b=-4，即a=b-4所以对任意成立，即,则整理得∴b=2,则a=-2所以（2）由（1）知，，∴, ∴,所以又（3）由（2）知所以所以又,又,为递增数列，所以所以由（2）可知，欲证，即证,则需证∵,∴所以=所以=2因为2018<所以,则>所以证得，即证得所以【点睛】本题主要考查数列综合，不等关系与不等式以及数列求和，放缩法证明不等式，转化化归能力，是难题三、填空题10．方程组的增广矩阵是______．【答案】【解析】试题分析：根据增广矩阵的定义可知为.【考点】本小题主要考查增广矩阵的定义和应用.点评：增广矩阵就是在系数矩阵的右边添上一列，这一列是线性方程组的等号右边的值。
上海市交大附中高考数学一模试卷解析版.doc
2019年上海市交大附中高考数学一模试卷一、选择题（本大题共4小题，共12.0分）1.已知定义域为R的函数，则此函数图象上关于原点对称的点有（）A. 7对B. 8对C. 9对D. 以上都不对【答案】B【解析】解：当x=0时，f（x）=-，此时（0，-）关于原点对称的点（0，）此时与f（x）没有交点，函数y=x-关于原点对称的函数为-y=-x-，即y=x+，x＞0，若函数图象上关于原点对称的点，等价为当x＞0时，f（x）=3与y=x+，x＞0的交点个数即可，作出函数f（x）在x＞0时的图象如图，由图象知，函数分别关于x=1，x=3，x=5，x=7，x=9对称，且函数的最大值为f（2k-1）=3，当y=x+=3时，得x=，即x=7，故当x＞0时，f（x）=3与y=x+，x＞0的交点个数有8个，即函数图象上关于原点对称的点有8对，故选：B．求出函数y=x-关于原点对称的函数为y=x+，x＞0，利用数形结合判断当x＞0时，f （x）=3与y=x+，x＞0的交点个数即可本题主要考查函数与方程的应用，利用对称性转化为两个图象交点个数是解决本题的关键．注意利用数形结合是解决本题的关键．2.某超市货架上摆放着某品牌红烧牛肉方便面，如图是它们的三视图，则货架上的红烧牛肉方便面至少有（）A. 8桶B. 9桶C. 10桶D. 11桶【答案】B【解析】解：易得第一层有4碗，第二层最少有3碗，第三层最少有2碗，所以至少共有9个碗．故选：B．主视图、左视图、俯视图是分别从物体正面、左面和上面看，所得到的图形．考查学生对三视图掌握程度和灵活运用能力，同时也体现了对空间想象能力方面的考查．如果掌握口诀“俯视图打地基，正视图疯狂盖，左视图拆违章”就更容易得到答案．3.已知f（x）=x2+3x，若|x-a|≤1，则下列不等式一定成立的是（）A. |f（x）-f（a）|≤3|a|+3B. |f（x）-f（a）|≤2|a|+4C. |f（x）-f（a）|≤|a|+5D. |f（x）-f（a）|≤2（|a|+1）2【答案】B【解析】解：∵|x-a|≤1，∴a-1≤x≤a+1，∵f（x）是二次函数，∴f（x）在区间[a-1，a+1]上单调时，|f（x）-f（a）|取得最大值为|f（a+1）-f（a）|或|f （a-1）-f（a）|，而|f（a+1）-f（a）|=|（a+1）2+3（a+1）-a2-3a）|=|2a+4|≤2|a|+4，|f（a-1）-f（a）|=|（a-1）2+3（a-1）-a2-3a|=|-2a-2|=|2a+2|≤2|a|+2．∴|f（x）-f（a）|≤2|a|+4，故选：B．结合二次函数的图象可知，当f（x）在区间[a-1，a+1]单调时，|f（x）-f（a）|的最大值为|f（a+1）-f（a）|或|f（a-1）-f（a）|，从而得出结论．本题考查了二次函数的性质，利用函数的最值研究恒成立问题的思路，同时结合函数图象分析问题是关键．4.若，且，，则的取值范围是（）A. B. [0，2]C. D.【答案】D【解析】解：∵，且，，∴•-•-•+||2≤0，∴4≥-•+•+•，∴2=||2+||2+||2+2•-2•-2•≤4+4+4-8=4，∴≤2，又由，得：=2，故≥-=2-2，故的取值范围是，故选：D．由，得：=2，故≥-=2-2，结合，得≤2，进而得到答案．本题考查的知识点是平面向量的数量积运算，向量的模，难度中档．二、填空题（本大题共12小题，共36.0分）5.已知集合A={x|0＜x≤2}，集合B={x|-1＜x＜2}，则A∪B=______．【答案】{x|-1＜x≤2}【解析】解：∵集合A={x|0＜x≤2}，集合B={x|-1＜x＜2}，∴A∪B={x|-1＜x≤2}．故答案为：{x|-1＜x≤2}．利用并集定义直接求解．本题考查并集的求法，是基础题，解题时要认真审题，注意并集定义的合理运用．6.若复数z=4+3i，其中i是虚数单位，则|z2|=______．【答案】25【解析】解：由z=4+3i，得z2=（4+3i）2=16+24i+9i2=7+24i，则|z2|=|7+24i|=．故答案为：25．直接利用复数代数形式的乘除运算化简，再由复数模的公式计算得答案．本题考查了复数代数形式的乘除运算，考查了复数模的求法，是基础题．7.函数，则f[f（-1）]=______．【答案】0【解析】解：f（-1）=f（2）=f（5）=5-4=1所以f[f（-1）]=f（1）=f（4）=0故答案为0先根据函数的解析式求出f（-1）的值，再求出f[f（-1）]=f（1）=f（4）=0．求分段函数的值，关键是判断出自变量所属的范围，然后将自变量的值代入相应段的解析式求出值．8.已知sin（α-）=，则cos（α-）=______．【答案】±【解析】解：∵sin（α-）=，∴cos（α-）=±=±．故答案为：±根据sin（α-）的值，利用同角三角函数间的基本关系求出cos（α-）的值即可．此题考查了运用诱导公式化简求值，以及同角三角函数间的基本关系，熟练掌握基本关系是解本题的关键．9.已知数列{a n}的前n项和为S n=n2+2n（n∈N*），则数列{a n}的通项公式a n=______．【答案】2n+1（n∈N*）【解析】解：当n≥2，且n∈N*时，a n=S n-S n-1=（n2+2n）-[（n-1）2+2（n-1）]=n2+2n-（n2-2n+1+2n-2）=2n+1，又S1=a1=12+2=3，满足此通项公式，则数列{a n}的通项公式a n=2n+1（n∈N*）．故答案为：2n+1（n∈N*）由数列的前n项和公式S n=n2+2n，表示出当n大于等于2时，前n-1项和S n-1，利用a n=S n-S n-1得出n大于等于2时的通项公式，把n=1代入此通项公式检验也满足，故得到数列的通项公式．此题考查了等差数列的通项公式，熟练掌握数列的递推式a n=S n-S n-1是解本题的关键，同时注意要把首项代入通项公式进行验证．10.已知实数x，y满足约束条件，则目标函数z=3x+y的取值范围为______．【答案】[1，6]【解析】解：由约束条件作出可行域如图，联立，解得A（2，0），联立，解得B（0，1）．化目标函数z=3x+y为y=-3x+z，由图可知，当直线y=-3x+z过B时，直线在y轴上的截距最小，z有最小值为1，当直线y=-3x+z过A时，直线在y轴上的截距最大，z有最小值为6．∴目标函数z=3x+y的取值范围为[1，6]．故答案为：[1，6]．由约束条件作出可行域，化目标函数为直线方程的斜截式，数形结合得到最优解，联立方程组求得最优解的坐标，代入目标函数得答案．本题考查简单的线性规划，考查了数形结合的解题思想方法，是中档题．11.已知函数f（x）=a sin2x+b cos2x（a，b∈R，ab≠0），若其图象关于直线对称，则直线ax+by+2=0的倾斜角α=______．【答案】【解析】解：∵函数y=a sin2x+b cos2x（a，b不全为0）的图象关于直线x=对称，设sinθ=，cosθ=，∴y=a sin2x+b cos2x=（sin2x+cos2x）=sin（2x+θ），当x=时，2x+θ=+θ=+kπ，（k∈Z），∴θ=-++kπ=+kπ，（k∈Z），不妨取k=0时，得θ=；∴sinθ==，cosθ==，解得a=，b=1；∴直线l：ax+by+c=0可化为：x+y+c=0，它的斜率为k=-，∴倾斜角是；故答案为：．化简函数y=a sin2x+b cos2x为一个角的一个角的函数形式，利用x=是函数y=a sin2x+b cos2x图象的一条对称轴，求出a，b的值，然后求直线l的斜率与倾斜角．本题考查了三角函数与向量知识的综合应用问题，是综合题目．12.鲁班锁是中国传统的智力玩具，起源于古代汉族建筑中首创的榫卯结构，这种三维的拼插器具内部的凹凸部分（即榫卯结构）啮合，十分巧妙，外观看是严丝合缝的十字立方体，其上下、左右、前后完全对称．从外表上看，六根等长的正四棱柱体分成三组，经90°榫卯起来，如图，若正四棱柱体的高为6，底面正方形的边长为1，现将该鲁班锁放进一个球形容器内，则该球形容器的表面积的最小值为______．（容器壁的厚度忽略不计）【答案】41π【解析】解：由题意，该球形容器的半径的最小值为=，∴该球形容器的表面积的最小值为=41π．故答案为41π由题意，该球形容器的半径的最小值为=，即可求出该球形容器的表面积的最小值．本题考查正棱柱的外接球，考查学生的计算能力，属于中档题．13.已知，且a0+a1+a2+…+a n=126，那么展开式中的常数项为______．【答案】20【解析】解：∵已知，且a0+a1+a2+…+a n=126，∴令x=1，可得a0+a1+a2+…+a n=2+22+…+2n==2n+1-2=126，∴n=6，那么=的展开式的通项公式为T r+1=•（-1）r•x3-r，令3-r=0，求得r=3，可得展开式中的常数项为=20，故答案为：20．由题意令x=1，可得n=4，再利用二项展开式的通项公式，求得展开式中的常数项．本题主要考查二项式定理的应用，注意根据题意，分析所给代数式的特点，通过给二项式的x赋值，求展开式的系数和，可以简便的求出答案，二项展开式的通项公式，属于基础题．14.已知正实数x，y满足xy+2x+3y=42，则xy+5x+4y的最小值为______．【答案】55【解析】解：∵正实数x，y满足xy+2x+3y=42，∴y=＞0，x＞0，解得0＜x＜21．则xy+5x+4y=3x+y+42=3x++42=3+31≥3×+31=55，当且仅当x=1，y=10时取等号．∴xy+5x+4y的最小值为55．故答案为：55．正实数x，y满足xy+2x+3y=42，可得y=＞0，解得0＜x＜21．则xy+5x+4y=3x+y+42=3x++42=3+31，再利用基本不等式的性质即可得出．本题考查了基本不等式的性质、不等式的解法，考查了推理能力与计算能力，属于中档题．15.已知等边△ABC的边长为2，点P在线段AC上，若满足等式=λ的点P有两个，则实数λ的取值范围是______．【答案】（-，0]【解析】解：设PA=x（0≤x≤2），则PC=2-x．∴=+=-+，又=2×2×cos60°=2，∴λ==-（-+）=-=x2-x=（x-）2-．令f（x）=（x-）2-，则f（x）在[0，]上单调递减，在（，2]上单调递增，且f（0）=0，f（）=-，f（2）=2．∵满足等式=λ的点P有两个，∴关于x的方程f（x）=λ在[0，2]上有两解，∴．故答案为：（-，0]．设PA=x，得出式关于x的函数，根据函数的单调性得出λ的范围．本题考查了平面向量的数量积运算，属于中档题．16.过直线l：x+y=2上任意点P向圆C：x2+y2=1作两条切线，切点分别为A，B，线段AB的中点为Q，则点Q到直线l的距离的取值范围为______．【答案】[，）【解析】解：∵点P为直线l：x+y=2上的任意一点，∴可设P（t，2-t），则过O、A、P、B的圆的方程为（x-）2+（y-）2=[t2+（2-t）2]，化简可得x2-tx+y2-（2-t）y=0，与已知圆的方程相减可得AB的方程为tx+（2-t）y=1，由直线OP的方程为（2-t）x-ty=0，联立两直线方程可解得x=，y=，故线段AB的中点Q（，），∴点Q到直线l的距离d==|2-|，∵t2-2t+2=（t-1）2+1≥1，∴0＜≤1，∴-1≤-＜0，∴1≤2-＜2，∴≤|2-|＜，即d∈[，）故答案为：[，）设P（t，2-t），可得过O、A、P、B的圆的方程与已知圆的方程相减可得AB的方程，进而联立直线方程解方程组可得中点Q的坐标，由点Q到直线的距离公式和不等式的性质可得．本题考查直线与圆的位置关系，涉及圆的相交弦和点到直线的距离公式，以及不等式求函数的值域，属中档题．三、解答题（本大题共5小题，共60.0分）17.在△ABC中，a、b、c分别为角A、B、C的对边，已知cos2A-3cos（B+C）=1．（1）求角A的值；（2）若a=2，求△ABC周长的取值范围．【答案】解：（1）△ABC中，cos2A-3cos（B+C）=1，（2cos2A-1）-3•（-cos A）=1，2cos2A+3cos A-2=0，解得cos A=或cos A=-2（不合题意，舍去），∴cos A=，A=；（2）a=2，A=，由正弦定理可得====；∴b=sin B，c=sin C，∴a+b+c=2+（sin B+sin C）=2+[sin（-C）+sin C]=2+（cos C+sin C）=2+4sin（C+），∵0＜C＜，∴＜C+＜，∴＜sin（C+）≤1，2＜4sin（C+）≤4，则4＜2+4sin（C+）≤6，即4＜a+b+c≤6，∴△ABC的周长的取值范围是（4，6]．【解析】（1）根据二倍角公式化简求解即可求出角A的大小；（2）由正弦定理求得b、c的值，再利用三角恒等变换计算a+b+c的取值范围．本题考查了正弦定理、两角和与差的正弦公式、三角函数的单调性应用问题，是中档题．18.在如图所示的组合体中，三棱柱ABC-A1B1C1的侧面ABB1A1是圆柱的轴截面，C是圆柱底面圆周上不与A、B重合的一个点．（Ⅰ）若圆柱的轴截面是正方形，当点C是弧AB的中点时，求异面直线A1C与AB1的所成角的大小；（Ⅱ）当点C是弧AB的中点时，求四棱锥A1-BCC1B1与圆柱的体积比．【答案】解：（Ⅰ）如图，取BC的中点D，连接OD，AD，则OD∥A1C，∴∠AOD（或其补角）为异面直线A1C与AB1的所成角，设正方形的边长为2，则△AOD中，OD=A1C=，AO=，AD=，∴cos∠AOD==∴∠AOD=；（Ⅱ）设圆柱的底面半径为r，母线长度为h，当点C是弧AB的中点时，，，，∴．【解析】（Ⅰ）取BC的中点D，连接OD，AD，则OD∥A1C，∠AOD（或其补角）为异面直线A1C与AB1的所成角，利用余弦定理，可求异面直线A1C与AB1的所成角的大小；（II）设圆柱的底面半径为r，母线长度为h，当点C是弧弧AB的中点时，求出三棱柱ABC-A1B1C1的体积，求出三棱锥A1-ABC的体积为，从而求出四棱锥A1-BCC1B1的体积，再求出圆柱的体积，即可求出四棱锥A1-BCC1B1与圆柱的体积比．本小题主要考查直线与直线的位置关系，以及几何体的体积等基础知识，考查空间想象能力、运算求解能力、推理论证能力，考查数形结合思想、化归与转化思想，属于中档题．19.一个创业青年租用一块边长为4百米的等边△ABC田地（如图）养蜂、产蜜与售蜜．田地内拟修建笔直小路MN，AP，其中M，N分别为AC，BC的中点，点P在BC上．规划在小路MN与AP的交点O（O与M、N不重合）处设立售蜜点，图中阴影部分为蜂巢区，空白部分为蜂源植物生长区，A，N为出入口（小路的宽度不计）．为节约资金，小路MO段与OP段建便道，供蜂源植物培育之用，费用忽略不计．为车辆安全出入，小路AO段的建造费用为每百米4万元，小路ON 段的建造费用为每百米3万元．（1）若拟修的小路AO段长为百米，求小路ON段的建造费用；（2）设∠BAP=θ，求cosθ的值，使得小路AO段与ON段的建造总费用最小．【答案】解：（1）在△AOM中，|AO|2=|AM|2+|OM|2-2|AM|•|OM|cos∠AMO，∴，化简得：|AM|2+2|AM|-3=0，∵|AM|＞0，∴|AM|=1，则|ON|=|MN|-|AM|=2-1=1，3×1=3，答：小路ON段的建造费用为3万元．（2）由正弦定理得：，则，，∴，设小路AO段与ON段的建造总费用为f（θ），则，，∴，若θ0满足，且，列表如下：θ（，θ0）θ0（θ0，）f'（θ）-0+f（θ）↘↗则当θ=θ0时，f（θ）有极小值，此时也是f（θ）的最小值，∴，答：当cosθ=，小路AO段与ON段的建造总费用最小．【解析】（1）根据余弦定理求出|AM|，即可求出|ON|=|MN|-|AM|=2-1=1，即可求出小路ON段的建造费用；（2）由正弦定理可得则，，，即可表示出，根据导数和函数最值得关系即可求出小路AO段与ON段的建造总费用最小．本题考查导数在实际问题中的运用：求最值，考查化简整理的运算能力，正确求出函数解析式和运用正余弦定理是解题的关键，属于中档题．20.过抛物线C：y2=2px（其中p＞0）的焦点F的直线交抛物线于A、B两点，且A、B两点的纵坐标之积为-16．（1）求抛物线C的方程；（2）当|AF|≠|BF|时，求的值；（3）对于x轴上给定的点D（n，0）（其中n＞2），若过点D和B两点的直线交抛物线C的准线P点，求证：直线AP与x轴交于一定点．【答案】解：（1）过抛物线C：y2=2px（其中p＞0）的焦点F（，0）的直线为x=my+，代入抛物线方程，可得y2-2pmy-p2=0，可设A（x1，y1），B（x2，y2），即有y1y2=-p2=-16，解得p=4，可得抛物线的方程为y2=8x；（2）由直线AB过抛物线的焦点F，可设A（ρ1，θ），B（ρ2，π+θ），由ρ=，可得+=+==，可得=•=1；（3）证明：设A（，y1），B（，y2），P（-2，s），由D（n，0），B，D，P三点共线可得=，可得s=，①设AP交x轴上的点为（t，0），即有=，代入①，结合y1y2=-16，可得=，即有8ny12-64nt=8ny12-（y1y2）2=8ny12-256，可得t=．即有直线AP与x轴交于一定点（，0）．【解析】（1）设直线AB的方程，联立抛物线方程，运用韦达定理，可得p=4，即有抛物线方程；（2）推得+=，即可得到所求值；（3）设A（，y1），B（，y2），P（-2，s），运用三点共线的条件：斜率相等，可得s，设AP交x轴上的点为（t，0），运用韦达定理，化简整理可得所求定点．本题考查直线和抛物线的位置关系，考查联立直线方程和抛物线方程，运用韦达定理和直线的斜率公式，考查化简运算能力，属于难题．21.已知数列{a n}为等比数列，a1=1，公比为q，S n为数列{a n}的前n项和．（1）若a3+a5=20，求；（2）若调换a5、a6、a7的顺序后能构成一个等差数列，求q的所有可能值；（3）是否存在正常数c、q，使得对任意正整数n，不等式总成立？若存在，求出q的取值范围；若不存在，请说明理由．【答案】解：（1）因为数列{a n}为等比数列，a1=1，公比为q，且q≠1，a3+a5=20，所以q2+q4=20，解得q2=4（-5舍去），则==1+q4=1+16=17；（2）若调换a5，a6，a7的顺序后能构成一个等差数列，即若调换q4，q5，q6的顺序后能构成一个等差数列，由等差数列的性质可得1+q=2q2或1+q2=2q或q+q2=2，解得q=1或-或-2；（3）假设存在正常数c，q，使得对任意正整数n，不等式总成立．由，即为＜0，等价为c＜S n＜2c，若q=1，可得c＜n＜2c，不成立；由a1=1，a n＞0，S n≥1，可得c＜1，当q＞1时，S2＞2＞2c不可能成立；当＜q＜1时，＞2可得q n＜2q-1，即n＞log q（2q-1），由＜q＜1，可得log q（2q-1）＞1，即当n＞log q（2q-1），S2＞2，所以S n＜2c不可能成立；当q=时，＜2c，即1-（）n＜c，可得（）n＞1-c，即当n＞log（1-c）时，S n＜2c不成立；当0＜q＜时，S n=＜，所以当＜c＜1时，c＜S n＜2c恒成立，综上可得，存在正常数c，q，使得对任意正整数n，不等式＞2总成立，且q的取值范围是（0，）．【解析】（1）运用等比数列的通项公式，解方程可得公比，求和公式计算即可得到所求值；（2）由等比数列的通项公式和等差数列中项的性质，解方程即可得到所求值；（3）假设存在正常数c，q，使得对任意正整数n，不等式总成立．由不等式，即为＜0，等价为c＜S n＜2c，讨论公比q，结合题意，推得存在，求得q的范围．本题考查等差数列和等比数列的通项公式和求和公式的运用，考查存在性问题的解法，以及分类讨论思想方法，化简整理和推理能力，属于难题．。
上海交通大学附属中学2018-2019学年高三第一学期摸底考试
上海交通大学附属中学2018-2019学年高三第一学期摸底考试英语试卷（考试时间120分钟；满分140分）第I卷Ⅰ. VocabularyDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.(A)1-5 BD A BC ABC D 6-10 B AB CB AC CTeenagers seem more likely to give in to peer influence than adults, but that may not be because teens are less 1 of making rational decisions themselves, studies on peer pressure suggest.Research finds people are strikingly susceptible to influences teenagers, but to what degree varies widely. In a growing body of work, scientists suggest that teens are more 2 to peer pressure than adults because they get greater pleasure from behavior they experience as rewarding. They tend to find being liked by other people very pleasing.Peer influence during adolescence is normal. During that time, people experience an increase in novelty-seeking, 3 by interest in exploring a new environment. This peer influence tends to 4 around age 15 and then decline. Teens get better at setting boundaries with peers by age 18, according to Laurence Steinberg, a psychology professor at Temple University.In years past, people thought teens didn’t have fully 5 frontal lobes (额叶), the part of the brain critical for decision-making and other more complex cognitive tasks. But an increasing amount of research seems to show that teens are able to make decisions as well as adults when they are not overwhelmed 6 with emotions.Peer pressure is often seen as negative, and indeed it can 7 teens into unhealthy behavior like smoking or speeding. But it can also lead to 8 in more useful social behavior. If peers value doing well in school or excelling at sports, for instance, it might encourage kids to study or train harder. And both peer pressure and learning to 9 it are important developmental steps to self-reliance, experts say.Facing the influence of friends represents an important developmental step for teens on their way to becoming independent-thinking adults, scientists say.In order for kids to develop the ability to stand up to peer pressure, parents have to let their children stand up to them, too, according to Dr. Steinberg. “If you’re the kind of parent that raises your children with the ‘do it because I said so’ 10 , you’re raising a child who’s going to be more susceptible to others saying, ‘Do this,’” he says.(B)1-5 CD C A D AC 6-10 ABC BC AB B BDStudents Honor 9/11 Through VolunteeringIn the days after Sept. 11, 2001, thousands poured into Ground Zero to lend their hands in one of the largest recovery efforts(恢复经济) in American history. Now, 12 years later, colleges are finding ways to channel（疏通）the same 1 into service projects in their own communities on September 11th."9/11 is such a(n) __2__ touchstone（试金石）for our country, I think people want to find ways to do something, and students as well," says Kevin Kruger, president of the student affairs group. "The idea of giving something back to the __3__ ties in well to（密切配合）the emotional significance of that."Though no corner of the country was untouched by the terrorist attacks, they especially rocked （晃动）New York University on 9/11. Less than two miles from Ground Zero, students__4__ the plane-on-tower impact from their dorm rooms. The university coordinated（协调）shelters and counseling（提供建议）in the days afterward.Because of this, NYU public affairs director Philip Lentz says the volunteer work the students do this week has a "special relevance（关联）." Students today __5__ at a rescue mission, wrote cards for soldiers and veterans（老兵）and made donations for the families of victims and first responders （现场目击者）on 9/11."NYU feels it has a special __6__ to offer this service opportunity to students that are here so they can give back to the community that was so devastated（毁灭）by the attacks," Lentz says.Similar deeds have been taking place in George Washington University in Washington, D.C. "For the past five years at GW, freshmen have boarded buses immediately after their official welcome __7__ in early September to head for the nation's financial capital and volunteer in __8__ that aid the environment, education, veterans and community organizations," says Amy Cohen, theuniversity's director for civic engagement and public service."We hope that students will learn that community __9__ is part of how we build strong communities and a vibrant __10__ society," Cohen wrote in an e-mail to USA TODAY. "We ask students to reflect on the tragedy of 9/11 and to use this day as a way to show civic engagement and community building."Ⅰ. Reading comprehension.Section ADirections:For each blank in the following passage there are four words or phrases marked A, B, C, D. Fill in each blank with the word or phrase that best fits the context.