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2023年上海交通大学博士生英语入学考试试题
2023年上海交通大学博士生英语入学考试试题第一部分：听力理解（共两节，满分20分）第一节（共5小题；每小题1分，满分5分）请听下面5段对话。
每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。
每段对话仅读一遍。
1. Where does this conversation most likely take place?- A. In a restaurant.- B. In a library.- C. In a hospital.2. What does the woman want to do?- A. Return the shirt.- B. Buy a new shirt.- C. Exchange the shirt.3. What does the man think the weather will be like tomorrow?- A. Sunny.- B. Cloudy.- C. Rainy.4. How many classes did the woman miss?- A. One.- B. Two.- C. Three.5. What does the woman imply about men?- A. They are careless.- B. They are forgetful.- C. They are helpful.第二节（共15小题；每小题1分，满分15分）请听下面5段对话或独白。
每段对话或独白后有几个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。
听完每段对话或独白前，你将有时间阅读各个小题，每小题5秒钟；听完后，各个小题将给出5秒钟的作答时间。
每段对话或独白读两遍。
听下面一段对话，回答第6和第7两个小题。
6. What does the woman want to do?- A. Go swimming.- B. Go hiking.- C. Go skiing.7. When does the conversation most probably take place?- A. In winter.- B. In spring.- C. In summer.听下面一段对话，回答第8和第9两个小题。
上海交通大学英语水平考试样题及答案
上海交通大学英语水平考试样题Part II Integrated Reading (30%)Section 1 Banked Cloze (10%)Directions: In this section, there is a passage with ten blanks. You are required to select one word for each blank from a list of choices given in a word bank following the passage. Read the passagethrough carefully before making your choices. You may not use any of the words in the bankmore than once. Give your answers to the questions on your ANSWER SHEET.Attention:You need to change the forms of the words in the word bank where necessary.(注意：请把答案写在答题卷上,否则以零分处理)A name might tell you something about a person's background. Names can be1) __________ of class and race. Data show African Americans are far more likely than other 2) __________ groups to give their children uncommon names. White people tend to 3) ________ more familiar names that were formerly popular with more affluent white people.The new study purports to show a link between name and outcome of life: The more 4) _________ your name, the more likely you are to land in juvenile hall. That's because we know that boys with uncommon names are more likely to come from a socio-economically 5) _________ background, which means that they also are more likely to get involved with crime. Even the researchers readily admit that it's not a name alone that 6）_______ a child's outcome, but rather the circumstance underlying the name.The researchers first assigned a popularity score to boys' names, based on how often they showed up in birth records in an undisclosed state from 1987 to 1991. Michael, the No. 1 boy's name, had a Popular Name Index score of 100; names such as Malcolm and Preston had index scores of 1. The researchers then assessed names of young men born during that time who landed in the juvenile justice system. They found that only half had a rating higher than 11. By 7) __________, in the general population, half of the names scored higher than 20. "A 10% increase in the popularity of a name is associated with a 3.7% 8) _________ in the number of juvenile delinquents who have that name."Still, the study theorizes that teenagers named Malcolm might also 9) ___________ because their peers treat them differently or they just don't like their names. And since the study's release last week, the name-crime 10) ___________ has been written or talked about in major media outlets.Section 2 True orFalse Judgement & Sentence Completion (10%)Directions:In this part, you will find 7 statements and 3 incomplete sentences followed by the reading passage.For questions 1-7, markY (for YES) if the statement agrees with the information given in the passage;N (for NO) if the statement contradicts the information given in the passage;For questions 8-10, complete the sentences with the information given in the passage.Attention: For questions 1-7, one more point will be deducted if you do n’t answereach one correctly.(注意: 1-7题中每答错一题倒扣1分, 不答不得分,答对得1分; 请把答案写在答题卷上,否则以零分处理)Who are smarter, men or women? It's a topic of common –– and often comic –– contemplation, but it has also become a serious policy issue for colleges and students in the United States.After years of concentrated effort to raise the academic achievement of girls, who in previous decades had often received less attention in the classroom and been steered away from college-prep courses, the nation can brag that female students have progressed tremendously. Though still underrepresented in calculus and other advanced-level science and math courses in high school, women now outnumber men applying to and graduating from college ––so much so that it appears some colleges are giving male applicants an admissions boost. As a result, the U.S. Commission on Civil Rights is examining whether colleges are engaging in widespread discrimination against women in an effort to balance their male and female populations.Consider some of the numbers at leading schools: At Vassar College in New York State, a formerly all-women's college that is still 60% female, more than two-thirds of the applicants last year were women. The college accepted 35% of the men who applied, compared with 20% of the women. Locally, elite Pomona College accepted 21% of male applicants for this year's freshman class, but only 13% of female applicants. At Virginia's College of William & Mary, 7,652 women applied for this year's freshman class, compared with 4,457 male applicants. Yet the numbers of each who gained admittance were nearly the same. That's because the college accepted 45% of the men and only 27% of the women.A 2007 analysis by U.S. News & World Report, based on the data sent by colleges for the magazine's annual rankings, found that the admissions rate for women averaged 13 percentage points lower than that for men. But percentages don't tell the whole story. It could be that the men were stronger candidates, or they might have applied in areas of engineering and science where women's numbers are still lower. But such justifications, even if true, are unlikely to fully explain these numbers. At schools such as the University of California, where admissions rely overwhelmingly on statistical measures of academic achievement such as grades and test scores, the disparities don't appear. Far more women than men applied to UCLA –– the UC's most selective campus –– last year. The university accepted about the same percentage of each, with a slight edge to the women. As a result, the freshman class has close to 800 more women than men.In recent years, several college leaders have admitted that their institutions give a boost to male applicants to maintain gender balance on campus. Most students of either sex, they point out, prefer suchbalance. If Vassar accepted equal percentages of each sex, women would outnumber men by more than 2 to 1.Jennifer Delahunty Britz, the dean of admissions at Kenyon