(A)Harvard LibraryIf we compare professors and students to the host of a university, then the library of a university can be compared to the hallway. The quality of a university, 1 , is in direct proportion to that of its library. At Harvard，the library is an essential part of everybody's life. Both the quantity and the 2 of the library make study a pleasant process.Harvard Library is not only the most ancient library in the United States, but the largest university library with the largest scale. In 1638 John Harvard 3 his whole library to the then Harvard College. After 300 years of development, the library now holds 10 million books and 4 more than 100 branch libraries. In addition to the libraries owned by each school, there are some branch libraries that are 5 in some aspects. While most of the branch libraries are on Harvard campus, some are as far as in Washington, D.C., or even in Florence of Italy. Yenching Library is famous for its 6 of East Asian literature. Lamont Library is the first library in the world that is 7 for undergraduates. Widener Library is the largest library in Harvard, only second to Library of Congress.What 8 to be mentioned is the system or rather theservice of the libraries. Usually the libraries are open from 9 a.m. to 5p.m.. The main libraries are open until 10 p.m.. The libraries forundergraduates will even be open all night during the 9period. The libraries also provide with students the service of 10 reading materials for all courses. At the beginning of a semester, each teacher will give a list of books to the librarians. The librarians are 11 to find out these books and put them at the places where students can easily find them.There is no limitation for the number of books that students can borrow. As the space for thelibrary is limited, many books are 12 in suburban library. Despite this, students can go to fetch the book at the 13 library within 24 hours after they submit request for that book. Even if there is only one book to be fetched from the suburban library, the libraries on campus will send someone to do the job. This kind of 14 which put readers in the first place is rare even in Ivy League. Therefore, study at Harvard will be a(n) 15 experience.A）1-5 BCADB 6-10 ACDAB 11-15 DCABD1. A. as a result B. to some extent C. on the contrary D. at all times2. A. influence B. discipline C. quality D. prospect3. A. donated B. assigned C. adapted D. distributed4. A. contains B. composes C. involves D. includes5. A. informative B. different C. secure D. peculiar6. A. collections B. documents C. phenomena D. exhibitions7. A. unusually B. formally C. specially D. especially8. A. remains B. happens C. appears D. deserves9. A. examination B. experiment C. vacation D. graduation10. A. confirming B. preparing C. selecting D. designing11. A. desperate B. willing C. reluctant D. responsible12. A. exhibited B. reserved C. stored D. classified13. A. appointed B. accepted C. expected D. restricted14. A. performance B. service C. activity D. response15. A. fortunate B. creative C. positive D. enjoyable(B)Instead of cruising in on a hoverboard, I rode my bike to the office today. The bicycle was invented in the 19th century. Instead of taking a pill for breakfast, I had a bacon roll, cooked using gas. Science fiction has 1 to us.Making predictions is tricky, especially about the future, as physicist Niels Bohr joked. In science fiction, you can't escape that 2 though. Since its birth in the 19th century, writers have 3 imagined the things to come: devices that humankind will invent to make life easier. But in so many instances, those promises have not come to pass. The biggest 4 are in travel--jet packs, hoverboards and flying cars are yet to fill the skies. Air travel has become significantly cheaper and wide-reaching, but only using distinctly 20th-century technology: commercial aero planes are much the same as they were 50 years ago.5 is what science fiction frequently delivers, but its arrival in the real world has been unpredictable. Domestic robots with a degree of intelligence are yet to6 , though robotic vacuum cleaners are commercially available--even if they are fairly hopeless. Video calls have now arrived--sort of--but conferencing on Skype is still dissatisfying. In mobiles, video call technology is now available, so when your dad rings to update you on his vegetable patch, he'll be able to7 your look of boredom.The truth is that we quickly 8 the astonishment of invention: our wonderment is soon replaced with the feeling of nothing new. We should ty to stay in that period of 9 . It is astonishing that the contents of every book ever written can be stored in a small box. Or that you can carry 10,000 albums on an object kept in your pocket. Or that almost all the information in the world can be accessed almost anywhere at any time. All these 10 are dependent on the emergence of the microchip and its place in computers. Yet sci-fi didn’t 11 the dominance of the computer in running our lives.But the real area where 12 far outstrips predictions is medicine. Sure, fiction would describe humans as ‘disease-free’ but without going into detail. “Disease-fee” humans are still absent, but the progress made in 13 life is breathtaking. With relative ease, we can sequence anyone's genome (基因组), giving a read-out of our entire genetic code. This means we can find out the underlying genetic cause of thousands of diseases in minutes.Photosensitive implants now exist that can replace damaged cells in the retina (视网膜) and can thus 14 sight to the blind. While the inventions of science fiction can show great ideas we’d like to happen, nothing 15 the inventiveness of people in the real world.B）1-5 BBDAC 6-10 ACCBD 11-15 ADACD1. A. tuned B. lied C. objected D. talked2. A. opportunity B. challenge C. Imagination D. conflict3. A. hesitantly B. critically C. temporarily D. tirelessly4. A. disappointments B. advancements C. enjoyments D. experiments5. A. Modernization B. Exploration C. Automation D. Transportation6. A. materialize B. identify C. honour D. liberate7. A. imagine B. feel C. see D. ignore8. A. arouse B. discover C. forget D. evaluate9. A. frustration B. amazement C. boredom D. limitation10. A. modes B. worries C. potentials D. actions11. A. predict B. overlook C. motivate D. prevent12. A. quality B. obstacle C. passion D. reality13. A. maintaining B. creating C. researching D. encountering14. A. show B. lend C. restore D. label15. A. guarantees B. overestimates C. releases D. OutperformsSection BDirections:Read the following three passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)In his book The Tipping Point Canadian author Malcolm Gladwell explains how a trend can take many forms. It can be a general change in social behaviour, an idea or a fashion. However, why do some trends catch on and others not? What makes one particular brand of training shoe suddenly become the must-have product? How do people find out about trends and what makes people want to buy into them? Is it simply a question of keeping up with other people?In his new work, Gladwell explores the moment when something becomes common and how products, ideas messages and forms of behaviour spread. He looks at the reasons why trends are similar in the way they develop to outbreaks of disease, or medical epidemics.Epidemics, like trends, start in a very small way, maybe from a single person with a virus, then spread very quickly until they take over the population and appear to be everywhere. Eventually, they will slowdown gradually or die out suddenly. Gladwell shows how these changes happen not gradually but at one dramatic moment.Gladwell identifies three types of people who are influential in the development of these kinds of social epidemics.Connectors are people in a community who have wide social circles. They know a lot of people and like to introduce people to catch other. The people they know also tend to come from a variety of social, cultural professional and economic circles.Mavens are people with a lot of knowledge or experts in a particular field. They wish to pass on their knowledge to others. Mavens collect and gather information so are the first to pick up on new trends.Salesmen are people with charisma and powerful negotiation skills. They have a soft influence over people rather than actual power. This means they are influential because people want to imitate them.Overall, Gladwell's book is a thought-provoking read for anyone interested in the origins oftrends. What's more, he writes in a clear style so even the most difficult ideas are easy to understand.71.According to Gladwell, which of the following is a similarity between trends and epidemics?A. Both of them start from nowhereB. Both of them die out in a short timeC. Both of them become popular overnightD. Both of them change he way people think72. What can be concluded from the passage about The Tipping Point?A. It is the writers first book to touch on social phenomenaB. It is intended to introduce the trends that once took overC. It deals with the ideas that most people identify withD. It explores How a trend originates and spreads73. The passage is most likely to beA. an adver sementB. a reviewC. a news reportD. a feature story74. Salesmen work in the development of trends by means ofA people intention to follow themB the way they gather informationD. their influence on the trendsC. their professional knowledge（B）(*Please purchase a ticket before boarding the coach75. On December 25th, 2014, the first coach from, Heathrow Terminal I to Reading departs at____.A.7:15B.7:00C.6:50D.6:3576. If you are to reach Terminal 2 of the Heathrow Airport before 10: 00 a.m., you need to get to Reading Station not later than____.A $. 30am B.8:45am C.9:00a,m. D.9:15a.m77. The information leaflet is produced by____.A. ReadingB. IntercityC. Railair LinkD. Heathrow Airport(C)As students are discussing their favorite colleges, there’s one characteristic they can’t control their race. That’s one reason voters, courts and politicians in six states have outlawed racial preferences in college admissions, while other colleges, fearful-of lawsuits, play down their affirmative action efforts these days. But make no mistake race still matters. How much depends on the school and the state.In: Texas, public universities have managed to reduce the effect of racial-preference bans by automatically admitting the top 10% of the graduating class of every high school, including those schools where most students are minorities. But Rice University in Houston, private and highly selective, has had to reinvent its admissions strategies to maintain the schools minority enrollment. Each February, 80 to 90 black, Hispanic(西班牙裔) and Native American kids visit Rice on an expenses-paid trip. Rice urges headmasters from high schools with large minority populations to recommend qualified students. And in the fall, Rice sends two recruiters on the road to find minority applicants; each recruiter visits about 80 mainly black or Hispanic high schools. Two weeks ago, Rice recruiter Tamara Siler dropped in on Westlake High in Atlanta, where 99% of the 1296 students are black. Siler went hearing literature and advice, and though only two kids showed up, she said: "Tm pleased I got two."Rice has also turned to some almost comical end-runs around the spirit of the law. The university used to award a yearly scholarship to a Mexican-American student; now it goes to a student who speaks Spanish really well. Admissions officers no longer know an applicant’s race. But a new essay question asks about each student "background" and "cultural traditions". When Rice officials read applications, they look for "diverse life experiences and what they awkwardly call "overcome students", who have triumphed over hardship.Last spring, admissions readers came across a student whose SAT score was lower than 1,200 and who did not rank in the top 10% of her class. Numerically speaking, she was far behind mostaccepted applicants: But her essay and recommendations indicated a strong interest in civil rights and personal experience with racial discrimination. She was admitted. All the newspapers say affirmative action is done, “says an experienced adviser at a large New York City high school. But nothing has changed. I have a(minority)kid at Yale with an SAT score in the high 900s.78. What does the word outlaw"(in Para. 1)most probably mean?A. supportB. consider D. hateC. ban79. What can we infer from the passage about affirmative action?A. It guarantees students, of different races to be admitted equally.B It discriminates against minority students in college admissions.C. It gives preference to minority students in college admissions.D. It is popular with American colleges but not with the American public80. Why does Rice University send two recruiters to find minority applicants?A. Rice has a large minority populationB: Rice wants to maintain its minority enrollmentC Minority students do not favor Rice very muchD. Minority students have better school performance81. Which of the following might be the best title of the passage?A: Here Comes Equality at LastB. Yes. Your Race Still MattersC. Well Done. Affirmative ActionD. Minorities Are Still a Minority in Universities(D)Direction: Read the following passage. Fill in each blank with a proper sentence given in the box.Sleep in a BoxHaving a newborn can be discouraging and troublesome. What do you need to buy? How will you get the baby to sleep? And how will you pay for everything? Could the answers to these worries lie in a “baby box"?The baby box has taken the world by storm, but what is it? Well, it originated in Finland in thel930s as a kind of basic items for parents-to-be. The box, provided by the government, contains supplies, such as bibs, nappies, and teething toys. It also comes with a small mattress, which is placed in the bottom of the box to create the baby’s first small bed. Now, the idea of putting a child to sleep inbox may shock some. 82_______ the box has been a huge success and is said to be one of the main reasons why the death rate of infants in Finland is so low.A few years ago, stories of the Finnish baby box went relating to viruses. Other countries around the world have since caught onto the idea and adapted it to suit local needs. For example, in South Africa, the box is made of plastic and can be used as a bath rather than a bed. A(83* The version tested in India includes other appropriate supplies, such as a mosquito het to protect babies from malaria(疟疾).In Canada, additions to the baby box include a bed-side assistance booklet “to help fathers connect with their babies, Written in the style of a car-repair manual, the booklet offers first-time dads helpful advice on matters such as how to burp(使打嗝)their child. 84________ I wanted to make that moment available to all parents,” said Morris, a father of a two-month baby boy.85_________ Many believe governments should focus on providing parents with adequate maternity and paternity Leaves(父母产假) and improving health care and education．Good things cone in small packages, though, and for such a simple idea the baby box really does do a lot of things!第II卷Ⅰ.GrammarDirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)E-cigarettes, widely prompted as an alternative (1)_____to smoking, are actually attractingyoung people who might not otherwise (2)_____(smoke) tobacco products, a new US study suggested Monday.E-cigarettes (3)_____(think) by some to be responsible for a decline in American youth cigarette smoking, but researchers from the University of California, San Francisco (UCSF) indicated the reality is the opposite.The USCF researchers concluded that many kids who went on (4)_____(smoke) regular cigarettes may not have used nicotine(尼古丁) at all if e-cigarettes did not exist. "We didn't find any evidence that e-cigarettes are causing youth smoking to decline," said lead author Lauren Dutra of the UCSF.