College in Ohio, a formerly all-male school, brought the matter to broad public attention in 2006 with an Op-Ed article for the New York Times describing the dilemma of her admissions office. "What messages are we sending young women that they must . . . be even more accomplished than men to gain admission to the nation's top colleges?" New York Times has long favored allowing colleges to use race as an admissions factor in order to diversify student populations.She also wrote that exposure to people of different backgrounds and viewpoints better educates all students –– not just those given a leg up. We are not in favor of accepting underqualified or clearly inferior students for the sake of diversity. But most colleges are inundated with applications from students who more than meet their standards; the differences among many of them are slight. It makes sense for colleges to pick a balanced population from within this group. At the same time, admissions officers should avoid rigid notions of what constitutes enough men on campus. It's not harming UCLA, or destroying college social life, to admit somewhat more women than men.Even if the Civil Rights Commission finds pervasive gender discrimination in admissions, there's little it could do about the situation. Such discrimination ––though not racial discrimination ––is legal for undergraduate admissions at private, nonprofit colleges, even those that receive federal funding. Commission documents on the inquiry suggest that colleges could find more "gender-neutral" ways of balancing their student numbers, perhaps by offering programs and extracurricular activities that attract men.Those might work for some schools but won't change the overall scenario. Not with college populations composed of 57% women nationwide. The issue we'd like the Commission on Civil Rights to investigate is: What's happening with the education of U.S. boys? Why are so few of them applying to and graduating from college?Theories and arguments abound. Some say that boys are more active and thus less able to sit still for long periods ––and as a result, more likely to be categorized as having attention deficit / hyperactivity disorder or needing special education. A 2008 study by researchers at Northwestern University found that when girls are involved in a language-related task –– such as reading –– they show more activity in areas of the brain involved in encoding language. Boys use more sensory information to do linguistic tasks. The study suggests boys might do better if they were taught language and arts in different ways. Race is a factor as well. The gender gap is starker among African American and Latino students.There may be no one reason –– or solution. But figuring out ways to help boys achieve in school is abetter response to the gender gap than making it easier for them to get into college later.1. As a result of the effort to raise the academic achievement of the girls for years, the girls have exceeded boys tremendously in all courses in colleges except calculus and other advanced-level science and math courses.2. Female students are facing the low admission rate because some colleges are engaging in discrimination against women to achieve the balance of their male and female populations.3. Although the men were traditionally considered stronger candidates in areas of engineering and science, the admission rate for men in these areas is still lower than that for women.4. Women have outnumbered men in gaining admittance in UCLA’s freshman class this year because their admissions greatly rely on grades and test scores of their applicants.5. Some college leaders hold that most college students prefer their policy of maintaining gender balance by admitting equal percentages of each sex.6. The dilemma of the dean of admissions at Kenyon College is whether to use gender as an admissions factor in order to achieve gender balance or use race as an admissions factor in order to diversify student populations.7. According to Jennifer Delahunty Britz, it is reasonable for colleges to pick a balanced population from the candidates who more than meet their standards.8. Actually the Civil Rights Commission can do little to change the situation of discrimination in college admission because such discrimination is _____________.9. The study shows that in doing linguistic tasks the boys use more sensory information, the girls show more _____________.10. Despite various theories and arguments about why so few boys apply to and graduate from college, the better solution to the problem is to __________________________________.Section 3 Cloze (10%)Directions:In this section there are 20 blanks in the following passage. For each blank there are four choices marked A), B), C) and D) on the right side of the paper. You should choose the ONE that best fits into the passage. Give your answers to the questions on your ANSWER SHEET.(注意：请把答案写在答题卷上,否则以零分处理)Part III Writing (30%)Section A (10%)In this Section,, you have 15 minutes to write an essay on the following topic. You should write at least 100 words. （请务必写在答题卷上，否则以零分处理）Your cousin, Ming Zhang, is going to take the national entrance examination to college in June. However, he is under great pressure and simply can’t concentrate on his study. Please drop him a note of about 100 words, giving him some tips as to how to deal with this situation.Section B (20%)In this Section, you have 30 minutes to write an essay on the following topic. You should write at least 200 words. （请务必写在答题卷上，否则以零分处理）Many college students complain of their heavy course load. They think some courses offered are time-consuming and not very useful. What do you think of the complaints? S hould college students’ opinions be considered in curriculum development and policy-making? Please write an essay of about 200 words to express your opinion and explain why with specific reasons.上海交通大学英语水平考试答题卷Part II Integrated Reading (30%)Section 1 Banked Cloze （10％）1) _________ 2) ___________ 3) ___________ 4)_______ 5)__________6) __________ 7) ____________ 8) ___________ 9)_________ 10) _________Section 2 True or False Judgement & Sentence Completion （10％） 1) _____ 2) _______ 3) _______ 4) ________ 5) _____ 6)_____ 7)_____8) _____________________________________________________________9) _____________________________________________________________10) ____________________________________________________________Part III Writing (30%) （请将作文写在答题卷背面) Section A （10%）Your cousin, Ming Zhang, is going to take the national entrance examination to college in June. However, he is under great pressure and simply can’t concentrate on his study. Please drop him a note of about 100 words, giving him some tips as to how to deal with this situation.Section B（10%）Key答案：Section 1: 1-5 CBBDC 6-10 ADACASection 2:1)Bandaged 2）triggered 3）probes 4）succession 5）principal 6）overlap 7）articulate 8) postdoctoral9）scientists have known for some time that conventional explanations for how parts of the brain work need to be revised10)there is a separation of tasks and a division of labor between two very different parts of the brain11)brain studies are shedding light on the pieces of the puzzle and might one day solve the mysterySection 3:1) I t’s basically the ability to c ommunicate successfully with people of other cultures. (2 points)2) Sensitivity to other cultures (1 point)3) Showing the bottom of your shoe or foot when crossing your legs (2 points)4) She did not remove her gloves when shaking hands with a business associate in Russia ( without realising that this isconsidered impolite). (2 points)5) Never make false assumptions about other cultures, and never lack sensitivity. Be open to learning about new cultures.And learn the local language. (3 points)Section 4:1) 全球经济的衰退对妇女和女孩所产生的影响尤其严重，这进而又波及到家庭、社区、乃至地区。
上海交通大学２０２２_年强基计划数学试题及解答
上海交通大学２０２２年强基计划数学试题及解答李发明(山东省泰安第一中学ꎬ山东泰安２７１０００)摘㊀要:本文给出上海交通大学２０２２年强基计划数学试题的回忆版及解答.关键词:上海交通大学ꎻ强基计划ꎻ数学试题中图分类号:Ｇ６３２㊀㊀㊀文献标识码:Ａ㊀㊀㊀文章编号:１００８－０３３３(２０２３)０７－００２６－０６收稿日期:２０２２－１２－０５作者简介:李发明ꎬ男ꎬ本科ꎬ从事高中数学教学研究.㊀㊀微信公众号 阿叶数学 发表了最新的上海交通大学强基计划数学试题ꎬ笔者给出解答ꎬ与广大数学爱好者及备考学子学习交流.试题共４５道单项选择题ꎬ这里学生只回忆了３９道.试题以高考考查范围为主ꎬ在技巧和方法上略有提高ꎬ个别试题的考点在新高考的省份已经被删除ꎬ如题４考查直线的参数方程㊁题７考查直线和圆的极坐标方程ꎬ另外题２７以高等代数中的多项式理论为背景考查ꎬ题３３以 米勒问题 为背景ꎬ题３４涉及到积化和差公式.整套试题难度介于高考与全国高中数学联赛一试之间ꎬ考点覆盖面广ꎬ具有很好的选拔功能ꎻ数学物理两科一起考ꎬ限时３小时ꎬ对于习惯了参加两个小时数学考试的学生来说ꎬ不论是能力上还是体力上都是巨大的考验.题１㊀等比数列ａｎ{}ꎬａ１＝－３ꎬＳ６Ｓ３＝７８ꎬｌｉｍｎңɕＳｎ＝(㊀).Ａ.不存在㊀Ｂ.２３㊀Ｃ.－２３㊀Ｄ.－２解析㊀因为Ｓ６Ｓ３＝７８ꎬ所以ｑʂ１.因为Ｓ６Ｓ３＝１－ｑ６１－ｑ３＝１＋ｑ３＝７８ꎬ所以ｑ＝－１２.所以ｌｉｍｎңɕＳｎ＝ｌｉｍｎңɕ－３１－－１２æèçöø÷ｎ[]１－－１２æèçöø÷＝－２.故选Ｄ.题２㊀集合Ａ＝１ꎬ２ꎬｔ{}ꎬＢ＝ａ２ａɪＡ{}ꎬＣ＝ＡɣＢꎬＣ中元素和为６ꎬ则元素积为(㊀㊀).Ａ.１㊀㊀㊀Ｂ.－１㊀㊀㊀Ｃ.８㊀㊀㊀Ｄ.－８解析㊀集合Ｂ的元素为１ꎬ４ꎬｔ２ꎬ所以ｔ<０.①ｔ２＝１时ꎬｔ＝－１符合ꎬ此时元素积为－８ꎻ②ｔ２＝２时ꎬｔ＝－２ꎬ不符ꎻ③ｔ２＝４时ꎬｔ＝－２ꎬ不符ꎻ④ｔ２ʂ１且ʂ２且ʂ４时ꎬｔ＋ｔ２＝－１ꎬ无解.综上所述ꎬ元素积为－８.故选Ｄ.题３㊀ｘꎬｙꎬｚ为正数ꎬ求１０ｘ２＋１０ｙ２＋ｚ２ｘｙ＋ｙｚ＋ｘｚ的最小值.㊀解析㊀因为１０ｘ２＋１０ｙ２＋ｚ２＝ｋｘ２＋ｋｙ２＋１０－ｋ()ｘ２＋１２ｚ２＋１０－ｋ()ｙ２＋１２ｚ２ȡ２ｋ２ｘｙ＋２(１０－ｋ)(ｙｚ＋ｘｚ)ꎬ所以ｋ２＝１０－ｋ()１２ꎬ解得ｋ＝２.所以１０ｘ２＋１０ｙ２＋ｚ２ｘｙ＋ｙｚ＋ｘｚ＝２ｘ２＋２ｙ２()＋８ｘ２＋１２ｚ２æèçöø÷＋８ｙ２＋１２ｚ２æèçöø÷ｘｙ＋ｙｚ＋ｘｚȡ４ｘｙ＋４ｙｚ＋４ｘｚｘｙ＋ｙｚ＋ｘｚ＝４.题４㊀直线ｋｘ＋４ｙ＝１垂直于ｘ＝２－３ｔｙ＝１＋４ｔ{(ｔ为参数)ꎬｋ＝(㊀㊀).Ａ.３㊀㊀Ｂ.－３㊀㊀Ｃ.１３㊀㊀Ｄ.－１３解析㊀ｘ＝２－３ｔꎬｙ＝１＋４ｔ{(ｔ为参数)化为普通方程即４ｘ＋３ｙ－１１＝０.所以ｋ＝－３.故选Ｂ.题５㊀ｆｘ()＝ｃｏｓωｘ－π６æèçöø÷ω>０()ꎬｆｘ()ɤｆπ４æèçöø÷对∀ｘɪＲ恒成立ꎬ则ω的最小值为(㊀㊀).Ａ.３２㊀㊀㊀Ｂ.１㊀㊀㊀Ｃ.１３㊀㊀㊀Ｄ.２３解析㊀因为ｆｘ()ɤｆπ４æèçöø÷对∀ｘɪＲ恒成立ꎬ所以πω４－π６＝２ｋπｋɪＺ().所以ω＝２３＋８ｋｋɪＺ().由ω>０ꎬ可得ｋ＝０时ꎬω的最小值为２３.故选Ｄ.题６㊀椭圆Ｃ:ｘ２４＋ｙ２４ｂ２＝１ꎬＰꎬＡꎬＢ在椭圆Ｃ上ꎬｋＡＰꎬｋＢＰ为相反数(ｋ与－ｋ)ꎬ则ｋＡＢ与(㊀㊀).Ａ.ｂꎬｋ有关ꎬ与Ｐ点无关Ｂ.Ｐ点ꎬｂꎬｋ均有关Ｃ.Ｐ点ꎬｋ有关ꎬ与ｂ无关Ｄ.Ｐ点ꎬｂ有关ꎬ与ｋ无关解析㊀当点Ｐ位于ｙ轴上时ꎬｋＡＢ＝０ꎬ其他情况ｋＡＢʂ０ꎬ所以与点Ｐ有关.取Ｐ１ꎬ３ｂ()ꎬ则直线ＡＰ的方程为ｙ－３ｂ＝ｋｘ－１().联立ｙ－３ｂ＝ｋｘ－１()ꎬｘ２４＋ｙ２４ｂ２＝１ꎬìîíïïï整理ꎬ得ｂ２＋ｋ２()ｘ２＋２３ｋｂ－２ｋ２()ｘ＋ｋ２－ｂ２－２３ｋｂ＝０.由韦达定理ꎬ得ｘＡ＝ｋ２－２３ｋｂ－ｂ２ｂ２＋ｋ２ꎬｙＡ＝－３ｋ２ｂ－２ｋｂ２＋３ｂ３ｂ２＋ｋ２.同理ｘＢ＝ｋ２＋２３ｋｂ－ｂ２ｂ２＋ｋ２ꎬｙＢ＝－３ｋ２ｂ＋２ｋｂ２＋３ｂ３ｂ２＋ｋ２.所以ｋＡＢ＝ｙＢ－ｙＡｘＢ－ｘＡ＝ｂ３.故选Ｄ.题７㊀ρ２ｃｏｓθ＋ρ－３ρｃｏｓθ－３＝０表示(㊀㊀).Ａ.一个圆㊀㊀㊀㊀Ｂ.一个圆与一条直线Ｃ.两个圆Ｄ.两条线解析㊀ρｃｏｓθ＋１()ρ－３()＝０表示直线ｘ＝－１和以原点为圆心ꎬ３为半径的圆.故选Ｂ.题８㊀ｂ＝ａ＝ｃ＝１ꎬａ ｂ＝１２ꎬ则ａ＋ｂ() ２ｂ－ｃ()的最小值为(㊀㊀).Ａ.３＋３㊀Ｂ.３－３㊀Ｃ.２＋２㊀Ｄ.２－２解析㊀ａ＋ｂ() ２ｂ－ｃ()＝３－ａ＋ｂ() ｃꎬ当且仅当ｃ与ａ＋ｂ共线同向时ꎬａ＋ｂ() ｃ取得最大值３.故选Ｂ.题９㊀１－ｘ()５＝ａ０＋ａ１ｘ＋ ＋ａ５ｘ５ꎬ求ａ２＋ａ４()ａ１＋ａ３＋ａ５()的值.解析㊀因为ａ１＝－Ｃ１５ꎬａ２＝Ｃ２５ꎬａ３＝－Ｃ３５ꎬａ４＝Ｃ４５ꎬａ５＝－Ｃ５５ꎬ所以ａ２＋ａ４()ａ１＋ａ３＋ａ５()＝－２４０.题１０㊀正四面体装水到高度的１２处ꎬ问倒置后高度至何处?解析㊀Ｖ空气Ｖ全部＝１８ꎬ所以Ｖ水Ｖ全部＝７８ꎬ所以新高度为３７２.题１１㊀使３ｘ－３＋ｘ－３()ｓｉｎｘ－３()＋ｋｃｏｓｘ－３()＝０有唯一解的ｋ(㊀㊀).Ａ.不存在㊀Ｂ.１个㊀Ｃ.２个㊀Ｄ.无穷多个解析㊀函数ｙ＝３ｘ－３＋ｘ－３()ｓｉｎｘ－３()＋ｋｃｏｓｘ－３()的零点个数⇔函数ｙ＝３ｘ＋ｘｓｉｎｘ＋ｋｃｏｓｘ的零点个数.易知该函数为偶函数ꎬ函数有唯一零点则必为ｘ＝０.所以１＋０＋ｋ＝０ꎬ解得ｋ＝－１ꎬ故ｋ只有唯一一个.故选Ｂ.题１２㊀两个圆柱体底面积Ｓ１ꎬＳ２ꎬ体积Ｖ１ꎬＶ２ꎬ侧面积相等ꎬＶ１Ｖ２＝３２ꎬ求Ｓ１Ｓ２.解析㊀Ｖ１Ｖ２＝３２ꎬ所以ｒ２１ｌ１ｒ２２ｌ２＝３２.侧面积相等ꎬ所以ｒ１ｌ１＝ｒ２ｌ２.所以ｒ１ｒ２＝３２.所以Ｓ１Ｓ２＝ｒ２１ｒ２２＝９４.题１３㊀双曲线ｘ２４－ｙ２１２＝１ꎬ焦点为ＡꎬＢꎬ点Ｃ在双曲线上ꎬｃｏｓøＡＣＢ＝３５ꎬ求әＡＢＣ的周长.解析㊀设点Ｃ在双曲线右支上ꎬＡＣ＝ｍꎬＢＣ＝ｎ.所以ｍ－ｎ＝４ꎬ８２＝ｍ２＋ｎ２－２ｍｎｃｏｓøＡＣＢ.{解得ｍ＝１０ꎬｎ＝６.所以周长为２４.题１４㊀Ａ＝１ꎬ２ꎬ ꎬ１００{}ꎬＢ＝３ｘｘɪＡ{}ꎬＣ＝２ｘｘɪＡ{}ꎬ求ＢɘＣ中元素个数.解析㊀由题知ꎬＢ＝３ꎬ６ꎬ ꎬ３００{}ꎬＣ＝２ꎬ４ꎬ ꎬ２００{}ꎬＢɘＣ为２００以内６的倍数ꎬ所以ＢɘＣ中元素个数为３３个.题１５㊀ｆｘ()＝ａｘ２２－１＋２ａ()ｘ＋２ｌｎｘａ>０()在１２ꎬ１æèçöø÷有极大值ꎬ则ａ的取值范围为(㊀㊀).Ａ.１ꎬ２()㊀㊀㊀㊀Ｂ.１ꎬ＋ɕ()Ｃ.２ꎬ＋ɕ()Ｄ.１ｅꎬ＋ɕæèçöø÷解析㊀ｆᶄｘ()＝ａｘ－１＋２ａ()＋２ｘꎬ只需ａｘ＋２ｘ＝１＋２ａ在１２ꎬ１æèçöø÷上有解.①ａȡ８时ꎬａｘ＋２ｘ在１２ꎬ１æèçöø÷上单调递增ꎬ只需ａ２＋４<１＋２ａ<ａ＋２ꎬ无解ꎻ②ａɤ２时ꎬａｘ＋２ｘ在１２ꎬ１æèçöø÷上单调递减ꎬ只需ａ＋２<１＋２ａ<ａ２＋４ꎬ解得１<ａ<２ꎻ③２<ａ<８时ꎬａｘ＋２ｘ在１２ꎬ１æèçöø÷上先单调递减后单调递增ꎬ只需２２ａ<１＋２ａ<ｍａｘａ＋２ꎬａ２＋４{}ꎬ无解.综上所述ꎬ故选Ａ.题１６㊀☉Ｏ１ꎬ☉Ｏ２与ｙ＝ｋｘꎬｘ轴的正半轴均相切ꎬｒ１ｒ２＝２ꎬ两圆交点Ｐ２ꎬ２()ꎬｋ＝(㊀㊀).Ａ.１㊀㊀㊀Ｂ.４３㊀㊀㊀Ｃ.３４㊀㊀㊀Ｄ.１２解析㊀交点Ｐ２ꎬ２()在ｙ＝ｘ上ꎬ所以ｋ>１.故选Ｂ.题１７㊀偶函数ｆｘ()满足ｆｘ＋４()＝ｆｘ()＋２ｆ２()ꎬ求ｆ２０２２()的值.解析㊀令ｘ＝－２ꎬ则ｆ２()＝ｆ－２()＋２ｆ２()ꎬ解得ｆ２()＝０.所以ｆｘ()的最小正周期为４.所以ｆ２０２２()＝ｆ(４ˑ５０５＋２)＝ｆ２()＝０.题１８㊀ｓｉｎ２０２２πｘ()＝ｘ２实根个数为(㊀㊀).Ａ.２０２２㊀㊀Ｂ.４０４４㊀㊀Ｃ.２０２３㊀㊀Ｄ.１０１１解析㊀由图象变换可知ꎬｙ＝ｓｉｎ２０２２πｘ()在－１ꎬ１[]上包含２０２２个周期ꎬ且每个周期都有两个交点.故选Ｂ.题１９㊀求方程ｓｉｎｘ＋ｃｏｓｘ＝π６的根.解析㊀考虑ｘɪ０ꎬπ２[]ꎬｓｉｎｘ＋ｃｏｓｘ＝２ｓｉｎｘ＋π４æèçöø÷ɪ１ꎬ２[]ꎬ所以ｓｉｎｘ＋ｃｏｓｘɪ１ꎬ２[].所以原方程无实数解.题２０㊀Ｆ１ꎬＦ２为双曲线两焦点(焦点在ｘ轴)ꎬ直线ＡＢ经过点Ｆ１且与双曲线左右两支交于点ＡꎬＢꎬ２ＡＦ１＝ＡＢꎬøＦ１ＡＦ２＝１２０ʎꎬ求双曲线的离心率.解析㊀设ＡＦ１＝ｘꎬ则ＡＦ２＝ｘ＋２ａꎬＡＢ＝２ｘꎬＢＦ２＝３ｘ－２ａꎬ在әＡＢＦ２中ꎬ３ｘ－２ａ()２＝２ｘ()２＋ｘ＋２ａ()２－２ ２ｘ ｘ＋２ａ()ｃｏｓ６０ʎꎬ即ｘ＝２ａ.在әＡＦ１Ｆ２中ꎬ２ｃ()２＝２ａ()２＋４ａ()２－２ ２ａ４ａｃｏｓ１２０ʎꎬ解得ｅ＝７题２１㊀ｆｘ()＝ｘ＋１＋ｘ－ｘ－２ꎬｆ[ｆｘ()]＋１＝０根的个数为(㊀㊀).Ａ.１㊀㊀㊀Ｂ.２㊀㊀㊀Ｃ.３㊀㊀㊀Ｄ.０解析㊀ｆｘ()＝－ｘ－３ꎬｘɤ－１ꎬｘ－１ꎬ－１<ｘɤ０ꎬ３ｘ－１ꎬ０<ｘɤ２ꎬｘ＋３ꎬｘ>２.ìîíïïïïï令ｔ＝ｆｘ()ꎬ则ｆｔ()＝－１ꎬ解得ｔ＝－２或０.当ｆｘ()＝－２时ꎬｘ＝－１ꎻ当ｆｘ()＝０时ꎬｘ＝－３或１３.故选Ｃ.题２２㊀әＡＢＣꎬＭ为平面上一点ꎬＡＭң＝２３ＡＢң＋１４ＡＣңꎬ则ＳәＡＢＭＳәＢＣＭ＝(㊀㊀).Ａ.３㊀㊀Ｂ.８㊀㊀Ｃ.８３㊀㊀Ｄ.３８解析㊀因为ＡＭң＝２３ＡＢң＋１４ＡＣңꎬ所以ＭＡң＋８ＭＢң＋３ＭＣң＝０.由奔驰定理ꎬ得ＳәＡＢＭＳәＢＣＭ＝３１.故选Ａ.题２３㊀Ａ＝ｘꎬｙ()ｘ２＋ｙ２ɤ３ꎬｘɪＺꎬｙɪＺ{}ꎬＡ中元素个数为(㊀㊀).Ａ.４㊀㊀㊀Ｂ.５㊀㊀㊀Ｃ.８㊀㊀㊀Ｄ.９解析㊀画图即得ꎬ故选Ｄ.题２４㊀ｔａｎ１５ʎ＋２２ｓｉｎ１５ʎ＝(㊀㊀).Ａ.３㊀㊀㊀Ｂ.２㊀㊀㊀Ｃ.２㊀㊀㊀Ｄ.１解析㊀ｔａｎ１５ʎ＝２－３ꎬｓｉｎ１５ʎ＝６－２４.故选Ｄ.题２５㊀空间中到正方体ＡＢＣＤ－Ａ１Ｂ１Ｃ１Ｄ１棱Ａ１Ｄ１ꎬＡＢꎬＣＣ１距离相等的点有(㊀㊀).Ａ.无数㊀㊀㊀Ｂ.０㊀㊀㊀Ｃ.２㊀㊀㊀Ｄ.３解析㊀体对角线Ｂ１Ｄ上的点均符合要求.故选Ａ.题２６㊀ａ>ｂ>０ꎬ则ａ＋４ａ＋ｂ＋１ａ－ｂ最小值为(㊀㊀).Ａ.２３㊀㊀Ｂ.３１０２㊀㊀Ｃ.３２㊀㊀Ｄ.４解析㊀ａ＋４ａ＋ｂ＋１ａ－ｂ＝ａ＋ｂ２＋４ａ＋ｂæèçöø÷＋ａ－ｂ２＋１ａ－ｂæèçöø÷ȡ２ａ＋ｂ２ ４ａ＋ｂ＋２ａ－ｂ２ １ａ－ｂ＝３２ꎬ当且仅当ａ＋ｂ２＝４ａ＋ｂꎬａ－ｂ２＝１ａ－ｂ时ꎬ即ａ＝３２２ꎬｂ＝２２时等号成立.故选Ｃ.题２７㊀多项式ｆｘ()ꎬｇｘ()ꎬ问两命题 ｆｘ()是ｇｘ()因式 ｆ[ｆｘ()]是ｇ[ｇｘ()]因式 的充分必要关系.解析㊀反例１:ｆｘ()＝ｘ＋１ꎬｇｘ()＝ｘ＋１()ｘ＋２()ꎬ此时ｆ[ｆｘ()]＝ｘ＋２ꎬｇ[ｇｘ()]＝ｘ２＋３ｘ＋３()ｘ２＋３ｘ＋４()ꎬ前推不出后ꎻ反例２:ｆｘ()＝ｘ＋１ꎬｇｘ()＝ｘｘ＋２()ꎬ此时ｆ[ｆｘ()]＝ｘ＋２ꎬｇ[ｇｘ()]＝ｘｘ＋２()ｘ２＋２ｘ＋２()ꎬ后推不出前.所以ꎬ前是后的既不充分也不必要条件.题２８㊀等势集合指两个集合间一一对应ꎬ下列为等势集合的是(㊀㊀).Ａ.０ꎬ１[]与Ｅ０ɤＥɤ１{}Ｂ.０ꎬ１[]与ａꎬｂꎬｃꎬｄ{}Ｃ.０ꎬ１()与０ꎬ１[]Ｄ.１ꎬ２ꎬ３{}与ａꎬｂꎬｃꎬｄ{}解析㊀０ꎬ１[]＝Ｅ０ɤＥɤ１{}ꎬ两者可通过对应关系ｙ＝ｘ建立一一对应.故选Ａ.题２９㊀ｆｘ()＝ｌｎｘ－ｍｘ２＋１－２ｍ()ｘ＋１ꎬ对∀ｘ>０ꎬｆｘ()ɤ０ꎬ求整数ｍ的最小值.解析㊀ｆᶄｘ()＝１ｘ－２ｍｘ＋１－２ｍ()＝－２ｍｘ－１()ｘ＋１()ｘꎬ①当ｍɤ０时ꎬｆｘ()在０ꎬ＋ɕ()上单调递增ꎬ不符合题意ꎻ②当ｍ>０时ꎬｆｘ()在０ꎬ１２ｍæèçöø÷上单调递增ꎬ在１２ｍꎬ＋ɕæèçöø÷上单调递减ꎬ所以ｆｘ()ｍａｘ＝ｆ１２ｍæèçöø÷＝ｌｎ１２ｍ－ｍ１２ｍæèçöø÷２＋１－２ｍ()１２ｍ＋１ɤ０ꎬ解得ｌｎ２ｍ－１４ｍȡ０.因为ｍ是整数ꎬ所以ｍｍｉｎ＝１.题３０㊀圆锥中ＰＯ为高ꎬＰＡ为母线ꎬＢ为底面上一点ꎬＯＢʅＢＡꎬＯＨʅＢＰ于点ＨꎬＡＯ＝２２ꎬＡＰ＝４ꎬ则ＶＰ－ＨＯＣ的最大值为(㊀㊀).Ａ.２６３㊀㊀Ｂ.３３㊀㊀Ｃ.６３㊀㊀Ｄ.２２注意㊀原题干中没有点Ｃꎬ我们不妨求一下ＶＰ－ＨＯＡ.设øＢＡＯ＝θꎬ则ＡＢ＝２２ｃｏｓθꎬＢＯ＝２２ｓｉｎθ.所以ＶＰ－ＨＯＡ＝ＶＡ－ＨＯＰ＝１３ ４ｓｉｎθ１＋ｓｉｎ２θ２２ｃｏｓθ＝８２３ １１ｔａｎθ＋２ｔａｎθɤ８２３ˑ１２２＝４３.题３１㊀数列ａｎ{}中ꎬａ１＝２ꎬａ２＝６ꎬａｎ＋２－２ａｎ＋１＋ａｎ＝２ꎬ求ð２０２２ｉ＝１１ａｉ.解析㊀因为ａｎ＋２－ａｎ＋１＝ａｎ＋１－ａｎ＋２ꎬ所以ａｎ－ａｎ－１{}是首项为４ꎬ公差为２的等差数列.所以ａｎ－ａｎ－１＝２ｎ.累加求和得ａｎ＝ｎｎ＋１().所以１ａｎ＝１ｎ－１ｎ＋１.所以ð２０２２ｉ＝１１ａｉ＝１－１２æèçöø÷＋１２－１３æèçöø÷＋ ＋１２０２２－１２０２３æèçöø÷＝２０２２２０２３.题３２㊀椭圆ｘ２ａ２＋ｙ２９＝１ａ>３()ꎬ弦ＡＢ中垂线过－ａ５ꎬ０æèçöø÷ꎬ求离心率ｅ的取值范围.注意㊀原题干弦ＡＢ应是不平行于ｙ轴的.设Ａｘ１ꎬｙ１()ꎬＢｘ２ꎬｙ２()ꎬ中点为ｘ０ꎬｙ０()ꎬ则ｘ２１ａ２＋ｙ２１９＝１ꎬｘ２２ａ２＋ｙ２２９＝１ꎬìîíïïïï两式相减得ｘ０ａ２＋ｋｙ０９＝０.又因为ｋｙ０ｘ０＋ａ５＝－１ꎬ两式联立ꎬ得ｘ０＝ａ３５９－ａ２().令－ａ<ａ３５９－ａ２()<ａꎬ解得ａ>３５２.所以ｅ＝ｃａ＝１－９ａ２>５５.所以ｅɪ５５ꎬ１æèçöø÷.题３３㊀椭圆ｘ２４＋ｙ２＝１的焦点为Ｆ１ꎬＦ２ꎬ点Ｐ在ｘ＋２３ｙ－４３＝０上ꎬ当øＦ１ＰＦ２最大时ꎬ则ＰＦ１ＰＦ２＝(㊀㊀).Ａ.１５３㊀㊀Ｂ.３５㊀㊀Ｃ.５３㊀㊀Ｄ.１５５解析㊀由米勒定理知ꎬ过点Ｆ１ꎬＦ２的圆与直线相切于点Ｐ时ꎬøＦ１ＰＦ２最大.由切割线定理知ꎬＡＰ２＝ＡＦ１ ＡＦ２.所以ＡＰ＝３５.所以ＰＦ１ＰＦ２＝ＡＰＡＦ２＝３５３３＝１５３.故选Ａ.题３４㊀әＡＢＣ中ꎬＡ＝３Ｂ＝９ＣꎬｃｏｓＡｃｏｓＢ＋ｃｏｓＢｃｏｓＣ＋ｃｏｓＣｃｏｓＡ＝(㊀).Ａ.１４㊀㊀Ｂ.－１４㊀㊀Ｃ.１３㊀㊀Ｄ.