(5)_____ some of the kids using e-cigarettes were also smoking cigarettes, we found that kids who were at low risk of starting nicotine with cigarettes were using e-cigarettes," Dutra said. "Recent declines in youth smoking are likely (6)_____ tobacco control efforts, not to e-cigarettes."The findings, published in U.S. journal Pediatrics, built on a growing body of evidence that adolescents who start with e-cigarettes are (7)_____(likely) to subsequently smoke traditional cigarettes.They found that cigarette smoking among U.S. adolescents declined during that decade, but did not decline faster (8)_____ the advent of e-cigarettes in the U.S. between 2007 and 2009."E-cigarettes are encouraging -- not discouraging -- youth to smoke and to consume nicotine, and (9)_____(expend) the tobacco market," said senior author Stanton Glantz, UCSF professor of medicine and director of the UCSF Center for Tobacco Control Research and Education.In August 2016, the U.S. Food and Drug Administration restricted e-cigarette purchases to adults ages 18 and older. The FDA will also require a warning label on e-cigarettes, starting August 2018, regarding the addictive nature of nicotine. However, the FDA's (10)_____(rule) does not regulate advertising or flavors, and e-cigarettes continue to be sold in flavors that appeal to youth, the UCSF researchers said.(B)There seems never (11)______(be) a civilization without toys, but when and how they developed is unknown. They probably came about just to give children something to do.In the ancient world, (12)______is today, most boys played with some kinds of toys and most girls with another. In societies (13)______ social roles are rigidly determined, boys pattern their play after the activities of their fathers and girls are (14)______ the tasks of their mothers. This is true because boys and girls are being prepared, even in play, (15)______(step) into the roles and responsibilities of the adult world.What is remarkable about the history of toys is not so much (16)______ they changed over the centuries but how much they (17)______(remain) the same.The changes have been mostly in terms of craftsmanship, mechanics, and technology. It is the universality of toys with regard to their development in all parts of the world and (18)______ persistence to the present that is amazing. In Egypt, America, China, Japan and among the Arctic people, generally the same kinds of toys (19)______(appear). Variations depended on local customs and ways of life (20)______ toys imitate their surroundings. Nearly every civilization had dolls, little weapons, toy soldiers, tiny animals and vehicles.(C)In a shocking turn of events, the Academy Award for Best Picture was mistakenly awarded to "La La Land," (21)______ cast(剧组演员) and crew took the stage and began giving speeches－until a moment later the producers realized actually the award (22)_______(mean) for "Moonlight”.Presenter Warren Beatty explained afterwards that he was handed the wrong envelope, which contained the winner for best actress Emma Stone (23)______(star) in " La la land” After staring at the card for several moments, in (24)______ appeared to be an attempt to build suspense, his co-presenter Faye Dunaway announced that “La La Land" had won best picture.Realizing the mistake, representatives of Price Waterhouse Coopers raced onstage to stop the acceptance speeches from the "La La Land” team, and called the "Moonlight" cast and crew to the stage. Barry Jenkins’ "Moonlight" had actually won best picture in a historic Oscar upset."La La land" came in with 14 nominations, a record that tied (25)_____with “Titanic” and “All About Eve”. Barry Jenkins tender, coming-of-age drama, made for just $1.5 million, is an unusually small Oscar winner. "Even in my wildest dreams this cannot be true, " said the astonished Jenkins once he reached the stage.Host Jimmy Kimmel had come forward(26)______(inform) the cast that "Moonlight" had indeed won, showing the inside of the envelope(27)_______ proof. And Producer Jordan Horwitz then graciously passed his statue to the "Moonlight" producers.Barry Jenkins, the writer-director of "Moonlight" and Tare Alvin McCraney, whose play it was based on, won for(28)_______(adapt) screenplay. “For all you people out there (29)_______feel like there isn’t a mirror out there for you, the academy has your back, the ACLU has your back and for the next four years we will not leave you alone, we will not forget you, " said Jenkins.Backstage, Oscar winner Emma Stone said, "I think everyone’s in a state of confusion still. Later the actress, who pledged her deep love of "Moonlight" added, "Is that(30)______(crazy)Oscar moment of all time? Cool!Ⅰ.Translation1．你是否具备了成为一名演员的必要素质？(take)2．不可否认的是均衡的饮食是保持健康的关键之一。
上海市交大附中2019届高三高考一模试卷数学试题
2019年上海市交大附中高考数学一模试卷一、选择题(本大题共4小题，共12.0分)1. 已知定义域为R的函数*(22,2],()21,055x k k k N f x x x ⎧∈-∈⎪=⎨-≤⎪⎩，则此函数图象上关于原点对称的点有( )A. 7对B. 8对C. 9对D. 以上都不对 【答案】B【解析】解：当0x =时，1(5)f x =-，此时1(0,)5-关于原点对称的点1(0,)5此时与()f x 没有交点， 函数2155y x =-关于原点对称的函数为2155y x -=--，即2155y x =+，0x >， 若函数图象上关于原点对称的点，等价为当0x >时，()f x =2155y x =+，0x >的交点个数即可， 作出函数()f x 在0x >时的图象如图，由图象知，函数分别关于1,3,5,7,9x x x x x =====对称，且函数的最大值为3(2)1f k -=， 当21355x y +==时，得21455x =，即7x =， 故当0x >时，()f x =2155y x =+，0x >的交点个数有8个， 即函数图象上关于原点对称的点有8对，故选：B ． 求出函数2155y x =-关于原点对称的函数为2155y x =+，0x >，利用数形结合判断当0x >时，()f x =2155y x =+，0x >的交点个数即可 本题主要考查函数与方程的应用，利用对称性转化为两个图象交点个数是解决本题的关键．注意利用数形结合是解决本题的关键．2. 某超市货架上摆放着某品牌红烧牛肉方便面，如图是它们的三视图，则货架上的红烧牛肉方便面至少有( )A. 8桶B. 9桶C. 10桶D. 11桶 【答案】B【解析】解：易得第一层有4碗，第二层最少有3碗，第三层最少有2碗，所以至少共有9个碗．故选：B ．主视图、左视图、俯视图是分别从物体正面、左面和上面看，所得到的图形．考查学生对三视图掌握程度和灵活运用能力，同时也体现了对空间想象能力方面的考查．如果掌握口诀“俯视图打地基，正视图疯狂盖，左视图拆违章”就更容易得到答案．3. 已知2(3)f x x x =+，若1x a -≤，则下列不等式一定成立的是( ) A.33()()f x f a a -≤+ B. 24()()f x f a a -≤+ C. ()()5f x f a a -≤+ D. 2|()()2|(1)f x f a a -≤+ 【答案】B【解析】解：∵1x a -≤，∴11a x a -≤≤+，∵()f x 是二次函数，∴()f x 在区间1,1[]a a -+上单调时，()()f x f a -取得最大值为|()(|1)f a f a +-或|()(|1)f a f a --， 而22()()()11313242())4f a f a a a a a a a +-+++--=+≤+=， 22|()()||()(11313||22||22|2|)2|f a f a a a a a a a a ---+---=--=+≤+=． ∴24()()f x f a a -≤+，故选：B ．结合二次函数的图象可知，当()f x 在区间1,1[]a a -+单调时，|()()|f x f a -的最大值为|()(|1)f a f a +-或|()(|1)f a f a --，从而得出结论．本题考查了二次函数的性质，利用函数的最值研究恒成立问题的思路，同时结合函数图象分析问题是关键．4. 若2a b c ===，且0a b ⋅=，()()0a c b c -⋅-≤，则a b c +-的取值范围是( )A. [0,2]B. [0,2]C. 2,2]D. 2,2] 【答案】D【解析】解：∵2a b c ===，且0a b ⋅=，()()0a c b c -⋅-≤，∴20a b a c b c c ⋅-⋅-⋅+≤，∴4a b a c b c ≥-⋅+⋅+⋅，∴222222244484a b c a b c a b a c b c +-=+++⋅-⋅-⋅≤++-=， ∴2a b c +-≤，又由0a b ⋅=，得：22a b +=， 故222a b c a b c +-≥+-=-，故a b c +-的取值范围是2,2]，故选：D ．由0a b ⋅=，得：22a b +=，故222a b c a b c +-≥+-=-，结合()()0a c b c -⋅-≤，得2a b c +-≤，进而得到答案．本题考查的知识点是平面向量的数量积运算，向量的模，难度中档．二、填空题(本大题共12小题，共36.0分)5. 已知集合02{|}A x x =<≤，集合12{|}B x x =-<<，则A B =______．【答案】{x|-1<x ≤2}【解析】解：∵集合02{|}A x x =<≤ }，集合12{|}B x x =-<<，∴1|}2{A B x x =-<≤．故答案为：2{|}1x x -<≤．利用并集定义直接求解．本题考查并集的求法，是基础题，解题时要认真审题，注意并集定义的合理运用．6. 若复数43z i =+，其中i 是虚数单位，则2z =______．【答案】25【解析】解：由43z i =+，得222431624972()4z i i i i =+=++=+，则272425z i =+==．故答案为：25．直接利用复数代数形式的乘除运算化简，再由复数模的公式计算得答案．本题考查了复数代数形式的乘除运算，考查了复数模的求法，是基础题．7. 函数4,(4)()(3)(4)x x f x f x x -≥⎧=⎨+<⎩，则[()]1f f -=______． 【答案】0【解析】解：12()())541(5f f f -===-=所以[()]()1140()f f f f -===故答案为0先根据函数的解析式求出1()f -的值，再求出[()]()1140()f f f f -===．求分段函数的值，关键是判断出自变量所属的范围，然后将自变量的值代入相应段的解析式求出值．8. 已知)in(1s 43πα-=，则)os(c 4πα-=______．【答案】【解析】解：∵)in(1s 43πα-=，∴cos 4(3)πα-==±．故答案为：3± 根据in 4(s )πα-的值，利用同角三角函数间的基本关系求出os 4(c )πα-的值即可． 此题考查了运用诱导公式化简求值，以及同角三角函数间的基本关系，熟练掌握基本关系是解本题的关键．9. 已知数列{}n a 的前n 项和为2*()2n S n n n N =+∈，则数列{}n a 的通项公式n a =______．【答案】*2)1(n n N +∈【解析】解：当2n ≥，且*n N ∈时，221()[()(2121)]n n n a S S n n n n -=-=+--+-22222)2(1n n n n n =+--++-21n =+，又211123S a ==+=，满足此通项公式，则数列{}n a 的通项公式*21()n a n n N =+∈． 故答案为：*2)1(n n N +∈由数列的前n 项和公式22n S n n =+，表示出当n 大于等于2时，前1n -项和1n S -，利用1n n n a S S -=-得出n 大于等于2时的通项公式，把1n =代入此通项公式检验也满足，故得到数列的通项公式． 此题考查了等差数列的通项公式，熟练掌握数列的递推式1n n n a S S -=-是解本题的关键，同时注意要把首项代入通项公式进行验证．10. 已知实数,x y 满足约束条件222441x y x y x y +≥⎧⎪+≤⎨⎪-≥-⎩，则目标函数3z x y =+的取值范围为______．【答案】[1,6]【解析】解：由约束条件222441x y x y x y +≥⎧⎪+≤⎨⎪-≥-⎩作出可行域如图，联立2224x y x y +=⎧⎨+=⎩，解得()2,0A ， 联立2241x y x y +=⎧⎨-=-⎩，解得()0,1B ． 化目标函数3z x y =+为3y x z =-+，由图可知，当直线3y x z =-+过B 时，直线在y 轴上的截距最小，z 有最小值为1，当直线3y x z =-+过A 时，直线在y 轴上的截距最大，z 有最小值为6．∴目标函数3z x y =+的取值范围为[1,6]．故答案为：[1,6]．由约束条件作出可行域，化目标函数为直线方程的斜截式，数形结合得到最优解，联立方程组求得最优解的坐标，代入目标函数得答案．本题考查简单的线性规划，考查了数形结合的解题思想方法，是中档题．11. 已知函数sin 2cos ()(2,,0)f x a x b x a b R ab =+∈≠，若其图象关于直线6x π=对称，则直线20ax by ++=的倾斜角α=______． 【答案】23π【解析】解：∵函数 sin 2cos 2y a x b x =+(,a b 不全为0)的图象关于直线6x π=对称， 设sin θ=，cos θ=，∴sin 2cos 222)y a x b x x x =+=+(n 2)x θ=+， 当6x π=时，2,32()x k k Z ππθθπ+=+=+∈， ∴,32()6k k k Z πππθππ=-++=+∈，不妨取0k =时，得6θπ=；∴1sin 2θ==，cos θ==，解得a =1b =；∴直线l ：0ax by c ++=可化为：0y c ++=，它的斜率为k =∴倾斜角是23π； 故答案为：23π． 化简函数sin 2cos 2y a x b x =+为一个角的一个角的函数形式，利用6x π=是函数sin 2cos 2y a x b x=+图象的一条对称轴，求出,a b 的值，然后求直线l 的斜率与倾斜角．本题考查了三角函数与向量知识的综合应用问题，是综合题目．12. 鲁班锁是中国传统的智力玩具，起源于古代汉族建筑中首创的榫卯结构，这种三维的拼插器具内部的凹凸部分(即榫卯结构)啮合，十分巧妙，外观看是严丝合缝的十字立方体，其上下、左右、前后完全对称．从外表上看，六根等长的正四棱柱体分成三组，经90︒榫卯起来，如图，若正四棱柱体的高为6，底面正方形的边长为1，现将该鲁班锁放进一个球形容器内，则该球形容器的表面积的最小值为______．(容器壁的厚度忽略不计)【答案】41π2=， ∴该球形容器的表面积的最小值为414414ππ⋅=． 故答案为41π2，即可求出该球形容器的表面积的最小值． 本题考查正棱柱的外接球，考查学生的计算能力，属于中档题．13. 已知232*012(1)(1)(1)(1)()n n n x x x x a a x a x a x n N ++++++++=++++∈，且012126n a a a a +++⋯+=，那么n 展开式中的常数项为______． 【答案】20 【解析】解：∵已知232*012(1)(1)(1)(1)()n n n x x x x a a x a x a x n N ++++++++=++++∈，且012126n a a a a +++⋯+=，∴令1x =，可得210122(12)2222212612n nn n a a a a +-+++⋯+=++⋯+==-=-，∴6n =，那么6n=的展开式的通项公式为316(1)r r r r T C x -+=⋅-⋅，令30r -=，求得3r =， 可得展开式中的常数项为3620C =，故答案为：20．由题意令1x =，可得4n =，再利用二项展开式的通项公式，求得展开式中的常数项．本题主要考查二项式定理的应用，注意根据题意，分析所给代数式的特点，通过给二项式的x 赋值，求展开式的系数和，可以简便的求出答案，二项展开式的通项公式，属于基础题．14. 已知正实数,x y 满足2342xy x y ++=，则54xy x y ++的最小值为______．【答案】55【解析】解：∵正实数,x y 满足2342xy x y ++=，∴42203x y x-=>+，0x >，解得021x <<． 则42216543423423[(3)]3133x xy x y x y x x x x -++=++=++=+++++33155≥⨯=，当且仅当1,10x y ==时取等号． ∴54xy x y ++的最小值为55．故答案为：55．正实数,x y 满足2342xy x y ++=，可得42203x y x-=>+，解得021x <<．则 42216543423423[(3)]3133x xy x y x y x x x x-++=++=++=+++++，再利用基本不等式的性质即可 得出．本题考查了基本不等式的性质、不等式的解法，考查了推理能力与计算能力，属于中档题．15. 已知等边ABC △的边长为2，点P 在线段AC 上，若满足等式PA PB λ⋅=的点P 有两个，则实数λ的取值范围是______． 【答案】1(,0]4-【解析】解：设02()PA x x =≤≤，则2PC x =-． ∴2x PB PA AB AC AB =+=-+， 又22cos602AB AC ⋅=⨯⨯︒=， ∴222211()224224()x x x x PA PB AC AC AB AC AB AC x x x λ=⋅=--+=-⋅=-=--． 令2(11(4))2f x x =--，则()f x 在1[0,]2上单调递减，在1(,2]2上单调递增， 且0(0)f =，()1124f =-，2(2)f =． ∵满足等式PA PB λ⋅=的点P 有两个，∴关于x 的方程()f x λ=在[0,2]上有两解，∴104λ-<≤． 故答案为：1(,0]4-． 设PA x =，得出式PA PB ⋅关于x 的函数，根据函数的单调性得出λ的范围．本题考查了平面向量的数量积运算，属于中档题．16. 过直线2l x y +=:上任意点P 向圆221C x y +=:作两条切线，切点分别为,A B ，线段AB 的中点为Q ，则点Q 到直线l 的距离的取值范围为______．【答案】[,2【解析】解：∵点P 为直线2l x y +=:上的任意一点，∴可设2(),P t t -，则过O A P B 、、、的圆的方程为222221()()[22()]24tt x y t t --+-=+-， 化简可得22()20x tx y t y -+--=，与已知圆的方程相减可得AB 的方程为21()tx t y +-=，由直线OP 的方程为(20)t x ty --=， 联立两直线方程可解得2244t x t t =-+，22244t y t t -=-+， 故线段AB 的中点222(,)244244t t Q t t t t --+-+， ∴点Q 到直线l的距离2122d t t ==--+， ∵222211)1(t t t -+=-+≥，∴210122t t <≤-+， ∴211022t t -≤-<-+，∴2112222t t ≤-<-+，∴21222t t ≤-<-+[,2d ∈故答案为：[,2设2(),P t t -，可得过O A P B 、、、的圆的方程与已知圆的方程相减可得AB 的方程，进而联立直线方程解方程组可得中点Q 的坐标，由点Q 到直线的距离公式和不等式的性质可得．本题考查直线与圆的位置关系，涉及圆的相交弦和点到直线的距离公式，以及不等式求函数的值域，属中档题．三、解答题(本大题共5小题，共60.0分)17. 在ABC △中，a b c 、、分别为角A B C 、、的对边，已知cos 23co 1)s(A B C -+=．(1)求角A 的值；(2)若2a =，求ABC △周长的取值范围．【答案】解：(1)ABC △中，cos 23co 1)s(A B C -+=，22cos 13()(co )s 1A A --⋅-=，22cos 3cos 20A A +-=， 解得1cos 2A =或cos 2A =- (不合题意，舍去)， ∴1cos 2A =，3A π=； (2) 2a =，3A π=，由正弦定理可得sin sin sin b c a B C A ====；∴b B =，c C =，∴2s n sin )i a b c B C ++=+22sin()sin 3(]C C π=+-+32)s sin 2C C =++24sin 6()C π=++， ∵203C π<<， ∴5666C πππ<+<， ∴1si 1n 6(2)C π+≤<， 24sin 6()4C π+≤<， 则(4664sin )2C π<+≤+，即46a b c <++≤，∴ABC △的周长的取值范围是(4,6]．【解析】(1)根据二倍角公式化简求解即可求出角A 的大小；(2)由正弦定理求得b c 、的值，再利用三角恒等变换计算a b c ++的取值范围．本题考查了正弦定理、两角和与差的正弦公式、三角函数的单调性应用问题，是中档题．18. 在如图所示的组合体中，三棱柱111ABC A B C -的侧面11ABB A 是圆柱的轴截面，C 是圆柱底面圆周上不与A B 、重合的一个点．(Ⅰ)若圆柱的轴截面是正方形，当点C 是弧AB 的中点时，求异面直线1AC 与1AB 的所成角的大小；(Ⅱ)当点C 是弧AB 的中点时，求四棱锥111A BCC B -与圆柱的体积比．【答案】解：(Ⅰ)如图，取BC 的中点D ，连接,OD AD ，则1OD AC ∕∕，∴AOD ∠ (或其补角)为异面直线1AC 与1AB 的所成角，设正方形的边长为2，则A O D △中，112OD AC ==，AO AD =，∴352cos AOD+-∠==∴AOD∠=；(Ⅱ)设圆柱的底面半径为r，母线长度为h，当点C是弧AB的中点时，AB BC==，111212))33A BCC BV h r h-=⋅⋅⋅=，2V r hπ=圆柱，∴111:2:3A BCC BVVπ-=圆柱．【解析】(Ⅰ)取BC的中点D，连接,OD AD，则1OD AC∕∕，AOD∠(或其补角)为异面直线1AC与1AB的所成角，利用余弦定理，可求异面直线1AC与1AB的所成角的大小；(II)设圆柱的底面半径为r，母线长度为h，当点C是弧弧AB的中点时，求出三棱柱111ABC A B C-的体积，求出三棱锥1A ABC-的体积为，从而求出四棱锥111A BCC B-的体积，再求出圆柱的体积，即可求出四棱锥111A BCC B-与圆柱的体积比．本小题主要考查直线与直线的位置关系，以及几何体的体积等基础知识，考查空间想象能力、运算求解能力、推理论证能力，考查数形结合思想、化归与转化思想，属于中档题．19. 一个创业青年租用一块边长为4百米的等边ABC△田地(如图)养蜂、产蜜与售蜜．田地内拟修建笔直小路,MN AP，其中,M N分别为,AC BC的中点，点P在BC上．规划在小路MN与AP的交点O(O与M N、不重合)处设立售蜜点，图中阴影部分为蜂巢区，空白部分为蜂源植物生长区，,A N为出入口(小路的宽度不计)．为节约资金，小路MO段与OP段建便道，供蜂源植物培育之用，费用忽略不计．为车辆安全出入，小路AO段的建造费用为每百米4万元，小路ON段的建造费用为每百米3万元．(1)若拟修的小路AOON段的建造费用；(2)设BAPθ∠=，求cosθ的值，使得小路AO段与ON段的建造总费用最小．【答案】解：(1)在AOM △中，2222cos AO AMOM AM OM AMO =+-⋅∠，∴222222cos 3AMAM π=+-， 化简得：2230AM AM +-=， ∵0AM >，∴1AM =，则211ON MN AM =-=-=，313⨯=，答：小路ON 段的建造费用为3万元．(2)由正弦定理得：sin sin sin()33AM AO OM θθ==-，则AO =OM =，∴sin sin 2sin sin ON MN AM θθθθθθ-=-=-=， 设小路AO 段与ON 段的建造总费用为()f θ，则9sin ()43sin f AO ON θθθθ-+=+=，63ππθ<<，∴2'()sin f θθθ=， 若0θ满足03cosθ=，且0ππθ<<，列表如下： 则当0θθ=时，()f θ有极小值，此时也是()f θ的最小值，∴03cos cos 4θθ==， 答：当3cos 4θ=，小路AO 段与ON 段的建造总费用最小．【解析】(1)根据余弦定理求出AM ，即可求出211ON MN AM =-=-=，即可求出小路ON 段的建造费用；(2)由正弦定理可得则AO =OM =，sin sin 2sin sin ON MN AM θθθθθθ-=-=-=，即可表示出9sin ()43sin f AO ON θθθθ-+=+=，根据导数和函数最值得关系即可求出小路AO 段与ON 段的建造总费用最小．本题考查导数在实际问题中的运用：求最值，考查化简整理的运算能力，正确求出函数解析式和运用正余弦定理是解题的关键，属于中档题．20. 过抛物线22C y px =:(其中0p >)的焦点F 的直线交抛物线于A B 、两点，且A B 、两点的纵坐标之积为16-．(1)求抛物线C 的方程；(2)当AF BF ≠时，求OF OFAF BF +的值；(3)对于x 轴上给定的点0(),D n (其中2n >)，若过点D 和B 两点的直线交抛物线C 的准线P 点，求证：直线AP 与x 轴交于一定点．【答案】解：(1)过抛物线22C y px =:(其中0p >)的焦点(,0)2P F 的直线 为2x P my =+，代入抛物线方程，可得2220y pmy p --=， 可设1122,,()(),A x y B x y ，即有21216y y p =-=-，解得4p =，可得抛物线的方程为28y x =；(2)由直线AB 过抛物线的焦点F ，可设12, ,,()()A B ρθρπθ+， 由1cos p ρθ=-，可得111cos 1cos 212AF BF p p p θθ-++=+==， 可得212OF OFp AF BF p+=⋅=； (3)证明：设121()8,A y y ，222()8,y B y ，,()2P s -， 由,0 ,(),,D n B D P 三点共线可得22228s n n y y =---，可得2228(2)8n s ny y --=-，① 设AP 交x 轴上的点为(),0t ， 即有211112288s y y y t y -=---， 代入①，结合1216y y =-，可得1222118(8)8y n n y y y t =--， 即有222211121()86488256ny nt ny y y ny -=-=-， 可得4t n=． 即有直线AP 与x 轴交于一定点4(,0)n ．【解析】(1)设直线AB 的方程，联立抛物线方程，运用韦达定理，可得4p =，即有抛物线方程；(2)推得112AF BF p+=，即可得到所求值； (3) 设121()8,A y y ，222()8,y B y ，,()2P s -，运用三点共线的条件：斜率相等，可得s ，设AP 交x 轴上的点为(),0t ，运用韦达定理，化简整理可得所求定点．本题考查直线和抛物线的位置关系，考查联立直线方程和抛物线方程，运用韦达定理和直线的斜率公式，考查化简运算能力，属于难题．21. 已知数列{}n a 为等比数列，11a =，公比为,n q S 为数列{}n a 的前n 项和．(1)若3520a a +=，求84S S ； (2)若调换567a a a 、、的顺序后能构成一个等差数列，求q 的所有可能值；(3)是否存在正常数c q 、，使得对任意正整数n ，不等式2n n S S c>-总成立？若存在，求出q 的取值范围；若不存在，请说明理由．【答案】解：(1)因为数列{}n a 为等比数列，11a =，公比为q ，且351,20q a a ≠+=，所以2420q q +=，解得24q = (5-舍去)， 则8484411111617S q qq S =+=+-=-=； (2)若调换567,,a a a 的顺序后能构成一个等差数列，即若调换456,,q q q 的顺序后能构成一个等差数列，由等差数列的性质可得212q q +=或212q q +=或22q q +=，解得1q =或12-或2-； (3)假设存在正常数,c q ，使得对任意正整数n ， 不等式2n n S S c>-总成立． 由2n n S S c >-，即为20n n S S c c-<-，等价为2n c S c <<，若1q =，可得2c n c <<，不成立；由11,0,1n n a a S =>≥，可得1c <，当1q >时，222S c >>不可能成立； 当112q <<时，121nq q->-可得21n q q <-， 即(log 21)q n q >-， 由112q <<，可得(og 1)l 21q q ->， 即当2(log 21,)2q n q S >->，所以2n S c <不可能成立； 当12q =时，11()22112nc -<-， 即11()2n c -<，可得1()12n c >-， 即当12(l g )o 1n c >-时，2nS c <不成立； 当102q <<时，1111n n q S q q-=<--， 所以当112(1)c q <<-时，2n c S c <<恒成立， 综上可得，存在正常数,c q ，使得对任意正整数n ， 不等式2n n S S c>-总成立， 且q 的取值范围是(10,2)． 【解析】(1)运用等比数列的通项公式，解方程可得公比，求和公式计算即可得到所求值；(2)由等比数列的通项公式和等差数列中项的性质，解方程即可得到所求值；(3)假设存在正常数,c q ，使得对任意正整数n ，不等式2n n S S c>-总成立．由不等式2n n S S c >-，即为20n n S S c c-<-，等价为2n c S c <<，讨论公比q ，结合题意，推得存在，求得q 的范围．本题考查等差数列和等比数列的通项公式和求和公式的运用，考查存在性问题的解法，以及分类讨论思想方法，化简整理和推理能力，属于难题．。