－１３解析㊀Ｃ＝π１３ꎬＢ＝３π１３ꎬＡ＝９π１３ꎬｃｏｓＡｃｏｓＢ＋ｃｏｓＢｃｏｓＣ＋ｃｏｓＣｃｏｓＡ＝ｃｏｓ９π１３ｃｏｓ３π１３＋ｃｏｓ３π１３ｃｏｓπ１３＋ｃｏｓπ１３ｃｏｓ９π１３＝１２(ｃｏｓ１２π１３＋ｃｏｓ６π１３＋ｃｏｓ４π１３＋ｃｏｓ２π１３＋ｃｏｓ１０π１３＋ｃｏｓ８π１３)＝１２ｓｉｎ２π１３ｓｉｎ２π１３(ｃｏｓ２π１３＋ｃｏｓ４π１３＋ｃｏｓ６π１３＋ｃｏｓ８π１３＋ｃｏｓ１０π１３＋ｃｏｓ１２π１３)＝１４ｓｉｎ２π１３(ｓｉｎ４π１３＋ｓｉｎ６π１３＋ｓｉｎ－２π１３＋ｓｉｎ８π１３＋ｓｉｎ－４π１３＋ｓｉｎ１０π１３＋ｓｉｎ－６π１３＋ｓｉｎ１２π１３＋ｓｉｎ－８π１３＋ｓｉｎ１４π１３＋ｓｉｎ－１０π１３)＝１４ｓｉｎ２π１３ ｓｉｎ－２π１３＝－１４.故选Ｂ.题３５㊀８个点将半圆分成９段弧ꎬ以１０个点(包括２个端点)为顶点的三角形中钝角三角形有(㊀)个.Ａ.５５㊀㊀㊀Ｂ.１１２㊀㊀㊀Ｃ.１５６㊀㊀㊀Ｄ.１２０解析㊀这１０个点没有三点共线ꎬ共构成Ｃ３１０＝１２０个三角形ꎬ其中同时选中两个端点时构成Ｃ２２Ｃ１８＝８个直角三角形.故钝角三角形的个数为１１２.故选Ｂ.题３６㊀ａ０＝１４ꎬａｎ＋１＝ａ２ｎ＋ａｎꎬð２０２２ｉ＝０１ａｉ＋１[]＝(㊀㊀).Ａ.１㊀㊀㊀Ｂ.２㊀㊀㊀Ｃ.３㊀㊀㊀Ｄ.４解析㊀因为ａｎ＋１＝ａｎａｎ＋１()ꎬ所以１ａｎ＋１＝１ａｎ－１ａｎ＋１.所以ð２０２２ｉ＝０１ａｉ＋１＝１ａ０－１ａ１æèçöø÷＋１ａ１－１ａ２æèçöø÷＋ ＋１ａ２０２２－１ａ２０２３æèçöø÷＝１ａ０－１ａ２０２３＝４－１ａ２０２３.易知ａｎ{}单调递增ꎬ且无上确界ꎬ所以４－１ａ２０２３[]＝３.故选Ｃ.题３７㊀ｆｘ()＝ｘ＋２ｘ＋１＋３ｘ的反函数为ｇｘ()ꎬ[ｇｘ２()]２＝１的根有(㊀)个.Ａ.１㊀㊀㊀Ｂ.２㊀㊀㊀Ｃ.３㊀㊀㊀Ｄ.４解析㊀由[ｇｘ２()]２＝１ꎬ得ｇｘ２()＝ʃ１.当ｇｘ２()＝１时ꎬ因为ｆ１()＝７ꎬ所以只需ｘ＝ʃ７ꎻ当ｇｘ２()＝－１时ꎬ因为ｆ－１()＝１３ꎬ所以只需ｘ＝ʃ３３.综上所述ꎬ有４个根使得[ｇｘ２()]２＝１.故选Ｄ.题３８㊀ｌｉｍｘң２ｆ５－ｘ()－３ｘ－２＝２ꎬｆ３()＝３ꎬｆｘ()在３ꎬｆ３()()处切线方程为(㊀㊀).Ａ.２ｘ＋ｙ＋９＝０㊀㊀㊀Ｂ.２ｘ＋ｙ－９＝０Ｃ.－２ｘ＋ｙ＋９＝０㊀㊀㊀Ｄ.－２ｘ＋ｙ－９＝０解析㊀ｌｉｍｘң２ｆ５－ｘ()－３ｘ－２＝ｌｉｍｘң２ｆ５－ｘ()－３３－５－ｘ()＝－ｌｉｍｘң２ｆ５－ｘ()－３５－ｘ()－３＝２ꎬ所以ｆᶄ３()＝－２.所以切线方程为２ｘ＋ｙ－９＝０.故选Ｂ.题３９㊀正方体ＢＤ１中ꎬＭ为Ｃ１Ｄ１中点ꎬＯＭʊ面βꎬβ过点Ｂ且异于平面Ｂ１ＢＣＣ１ꎬＰɪβ且Ｐ在正方体内(包括边)ꎬ则直线Ａ１Ｐ与平面Ｂ１ＢＣＣ１所成角的正切值最大为(㊀㊀).Ａ.３㊀㊀Ｂ.１２㊀㊀Ｃ.２２㊀㊀Ｄ.２注意㊀原题干没有点Ｏꎬ而且把点Ｏ放到很多位置都不合适.参考文献:[１]中华人民共和国教育部.普通高中数学课程标准(２０１７年版２０２０年修订)[Ｍ].北京:人民教育出版社ꎬ２０２０.[责任编辑:李㊀璟]。
上海交大大学物理考卷汇总
（本小题 分） 3、
12 如图所示，悬挂的轻弹簧下端挂着质量为 m1、m2 的两个
物体，开始时处于静止状态．现在突然把
m 1
与
m 2
间的连线剪断，求
m 1
的最
大速度为多少？设弹簧的劲度系数 k＝8.9×104 N/m，m1＝0.5 kg，m2＝0.3
kg．
1
m2
8
8
（本小题 分） 4少、功？ (电6子静止要质使量电m子e的＝速9.度11从×1v01-=311k.2g×) 10 m/s 增加到 v2 =2.4×10 m/s 必须对它作多
运动动能之比 EKA/EKB 为
1
(A) ．
(B)
2
2/2．
(C) 2 ．
(D) 2．
A
mB
选：________
4、一根细绳跨过一光滑的定滑轮，一端挂一质量为 M 的物体，另一端被人用双手拉着，人
的质量 m
=
1 2
M
．若人相对于绳以加速度
a0 向上爬，则人相对于地面的加速度（以竖直向
上为正）是
(A) (2a + g) / 3．
（本小题 分） 5、
12 一水平放置的飞轮可绕通过中心的竖直轴转动，飞轮的辐条上装有一个
小滑块，它可在辐条上无摩擦地滑动．一轻弹簧一端固定在飞轮转轴上，另一端与滑块联
接 f 的．函当数飞关轮系以．角速度ω 旋转时，弹簧的长度为原长的 f 倍，已知ω ＝ω 0 时，f ＝f0，求ω 与
05 年大学物理（力学）期中考试试卷(144A)
A
B
选：________
二、填空题（共34 分）
（本小题 分） 1、
4 一质点沿直线运动,其运动学方程为 x = 6 t－t2 (SI)，则在 t 由 0 至 4s 的
上海交大外语测试题及答案
上海交大外语测试题及答案一、选择题（每题2分，共20分）1. The book you gave me is one of the most interesting booksI have ever read.A. thatB. whichC. whatD. it答案：B2. The number of the people who were injured in the accident was 20.A. fewB. littleC. lessD. fewer答案：D3. He is the only one of the students who has passed the exam.A. thatB. whichC. whoD. whom答案：C4. The reason he was late was because he missed the bus.A. thatB. whyC. whichD. because答案：B5. The old man lives by himself. He doesn’t have anyone to look after him.A. himselfB. himselfC. himselfD. himself答案：A6. The teacher told us that light travels faster than sound.A. thatB. whichC. whatD. it答案：A7. The reason why he was late was that he missed the bus.A. thatB. whyC. whichD. because答案：A8. The news that he told us was true.A. whatB. whichC. thatD. it答案：C9. The boy is too young to go to school.A. enoughB. moreC. tooD. so答案：A10. He is the tallest boy in his class.A. tallerB. the tallestC. more tallD. the taller答案：B二、填空题（每题2分，共20分）1. The teacher asked the students to ________ (保持安静) during the exam.答案：keep quiet2. The ________ (会议) will be held in the school hall tomorrow.答案：meeting3. She is very ________ (擅长) at playing the piano.答案：good4. He is ________ (对…感兴趣) painting.答案：interested in5. I ________ (收到) a letter from my brother yesterday. 答案：received6. The ________ (问题) was too difficult for him to solve. 答案：question7. The ________ (孩子) are playing in the park.答案：children8. He is ________ (负责) for the project.答案：responsible9. She is ________ (担心) about her son’s health.答案：worried10. The ________ (事件) happened last night.答案：event三、阅读理解（每题2分，共20分）阅读以下短文，并回答后面的问题。
高等数学考试试卷四套【上海交通大学】
（C） a 9 ， b 12 ；
（D） a 9 ， b 12 。
2. 设 x 0 时， ln cos x axk ，则常数 a 和 k 的值分别为
（）
（A） a 1 ， k 2 ； 2
（B） a 1 ， k 2； 2
（C） a 1 ， k 1； 2
（D） a 1 ， k 1。 2
11.
用极限定义证明：
lim
x1
2
arctan 1 x2
x
。
12.
求
lim
xln
ln ln
x1 x1
。
x0
13. 求 lim x0
1 x2 sin2 x tan2 x 。
x2 ln2 1 x
四、（每小题 8 分，共 16 分）
14. 已知 f x
e
x
,
1 2
x2
1
，求证：
（1）当 x 1,0 时， ex 1 x2 1 ；
2
（2）若函数 g x 在 R 上可导，且 g x f x ，则 g 0 1。
2
上海交通大学《高等数学》考试试卷 二
一、单项选择题（每小题 3 分，共 15 分） 1. 当 x 0 时，与 x 等价的无穷小量是
[
x ] 是取整函数），
g
x
x, 0,
x 1， x 1
则方程 g( f (x)) 0 的解集为：___________________。
7. lim( 1 1 1 1 )
。
n n2 1 n2 2 n2 3
交大强基计划面试题目(3篇)
第1篇一、面试概述上海交通大学强基计划面试作为选拔具有学科特长和创新潜质学生的关键环节，旨在考察学生的综合素质、学科素养、创新思维和实践能力。
以下为2023年上海交通大学强基计划面试题目及解析，供考生参考。
二、面试题目1. 开场白（1）请做简短的自我介绍。
（2）请谈谈你对强基计划的理解。
2. 学科素养类题目（1）数学类1）已知函数f（x）=（x-1）lnx+2，求f（x）的单调性。
2）已知等差数列{an}的前n项和为Sn，若S10=40，S20=100，求该数列的通项公式。
（2）物理类1）在平直导轨上放置一个匀强磁场，磁场方向垂直于导轨平面。
一导体棒在导轨上以恒定速度v向右运动，导体棒与导轨接触良好，求导体棒中感应电流的大小。
2）一个质点在水平面上做匀速圆周运动，其运动方程为x=10cosωt，y=10sinωt，其中ω为角速度。
求该质点运动的周期和速度大小。
（3）化学类1）下列物质中，属于非电解质的是（）A. 氢氧化钠B. 氯化钠C. 二氧化硫D. 硫酸2）已知某有机物A在酸性条件下与NaOH反应，生成一种醇B和一种醛C。
B在酸性条件下与AgNO3反应，生成白色沉淀。
C在银镜反应中生成银镜。
推测A的结构简式。
（4）生物类1）下列关于基因突变的说法，正确的是（）A. 基因突变是可逆的B. 基因突变是随机发生的C. 基因突变会导致生物体性状发生改变D. 基因突变具有普遍性2）人体免疫系统包括哪些组成部分？（5）历史类1）简述鸦片战争对中国的影响。
2）秦始皇统一六国后，采取了一系列措施巩固统一，请列举其中的两项。
（6）哲学类1）请简述马克思主义哲学的基本特征。
2）请谈谈你对“实践是检验真理的唯一标准”这一观点的理解。
3. 创新思维与实践能力类题目（1）请结合所学知识，谈谈你对人工智能在医疗领域的应用前景。
（2）请谈谈你对我国“天问一号”探测器火星探测任务的看法。
（3）请简述我国在抗击新冠疫情中采取的防控措施，并分析其有效性。
上海交大考研英语真题
上海交大考研英语真题Since its establishment in 1896, Shanghai Jiao Tong University (SJTU) has been at the forefront of higher education in China. As one of the oldest and most prestigious universities in the country, SJTU attracts thousands of students each year, with many aspiring to pursue postgraduate studies. One of the crucial aspects of the postgraduate admissions process is the English language examination, which tests the applicants' proficiency in reading, writing, listening, and speaking. In this article, we will explore the SJTU postgraduate English exam, its format, and some tips for success.The SJTU postgraduate English exam is designed to evaluate the applicants' English language abilities and determine their suitability for postgraduate studies. The exam consists of four sections: reading comprehension, listening comprehension, writing, and oral examination. Each section assesses different skills and requires a specific approach for effective performance.The reading comprehension section is designed to assess the applicants' ability to understand and analyze academic texts. It includes multiple-choice questions, where candidates must choose the correct answer based on their understanding of the given passage. To excel in this section, it is essential to develop excellent reading skills, such as skimming and scanning, and to pay attention to key details and main ideas.The listening comprehension section evaluates the applicants' ability to comprehend spoken English in various academic contexts. It includes multiple-choice questions, where candidates listen to audio clips and must select the correct answer based on what they hear. To succeed in this section,it is crucial to practice listening to a wide range of English speakers, such as TED Talks, podcasts, and academic lectures, to become accustomed to different accents and speech patterns.The writing section requires candidates to express their ideas clearly and concisely in written form. It