2019学年交大附中高一上英语摸底考
上海交通大学附属中学2019-2020学年度第一学期高一英语摸底考试试卷第I卷I. Listening Comprehension（30’）（略）II. Grammar and V ocabulary（30’+10’+10’）Section ADirections: Beneath each of the following sentences there are four choices marked A, B, C and D. Choose the answer that best completes the sentence.21.Have you ever felt in a situation ________ you see an acquaintance and have his or her name on the tip of your tongue?A. whichB. thatC. on whichD. where22.________ Albert Einstein left behind is the most profound ideas ________ form the foundation of modem physics today.A. That; whatB. That; whichC. What; whichD. What; that23. The state government declared that they would construct a national park in ________ used to be a small villageA. whatB. whichC. whereD. that24.Terry received about ten gifts on his birthday, ________ were from his lovely classmates.A. most of themB. one of whichC. most of whichD. and most of which25. “Climate change is no longer something to be joked about in Iceland or anywhere,” Gudni Johannesson, Iceland’s president. said in an interview. that most Icelanders believe human activity plays a role in it.A. addedB. to addC. addingD. adds26. ---You ________ here all the way through the thick snow last night .There was nothing important.---Yes, but I didn’t know.A. didn’t need to comeB. don’t need to comeC. needn’t have comeD. needn’t come27.Wth the population of those ever 60 ________ to double to one-third by 2050, the strategy of some Internet company for attracting the elderly is wise.A. expectB. expectedC. expectingD. being expected28.The reason ________ the TV networks are forced to come up with better shows is ________ nowadays more and more young parents prefer to spend time reading stories to their kids rather than root themselves in front of the TV.A. why; becauseB. that; becauseC. that; thatD. why; that29.Singapore is a playground for the wealthy, so it’s surprising that in the past five years, most of the purchasing desire ________ from those at the bottom of the economic pyramid.A. cameB. comesC. has comeD. have come30.The findings were published last week as part of the household expenditure survey, which is a detailed study ________ every five years.A. to be conductedB. having been conductedC. being conductedD. conducted31.Only when you leave your parents for college education ________ how much you love them.A. do you realizeB. you realizeC. you will realizeD. will you realize32.________ the Forbidden City approaches its 600th birthday next year, a dramatic change has been taking place.A. BeforeB. AsC. WhileD. Until33.Of all the jobs I’ve had, ________ was my experience at Pennsylvania Railway Station ________ impressed me most.A. it: whereB. what; whichC. it; thatD. that; which34.That multinational company is adopting an aggressive expanding strategy, and so far it has recruited ________ in the year of 2015 as they did two years ago.A. three times as many new employeesB. three times many new employeesC. three times as many as new employeesD. three times more new employees than35.Afterschool we went to the reading room to do some reading, only ________ that it ________.A. being told; was decoratedB. telling, had decoratedC. to be told; was being decoratedD. told; had been decoratingst night, I was packing my bag and texting a message to my boss ________ I heard a cry for help from outside the office.A. whenB. asC. beforeD. while37.Until Alice told me that astonishing secret ________.A. I didn’t have any idea what had happened to our companyB. did I have no idea what had happened to our companyC. didn’t I have any idea what had happened to our companyD. had I no idea what had happened to our company38.As a high school principal put it, “education in high school should not be isolated. It ________ to be linked withuniversity study. Since higher education in China is experiencing reform, high schools ________ change too.”A. needs; have toB. need; mustC. need; canD. needs; shall39.Ms. Shi and Mr. Zhou are an elderly couple in their 70s ________ enthusiasm for the square dancing is matched only by that for their smart phones.A. whenB. whichC. whoseD. during which40.Without your encouragement and support, we ________.A. should not succeedB. would not succeedC. would have succeededD. would not have succeeded41.Traditional Chinese medicine ________ effectively applied for thousands of years before its market was strongly impacted by western medicine in modernized China.A. had been beingB. had beenC. wasD. has been42.Many of the procrastinators (拖延症患者) often care too much about the result of ________ they are doing and insist on it being perfect.A. howeverB. no matter whatC. whicheverD. whatever43.There is no agreement among scientists ________ the active ingredients (成分) in many chemical sunscreens are safe.A. whoseB. thatC. whoD. as44.There is currently no effective vaccine or treatment for most mosquito-transmitted diseases, ________ controlling the insect’s population one of the most effective control methodsA .leaving B. leaves C. to leave D. has left45.The effect of the typhoon named Lingling on Shanghai was much smaller than ________ of Lekima.A. itB. thoseC. thatD. what46.The American Academy of Dermatology (美国皮肤病协会)’s official position on sunscreen is that everyone, ________ age, gender or race, should wear it because anyone can get skin cancer.A. according toB. instead ofC. regardless ofD. because of47.The number of deaths from a powerful typhoon sweeping across China’s east coast ________ to 30 on Sunday.A. raisedB. roseC. arousedD. arose48.By learning “the decoy effect (诱饵效应), you may become less ________ to its unconscious influence.A. sensibleB. sensationalC. sensitiveD. superior49.A video featuring Nezha and Monkey King, was ________ on Monday to promote the animated film Nezha, which hit the big screens across China on Friday.A. relievedB. releasedC. reviewedD. received50.Police on Saturday arrested a 21-year-old Texas man ________ of opening fire with a rifle at a Wal-Mart store in El Paso, Texas.A. sustainedB. suspendedC. suspectedD. suspiciousSection BDirections: Complete the following passage by using the words in the box. Each word can only be used once. Note that there is one word more than you need.(A)One recent study showed the benefits to your brain that learning a language can have and how to improve your brain’s ability to learn English. But what are the best ways to actually go about learning English?Learning a language is markedly different from __51__ historical facts or solving a complicated maths problem. As a result. you may need to decide which of the following __52__ work to improve your English learning.Talk it outYou’re never going to do well in English unless you practice using it __53__. If you have a classmate, friend or family member who already speaks the language fluently, ask them to help you. This gives you the __54__ to hear how words and phrases should be spoken. In addition. if you have difficulty with pronunciation, then a study buddy can help you with these problems.Write it downWhether you’re travelling on the bus or train, or watch ng television with your family, try to note down any new words that __55__ repeatedly. Keep a notebook at hand so that you can seize the opportunities to accumulate new words __56__. During your next study session, review these words and phrases and try to commit to memory their definitions.Take your timeWhen you’re learning something new, you are __57__ to get frustrated if you think you aren’t progressing quickly enough. Don’t worry, just take your time because English isn’t something you can learn overnight. Allow yourself to __58__ at times on the dictionary at the start of English learning instead of getting annoyed with yourself. While you’ll have to re tum to it later, you may find it easier the second time around.To sum up, the more you’re exposed to English, the more your skills will improve. Don’t be afraid to asksomeone to __59__ themselves when they ask you a question that you don’t understand. Listen for words that you know and try to work out what’s being said based on the text, etc. These situations above can __60__ the best learning experiences.(B)Study habits of effective studentsThe key to becoming an effective student is learning how to study smarter, not harder. While some students are able to breeze through school with minimal effort, the vast __61__ of successful students achieve their success by applying effective study habits. The following are some of the study habits __62__ by successful students.1.Don’t attempt to __63__ all of your study into one period of time.Ever find yourself up late at night spending more energy trying to keep your eyelids open than you are studying? If so, It’s time for a change. Successful students __64__ divide their work over shorter periods of time. If you want to become a successful student, then you need to learn to be consistent in your studies and to have __65__, but shorter, study periods.2.Plan when you’re going to study.Successful students schedule specific times throughout the week when they are going to study--and then they __66__ to their schedule. Even is you’re all caught up with studies, setting as idea period of time a few days a week to review your courses will help you develop habits that will enable you to succeed in your education in the long term.3.Make sure you concentrate on your studyEveryone gets __67__ by something. Maybe it’s the TV. Or maybe it’s your family. Or maybe it’s just too quiet. Some people actually study better with a little background noise. When you’re not paying attention while studying, you either lose your train of thought or are unable to focus--both of which will lead to very __68__ studying. Before you start studying, find a place where you won’t be disturbed.4.Review your notes, schoolwork and other class materials over the weekend.Successful students review what they’ve learned during the week over the weekend. This way they’ve well __69__ to continue learning new concepts that build upon previous coursework and knowledge __70__ the previous week.We’re confident that if you develop the habits out in ed above, you’ll see a major improvement in your academic performance.III. Reading Comprehension (15’+30’)Section ADirections: For each blank in the following passage there are four words or phrases marked A, B, C and D. Fill in each blank with the word or phrase that fits the context.A recent article in The Wall Street journal says that Chinese students in American universities are not getting the most out of their educational opportunities. The article says that __71__ Chinese students work hard, many are not acquiring the soft skills that come with fully participating in campus life.Soft skills refer to things like socialization and learning to be __72__. These are the skills students develop by __73__ socially with American and other international students and by learning how to handle problems in a new __74__ and make their own decisions. A large number of Chinese students, __75__, tend to self-segregate, that is, they just __76__ other Chinese students and __77__ the campus culture and even the wider American culture that surrounds them.Jocelyn Jia, a 22-year-old from Hainan studying at the university of north Carolina at Chapel Hill, says, “If you just come to study and hangout with Chinese people, all you bring back to China is the __78__. It’s just a piece of paper. That’s it” Jocelyn studies hard, but she likes to __79__, too. She’s taking every opportunity to make American friends and experience things she couldn’t have at a(n) __80__ university.Chinese companies want to hire “haigui” like Jocelyn. Ken Chen of a consulting firm in Shanghai says an American college education teaches you how to socialize, develop your __81__ and know how to think and solve problems. Mr. Chen says these are the kinds of people he is looking for.An American education isn’t __82__, though. It can cost as much as U.S. $200,000 for a four-year program. But Charlotte Fan, a graduate of Duke University from Shanghai, says the __83__ was worth it. She’s now working for an American company and, in the Wall Street Journal article, is quoted as saying. “I’ve learned a lot and changed a lot in college, not just to learn knowledge, but more importantly the way of thinking, creativity, communication--the soft skills you never learn from __84__ but learn from day-to-day life and from interacting with all the smart kids around you in school. Those sorts of things are what a Chinese education doesn’t __85__.”71.A. if B. while C. as D. unless72.A. enjoyable B. permanent C. intelligent D. independent73.A. mixing B. combining C. cooperating D. conflicting74.A. society B. environment C. class D. organization75.A. however B. in addition C. as a result D. for instance76.A. take pity on B. show respect to C. rely on D. hangout with77.A. ignore B. admire C .require D. challenge78.A. diploma B. proof C. document D. title79.A. have fun B. have a rest C. do research D. take a trip80.A. average B. Chinese C. traditional D. prestigious81.A. social wellbeing B. financial literary C. physical strength D. emotional intelligence82.A. adequate B. cheap C. worthwhile D. extensive83.A. time B. effort C. investment D. degree84.A. teachers B. books C. movies D. friends85.A. allow for B. know about C. focus on D. seek outSection BDirections: Read the following four passages. Each passage is followed by several questions or unfinished statements. For each of them there are four choices marked A, B, C and D. Choose the one that fits best according to the information given in the passage you have just read.(A)“I Went Skydiving at 84!”As a young girl growing up in the 1930s, I always wanted to fly a plane, but back then it was almost unheard of for a woman to do that. I got a taste of that dream in 2001, when my husband arranged for me to ride in a hot air balloon for my birthday. But the experience turned out to be very dull. Around that time, I told my husband that I wanted to skydive. So when our retirement community announced that they were having an essay competition and the topic was an experience of a lifetime that you wanted to have. I decided to write about my dream.In the essay, I wrote about my desire to skydive, stating George Brush Sr. did it at age 80. Why not me? I was just 84 and in pretty good health. A year went by and I heard nothing. But then at a community party in late April 2009, they announced that l was one of the winners. I just couldn’t believe it.One June 11, 2009, nearly 40 of my family and friends gathered in the area close to where I would land while I headed up in the airplane. My instructor, Jay, guided me through the experience. The plane was the noisiest one I had ever been in, but I wasn’t frightened—I was really just looking forward to the experience. When we reached 13,000 feet, Jay instructed me to throw myself out of the plane. When we first hit the air, the wind was so strong that I could hardly breathe. For a second I thought, “What have I gotten myself into?” But then everything got calmer We were in a free fall for about a minute before Jay opened the parachute (降落伞), then we just floated downward for about five minutes. Being up in the clouds and looking at the view below was unlike anything I have ever felt—much better than the hot air balloon. I was just enjoying it.Skydiving was really one of the greatest experiences of my life. I hope other people will look at me and realize that you don’t stop living just because you are 84 years old. If there’s something you want to experience, GO AHEAD! If it’s something that is possible, make it happen.86.What happened to the author in 2001?A. She flew an airplaneB. She entered a competitionC. She went on a hot air balloon rideD. She moved into a retirement community87.The author mentioned George Bush Sr. in her essay to ________.A. build up her own reputationB. show her admiration for himC. compare their health conditionD. make her argument persuasive88.How did the author feel in mediately after she jumped out of the plane?A. ExcitedB. ScaredC. NervousD. Regretful89.What did the author enjoy most when she was skydiving?A. The beautiful cloudsB. The wonderful viewC. The company of JayD. The one-minute freefall(B)WELCOMEWelcome to Windsor Castle, the oldest and largest occupied castle in the world. Windsor is one of the official residences of the Queen, who sometimes stays here.Audio toursFree audio tours are available on leaving the Admission Centre at the start of your visit. There is a descriptive audio tour for blind and poor-sighted visitors.Guided toursVisitors can explore the history of the Castle through a tour of the Precincts with an expert guide. Tours depart at regular intervals throughout the day from the Courtyard and finish at the entrance to the State Apartments. Visitors with childrenFor those visiting with children, a special family tour and various activities are offered during school holidays and at weekends and baby carriers are also available.St George’s ChapelVisitors arriving at the Castle after 15:00 from March to October are advised to visit St George’s Chapel first before it closes.ShoppingShops offer a wide range of souvenirs designed for the Royal Collection, including books, postcards, china, jewellery, and children’s toys. Please ask at the Middle Ward shop about our home delivery service. RefreshmentsBottled water can be purchased from the Courtyard and Middle Ward shops. From April to September ice cream is also available, visitors wishing to leave the Castle for refreshments in the town may obtain re-entry permit from the castle shops. Eating and drinking are not permitted in the State Apartments or St George’s Chapel. Photography and mobile phonesNon-commercial photography and filming are welcomed in the Castle. Photography, video recording and filming are not permitted inside the State Apartments or St George’s Chapel. Mobile phone must be switched off inside the State Apartments and St George’ Chapel in consideration of other visitors.SecurityAs Windsor Castle is a working royal palace, visitors and their belongings should get through airport style security checks For safety and security reasons a one-way system operates along the visitor route.90.A visitor can apply for a free audio tour ________.A. in the CourtyardB. in the State ApartmentsC. at the Admission CenterD. at St George’s Chapel91.Who can get re-entry permits?A. Visitors expecting to eat outside the Castle.B. Visitors buying gifts in the castle shops.C. Visitors buying water from the Courtyard.D. Visitor seating outside St George’s Chapel92.Why are visitors required to turn off their mobile phone?A. To ensure the safety of others,B. To ensure the security of the Castle.C. To prevent them from disturbing others.D. To prevent the use of the built-in cameras.(C)Not exactly, but Dr. Joseph Bell, the man who inspired the character of Sherlock Holmes, shared many qualities with the famous detective. Arthur Conan Doyle, the writer and creator of Holmes, met Dr. Bell in 1877 at the University of Edinburgh Medical School. Conan Doyle was studying to be a doctor and Bell was one of his professor.Bell was 39 years old when Conan Doyle first attended one of his lectures. He is said to have walked with great energy. His nose and chin were angular and his eyes twinkled with intelligent humor. Bell, who was a brilliant doctor, liked writing poetry, playing sport and bird-watching.By the end of Conan Doyle’s second year, Bell had selected him to serve as his assistant. Being on award withBell, where he had plenty of opportunity to observe, only increased Conan Dovle’s admiration for the great doctor. Amongst other things he was able to witness Dr. Bell’s remarkable ability to quickly deduce (推断) a great deal about the patient.Dr. Bell observed the way a person moved. The walk of a sailor, who had spent many years at sea, varied greatly from that of a soldier. If he identified a personas a sailor, he would look for any tattoos (纹身) that might assist him in knowing where their travels had taken them. He trained himself to listen differences in his patients accents to help him identify where they were from. Bell studied the hands of his patients because calluses (老茧) or other marks could help him determine their occupation.Conan Doyle published the first Ho lanes story in 1887. His innovation in creating a character that would appear over and over in a series of self-contained stories meant that Holmes s popularity grew with each book. Perhaps the most famous was The Hound of the Baskervilies, which has been made into several films. Soon the character was so beloved that people refused to believe he wasn’t a real person: letters addressed to “Sherlock Holmes, Consulting Detective” arrived daily at Baker Street and Scotland Yard, each begging him take on a real case.93.What can be learned about Dr Joseph Bell from the passage?A. He used to be a famous detectiveB. He first created Sherlock HolmesC. He took interest in a variety of thingsD. He looked serious and unapproachable94.In Paragraph 4, the author talks mainly about ________.A. how Dr Joseph Bell got to be liked by patientsB. what kind of patients Dr Joseph Bell was good at treatingC. what contribution Dr Joseph Bell did to Conan Doyle’s bookD. how Dr Joseph Bell got clues about patients through observation95.Why did the author mention letter addressed to Sherlock Holmes in the last paragraph?A. To illustrate how popular Sherlock Holmes wasB. To tell readers where Sherlock Holmes actually lived.C. To show why readers refused to believe in Conan DoyleD. To present away Sherlock Holmes drew people’s attention96.Which of the following might be the best title of the passage?A. Dr Joseph Bell: the man who w role Sherlock HolmesB. How Conan Doyle created Sherlock Holmes?C. Sherlock Holmes: the man who lives foreverD. Was Sherlock Holmes a real person?(D)If English means endless new words, difficult grammar and sometimes strange pronunciation, you are wrong. Haven’t you noticed that you have become smarter since you started to learn a language?According to a new study by a British university, learning a second language can lead to an increase in your brain power. Researchers found that learning other languages changes grey matter. This is the area of the brain which processes information. It is similar to the way that exercise builds muscles. The study also found the effects are greater, the younger people learn a second language.A team led by Dr. Andrea Mechelli, took a group of Britons who only spoke English. They were compared with a group of “early bilinguals” who had learnt a second language before the age of five, as well as a number of later learners.Scans showed that grey matter density in the brain was greater in bilinguals than in people without a second language. But the longer a person waited before mastering a new language. the smaller the difference.“Our findings suggest that the structure of the brain is changed by the experience of learning a second language.” said the scientists. It means that the change itself increases the ability to learn.Professor Dylan Vaughan Jones of the University of Wales, has researched the link between bilingualism and math skills. “Having two languages gives you two windows on the world and makes the brain more flexible” he said, “You are actually going beyond language and have a better understanding of different ideas.”The findings were matched in a study of native Italian speakers who had learned English as a second language between the ages of 2 and 34. Reading, writing and comprehension were all tested. The results showed that the younger they started to learn, the better. “Studying a language means you get an entrance to another world,” explained the scientists.97.The main subject of this passage is ________.A. the strategy for learning a second languageB. men’s ability to learn a second languageC. how language leaning helps brainpowerD. the relationship between language learning and math study98. In the second paragraph, they writer mentions “exercise” in order to ________.A. suggest that language learning involves physical labor.B. prove that one needs more practice when he(she) is learning a languageC. show that language learning is a process of accumulationD. make people believe language learning helps grey matter work well99.We may learn from the scientific findings that ________.A. the earlier you start to learn a second language, the higher the grey matter density is.B. there is no difference between a later second language learner and one knowing no second language.C. the experience of learning a second language has an unknown effect on people’s brainD. the ability to learn a second language is changing all the time100.In the last two paragraphs, the author tries to tell us that ________.A. learning a second language is the same as studying mathsB. early learning of a second language helps in studying other subjectsC. Italian is the best choice for you as a second languageD. you’d better choose the ages between 2 and 34 to learn a second language第Ⅱ卷Translation (7’+18’)I. DictationDirections: Translate the following phrases into English according to the Chinese. (7’)1.占据我的空闲时间2.详细描述这个过程3.必定会满足学生的要求4.除了笔友的激励和支持5.难度更高的阅读材料6.向商店抱怨产品的质量7.抽出时间写老师布置的作文II. Translation（3’+3’+3’+4’+5’）Directions: Translate the following sentences into English, using the words given in the brackets.1.尽管看起来很年轻，她绝不是一名没有经验的物理老师。
2018-2019 学年上海交通大学附属中学第一学期 高一化学摸底考试卷(解析版)
.2018-2019 学年上海交通大学附属中学第一学期高一化学摸底考试卷相对质量:H斗，C-12 ，N-14 ，0 -16，Na-23 ，S-32，Cl-35.5，K-39，Ca-40一、选择题(只有一个正确答案)1.下列资源的利用过程中发生了化学变化的是A . 铁矿炼铁B. 干冰制冷 C . 海水晒盐 D. 风能发电【答案】A【解析】略2. 氨气密度比空气小，极易溶于水，以下收集氨气的方法正确的是【答案】B【解析】氨气在常温下是一种极易溶与水的气体，所以不能用排水法收集，它的密度比空气小可以用向下排空气法收集．3. 下列实验操作、现象与结论对应关系不正确的是【答案】A【解析】A、醋酸和氢氧化钠溶液反应生成醋酸钠和水，反应无明显现象，但二者之间发生了反应，故A错误；B、活性炭具有吸附性，能吸附色素和异味，所以向红墨水中加入活性炭，过滤，看到的现象是红墨水变为无色，从而证明活性炭具有吸附性，故B正确；C、黄铜是铜的合金，合金的硬度大，所以用黄铜片在铜上刻划，铜片上有划痕，故C正确；D 、电解水实验中可观察到电极上有气泡产生，这是因为电解水生成氢气和氧气，故D 正确．由于本题选择不正确的，故选：A ．4. KCl 与 KN03 在不同温度的溶解度数据如右表。
则下列说法正确的是A. KN03 比KCl 的溶解度大B. 两物质的溶解度相等的温度在 20-30℃间C. 在 200C 时， 10g 水中加入 5gKCl 可得到 33.3% 的 KCl 溶液D. 在 50℃时，两物质各 5g 分别加入 10g 水中，充分溶解，均有固体剩余 【答案】B【解析】A 、没有指明温度无法比较溶解度的大小，故A 错误；B 、分析图表，KNO3和NaCl 的溶解度曲线在20℃～30℃温度范围内有相同的时候，所以两种物质的溶解度曲线在此范围内相交，故B 正确；C 、20℃时KCl 的溶解度是33g ，相当于100g 溶液最多溶解氯化钾33g ；10g 水中加入5gKCl ，溶解3gKCl ，溶液中溶质的质量分数为3g ，3g+10g ×100%=23%，故C 错误；D 、50℃时KCl 溶解度是41g ，相当于100g 溶液最多溶解氯化钾41g ，10g 水中最多溶解氯化钾4.1g ，有固体剩余；50℃时硝酸钾溶解度是88g ，相当于100g 溶液最多溶解硝酸钾88g ，10g 水中最多溶解硝酸钾8.8g ，无固体剩余，故D 错误．故选：B ．5. 取四朵用石蕊熔液染成的紫色干燥纸花进行以下实验，下列分析错误的是 A. ①说明酸溶液可以使石恋变红B. ①④对比说明④中产生了与盐酸性质相似的物质C. ②④对比说明水在石蕊变色过程中不发挥任何作用D. ②③④对比说明二氧化碳能和水反应【答案】A【解析】：A、喷洒稀盐酸纸花变红说明了酸溶液可以使石蕊变红，故A说法正确B、纸花喷水后放入CO2中，纸花变红说明了纸花喷水后生成了与盐酸性质相似的物质，故B说法正确；C、喷洒水纸花不变色、喷水后放入CO2中纸花变红不能说明水在石蕊变色过程中不发挥任何作用，故C说法错误；D、喷洒水纸花不变色、放入干燥二氧化碳中纸花不变色、喷水后放CO2中纸花变红说了二氧化碳能和水反应，故D说法正确．故选C．6. 向不饱和的 KN03熔液中，逐渐加 KN03晶体，下列图象中符合溶被中溶质质量变化规律的是【答案】C【解析】A、不饱和KNO3溶液中含有一定量的溶质硝酸钾，所以加入硝酸钾之前，不饱和的硝酸钾溶质的质量不为0，故选项错误；B、向一定量不饱和KNO3溶液中逐渐加入KNO3固体时，硝酸钾能够继续溶解，直到达到饱和状态．故选项错误；C、向一定量不饱和KNO3溶液中逐渐加入KNO3固体时，硝酸钾能够继续溶解，达到饱和状态时不再溶解．故选项正确；D、在一定温度下，在一定量的溶剂里，KNO3不能无限溶解．故选项错误．故选C．7.类推是常用的思维方法，以下类推成立的是A . 单质由同种元素组成，所以由同种元素组成的物质一定是单质B. 分子可以构成物质，所以物质一定由分子构成C. 燃烧有发光、发热，所以发光、发热变化一定是化学变化D. 常温下，酸溶液的 pH 小于 7，所以醋酸溶液的pH 一定小于 7【答案】D【解析】A、由同种元素组成的纯净物是单质，故A错；B、构成物质的基本微粒有分子、原子、离子，故B错；C、灯泡发光放热，属于物理变化，故C错；D、醋酸溶液属于酸，因为常温下，酸溶液的pH小于7，所以醋酸溶液的pH一定小于7，故D正确．8. 将一定量的乙醇 (C2H5OH）和氧气置于一个封闭的容器中引燃，测得反应前后各物质的质量如下表：下列判断正确的是A. 无论如何改变氧气的起始量，均有 X 生成B. X 一定是该反应的催化剂C. X 可能含有氢元素D. 表中 a 的值为 5.6【答案】C【解析】略9. 在隔绝空气情况下，用木炭还原氧化铜.下列叙述正确的是A. 反应前后固体的质量不变B. 反应后固体减轻的质量等于氧化铜中氧元素的质量C. 反应前后固体中铜元素的质量保持不变D. 反应中消耗的氧化铜与木炭的物质的量一定相等【答案】C【解析】利用质量守恒定律解答10. 下列四个图像能正确反映其对应实验操作的是A :①高温般烧一定质量的石灰石B ②用等质量、等浓度的双氧水分别制取氧气C. ③向一定体积的稀盐酸中逐滴加入氢氧化钠溶液D ④某温度下，向一定量饱和硝酸钾溶液中加入硝酸钾固体【答案】C【解析】A、石灰石开始具有一定的质量，高温煅烧后，会分解放出二氧化碳和氧化钙，二氧化碳逸到空气中，使固体质量减少，石灰石分解完后，固体质量不再减少，图象应该从纵轴的某个部位开始逐渐的减少，然后转成水平，故A 错误B、催化剂只会改变反应的速率，不会改变氧气量的多少，加催化剂和不加催化剂放出的氧气量相同，只是反应时间的不同，水平线应该重合，故B错误C、锌的活动性比铁强，锌与稀硫酸反应比铁剧烈；等质量两金属完全反应后，根据反应的化学方程式可知，铁产生氢气质量大于锌；故C正确D、温度一定，饱和溶液中的溶质质量分数就不变，所以图象应该是从y轴的某点开始的一条水平线，故D错误11.右图是 R 原子结构示意图和磷元素的相关信息，下列说法错误的是A，X=8B，磷元素的相对原子质量为15C，两种元素可以形成化学式为P2R 5D，磷可以在R的单质中剧烈燃烧【答案】B【解析】A、X=2+6=8，是氧元素，故A正确；B、磷元素的相对原子质量是30.97，故B错误；C、R原子的最外层电子数是6，在化学反应中易得到两个电子，表现出的化合价是-2，磷元素的化合价是+5，故能形成的化合物的化学式是P2O5，故C正确；D、R是氧元素，形成的单质是氧气，磷能在氧气中燃烧，故D正确．12.参阅下列有关元素E两种同位素的资料同位素同位素的相对原子质量丰度103E 103 20%105E 105 80%元素E的相对平均原子量的是A.103.4B. 103.6 C 104.0 D 104.6 【答案】D【解析】略13. 氯元素的天然同位素有3517Cl 和3717Cl，氯元素的相对原子质量为 35.5.则天然氯元素中，3517Cl 和3717Cl 的原子数目之比约为A. 3 : 1B. 1 : 3C. 3: 2D. 4: 1 【答案】A【解析】氯元素的相对原子质量35.5是质量数分别为3537的核素的平均值，可以采用十字交叉法计算其原子个数比；，3717Cl和3517Cl的原子个数之比为0.5：1.5=1：314. X 元素组成三种气态单质都是双原子分子它们的相对分子质量分别是 32、34、36现有这三种单质的混合气体，分子数之比为 15 :4: 1，下列说法正确的是A. 若该容器中的 X2全部转化成同素异形体元，则 X3的分子有 21 种B. 质量数为 16 的同位素的丰度为 85%C. 该元素的相对原子质量为 17D. 该元素所含三种同位素的原子数之比为 15:4 : 1 【答案】B【解析】略15. 一个12C 原子的质量为 a kg，一个12C I602分子的质量为 bkg ，若以12C I602中的一个氧原子质量的 1/16 作为相对原子质量标准，则12C I602的相对分子质量为【答案】A【解析】由题意可知：12CO2分子中的1个氧原子质量为：(b-a)/2 kg根据相对原子质量的求法可知12CO2的相对分子质量= bkg/ (b-a)/2 kg× 1/16 = 32b /b-a ；16. X、Y、Z和R分别代表四种元素，如果a X m+、b Y n+、c Z n- d R m- 四种离子的电子层结构相同，则下列关系式正确的是A . a-c=m-n B. a-b=n-m C. c+d=m+n D. b-d=n+m【答案】D【解析】四种离子的电子层结构相同即离子核外电子总数相同，所以正确选项为D；17. 己知某种元素的一种原子的核内质子数是m ，中子数是n ，下列说法正确的是A . 该元素的相对原子质量是m+nB. 该元素的质量数是m+nC. m+n均可写在元素符号的左下角D. 若C-12 的质量是wg ，则该原子的质量是(m+n)w/ 12 g【答案】D【解析】考查相对原子质量概念辨析。