typically includes tasks such as summarizing a given passage, writing an argumentative essay, or analyzing a given topic. To excel in this section, candidates must develop strong writing skills, such as organizing their ideas effectively, using appropriate vocabulary and grammar, and presenting a coherent and well-structured piece of writing.The oral examination section assesses the applicants' ability to communicate effectively and fluently in English. It typically includes tasks such as giving a presentation on an assigned topic, engaging in a discussion or debate, or answering interview-style questions. To succeed in this section, candidates must practice speaking English regularly, improve their pronunciation and intonation, and be confident in expressing their thoughts and opinions.In addition to understanding the format of the SJTU postgraduate English exam, it is essential for applicants to prepare thoroughly to maximize their chances of success. Here are some tips to help candidates prepare effectively:1. Start Early: Give yourself enough time to prepare for the exam. Begin practicing as soon as possible to improve your skills gradually.2. Take Practice Tests: Familiarize yourself with the exam format by taking practice tests. This will help you understand the types of questions and tasks you will encounter, as well as identify areas for improvement.3. Develop a Study Plan: Create a study plan and stick to it. Allocate specific time slots for each section of the exam and focus on improving your weaknesses while maintaining your strengths.4. Expand Your Vocabulary: Enhance your vocabulary by reading extensively. Read a variety of texts, including newspapers, magazines, academic articles, and novels, to expose yourself to different writing styles and vocabulary.5. Seek Feedback: Practice your writing and speaking skills regularly and ask for feedback from teachers, peers, or English language professionals. This will help you identify areas for improvement and refine your language abilities.6. Stay Calm and Confident: On the day of the exam, stay calm and confident. Take deep breaths, read the instructions carefully, and approach each section with a positive mindset.In conclusion, the SJTU postgraduate English exam plays a vital role in the admissions process for aspiring postgraduate students. By understanding the exam format and preparing effectively, candidates can increase their chances of success and pave the way for their academic journey at Shanghai Jiao Tong University.。
上海交大考研试题(高代)
上海交通大学研究生入学试题（高等代数）JDy97-1方程组⎩⎪⎨⎪⎧3x 1+4x 2-5x 3+7x 4=02x 1-3x 2+3x 3-2x 4=04x 1+11x 2-13x 3+16x 4=07x 1-2x 2+ x 3+3x 4=0是否有非零解？ 若有，求其通解，并写出解空间维数。
（14分）JDy97-2用正交线性变换把二次型 x 12+2x 22+3x 32 -4x 1x 2 - 4x 2x 3化为标准形，并写出该变换。
（14分）JDy97-3证明：矩阵A 是正定或半正定实对称的充要条件是：存在实矩阵S ，使得A=S T S ，其中S T 表示S 的转置矩阵。
（14分）JDy97-4设A, B 为n 阶方阵，AB=BA ，且A k =0，对某一个k ≥1整数，证明 |A+B|=|B|。
（14分） JDy97-5设R n [x]为次数<n 的多项式线性空间，δ 为求导变换（即δf(x)=f ’(x)），求证 ι-δ 为非退化线性变换（其中 ι 为恒等变换），并求出 δ 的所有不变子空间。
（14分）JDy97-6已知线性无关向量组e 1,e 2,…,e s 和两个非零向量的正交组f 1,f 2,…,f s 与g 1,g 2,…,g s 使得f k 和g k (k=1,2,…,s)可由e 1,e 2,…,e k 线性表示，求证f k =a k g k (k=1,2,…,s)，其中a k ≠0。
（14分） JDy97-7(1) 设J(x)为方阵X 的若当标准形，证明J(A+aE)=J(A)+aE ，其中A 是任一方矩阵，a 是一个数。
（8分）(2) 求幂等方阵A （即满足条件A 2=A ）的若当标准形。
（8分）JDy98-1叙述下列概念：1）数域；2）对称多项式；3）向量的线性相关；4）矩阵的秩；5）欧氏空间。
（每小题4分，共20分）JDy98-2求线性方程组的解：⎩⎪⎨⎪⎧(α+β)x 1+αβx 2 =0x 1 +(α+β)x 2+αβx 3 =0x 2 +(α+β)x 3+αβx 4 =0 … …. … x n-1+(α+β)x n =0JDy98-3求出一切仅与自己相似的n 阶复方阵。
上海交通大学试卷(A卷)
班级号_______________________ 学号______________ 姓名 课程名称 离散数学 成绩一、选择题（40’，每题2’， 每题只有一个选项是正确的，请将答案写在题号前的括号里） （ ）1．下列命题不含联结词的（称为原子命题）是____________：A. “小明和小华是兄弟”。
B. “他个子不高也不漂亮”。
C. “小张或小王能解出这道题”。
D. “小张可能去体育场也可能在家里电视屏幕上观看这场球赛”。
（ ）2．使得p q p q →→∧))((的真值为F 的是下列情形____________：A. ),(),(F F q p =B. ),(),(T F q p =C. ),(),(F T q p =D. ),(),(T T q p =（ ）3．下列公式中____________不是永真式：A. )(q p p →→⌝B. )(q p p →⌝→C. ()()q q p q p ⌝∧→∨→)(D. ()()q q p q p ⌝∨→∨→)(（ ）４．),,()(),,())((z y x P z z y x P y x ∃→∀∃的前束范式为___________：A. )),,(),,()()()((z w v P u y x P z y x ∨⌝∃∀∃B. )),,(),,()()()((z w v P u y x P z y x ∨⌝∃∃∀C. )),,(),,()()()((z w v P u y x P z y x →∃∀∃D. 以上都不对（ ）5．下式不一定成立的是___________：A ．)()()()())()()((x Q x x P x x Q x P x ∀∧∀=∧∀B ．)()()()())()()((x Q x x P x x Q x P x ∃∨∃=∨∃C ．)()()()())()()()((x Q x x P x y Q x P y x ∀∨∀=∨∀∀D ． )()()()())()()((x Q x x P x x Q x P x ∃∧∃=∧∃上 海 交 通 大 学 试 卷（ A 卷）（ 20_07_ 至 20_08_ 学年 第_2__学期 ）我承诺，我将严格遵守考试纪律。
上海交大大学物理考卷汇总
上海交大大学物理考卷汇总（考试时间：90分钟，满分：100分）一、选择题（共5题，每题4分，共20分）1. 关于牛顿第一定律，下列说法正确的是（）2. 在下列哪种情况下，物体的动能不变？（）4. 在简谐振动中，位移与时间的关系是（）5. 关于电磁感应定律，下列说法正确的是（）二、填空题（共5题，每题4分，共20分）6. 力的单位是______，能量的单位是______。
7. 一个物体做匀速直线运动，当速度为5m/s时，其加速度为______。
8. 在自由落体运动中，物体的初速度为______，加速度为______。
9. 一个电容器的电容为C，电压为U，则其储存的电场能量为______。
10. 根据欧姆定律，电流I与电压U和电阻R的关系是______。
三、计算题（共3题，每题10分，共30分）11. 一个物体从静止开始做匀加速直线运动，加速度为2m/s²，求物体在第3秒末的速度和位移。
12. 一个电阻R=10Ω，电容C=5μF的串联电路，接在电压U=100V的电源上，求电路中的时间常数τ。
13. 一个质量为m的物体在水平面上受到一个恒力F的作用，求物体在力F作用下的加速度。
四、简答题（共2题，每题10分，共20分）14. 简述牛顿第三定律的内容及其在生活中的应用。
15. 解释什么是电磁感应现象，并举例说明。
五、分析题（共1题，共10分）16. 一个小球从高度h自由落下，求其在落地前的速度、位移以及落地时的动能。
假设空气阻力不计，重力加速度为g。
六、作图题（共2题，每题5分，共10分）17. 请画出物体做匀速圆周运动时的速度、加速度和力的矢量图。
18. 请画出LC振荡电路中的电容器充电和放电过程中的电压、电流变化图。
七、实验题（共2题，每题10分，共20分）19. 描述如何用弹簧测力计测量一个物体的重量，并简述实验步骤。
20. 设计一个验证欧姆定律的实验，包括实验器材、步骤和数据处理。
八、推导题（共1题，共10分）21. 从牛顿第二定律推导出动能的表达式。
上海交通大学mpa政治试题及答案
上海交通大学mpa政治试题及答案上海交通大学MPA政治试题及答案一、单项选择题（每题1分，共20分）1. 马克思主义哲学认为，世界的真正统一性在于它的（）。
A. 物质性B. 多样性C. 客观性D. 可知性答案：A2. 辩证唯物主义认为，物质的唯一特性是（）。
A. 客观实在性B. 运动性C. 多样性D. 可分性答案：A3. 唯物辩证法认为，事物发展的根本规律是（）。
A. 对立统一规律B. 质量互变规律C. 否定之否定规律D. 因果律答案：A4. 马克思主义哲学认为，认识的本质是（）。
A. 主观符合客观B. 主观创造客观C. 主观决定客观D. 客观决定主观答案：A5. 马克思主义哲学认为，社会历史发展的根本动力是（）。
A. 阶级斗争B. 社会基本矛盾C. 人民群众D. 英雄人物答案：B6. 马克思主义哲学认为，人民群众是历史的（）。
A. 创造者B. 旁观者C. 领导者D. 被领导者答案：A7. 马克思主义哲学认为，社会存在决定社会意识，社会意识是社会存在的（）。
A. 反映B. 创造C. 决定D. 否定答案：A8. 马克思主义哲学认为，经济基础决定上层建筑，上层建筑对经济基础具有（）。
A. 决定作用B. 反作用C. 创造作用D. 否定作用答案：B9. 马克思主义哲学认为，人的价值在于（）。
A. 个人利益的实现B. 社会地位的提高C. 个人对社会的责任和贡献D. 个人能力的发挥答案：C10. 马克思主义哲学认为，自由是对必然的认识和对客观世界的（）。
A. 改造B. 适应C. 顺从D. 利用答案：A11. 马克思主义哲学认为，真理是（）。
A. 主观的B. 客观的C. 主观与客观的统一D. 绝对的答案：C12. 马克思主义哲学认为，实践是检验真理的唯一标准，这是因为实践具有（）。
A. 客观性B. 社会历史性C. 直接现实性D. 能动性答案：C13. 马克思主义哲学认为，社会基本矛盾是（）。
A. 经济基础与上层建筑的矛盾B. 人与自然的矛盾C. 个人与社会的矛盾D. 先进与落后的矛盾答案：A14. 马克思主义哲学认为，阶级斗争是阶级社会发展的（）。
上海交通大学试卷
上海交通大学试卷（2019至2020学年第1学期）班级号学号姓名考试时间2019/12/3113：10–15：10地点东上院507/508课程名称初等数论成绩第1题：选择题[共21分]1.1[3分]15125与25256能否表示成两个整数的平方和？（）(A)都不能(B)仅15125能(C)仅25256能(D)都能1.2[3分]令k为三维实空间中一条直线上的全体整点的集合的势。
k的可能取值有多少种？（）(A)2种(B)3种(C)可数无穷种(D)不可数多种1.3[3分]下面各数中哪一个没有原根？（）(A)4(B)8(C)9(D)181.4[3分]最小的可以被所有判别式为−100的整正定二元二次型表出的(正)整数为哪一个？（）(A)5(B)25(C)100(D)不存在1.5[3分]令A为一个正整数集合，令αn表示A中不超过n的元素的个数，并且令α˙=lim sup n→∞αnn >0。
∑a∈A 1a等于多少？（）(A)π2+π4+π61−α(B)11−α2(C)∞(D)具体取值不能仅由α决定1.6[3分]225+1含有下述哪一个素因子？（）(A)2(B)11(C)101(D)6411.7[3分]实数轴上是否存在一族开区间，使得每个有理数都只被其中有限个区间覆盖，每个无理数都被其中无限个区间盖住？（）(A)存在(B)不存在(C)存在性与选择公理等价(D)由Godel不完全性定理可知这无法判定我承诺，我将严题号123456合计格遵守考试纪律。
得分承诺人：批阅人第2题：填空题[共30分]2.1[5分]11x+8y=600的正整数解(x,y)的个数为。
2.2[5分]72020在十进制展开中最后两位是。
2.3[5分]称2的幂次或者2的幂次的3倍为一个好数。