上海交大附中高三(上)摸底数学试卷(解析版)
上海交大附中高三（上）摸底数学试卷参考答案与试题解析一、填空题（本大题共14题，每题4分，满分56分）1．已知全集U=R，集合A={x|x≤﹣2，x∈R}，B={x|x＜1，x∈R}，则（∁U A）∩B={x|﹣2＜x＜1}．【考点】交、并、补集的混合运算．【专题】集合．【分析】根据全集U及A求出A的补集，找出A补集与B的交集即可．【解答】解：∵全集U=R，集合A={x|x≤﹣2}，∴∁U A={x|x＞﹣2}，∵B={x|x＜1}，∴（∁U A）∩B={x|﹣2＜x＜1}．故答案为：{x|﹣2＜x＜1}【点评】此题考查了交、并、补集的混合运算，熟练掌握各自的定义是解本题的关键．2．已知互异的复数a，b满足ab≠0，集合{a，b}={a2，b2}，则a+b=﹣1．【考点】集合的相等．【专题】集合．【分析】根据集合相等的条件，得到元素关系，即可得到结论．【解答】解：根据集合相等的条件可知，若{a，b}={a2，b2}，则①或②，由①得，∵ab≠0，∴a≠0且b≠0，即a=1，b=1，此时集合{1，1}不满足条件．若b=a2，a=b2，则两式相减得a2﹣b2=b﹣a，∵互异的复数a，b，∴b﹣a≠0，即a+b=﹣1，故答案为：﹣1．【点评】本题主要考查集合相等的应用，根据集合相等得到元素相同是解决本题的关键，注意要进行分类讨论．3．若不等式ax2+5x﹣2＞0的解集是，则不等式ax2﹣5x+（a2﹣1）＞0的解集是．【考点】一元二次不等式的应用．【分析】先由二次不等式的解集形式，判断出，2是方程ax2+5x﹣2=0的两个根，利用韦达定理求出a的值，再代入不等式ax2﹣5x+a2﹣1＞0易解出其解集．【解答】解：∵ax2+5x﹣2＞0的解集是，∴a＜0，且，2是方程ax2+5x﹣2=0的两根韦达定理×2=，解得a=﹣2；则不等式ax2﹣5x+a2﹣1＞0即为﹣2x2﹣5x+3＞0，解得故不等式ax2﹣5x+a2﹣1＞0的解集．故答案为：【点评】本题考查的知识点是一元二次不等式的解法，及“三个二次”（三个二次指的是：二次函数，一元二次不等式，一元二次方程）之间的关系，“三个二次”之间的关系及应用是数形结合思想的典型代表．4．设等差数列{a n}的前n项和为S n，若S10=10，S20=30，则S30=60．【考点】等差数列的性质．【专题】计算题；等差数列与等比数列．【分析】由给出的数列是等差数列，可知数列的第一个10项和，第二个10项和，…仍然构成等差数列，结合S10=10，S20=30，列式求解S30的值．【解答】解：∵数列{a n}是等差数列，则S10，S20﹣S10，S30﹣S20仍然构成等差数列，由S10=10，S20=30，得2×20=10+S30﹣30，∴S30=60．故答案为：60．【点评】本题考查了等差数列的性质，考查了等差数列的前n项和，关键是对性质的理解与运用，是中档题．5．在△ABC中，已知角A，B，C所对的边分别为a，b，c，且c（acosB﹣bcosA）=2b2，则=．【考点】余弦定理；正弦定理．【专题】解三角形．【分析】由条件利用正弦定理和余弦定理代入进行化简即可．【解答】解：∵c（acosB﹣bcosA）=2b2，∴由余弦定理可得ac•﹣bc•=2b2，即a2+c2﹣b2﹣b2﹣c2+a2=4b2，即a2=3b2，则a=b，∴=．再利用正弦定理可得=，故答案为：【点评】本题主要考查正弦定理和余弦定理的应用，比较基础．要求熟练掌握相应的公式．6．若点A（2，3）与点B（1，y0）位于直线l：x﹣2y+5=0的两侧，则y0的取值范围是（3，+∞）．【考点】二元一次不等式（组）与平面区域；直线的斜率．【专题】直线与圆．【分析】由不等式与平面区域的关系可得y0的不等式，解不等式可得．【解答】解：∵点A（2，3）与点B（1，y0）位于直线l：x﹣2y+5=0的两侧，∴（2﹣2×3+5）（1﹣2y0+5）＜0，解得y0＞3故答案为：（3，+∞）【点评】本题考查不等式与平面区域，属基础题．7．将一枚质地均匀的一元硬币抛3次，恰好出现一次正面的概率是．【考点】相互独立事件的概率乘法公式．【专题】计算题．【分析】掷一枚硬币，正面向上的概率是，将一枚质地均匀的一元硬币抛3次，相当于做了三次独立重复试验，利用独立重复试验的概率公式写出结果．【解答】解：由题意知掷一枚硬币，正面向上的概率是，将一枚质地均匀的一元硬币抛3次，相当于做了三次独立重复试验，∴恰好出现一次正面的概率是故答案为：【点评】本题考查独立重复试验的概率公式，解题的关键是看出试验符合什么条件，注意应用概率的公式，本题是一个基础题．8．已知b∈R，若（1+bi）（2﹣i）为纯虚数，则|1+bi|=．【考点】复数求模．【专题】数系的扩充和复数．【分析】通过化简可知（1+bi）（2﹣i）=（2+b）+（2b﹣1）i，利用纯虚数的定义计算即可．【解答】解：∵（1+bi）（2﹣i）=（2+b）+（2b﹣1）i为纯虚数，∴，解得b=﹣2，∴|1+bi|===，故答案为：．【点评】本题考查复数求模，弄清纯虚数的概念是解决本题的关键，注意解题方法的积累，属于基础题．9．已知，且x+2y=1，则的最小值是．【考点】两向量的和或差的模的最值．【专题】计算题．【分析】根据要求的向量可以表示成两个向量的和的形式，把两个向量的系数用一个字母来表示，求向量的模长，利用二次函数的最值，做出结果．【解答】解：∵x+2y=1∴•===84y2﹣72y+16∴当y=时，原式=，故答案为：，【点评】本题考查向量的模长的最值，本题解题的关键是表示出向量的模长，再用函数求最值的方法来求解，这是这一类题目共同的特征．10．已知一圆锥的底面是半径为1cm的圆，若圆锥的侧面积是底面积的3倍，则该圆锥的体积是cm3．【考点】棱柱、棱锥、棱台的体积．【专题】空间位置关系与距离．【分析】由已知中，圆锥的底面半径为1，侧面积是底面积的3倍，分析圆锥的母线长，进而求出圆锥的高，结合圆锥的体积公式即可获得问题的解答．【解答】解：∵圆锥的底面半径r=1cm，侧面积是底面积的3倍，∴圆锥的母线长l=3cm，故圆锥的高h==2cm，故圆锥的体积V=Sh=πr2•h==cm3，故答案为：．【点评】本题考查的是圆锥的体积求解问题．在解答的过程当中充分体现了圆锥体积公式的应用以及转化思想的应用．值得同学们体会反思．11．抛物线y2=4x的焦点为F，过点P（2，0）的直线与该抛物线相交于A，B两点，直线AF，BF 分别交抛物线于点C，D．若直线AB，CD的斜率分别为k1，k2，则=．【考点】直线与圆锥曲线的关系．【专题】直线与圆；圆锥曲线的定义、性质与方程．【分析】设AF的方程是y=（x﹣1），与抛物线方程联立，求出C的坐标，同理求出D的坐标，可得k2，即可求出．【解答】解：设A（x1，y1），B（x2，y2），C（x3，y3），D（x4，y4），∴AF的方程是y=（x﹣1）设k0=，则AF：y=k0（x﹣1），与抛物线方程联立，可得k02x2﹣（2k02+4）x+k02=0，利用韦达定理x3x1=1∴x3=，∴y3=k0（x3﹣1）=﹣即C（，﹣）同理D（，﹣）∴k2==2k1，∴=．故答案为：．【点评】本题考查直线与抛物线的位置关系，考查斜率的计算，考查学生的计算能力，属于中档题．12．已知f（x）=x2﹣3x+4，若f（x）的定义域和值域都是[a，b]，则a+b=5．【考点】函数的值域；函数的定义域及其求法．【专题】函数的性质及应用．【分析】因为定义域和值域都是[a，b]，说明函数最大值和最小值分别是a和b，所以根据对称轴进行分类讨论即可．【解答】解：∵f（x）=x2﹣3x+4=+1，∴x=2是函数的对称轴，根据对称轴进行分类讨论：①当b＜2时，函数在区间[a，b]上递减，又∵值域也是[a，b]，∴得方程组即，两式相减得（a+b）（a﹣b）﹣3（a﹣b）=b﹣a，又∵a≠b，∴a+b=，由，得3a2﹣8a+4=0，∴a=∴b=2，但f（2）=1≠，故舍去．②当a＜2＜b时，得f（2）=1=a，又∵f（1）=＜2，∴f（b）=b，得，∴b=（舍）或b=4，∴a+b=5③当a＞2时，函数在区间[a，b]上递增，又∵值域是[a，b]，∴得方程组，即a，b是方程x2﹣3x+4=x的两根，即a，b是方程3x2﹣16x+16=0的两根，∴，但a＞2，故应舍去．故答案为：5【点评】本题考查了二次函数的单调区间以及最值问题，属于基础题．13．关于函数f（x）=cos（2x﹣）+cos（2x+），有下列说法（1）y=f（x）的最大值为；（2）y=f（x）是以π为最小正周期的函数；（3）y=f（x）在区间（，）上单调递减；（4）将函数y=cos2x的图象向左平移个单位后，将与已知函数的图象重合．其中正确说法的序号是（1）（2）（3）．【考点】两角和与差的余弦函数．【专题】三角函数的图像与性质．【分析】由三角函数公式化简可得f（x）=sin（2x+），由三角函数的性质逐个选项验证可得．【解答】解：化简可得f（x）=cos（2x﹣）+cos（2x+）=cos（2x+﹣）+cos（2x+）=sin（2x+）+cos（2x+）=sin（2x++）=sin（2x+）∴函数f（x）的最大值为，（1）正确；函数的周期T==π，（2）正确；由2kπ+＜2x+＜2kπ+可得kπ+＜x＜kπ+，当k=0时可得函数y=f（x）在区间（，）上单调递减，（3）正确；（4）y=cos2x的图象向左平移个单位后，可得y=cos2（x+）=cos（2x+）≠sin（2x+），错误；综上可知（1）（2）（3）正确，故答案为：（1）（2）（3）．【点评】本题考查三角函数的图象和性质，涉及两角和与差的三角函数公式和诱导公式，属中档题．14．定义在实数集R上的函数f（x），如果存在函数g（x）=Ax+B（A、B为常数），使得f（x）≥g（x）对一切实数x都成立，那么称g（x）为函数f（x）的一个承托函数．给出如下四个命题：①对于给定的函数f（x），其承托函数可能不存在，也可能有无数个；②定义域和值域都是R的函数f（x）不存在承托函数；③g（x）=2x为函数f（x）=|3x|的一个承托函数；④为函数f（x）=x2的一个承托函数．其中正确的命题有①③．【考点】函数最值的应用．【专题】压轴题；新定义．【分析】函数g（x）=Ax+B（A，B为常数）是函数f（x）的一个承托函数，即说明函数f（x）的图象恒在函数g（x）的上方（至多有一个交点）①举例可以说明，如f（x）=cosx，则g（x）=B （B＜﹣1）就是它的一个承托函数，且有无数个，反例如y=tanx或y=lgx就没有承托函数；②f（x）=2x+3的定义域和值域都是R，存在一个承托函数y=2x+1，故命题②不正确；③要说明g（x）=2x为函数f（x）=|3x|的一个承托函数；即证明F（x）=e x﹣2x 的图象恒在x轴上方；④举反例即可．【解答】解：①如f（x）=sinx，则g（x）=B（B＜﹣1）就是它的一个承托函数，且有无数个，再如y=tanx．y=lgx就没有承托函数，∴命题①正确；②f（x）=2x+3的定义域和值域都是R，存在一个承托函数y=2x+1，故命题②不正确；③令F（x）═|3x|﹣2x=，可见在x≥0时，函数F（x）单调递增，最小值F（0）=0，在x＜0时，函数F（x）单调递减，最小值大于F（0）=0，∴F（x）≥0在R上恒成立，符合定义∴命题③正确；④x=1时，g（1）=，f（1）=1，显然g（1）＜f（1），当x=时，g（）=，f（）=，显然g（）＞f（），命题④不正确．故答案为：①③【点评】本题是新定义题，考查对题意的理解和转化的能力，要说明一个命题是正确的，必须给出证明，如③，对于存在性命题的探讨，只需举例说明即可，如①，对于不正确的命题，举反例即可，如②③，属于中档题．二、选择题（本大题共4题，每题5分，满分20分）15．在（1+x）6（2+y）4的展开式中，含x4y3项的系数为（）A．210 B．120 C．80 D．60【考点】二项式定理的应用．【专题】二项式定理．【分析】利用二项展开式的通项公式求得（1+x）6（2+y）4的展开式中，含x4y3 的项，可得含x4y3项的系数．【解答】解：在（1+x）6（2+y）4的展开式中，含x4y3 的项为•x3••2•y3=120x4y3，故含x4y3项的系数为120，故选：B．【点评】本题主要考查二项式定理的应用，二项展开式的通项公式，二项式系数的性质，属于基础题．16．已知a、b、c是△ABC的三边长，且满足=0，则△ABC一定是（）A．等腰非等边三角形 B．等边三角形C．直角三角形D．等腰直角三角形【考点】高阶矩阵．【专题】选作题；矩阵和变换．【分析】方程化为2a2+2b2+2c2﹣2ab﹣2bc﹣2ca=0，配方可得结论．【解答】解：方程化为2a2+2b2+2c2﹣2ab﹣2bc﹣2ca=0，所以（a﹣b）2+（b﹣c）2+（a﹣c）2=0，所以a=b=c，故选：B．【点评】本题考查高阶矩阵，考查学生的计算能力，比较基础．17．甲乙两人进行相棋比赛，甲获胜的概率是0.4，两人下成和棋的概率是0.2，则甲不输的概率是（）A．0.6 B．0.8 C．0.2 D．0.4【考点】概率的基本性质．【专题】计算题．【分析】欲求甲不输的概率，利用等量关系：甲获胜的概率是0.4，两人下成和棋的概率是0.2，把相关数值代入即可求解．【解答】解，根据题意，甲获胜的概率是0.4，两人下成和棋的概率是0.2所以甲不输的概率为0.4+0.2=0.6．故选A．【点评】本题考查了等可能事件的概率，解答本题的关键是要判断出“甲获胜的概率，和棋的概率和乙获胜的概率的和是1”．18．圆ρ=（cosθ+sinθ）的圆心坐标是（）A．（1，）B．（，）C．（，）D．（2，）【考点】简单曲线的极坐标方程．【专题】坐标系和参数方程．【分析】利用化为直角坐标方程，进而得出．【解答】解：圆ρ=（cosθ+sinθ）即（cosθ+sinθ），∴，化为．∴圆心坐标是，∴=1，θ=arctan1=．极坐标为．【点评】本题考查了极坐标与直角坐标方程的互化，属于基础题．三．解答题（本大题共五题，满分74分，12+14+14+16+18=74）19．已知角α的终边经过点P（，﹣）．（1）求sinα的值．（2）求式•的值．【考点】任意角的三角函数的定义；运用诱导公式化简求值．【专题】计算题．【分析】（1）求出|OP|，利用三角函数的定义，直接求出sinα的值．（2）利用诱导公式化简表达式，根据角的终边所在象限，求出cosα=，可得结果．【解答】解：（1）∵|OP|=，∴点P在单位圆上．由正弦函数的定义得sinα=﹣（2）原式==..由余弦的定义可知，cosα=即所求式的值为【点评】本题考查任意角的三角函数的定义，运用诱导公式化简求值，考查计算能力，推理能力，是基础题．20．已知函数f（x）=|3x+2|．（Ⅰ）解不等式f（x）＜4﹣|x﹣1|；（Ⅱ）已知m+n=1（m，n＞0），若|x﹣a|﹣f（x）≤+（a＞0）恒成立，求实数a的取值范围．【考点】绝对值不等式的解法．【专题】不等式的解法及应用．【分析】（Ⅰ）把要解的不等式等价转化为与之等价的三个不等式组，求出每个不等式组的解集，再取并集，即得所求．（Ⅱ）由条件利用基本不等式求得+≥4，结合题意可得|x﹣a|﹣|3x+2|≤4恒成立．令g（x）=|x﹣a|﹣|3x+2|，利用单调性求得它的最大值，再由此最大值小于或等于4，求得a的范围．【解答】解：（Ⅰ）不等式f（x）＜4﹣|x﹣1|，即|3x+2|+|x﹣1|＜4，∴①，或②，或③．解①求得﹣＜x＜﹣，解②求得﹣≤x＜，解③求得x∈∅．综上可得，不等式的解集为（﹣，）．（Ⅱ）已知m+n=1（m，n＞0），∴+=（m+n）（+）=2++≥2+2=4，当且仅当m=n=时，取等号．再根据|x﹣a|﹣f（x）≤+（a＞0）恒成立，可得|x﹣a|﹣f（x）≤4，即|x﹣a|﹣|3x+2|≤4．设g（x）=|x﹣a|﹣|3x+2|=，故函数g（x）的最大值为g（﹣）=+a，再由+a≤4，求得0＜a≤．【点评】本题主要考查绝对值不等式的解法，函数的恒成立问题，基本不等式的应用，体现了转化、分类讨论的数学思想，属于中档题．21．如图，在直三棱柱ABC﹣A1B1C1中，∠ACB=90°，AC=BC=CC1=2．（1）证明：AB1⊥BC1；（2）求点B到平面AB1C1的距离；（3）求二面角C1﹣AB1﹣A1的大小．【考点】二面角的平面角及求法；点、线、面间的距离计算．【专题】综合题．【分析】（1）以C点为坐标原点，CA，CB，CC1为X，Y，Z轴正方向建立空间坐标系，分别求出AB1与BC1的方向向量，代入数量积公式，得到其数量积为0，即可得到AB1⊥BC1；（2）求出平面AB1C1的一个法向量，则AB的方向向量，代入到公式，即可求出点B到平面AB1C1的距离；（3）结合（2）的结合，再求出平面AB1A1的一个法向量，代入向量夹角公式，即可得到二面角C1﹣AB1﹣A1的大小．【解答】证明：（1）如图建立直角坐标系，其为C为坐标原点，题意A（2，0，0），B（0，2，0），A1（2，0，2），B1（0，2，2），C1（0，0，2）．∵，∴∴AB1⊥BC1解：（2）设的一个法向量，由得令∵，∴点B到平面AB1C1的距离．（3）解设是平面A1AB1的一个法向量由∴令∵，∴二面角C1﹣AB﹣A1的大小为60°．【点评】本题考查的知识点是二面角的平面角及求法，点到面的距离，异面直线的夹角，其中建立适当的空间坐标系，将问题转化为向量夹角及向量长度问题是解答本题的关键．22．已知F1，F2为椭圆E的左右焦点，点P（1，）为其上一点，且有|PF1|+|PF2|=4（Ⅰ）求椭圆C的标准方程；（Ⅱ）过F1的直线l1与椭圆E交于A，B两点，过F2与l1平行的直线l2与椭圆E交于C，D两点，求四边形ABCD的面积S ABCD的最大值．【考点】直线与圆锥曲线的综合问题．【专题】圆锥曲线中的最值与范围问题．【分析】（I）设椭圆E的标准方程为，由已知|PF1|+|PF2|=4，，由此能求出椭圆E的标准方程．（II）由题意可知，四边形ABCD为平行四边形，S△ABCD=4S△OAB，设直线AB的方程为x=my﹣1，且A（x1，y1），B（x2，y2），由，得（3m2+4）y2﹣6my﹣9=0，由此利用弦长公式能求出S△BCD的最大值．【解答】解：（I ）设椭圆E 的标准方程为，由已知|PF 1|+|PF 2|=4，得2a=4，∴a=2，…又点P （1，）在椭圆上，∴，∴b=， 椭圆E 的标准方程为=1．…（II ）由题意可知，四边形ABCD 为平行四边形，∴S ▱ABCD =4S △OAB ，设直线AB 的方程为x=my ﹣1，且A （x 1，y 1），B （x 2，y 2），由，得（3m 2+4）y 2﹣6my ﹣9=0， ∴y 1+y 2=，y 1y 2=﹣，… S △OAB =+=|OF 1||y 1﹣y 2|= ==6，…令m 2+1=t ，则t ≥1，S △OAB =6=6，…又∵g （t ）=9t+在[1，+∞）上单调递增 ∴g （t ）≥g （1）=10，∴S △OAB 的最大值为．∴S ▱ABCD 的最大值为6．…【点评】本题考查椭圆方程的求法，考查三角形面积的最大值的求法，解题时要认真审题，注意椭圆弦长公式的合理运用．23．给定数列{c n }，如果存在常数p 、q 使得c n+1=pc n +q 对任意n ∈N *都成立，则称{c n }为“M 类数列”． （1）若{a n }是公差为d 的等差数列，判断{a n }是否为“M 类数列”，并说明理由；（2）若{a n }是“M 类数列”且满足：a 1=2，a n +a n+1=3•2n ．①求a 2、a 3的值及{a n }的通项公式；②设数列{b n }满足：对任意的正整数n ，都有a 1b n +a 2b n ﹣1+a 3b n ﹣2+…+a n b 1=3•2n+1﹣4n ﹣6，且集合M={n|≥λ，n ∈N *}中有且仅有3个元素，试求实数λ的取值范围．【考点】数列的应用．【专题】点列、递归数列与数学归纳法．【分析】（1）通过a n+1=a n +d 与c n+1=pc n +q 比较可知p=1、q=d ，进而可得结论；（2）①通过a 1=2、a n +a n+1=3•2n 计算出a 2、a 3的值，进而利用数列{a n }是“M 类数列”代入计算可知数列{a n }是以首项、公比均为2的等比数列，计算可得结论；②通过①可知2b n +22b n ﹣1+23b n ﹣2+…+2n b 1=3•2n+1﹣4n ﹣6，利用2b n =（2b n +22b n ﹣1+23b n ﹣2+…+2n b 1）﹣（22b n ﹣1+23b n ﹣2+…+2n b 1）计算可知b n =2n ﹣1，从而M={n|≥λ，n ∈N *}，分别计算出当n=1、2、3时λ的值，进而可得结论．【解答】（1）结论：公差为d 的等差数列是“M 类数列”．理由如下：∵数列{a n }是公差为d 的等差数列，∴a n+1=a n +d ，此时p=1、q=d ，即公差为d 的等差数列是“M 类数列”；（2）①∵a 1=2，a n +a n+1=3•2n ，∴a 2=3•2﹣a 1=4， =8，又∵数列{a n }是“M 类数列”，∴，即，解得：p=2，q=0，即a n+1=2a n ， 又∵a 1=2，∴数列{a n }是以首项、公比均为2的等比数列，∴数列{a n }的通项公式a n =2n ； ②由①可知a 1b n +a 2b n ﹣1+a 3b n ﹣2+…+a n b 1=3•2n+1﹣4n ﹣6，即2b n +22b n ﹣1+23b n ﹣2+…+2n b 1=3•2n+1﹣4n ﹣6，∴2b n ﹣1+22b n ﹣2+23b n ﹣3+…+2n ﹣1b 1=3•2n ﹣4（n ﹣1）﹣6=3•2n ﹣4n ﹣2，∴22b n ﹣1+23b n ﹣2+…+2n b 1=3•2n+1﹣8n ﹣4，∴2b n =（2b n +22b n ﹣1+23b n ﹣2+…+2n b 1）﹣（22b n ﹣1+23b n ﹣2+…+2n b 1）=（3•2n+1﹣4n ﹣6）﹣（3•2n+1﹣8n ﹣4）=4n ﹣2，即b n =2n ﹣1，∴集合M={n|≥λ，n ∈N *}={n|≥λ，n ∈N *}，当n=1时，λ≤=；当n=2时，λ≤=；当n=3时，λ≤=；当n ≥4时，λ≤=；又∵集合M={n|≥λ，n ∈N *}中有且仅有3个元素，∴＜λ≤，故实数λ的取值范围是（，]．【点评】本题是一道关于数列与不等式的综合题，考查数列的通项，考查运算求解能力，注意解题方法的积累，属于难题．。
上海市交大附中2019届高三数学一模试题(含解析)
上海市交大附中2019届高三高考一模试卷数学试题一、选择题(本大题共4小题，共12.0分)1.已知定义域为的函数，则此函数图象上关于原点对称的点有( )A. 7对B. 8对C. 9对D. 以上都不对【答案】B【解析】【分析】求出函数y x关于原点对称的函数为y x，x＞0，利用数形结合判断当x＞0时，f （x）＝3与y x，x＞0的交点个数即可【详解】当时，，此时关于原点对称的点此时与没有交点，函数关于原点对称的函数为，即，，若函数图象上存在关于原点对称的点，等价为当时，与，的交点个数即可，作出函数在时的图象如图，由图象知，函数分别关于对称，且函数的最大值为，当时，得，即，故当时，与，的交点个数有8个，即函数图象上关于原点对称的点有8对，故选：B．【点睛】本题主要考查函数与方程的应用，利用对称性转化为两个图象交点个数是解决本题的关键．注意利用数形结合，是中档题2.某超市货架上摆放着某品牌红烧牛肉方便面，如图是它们的三视图，则货架上的红烧牛肉方便面至少有( )A. 8桶B. 9桶C. 10桶D. 11桶【答案】B【解析】【分析】主视图，左视图，俯视图是分别从物体正面，左面和上面看，所得到的图形【详解】易得第一层有桶，第二层最少有桶，第三层最少有桶，所以至少共有桶。
故选【点睛】本题主要考查了由三视图判断几何体，熟练掌握读图的方法是解题的关键，主视图，左视图，俯视图是分别从物体正面，左面和上面看，属于基础题。
3.已知，若，则下列不等式一定成立的是( )A. B.C. D.【答案】B【解析】【分析】先令a=0,排除A，C,D,再利用绝对值三角不等式证明选项B成立【详解】令a=0，则，即-1≤x≤1,≤4,此时A,C,D不成立，下面证明选项B成立=≤≤=≤≤故选：B．【点睛】本题考查了绝对值三角不等式的应用，特值法，结合二次函数最值分析问题，准确推理计算是关键，是基础题．4.若，且，，则的取值范围是( )A. B.C. D.【答案】D【解析】如图所示：，，，∵，∴点C在劣弧AB上运动，表示C、D两点间的距离。
2018-2019学年交大附中高三英语第一学期摸底考试卷,含答案及解析
2018-2019学年交大附中高三英语第一学期摸底考试卷I.Listening Comprehension(略)II.Grammar and Vocabulary(20分)Section ADirections:After reading the passage below,fill in the blanks to make the passage coherent and grammatically correct.For the blanks with a given word,fill in each blank with the proper form of the given word;for the other blanks,use one word that best fits each blank.(A)Space is a dangerous place,not only because of meteors(流星)but also because of rays from the sun and other stars.The atmosphere again acts(21)our protective blanket on earth.Light gets through,and this is essential for plants(22)(make)the food which we eat.Heat,too,makes our environment endurable. Various kinds of rays come through the air from outer space,but enormous quantities of radiation from the sun(23) (screen)off.As soon as men leave the atmosphere,they are exposed to this radiation but their spacesuit or the walls of their spacecraft,(24)they are inside,do prevent a lot of radiation damage.Radiation is(25)(great)known danger to explorers in space.The unit of radiation is called"rem". Scientists have reason to think that a man can put up with far more than0.1rem without(26)(damage); the figure of60rems has been agreed on.The trouble is(27)it is extremely difficult to be sure about radiation damage-a person may feel perfectly well,but the cells of his or her sex organs may be damaged,and this will not be discovered(28)the birth of deformed children or even grandchildren.Missions of the Apollo flights have had to cross belts of high radiation and,during the outward and return journeys,the Apollo crew accumulated(积累)a large amount of rems.So far,no dangerous amounts of radiation have been reported,but the Apollo missions have been quite short.We simply don't know yet(29)men are going to get on when they spent weeks and months outside the protection of the atmosphere,working in a space laboratory.Drugs might help to decrease the damage(30)(do)by radiation,but no really effective ones have been found so far.(B)Living JewelsBefore I went to the British Koi Keepers Annual Show,I didn’t understand(31)people could take fish so seriously.However,the more I learned about koi,the more interested I became.As one expert told me, "Collecting koi is far more addictive than you might think.They’re as beautiful as butterflies and very calming to watch."Freddie Mercury,the lead singer of Queen,would have agreed the pool in his specially-built Japanese garden was home to89koi,(32)cost up to$10,000each.At the show I met koi enthusiast Jean Kelly.“Koi are getting more and more expensive,”she told me.“One recently sold for$250,000.”I was shocked that's almost as much as I paid for my house.Well,that was a record,(33)(admit)Jean.The normal price is nowhere near as high as that.Nevertheless,serious collectors can pay up to$15,000for a fully(34)(grow)koi,which is nearly as expensive as a new luxurious car,and the bigger they are,the more they cost.The cheapest I(35)find was$75each,but they were only about twice as big as my goldfish.Jean wasn’t impressed by one of the koi on sale either.“Actually,these koi aren’t any nicer than (36),”she commented.“(37)they are slightly bigger than the ones I’ve got,I paid considerable less than this.”I wasn’t quite as enthusiastic as Jean,but I did consider(38)(buy)one.Then I remembered that all but5of Freddie Mercury's koi died when someone accidentally turned off the electricity supply to their pool.Jean assured me that with all the new equipment available the survival rate was getting better and better,and that looking(39)koi was no harder than taking care of any other pet.However,in the end I decided to stick with my goldfish.They’re not nearly as beautiful as koi——but they’re a great deal cheaper(40) (replace)!Section B(10分)Directions:Complete the passage with the words in the box.Each word can only be used once.Note that there is one word more than you need.A.associatedB.likelyC.decreasesD.abstractE.limitF.funG.contributes H.consistently I.favorably J.reasoned K.averageThe Beatles sang that money can't buy you love.But what about happiness?Research(41)_____shows that the more money people have,the more likely they are to report being satisfied with their lives.And that makes sense:money buys you things that make life easier and more satisfying;the easier your life, the happier you tend to be.That relationship isn't entirely linear,since there's a(n)(42)_____to how much wealth can please you;the happiness benefit of an increasing income is especially powerful among people who don't have much money to start with,and(43)_____as wealth increases.But studies also reveal that as(44)_____income levels have risen over time—in the U.S.and European nations,for example—residents of those countries have not reported being any happier than people were30or40years ago.It's a paradox that while income and happiness may be(45)_____within a population at any given moment,overall economic growth does not appear to correspond to a boost in national satisfaction over time.(See a gallery of things money can buy.) To understand why,researchers at the University of Warwick and Cardiff University decided to break down how individual people evaluate their income.What does wealth mean to people?Previous work has suggested that people tend to value their own wealth more—and are happier—when it compares(46)_____to everyone else's. The so-called reference-income hypothesis holds that it's not simply how much money you make that(47)_____to satisfaction,but how much more money you make than,say,the national average.The higher your salary than the norm,the happier you tend to be.That could explain in part why populations as a whole do not experience sunnierdispositions with economic growth,since a majority of individuals may not fall above the national income average.But the reference-income hypothesis is rather(48)_____.The researchers wondered whether there was a more nuanced way to capture how people valued their income.They(49)_____that people tend to make specific comparisons of personal wealth,not only with the average income of the larger population,but with the individual incomes of their neighbors,colleagues at work or friends from college.And the higher their rank,the greater their sense of happiness and self-worth would(50)_____be."For example,people might care about whether they are the second most highly paid person,or the eighth most highly paid person,in their comparison set,"write the authors, Chris Boyce,a psychologist at the University of Warwick,and Simon Moore,a psychologist at Cardiff University.III.Reading Comprehension(45分）Section ADirections:For each blank in the following passage there are four words or phrases marked A,B,C and D.Fill in each blank with the word of phrase that best fits the context.The beauty,majesty,and timelessness of a primary rainforest are indescribable.It is impossible to(51)______ on film,to describe in words,or to explain to those who have never had the awe-inspiring experience of standing in the heart of a primary rainforest.Rainforests have(52)______over millions of years to turn into the incredibly complex environments they are today.Rainforests represent a store of living and(53)______renewable natural resources that for eons,by virtue of their richness in both animal and plant species,have(54)______a wealth of resources for the survival and well-being of humankind.These resources have included basic food supplies,clothing,shelter,fuel,spices, industrial raw materials,and medicine for all those who have lived in the majesty of the forest.(55)______,the inner dynamics of a tropical rainforest is an intricate and fragile system.Everything is so(56)______that upsetting one part can lead to unknown damage or even destruction of the whole.Sadly,it has taken only a century of human intervention to destroy what nature designed to(57)______forever.The scale of human(58)______on ecosystems everywhere has increased enormously in the last few decades. Since1980the global economy has tripled in size and the world population has increased by30percent. Consumption of everything on the planet has risen——at a cost to our(59)______.In2001,the World Resources Institute estimated that the demand for rice,wheat,and corn is expected to grow by40%by2020,increasing irrigation water demands by50%or more.They further reported that the demand for wood could double by the year2050;(60)______,it is still the tropical forests of the world that supply the bulk of the world's demand for wood.In1950,about15percent of the Earth's land surface was covered by rainforest.Today,more than half has already gone up in(61)______.In fewer than fifty years,more than half of the world's tropical rainforests have fallen(62)______to fire and the chain saw,and the rate of destruction is still accelerating.Unbelievably,more than 200,000acres of rainforest are burned every day.That is more than150acres lost every minute of every day,and 78million acres lost every year!More than20percent of the Amazon rainforest is already gone,and much more is severely threatened as the destruction continues.It is estimated that the Amazon alone is vanishing at a rate of 20,000square miles a year.If nothing is done to curb this(63)______,the entire Amazon could well be gone withinfifty years.Massive(64)______brings with it many ugly consequences-air and water pollution,soil erosion,malaria epidemics,the release of carbon dioxide into the atmosphere and the(65)______of biodiversity through extinction of plants and animals.Fewer rainforests mean less rain,less oxygen for us to breathe,and an increased threat from global warming.51.A.present B.capture C.claim D.prove52.A.changed B.evolved C.expanded D.existed53.A.energizing B.healing C.isolating D.breathing54.A.contributed B.stored C.reduced D.affected55.A.However B.Furthermore C.Therefore D.Otherwise56.A.active B.sensitive C.interdependent D.delicate57.A.restore B.support C.revive st58.A.pressure B.power C.concern D.strength59.A.existence B.ecosystem C.planet D.survival60.A.unfortunately B.consequently C.naturally D.similarly61.A.store B.food C.smoke D.wealth62.A.subject B.down C.apart D.victim63.A.trend B.practice C.decrease D.attitude64.A.destruction B.industrialization C.modernization D.deforestation65.A.appearance B.explosion C.loss D.increaseSection BDirections:Read the following three passages.Each passage is followed by several questions or unfinished statements.For each of them there are four choices marked A,B,C and D.Choose the one that fits best according to the information given in the passage you have just read.(A)The definition of the standard kilogram is fundamentally imperfect.Getting the definition right is a challenge that has tried the patience and intelligence of scientists for decades.Scientists use just seven basic units to define all the other quantities we use---quantities such as speed, density,or electric power.All of those basic units except the kilogram are themselves defined in terms of natural properties that are beyond human control.For example,the standard second(time)is defined as a specific number of vibration of a type of radiation released by atoms of a special metal.The standard meter(length),in turn,is defined as the length of the path light travels in a vacuum during a specific fraction of a second.Not so the kilogram.This orphan of the basic unit family is simply the mass of a small platinum-iridium alloy cylinder(铂-铱合金筒)locked away by the international Bureau of Weighs&Measures in France.Embarrassingly,the last time the copies were brought for a checkup in the1980s,officials found that some copies had gained about20parts per billion in weight compared to the master cylinder since the previous checkup in the1940s.This implies that the master cylinder itself may be an inconstant standard.No one knows what causes the weight changes.But the uncertainty can’t be tolerated when precision(精密度) in research and some manufacturing now demands accuracy to a few parts per billion.Several efforts in several different countries are under way to redefine the kilogram in terms of basic physical quantities such as counting the actual number of atoms of a specific substance in a kilogram or the electromagnetic force that balances a kilogram mass against gravity.A project of the latter type at the NIST laboratories in Gaithersburg hopes eventually to define mass in terms of electrical units.So far,none of these redefinition projects has borne fruit.They require precision of measurement and control of experimental conditions.The slightest pollution,tiny vibrations,or other influences---even changes in weather---can ruin results.You’ve got to hand it to scientists who are willing to devote many years to such painstaking but fundamentally important research.66.Which of the following best paraphrases the sentence“Not so the kilogram.”In paragraph4?A.The kilogram is not as accurate as the standard second.B.The kilogram is not universally accepted in the world.C.The kilogram is not defined in terms of natural properties.D.The kilogram is not well defined as time and length.67.Which of the following can NOT be concluded from the passage?A.Experiments are being carried out to redefine the kilogram.B.The uncertainty in the standard kilogram can seriously affect some research.C.The redefinition of the standard kilogram is quite complicated.D.Scientists will achieve success in redefining the kilogram in the near future.68.According to the passage,to define the weight of mass in terms of electrical units_______.A.is one of the best methods to redefine the kilogramB.has been accepted as the only possible redefinition projectC.is not as simple as what people can understandD.has been considered by some scientists as a better approach69.We can know from the passage that the redefinition of the kilogram is_________.A.more important in keeping market honestyB.worth years of scientists’painstaking researchC.the urgent requirement of business and manufacturing.D.bring about important and fruitful results(B)Stewart Island Ferry ServicesWhile most visitors spend at least one night on Stewart Island,it is also readily accessible by ferry as a day excursion from Invercargill and Bluff.Experience Foveaux Strait in comfort and style on board our express catamarans.During the one-hour crossing between Bluff and Stewart Island keep a lookout for wildlife,especially seabirds.Watching mollymawks (albatross)soaring behind the ferry is a fantastic sight.Interesting landmarks commonly seen include Dog Island Lighthouse,Ruapuke Island,Titi Islands and Mt Anglem-Stewart Island’s highest point.●Free tea and coffee on board●Interpretation handouts are available(English only).●Wheelchair access available●Personal baggage is carried free on the ferries-max.two bags per person(one stowed and onesmall carry-on).Additional baggage is by prior arrangement.●Vehicle parking available at Bluff(extra cost-reservations recommended)FERRY TO STEWART ISLAND Depart BluffAll year9:30amSep-May5:00pmOct–Apr11:00amJun–Aug4:30pmLate Dec–mid Jan8:00am FERRY TO BLUFF Depart Stewart IslandAll year8:00amSep–May3:30pmOct–Mar6:00pmApr5:00pmJun-Aug3:00pmLate Dec–mid Jan9:30amOther departures as locally advertisedDuration1hrCheck-in30minutes prior to the scheduleddeparture time.(Check-in and boarding gates are closed10minutes prior to times stated above.)“20%Multi-Purchase REWARD”on Return Ferry ServicesBuy2or more different excursions and SAVE20%off all lower priced!Kids Go FREE on selected departures during NZ School Holidays!Kids Go FREE for travel20April-5May2013.70.If a traveler plans to leave a car at Bluff,he had better________.A.refer to the handouts firste wheelchair accessC.make a reservationD.park it30minutes before departure time71.John,who went to Stewart Island on Dec.28th,got to the ferry dock at7:55am.When did he most probably leave Bluff？A.At8:00a.m.B.At9:30a.m.C.At11:00a.m.D.At3:00p.m.72.Which of the following is false about the ferry services？A.Tea and coffee are free for passengers.B.Children go free for travel for about15days.C.Travelers are sure to see some seabirds during the crossing.D.Passengers have to pay extra cost for extra pieces of luggage.（C）Like every dog,every disease now seems to have its day.World Tuberculosis(infections disease in which growths appear on the lungs)Day is on Saturday March24th.Tuberculosis was once terribly fashionable.Dying of"consumption"seems to have been a favorite activity of garret-dwelling19th-century artists,h has,however,been neglected of late.Researchers in the field never tire of pointing out that TB kills a lot of people.According to figures released earlier this week by the World Health Organization,1.6million people died of the disease in2005,compared with about3m for AIDS and l m for malaria. But it receives only a fraction of the research budget devoted to AIDS.America’s National Institutes of Health,for example,spends20times as much on AIDS as on TB.Nevertheless,everyone seems to getting in on the TB-day act this year.The Global Fund an international organization responsible fur fighting all three diseases but best known for its work on AIDS,has used the occasion to trumpet its tuberculosis projects.The fund claims that its anti-TB activities since it opened for business in2002have saved the lives of over1m people.The World Health Organization has issued a report that contains some good news.Although the number of TB cases is still rising,the rate of illness seems to have stabilized;the caseload,in other words,is growing only because the population itself is going up.Even drug companies are involved.In the nm-up to the day itself,Eli Lilly announced a$50m boost to its MDRTB Global Partnership.MDR stands for multi-drug resistance,and it is one of the reasons why TB is back in the limelight.Careless treatment has caused drug-resistant strains to evolve all over the world.The course of drugs needed to clear the disease completely takes six mouths,anti persuading people lo stay that course once their symptoms have gone is hard.Unfortunately,those infected with MDR have to be treated with less effective,more poisonous and more costly drugs.Naturally,these provoke still more.non-compliance and thus still more evolution.The other reason TB is back is its relationship to AIDS.The Global Fund’s joint responsibility for the diseases is no coincidence.AIDS does not kill directly.Rather,HIV,the virus that causes it,weakens the body’s immune system and exposes the sufferer to secondary infections.Of these,TB is one of the most serious.It kills200000 AIDS patients a year.However,some anti-TB drugs interfere with the effect of some anti-HIV drugs.Conversely, in about20%of cases where a patient has both diseases,anti-HIV drugs make the tuberculosis worse.The upshot is that125years after human beings worked out what caused TB,it is still a serious threat.73.The first sentence“Like every dog,every disease now seems to have its day.”means______.A.every dog enjoys good luck or success sooner or laterB.human beings can deal with problems caused by diseaseC.Tuberculosis becomes a serious infectious diseaseD.people attach importance to Tuberculosis recently74.By referring to AIDS in Paragraph2,the author intends to show______.A.the US government is reluctant to spend millions of dollars on TuberculosisB.the death rate of AIDS is higher than that of TuberculosisC.the officials did not pay much attention to the research of Tuberculosis in the pastpared with AIDS,Tuberculosis can be cured effectively75.Which of the following best defines the word“upshot”(Line6,Para5)?A.Outcome.B.Uphold.C.Achievement.D.Project76.Which of the following proverbs is closest in meaning to the message the passage tries to convey?A.Forgive and forget.B.Forgotten,but not gone.C.When the wound is healed,the pain is forgotten.D.Every dog is brave at his own door.Section CDirections:Read the passage carefully.Fill in each blank with a proper sentence given in the box. Each sentence can be used only once.Note that there are two more sentences than you need.A.The critical abilities are beginning to develop in adolescence.B.Their view on life usually falls in two extremes.C.Of all periods of life,this is what may best be called the plastic age.D.They are basically timid or self-conscious.E.Despite that,it is also in this period that strong ties between teachers and students develop.F.Fundamentally they want to be kept-busy but they refuse to admit it.Adolescents generally refer to boys and girls on the high-school level-more specifically,the second,third, and the fourth years of high school.In dealing with students at this level,we must bear in mind that to some degree they are at a difficult stage,generally called adolescence.Students at this level are likely to be confused mentally.They usually find it hard to concentrate on what they intend to do and often have romantic dreams.