把100颗一模一样的珠子分成大小不一的若干堆，使得每一堆里头的珠子个数都是好数。
这种分法的个数为。
2.4[5分]模257的原根共有个。
2.5[5分](1747)=（填一个整数）。
上海交通大学国际本科生招生考试数学科考试试卷
上海交通大学国际本科生招生考试数学科考试试卷（样卷）SJTU International Undergraduate Entrance Examination(Mathematics sample exam papers)第一部分: 下列问题有且仅有一个正确答案(每题3分, 共42分)Section 1: The following problems have one and only one correct answer.(3 points for each, 42 points total)1.设集合A={1,2,4},B={2,4,5}, 则A∩B=（）.If set A={1,2,4},B={2,4,5}, then A∩B=（）.（A）{2,4}（B）{1,2,4,5}（C）{1}（D）{1,5}2.函数y=(x−1)12+(4−x)−32的定义域为（）.The domain of the function y=(x−1)12+(4−x)−32is（）.（A）[1,4)（B）(−∞,1)（C）[4,+∞)（D）(1,4]3.下列公式中，正确的是（）.In the following formulae, t he one that must be correct is（）.（A）cos2x=2cos2x−1（B）cos2x=2sin2x−1（C）sin2x=2cos2x−1（D）sin2x=2sin2x−14.设m是实常数. 若直线l1:2x+my+1=0与直线l2:y=3x−1平行，则m=（）.Let m be a real number. If line l1:2x+my+1=0is parallel to line l2:y=3x−1, then m=（）.（A）−23（B）23（C）6（D）−65.设平面上的动点P 到定点F(2,0)的距离等于P到直线x+2=0的距离，则点P的轨迹方程为（）.If the distance from moving point P to point F(2,0)equals to the distance from P to the straight line x+2=0, then the trajectory equation of P is（）.（A）y2=8x（B）y2=−8x（C）x2=8y（D）x2=−8y6.下列函数中，在其定义域上是单调递减的函数是（）.In the following functions, the one that is decreasing in its domain is（）.（A ）y =2−x （B ）y =cot x （C ）y =1x 2+1（D ）y =x7. 下列选项中，正确的是（ ）.Among the following options, t he correct one is （ ）. （A ）y =x 3+1x 和 y =log 2(x +√x 2+1) 均是奇函数y =x 3+1xand y =log 2(x +√x 2+1) are both odd functions（B ）y =x 3+1x是奇函数，但 y =log 2(x +√x 2+1) 不是奇函数y =x 3+1xis an odd function but y =log 2(x +√x 2+1) is not an odd function（C ）y =log 2(x +√x 2+1)是奇函数，但 y =x 3+1x不是奇函数y =log 2(x +√x 2+1) is an odd function but y =x 3+1x is not an odd function （D ）y =x 3+1x 和 y =log 2(x +√x 2+1) 均不是奇函数neither y =x 3+1x nor y =log 2(x +√x 2+1) is an odd function8. 已知 {a n } 是等差数列, 且 a 2=12,a 8=18, 则 a 5=（ ）.Given that {a n } is an arithmetic sequence, and a 2=12,a 8=18, then a 5=（ ）. （A ）15 （B ）6√6 （C ）30 （D ）2169. 若函数 f (x ) 的反函数 f −1(x )=x 2 (x >0), 则 f (4)=（ ）.If the inverse function of f (x ) is f −1(x )=x 2 (x >0), then f (4)=（ ）. （A ）2 （B ）−2 （C ）16 （D ）−16 10. arctan (tan5π6)=（ ）.（A ）−π6（B ）π6（C ）−5π6（D ）5π611. 已知椭圆 Γ：x 2a 2+y 2b 2=1 的一个焦点是(−2√3,0). 若a =2b , 则b =（ ）.Let (−2√3,0) be one focus of the ellipse Γ：x 2a 2+y 2b 2=1. If a =2b , then b =（ ）. （A ）2 （B ）√605 （C ）4 （D ）12512.设a,b均为正实数, 则“a+b≤2” 是“a2+b2≤2” 的（）.Let a,b be positive real numbers, then statement “a+b≤2” is a（）for statement “a2+ b2≤2”.（A）必要但非充分条件necessary but not sufficient condition（B）充分但非必要条件sufficient but not necessary condition（C）既非充分又非必要条件neither sufficient nor necessary condition（D）充分且必要条件sufficient and necessary condition13.函数sin(2x+3)的导数是（）.The derivative of function sin(2x+3)is（）.（A）2cos(2x+3)（B）cos(2x+3)（C）-2cos(2x+3)（D）−cos(2x+3) 14.曲线y=x3+3x+1在点P(0,1)处的切线方程是（）.The tangential equation of curve y=x3+3x+1at point P(0,1)is （）.（A）3x−y+1=0（B）x−3y+3=0（C）3x+y−1=0（D）x+3y−3=0第二部分: 下列问题有且仅有一个正确答案(每题4分, 共48分)Section 2: The following problems have one and only one correct answer.(4 points for each, 48 points total)15.不等式1x−2<1x的解集为（）.The solution set of the inequality1x−2<1xis（）.（A）(0,2)（B）(1,3)（C）(−∞,−1)（D）(2,+∞)（E）(−1,0)16.已知等比数列{a n}的首项a1=1, 公比q=2, 则{a n}的前8项的和S8=（）.If the first term a1of the geometric sequence {a n}is 1, and the common quotient q=2, then the sum S8of the first 8terms of {a n}is（）.（A）255（B）127（C）63（D）511（E）51217.已知实数a,b满足22a−b=4a+b=3, 则a=（）.If real numbers a,b satisfy 22a−b =4a+b =3, then a =（ ）. （A ）log 43 （B ）log 23 （C ）log 32 （D ）log 34 （E ）log 42 18. 已知 a,b,1,2 的中位数是 3，平均数是 4，则 ab =（ ）.Let the median of a,b,1,2 be 3，the average of a,b,1,2 be 4，then ab =（ ）. （A ）36 （B ）22 （C ）30 （D ）40 （E ）4219. 已知点 P 在曲线 C:2x 2−4x +2y 2−12y =5 上，点 Q 在直线 x +y +3=0上，则点P 和 Q 之间点距离 |PQ | 的最小值为（ ）.If point P is on the curve C:2x 2−4x +2y 2−12y =5, and point Q is on the line x +y +3=0, then the minimum distance |PQ | between points P and Q is （ ）. （A ）√2 （B ）√22（C ）1 （D ）0 （E ）2 20. 设复数 z =√3+i , 其中 i 是虚数单位, 则 z 5=（ ）.Let complex number z be defined as z =√3+i , where i is the unit of imaginary numbers, then z 5=（ ）.（A ）−16√3+16i （B ）16√3+16i （C ）−16√3−16i （D ）16√3−16i （E ）16√3+16√3i21. 在所有两位数中，个位数和十位数之和事偶数的数有（ ）.In all two-digit numbers, the number of those which the sum of its ones digit and its tens digit is an even number is （ ）.（A ）45 （B ）25 （C ）40 （D ）20 （E ）5022. 若实数 x,y 满足 sinx cosy =45, siny cosx =15, 则 cos2x =（ ）.If real numbers x,y satisfy sinx cosy =45, siny cosx =15, then cos2x =（ ）. （A ）−35（B ）35（C ）45（D ）−45（E ）2523. 三位同学参加跳过、跳远和铅球项目的比赛. 若每人都选择两个项目, 则有且仅有两人选择的项目相同的概率是（ ）.Three students participated in high jump, long jump and shot put competitions. If everyone chooses two of these three items, then the probability that there are exactly two people choosing same items is （ ）.（A ）23（B ）13（C ）29（D ）19（E ）1624. 设双曲线 C ：x 2−y 23=1 的左右焦点分别为 F 1 和 F 2 . 若点 P 在 C 上，且sin ∠PF 2F 1sin ∠PF 1F 2=2, 则 cos ∠F 1PF 2=（ ）.Let the foci of the hyperbola C ：x 2−y 23=1 be F 1 and F 2, respectively. If point P is onC , such thatsin ∠PF 2F 1sin ∠PF 1F 2=2, then cos ∠F 1PF 2=（ ）.（A ）14（B ）−12（C ）16（D ）−15（E ）1325. 设 P −ABC 是棱长为 6 的正四面体，点 D,E,F 分别是三角形 ∆PAB ∆PBC ∆PAC的重心, 则三棱锥 P −DEF 的体积为（ ）.Let P −ABC be a tetrahedron whose edges have a length of 6 . If points D,E,F are the barycenter of triangles ∆PAB ∆PBC ∆PAC respectively, then the volume of the trigonal pyramid P −DEF is （ ）.（A ）4√23 （B ）√23 （C ）3√22（D ）2√2 （E ）4√226. 设数列{a n },{b n } , 和 {c n } 满足: 对任意正整数n , a n+1=(−1)n (a n 2+1) , b n =a n a n+1, c n =cos a n . 下列论断中正确的的是（ ）.Let sequences {a n },{b n }, and {c n } satisfy: for an arbitrary integer n , a n+1=(−1)n (a n 2+1) , b n =a n a n+1, c n =cos a n , then the one that must be correct in the following statements is （ ）.（A ）{b n } 是单调递减数列 {b n } is a decreasing sequence （B ）{b n } 是单调递增数列 {b n } is an increasing sequence （C ）{c n } 是单调递增数列 {c n } is an increasing sequence （D ）{a n } 是单调递增数列 {a n } is an increasing sequence （E ）{c n } 是单调递减数列 {c n } is a decreasing sequence第三部分: 下列问题有且仅有一个正确答案 (每题5分, 共10分) Section 3: The following problems have one and only one correct answer.(5 points for each, 10 points total)27. 设 A,B,C 是三角形 ∆ABC 的三个顶点，且对任意的实数 λ 恒有 |BA⃗⃗⃗⃗⃗ −λBC ⃗⃗⃗⃗⃗ |≥2|BC ⃗⃗⃗⃗⃗ |. 若 |BC⃗⃗⃗⃗⃗ |=1, 则三角形 ∆ABC 周长的最小值为（ ）. Let points A,B,C be the three vertices of triangle ∆ABC , such that for an arbitrary realnumber λ , the following always holds true: |BA⃗⃗⃗⃗⃗ −λBC ⃗⃗⃗⃗⃗ |≥2|BC ⃗⃗⃗⃗⃗ | . If |BC ⃗⃗⃗⃗⃗ |=1 , then the minimum value of the perimeter of the triangle ∆ABC is （ ）.（A ）1+√17 （B ）1+√12 （C ）1+√7 （D ）1+√22 （E ）1+√27 28. 已知实数 x,y,z 满足 x 2+y 2+z 2=1, 则 xy +2yz 的最大值为（ ）.If x,y,z are all real numbers, and x 2+y 2+z 2=1, then the maximum value of xy +2yz is （ ）. （A ）√52 （B ）√22 （C ）√32 （D ）2 （E ）12参考答案：1~28：A。
上海交通大学英语水平考试样题及答案