(77)They lack frankness and are usually very easily affected by their own emotions but hate to admit it.They are driven either by greater ambition,probably beyond their capability,or by extreme laziness caused by the fear of not succeeding or achieving their objectives.(78)They are willing to work,but they hate to work without obtaining the results they think they should obtain.Regarding school issues,although they seldom say so,they really want to be consulted and given an opportunity to direct their own affairs,but they need a good amount of guidance.They seldom admit that they need this guidance and they frequently rebel against it,but if it is intelligently offered they accept it with enthusiasm.As to persona]beliefs,most of adolescents are trying to form political ideas and they have a tendency to be sometimesextremely idealistic,and at other times conventional,blindly accepting what their fathers and grandfathers believed in.(79)On the one hand they are too modest,and on the other hand unreasonably boastful.They tend to be influenced more by a strong character than by great intelligence.(80)Having a better understanding of the characteristics and needs of young people at this age is a task that falls on both educators and the other people involved.It may also help the young go through this difficult and critical stage of life in a more constructive manner.【答案】77-80DFBC【解析】青春期的孩子要谨慎对待第一段引出话题，青春期是一个困难的时期to some degree...at a difficult stage...第二段描述了青春期的孩子们的各种纠结和扭吧77题的提示在后面，他们不愿坦诚，易受情绪影响又羞于承认，与这些描述相关就是they basically timid and self-conscious78题的提示也是在后面,they are willing to work,和前面的they want to be kept busy呼应第三段描述了青春期的孩子们还是很希望能参与到学校生活中并起主导作用，尽管他们不承认，他们需要良好的引导，需要一位强有力的人物的影响。
精品解析：【全国百强校】上海市交大附中2019届高三高考一模试卷数学试题(解析版)
上海市交大附中2019届高三高考一模试卷数学试题注意事项：1．答卷前，考生务必用黑色字迹的钢笔或签字笔在答题卡上填写自己的准考证号、姓名、试室号和座位号。
用2B型铅笔把答题卡上试室号、座位号对应的信息点涂黑。
2．选择题每小题选出答案后，用2B型铅笔把答题卡上对应题目选项的答案信息点涂黑，如需改动，用橡皮擦干净后，再选涂其他答案，答案不能答在试卷上。
3．非选择题必须用黑色字迹钢笔或签字笔作答，答案必须写在答题卡各题目指定区域内的相应位置上；如需改动，先划掉原来的答案，然后再写上新的答案；不准使用铅笔和涂改液。
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4．考生必须保持答题卡整洁。
考试结束后，将试卷和答题卡一并交回。
一、选择题(本大题共4小题，共12.0分)1.已知定义域为的函数，则此函数图象上关于原点对称的点有( )A. 7对B. 8对C. 9对D. 以上都不对【答案】B【解析】【分析】求出函数y x关于原点对称的函数为y x，x＞0，利用数形结合判断当x＞0时，f（x）＝3与y x，x＞0的交点个数即可【详解】当时，，此时关于原点对称的点此时与没有交点，函数关于原点对称的函数为，即，，若函数图象上存在关于原点对称的点，等价为当时，与，的交点个数即可，作出函数在时的图象如图，由图象知，函数分别关于对称，且函数的最大值为，当时，得，即，故当时，与，的交点个数有8个，即函数图象上关于原点对称的点有8对，故选：B．【点睛】本题主要考查函数与方程的应用，利用对称性转化为两个图象交点个数是解决本题的关键．注意利用数形结合，是中档题2.某超市货架上摆放着某品牌红烧牛肉方便面，如图是它们的三视图，则货架上的红烧牛肉方便面至少有( )A. 8桶B. 9桶C. 10桶D. 11桶【答案】B【解析】【分析】主视图，左视图，俯视图是分别从物体正面，左面和上面看，所得到的图形【详解】易得第一层有桶，第二层最少有桶，第三层最少有桶，所以至少共有桶。
【化学】2020-2019学年度上海交通大学附中第一学期高三摸底考试
2020-2019学年度上海交通大学附中第一学期高三摸底考试化学试卷（满分150分，120分钟完成，答案一律写在答题纸上）相对原子质量：H-1 Li-7 Be-9 C-12 N-14 O-16 Na-23 Mg-24 Al-27 S-32 Cl-35.5 K-39 Ca-40 Fe-56 Cu-64 Zn-65一、选择题(本题共48分，每小题3分，只有一个正确选项)1．据06年4月9日CCTV“每周质量报告”节目报导，染发剂中的对苯二胺会致癌。
下列关于对苯二胺的叙述中，不正确的是（）。
A. 该物质属于芳香族化合物B. 该物质属于烃的衍生物C. 该物质的分子量比苯大32D. 该物质不属于苯的同系物2．以下是人们对原子结构的认识所经历的几个重要历史阶段，其中先后顺序正确的是（）①道尔顿提出的原子论②汤姆孙提出的葡萄干面包原子摸型③德谟克里特的古典原子论④卢瑟福的原子结构行星模型A.①②③④B.③①②④C.③②①④D. ③④②①3．以下说法中，违背科学规律的是（）A. 改变核外电子数可使原子与离子相互转化B. 改变核内中子数可使不同的同位素相互转化C. 改变核内质子数可使不同的元素相互转化D. 改变离子的电荷数可使一种元素的阳离子转化为另一种元素的阴离子4．不能促进水的电离，即不能增大水的电离程度的方法或途径是（）A. 在水中加入一小粒钠B. 在水中溶入纯碱C. 在水中通入SO2气体D. 在水中放入一块红热的铜5．1molCH3COOH分别与1molC2H518OH和1molC2H516OH发生酯化反应，两者生成水的质量（）A.前者大B.后者大C.相等D.不能判断6．将铁和铝的混合粉末溶于足量盐酸中，通入足量氯气，再加入过量的NaOH溶液，最后所得的溶液中大量存在的离子是（）A. Na+、Fe2+、Cl-、AlO2-B. Na+、Fe3+、Cl-、OH-C. Na+、Fe3+、Cl-、AlO2-D. Na+、OH-、Cl-、AlO2-7．设N A为阿伏加德罗常数，下列叙述中不正确的是（）A. 在标准状况下，N A个水分子所占的体积约为18mLB. 5.6g铁与足量的硫完全反应，失去电子的数目约为0.2N AC. 1L 0.01mol/L的氯水中含有的分子总数大大超过0.01N AD. 含N A个氧原子的O2与含N A个氧原子的O3的质量之比为2:38．在一定体积的密闭容器中发生下列反应：N2 + 3H22NH3，其中N2的起始浓度为1mol/L。
上海交通大学附属中学高二上开学摸底考试数学试题(无答案)
上海交通大学附属中学高二上开学摸底考试数学试题（无答案）上海交大大学附属中学2019-2019学年度第一学期高二数学摸底考试试卷 一、填空题。
1.若集合{}{}{}，，，，，，，210200===B A B m A 则实数=m ________.2.已知关于x 的二元一次方程组⎩⎨⎧=+=+222111cy b x a cy b x a 的增广矩阵是 ⎝⎛11 11- ，⎪⎪⎭⎫31则此方程组的解是________. 3.函数()2log 2-=x y 的定义域是_____________.4.已知向量b a 、均为单位向量,若它们的夹角是60°，则b a 3-等于__________. 5.函数()⎪⎭⎫⎝⎛+⎪⎭⎫ ⎝⎛-=x x x f 4sin 4sin 2ππ的最小正周期为_________. 6.等差数列{}na 中,，12876=++a a a,则该数列的前13项的和=13s _________.7.已知函数()241+=xx f ，若函数()41-+=m x f y 为奇函数，，，πAO m AC BC AB C B A 2sin cos sin cos 3=+=则实数=m ________.二、选择题。
13.若平面向量()x ，1=和()x x -+=，32互相平行,其中，R x ∈=b a A.52 B.522或 C.02或- D.102或14.已知△ABC 两内角A 、B 的对边边长分别为b a 、,则“A=B ”是“B b A a cos cos =”A.充分非必要条件B.必要非充分条件C.充要条件D.既非充分也非必要条件15.函数()123+-=a ax x f ,若存在()，，110-∈x 使()00=x f ,那A.511＜＜a - B.1-＜a C.511＞或＜a a -D.51＜a 16.定义域为[]b a ，的函数()x f y =图像的两个端点为A 、B,向量()λλ-+=1()y x M ，是()x f 图像上任意一点,其中()[]101，，∈-+=λλλb a x .若不等式k MN ≤恒成立,则称函数()x f 在[]b a ，上满足“k 范围线性近似”,其中最小的的正实数k 称为该函数的线性近似阈值。
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2019-2020学年上海交通大学附属中学第一学期高三英语摸底考命题人：李剑诗颜秉蕾审卷人：朱雪艳(满分150分，考试时间120分钟，答案一律写在网上阅卷答题纸上)第I卷I. Listening Comprehension (25’)Part A Short ConversationsDirections: In Part A, you will hear ten short conversations between two speakers. At the end of each conversation, a question will be asked about what was said. The conversations and the questions will be spoken only once. After you hear a conversation and the question about it, read the four possible answers on your paper, and decide which one is the best answer to the question you have heard.1. A. In the kitchen. B. At home. C. In a fashion shop. D. In a net bar.2. A. 500 yen. B. 1500 yen. C. 2500 yen. D. 5000 yen.3. A. He will pay for the lunch. B. Sue likes Spanish food very much.C. He doesn’t like Spanish food at all.D. Both of them should treat Sue well at dinner.4. A. Boss and employee. B. Doctor and patient.C. Teacher and student.D. Interviewer and interviewee.5. A. She doesn’t have time to find a new flat.B. She has paid three months, rent in advance.C. She is unlikely to find such a satisfactory flat.D. She doesn’t like the idea of decorating an empty flat.6. A. Mike. B. Sandy. C. An unexpected friend. D. A handyman.7. A. Make a recovery plan. B. Find a full-time job.C. Drop out of school.D. Resign from her present job.8. A. The woman was fully absorbed in the music.B. The woman couldn’t understand the music very well.C. The woman lost her way to the conceit that evening.D. The concert was no better than what the woman imagined.9. A. Extreme sports. B. Travel insurance.C. Travel arrangements.D. Courage and safety.10. A. She is talkative. B. She is quiet. C. She is active. D. She is sociable.Part B PassagesDirections: In Section B, you will hear two short passages and one longer conversation. After each passage or conversation, you will be asked several questions. The passage and the conversations will be read twice, but the questions will be spoken only once. When you hear a question, read the four possible answers on your paper and decide which one would be the best answer to the question you have heard.Questions 11 through 13 are based on the following passage.11. A. 28 billion copies. B. 567 million copies.C. 1953 million copies.D. 2015 million copies.12. A. Interviewed the vice-president of the Commercial Press in China.B. Completed data investigation, collection and examination for the records.C. Compared the sales volumes of the Secret Garden and Harry Potter series.D. Delivered enough copies of Xinhua Dictionary to the presentation ceremony.13. A. It contains colorful cultures of many countries.B. It is the world’s most popular dictionary.C. It is a useful tool for learners of the Chinese language.D. It has influenced several generations of Chinese people.Questions 14 through 16 are based on the following passage.14. A. Over a billion people do not have enough safe drinking water.B. Diseases and 6acteria in the water kill millions of people every day.C. People in developed countries take their clean drinking water for granted.D. Clean, bottled water is expensive to transport to poor rural villages.15. A. It is a plastic straw.B. It uses batteries or electricity.C. It can be used for one year.D. It’s portable and cheap.16. A. Appeal to the government to supply clean water for everyone.B. Provide easy access to clean water to destroy the bacteria.C. Offer the WaterTube free to people in. developing countries.D. Sell the WaterTube to every person who needs one.Questions 17 through 20 are based on the following conversation.17. A. A little restaurant. B. A private organization.C. An ice cream shop.D. A snack bar.18. A. More flexible working time.B. Less conflicts with consumers.C. Closer relationship with customers.D. More freedom to make financial decisions.19. A. A program of the Small Business Administration.B. A grant from a private organization.C. Savings in his own bank account.D. Loans from the bank.20. A. He found owing his own business is rewarding.B. He didn’t recommend others to have their own business.C. He chose the location to compete with bigger businesses.D. He found managing a small business is high risky.II. Grammar and Vocabulary (10’+10’+10’)Section ADirections:After reading the passage below, fill in the blanks to make the passage coherent and grammatically correct. For the blanks with a given word, fill in each blank with the proper form of the given word; for the other blanks, use one word that best fits each blank.(A)"Monday morning feeling" could be the very crushing pain in the chest (21) __________ leaves you sweating and gasping for breath. Recent research from Germany and Italy shows that heart attacks are more common on Monday mornings.A study of 11,000 participants proved 8 am on a Monday morning as (22) __________ (stressful) time for the heart, and both studies showed that Sunday is the least stressful day.The findings could lead to a better understanding of what is the immediate cause of heart attacks, according to Dr. Stefan Willich of the Free University. " We don't know what actually causes heart attacks, so we can 't make specific recommendations about (23) __________ to do to prevent them," he said.Monday mornings have a double helping of stress for the working body (24) __________ it makes a rapid change from sleep to activity, and from the relaxing weekend to the pressures of work. Willich explained. “It is the unfavorable effect in the blood system and increase of the risk of a clot (血凝块) in the arteries (动脉) (25) __________ will cause a heart attack. "When people return to work after a weekend off, they have a higher workload, more stress, more anger and more physical activity," said Willich. "We need to know how these events cause changes in the body (26)__________ we can understand if they cause heart attacks."But (27) __________ it is tempting to believe that returning to work increases the risk of a heart attack, both Willich and the Italian researchers admit that it is only a partial answer. Both studies showed that the over 65s are also vulnerable on Monday morning (28) __________ __________ most no longer work. The reason for this is not clear, but the Italian team speculated that the social interactions — the thought of (29) __________ (face) with another week and all its pressures — may play a part.What is clear, however, is that the Monday morning peak seems to be consistent from the northern Germany to southern Italy (30) __________ the differences in diet and lifestyle.(B)A trail of hot springs dot the northern Kapong District. For tree worshipers, it's a site best described as awesome. Visitors can enjoy the ancient hot springs, (31) __________ (understand) their therapeutic properties from knowledge (32) __________ (pass) down from one generation to another. Rain, drizzle and cloudy skies are typical in Phang Nga, making secluded places even more mesmerizing in scenery.Visit Phang Nga for a few days and you will immediately realise that once (33) __________ (overlook) things turn out to be hidden gems and one (34) __________ have planned for more time to enjoy them all. The ever-famous Phang Nga bay is in fact best seen not from the middle of the bay, but instead from the (35) __________ (elevate) shores of Samed Nang Chee. You can’t pick the best weather, (36) __________ even on partly cloudy days, the magnificent natural limestone structures of the bay is simply spectacular.If you've heard about the trading routes of the Thai south and the Malay peninsula, you will notice a remnant of this direct link between Phuket (普吉) and Phang Nga (攀牙). (37) __________ the major trading hub of Phang Nga in the old days, the district of Takua Pa boasts a small but untainted stretch of an old Sino-English community. These original century-old shophouses are “so authentic” here a local told me, it can overwhelm Phuket people with nostalgia.However, the town centre of Phang Nga is not Takua Pa, though. The story has it (38) __________ back in 1809, the Siam-Burmese wars drove people down to Phang Nga bay，hence the new settlement that has now become the province's municipal seat. It's still small in size, but with newer natural charms. Mountains (39) __________ (surround) Phang Nga with the most magnificent limestone peaks (40) __________ create wonderfully amazing signature views. Driving through the town's small parallel streets and looking up, one can only marvel at Mother Nature. Perpetual rain and misty mornings to virtual greenness --- Phang Nga people will ensure you get all that。