上海交通大学英语水平考试样题学生姓名：________________ 年级：____________学号：学号： _____________ 班级代号：_______________ 考试地点: 授课教师：授课教师： Part I Listening （40％）Section 1 Long Conversations （10％）Directions: In this section, you will hear two long conversations. At the end of each conversation, you will hear five questions. Both the conversations and the questions will will be be be spoken spoken spoken ONLY ONLY ONLY ONCE. ONCE. ONCE. After After After you you you hear hear hear a a a question, question, question, you you must must choose choose choose the the the best best answer from the four choices.(注意：请把答案写在答题卷上,否则以零分处理) Conversation 1 1. A) It is exaggerated. B) It is self-important. C) It is a move toward the concepts she teaches. D) It doesn’t give a clear idea of what the department does . 2. A) S he didn’t agree with him . B) It illustrates one of her basic ideas. C) The man was an expert on people management. D) It shows how some people do not understand people management. 3. A) Worrying can cause needless stress. B) It is important to remember other things as well. C) They can stop you thinking about more basic things. D) We can’t solve them, so there’s no point in worrying.4. A) Completely. B) In no way at all. C) With respect to relationships. D) With respect to professional questions. 5. A) By giving them a written warning. B) By sacking people who break the rules. C) By following organizational procedures. D) By understanding the employee’s personal circumstances . passage twice.work," said Denise Denise Harris. Harris. Harris. "I still "I still get get seizures. seizures. So So now, now, now, when they remove when they remove the part that the seizure is 2) ____________ from, it's supposed to stop." But while Harris i s is is in the in the hospital, she is also helping helping scientists scientists scientists understand how understand how the brain comprehends and uses uses language. language. For For the study the study , , researchers are researchers are monitoring the the implanted implanted implanted 3) 3) ____________ ____________ on on on a a a part part of of the the the frontal frontal frontal lobe lobe lobe called called called Broca's Broca's Broca's area, area, named after 19th century French physician Pierre Paul Broca. He was the first doctor to recognize the major role of that area in language. Through the implant process, called Intra-cranial Electrophysiology Electrophysiology, or ICE, the , or ICE, the researchers researchers have have have found that found that Broca's area processes three different language language functions functions in 4) ____________ –––– within a quarter of a second. within a quarter of a second. It is the first time the technique has been used to document how the brain processes grammar and produces words.Eric Halgren of the University of California, San Diego, School of Medicine, is one of the 5) ____________ investigators of the study . "What "What we we we were were were able able able to to to find find find was was was that that that within within within a a a centimeter, centimeter, centimeter, around around around less less less than than than an an inch, certainly, and probably half an inch, there were different regions - perhaps they 6) ____________ ____________ some some some –––– but but they they they were were were doing, doing, doing, at at at different different different times, times, times, different different different processes, processes, all within this small area." The The first first first function deals with recognizing a word, the second with understanding function deals with recognizing a word, the second with understanding the word's context i n a sentence, and the in a sentence, and the third third lets lets lets us 7) ____________ the word by us 7) ____________ the word by speaking. Harvard University brain expert Steven Pinker is another of the study's authors. Ned Ned Sahin, Sahin, Sahin, a a a 8) 8) 8) ____________ ____________ ____________ fellow fellow fellow at at at Harvard Harvard Harvard and and and the the the University University University of of California, San Diego, School of Medicine was the first author of the paper outlining the work, which was published in the journal Science . According to Sahin, 9)___________________________________________ _____________________________________________________________________ _____________. "Nearly every introductory introductory textbook as textbook as well as people practicing in in the the the field field field in in speech pathology , , for for for instance, instance, instance, teach and believe that 10) ______________________ teach and believe that 10) ______________________ ____________________________________________________________________ _______________ –– Broca's area and Wernicke's area, where Broca's area is responsible responsible for for for producing, producing, producing, for for for speaking, speaking, speaking, and and and Wernicke's Wernicke's Wernicke's for for for comprehending," comprehending," comprehending," said said Sahin. This study shows that Broca's area is involved in both speaking and comprehension, illustrating that parts of the brain perform more than one task."Here's "Here's an an an example example example of of of one one one relatively relatively relatively small small small part part part of of of the the the brain brain brain that's that's that's doing doing doing three three very different things at three different times, but all within the space of a quarter of a second." But Eric Halgren points out that despite our growing knowledge, much about the human brain remains unknown. "How does this h unk of hunk of flesh, which is not much different from a muscle muscle –––––– it's it's just a bowl of porridge –––– how does it produce the mind? how does it produce the mind? It's a total mystery". He says 11) ______________________________________________________ ________________________________________. ONLY ONCE.__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 3) It is no coincidence that the relationship between our countries has accompanied a period of positive change. ___________________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4) 4) And And yet yet the the the success success success of of that that engagement engagement engagement depends depends upon understanding -- -- on on sustaining sustaining an an an open open open dialogue, dialogue, dialogue, and and learning about about one one one another another and from from one one another. For just as that American table tennis player pointed out, we share much in common as human beings, but our countries are different in certain ways. _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 5) 5) For For For a a a variety variety variety of of of reasons, reasons, reasons, production production production of of of the the the H1N1 H1N1 H1N1 vaccine vaccine vaccine has has has lagged lagged lagged behind behind demand. demand. The The The vaccine vaccine vaccine for the so-called swine for the so-called swine flu flu is is is made made made in in in the the the same way as same way as the seasonal flu vaccine - in chicken eggs. But the government's top infectious disease expert, Dr. Anthony Fauci, said the goal is to perfect new ways to make a vaccine. "What "What we we we really really really want want want to to to do do do is is is get get get away away away from from from that that that and and and get get get it it it to to to be be be 21st 21st 21st century century technology technology - - - molecular molecular molecular biology biology biology, , , recombinant recombinant recombinant DNA DNA DNA technology technology technology, , , where where where you you you have have very very good good good control control control over over over the the the process. process. process. It's It's It's rapid, rapid, rapid, it's it's it's consistent, consistent, consistent, and and and it it it proves proves proves to to to be be something something that that that we we we can can can rely rely rely on." on." on." _____________________________________ _____________________________________ __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ __________________________________________________________________ Part II Integrated Reading (30%)Section 1 Banked Cloze (10%)Directions: In this section, there is a a passagepassage with ten blanks. You are required tochoices. You may not use any of the words in the bank more than once. Give your answers to the questions on your ANSWER popular connect favorite race affect compare decrease deprivation act out signify effect derive increase major concludeY (for YES) if the statement agrees with the information given in the passage; N (for NO) if the statement contradicts the information given in the passage; For questions 8-10, complete the sentences with the information given in the passage.Attention: For questions 1-7, one more point will be deducted if youdo n’t an swer each one correctly.(注意: 1-7题中每答错一题倒扣1分, 不答不得分,答对得1分; 请把答案写在答题卷上,否则以零分处理)Who are smarter, m en or women? It's a topic of common men or women? It's a topic of common –––– and often comic and often comic –– contemplation, but it has also become a serious policy issue issue for colleges and students for colleges and students in the United States. After After years years years of of of concentrated concentrated concentrated effort effort effort to to to raise raise raise the the the academic academic academic achievement achievement achievement of of of girls, girls, who who in previous decades in previous decades h ad often received had often received l ess attention less attention in the classroom a nd been and been steered away from college-prep courses, the nation can brag that female students have progressed tremendously. Though still underrepresented in calculus and other advanced-level science and math courses in high school, women now outnumber men applying to and g raduating graduating graduating from college from college –––– so so much so that that it appears some colleges it appears some colleges are giving male applicants an admissions boost. As a result, the U.S. Commission on Civil Rights is examining whether colleges are engaging in widespread discrimination against women in an effort to balance their male and female populations. Consider Consider some some some of of of the the the numbers numbers numbers at at at leading leading leading schools: schools: schools: At At At Vassar Vassar Vassar College College College in in in New New York State, State, a a formerly all-women's all-women's college college college that that is is still still still 60% 60% female, female, more more more than than two-thirds of the applicants last last year year year were women. were women. The college accepted 35% of the men who applied, compared with 20% of the women. women. Locally, elite Pomona College Locally, elite Pomona College accepted accepted 21% 21% 21% of of of male male male applicants applicants applicants for for for this this this year's year's year's freshman freshman freshman class, class, class, but but but only only only 13% 13% 13% of of female female applicants. applicants. applicants. At At At Virginia's Virginia's Virginia's College College College of of of William William William & & & Mary, Mary, Mary, 7,652 7,652 7,652 women women women applied applied for this year's year's freshman class, compared freshman class, compared w ith 4,457 with 4,457 male applicants. Yet the numbers of of each each each who who who gained gained gained admittance admittance admittance were were were nearly nearly nearly the the the same. same. same. That's That's That's because because because the the the college college accepted 45% of the men and only 27% of the women. A A 2007 2007 2007 analysis analysis analysis by by U.S. News & World Report , , based based based on on on the the the data data data sent sent sent by by colleges for the magazine's annual rankings, found that the admissions rate for women averaged 13 percentage points lower lower than that than that for for men. But percentages don't men. But percentages don't tell tell the the whole whole story. story. story. It It It could could could be be that that the the the men men men were were were stronger stronger stronger candidates, candidates, candidates, or or or they they they might might might have have applied applied in in in areas areas areas of of of engineering engineering engineering and and and science science science where where where women's women's women's numbers numbers numbers are are are still still still lower. lower. But But such such such justifications, justifications, justifications, even even even if if if true, true, true, are are are unlikely unlikely unlikely to to to fully fully fully explain explain explain these these these numbers. numbers. numbers. At At schools schools such as the University of California, where admissions rely overwhelmingly such as the University of California, where admissions rely overwhelmingly on on statistical statistical statistical measures measures measures of of of academic academic academic achievement achievement achievement such such such as as as grades grades grades and and and test test test scores, scores, scores, the the disparities disparities don't don't don't appear. appear. appear. Far Far Far more more more women women women than than than men men men applied applied applied to to to UCLA UCLA UCLA –––– the the UC's UC's most selective campus –– last year. The university accepted about the same percentage of each, with a slight edge to the women. As a result, result, the the the freshman class freshman class has close to 800 more women than men. In recent years, several college leaders have admitted that their institutions give a boost boost to to to male male male applicants applicants applicants to to to maintain maintain maintain gender gender gender balance balance balance on on on campus. campus. campus. Most Most Most students students students of of either sex, they point out, prefer such balance. If Vassar accepted equal percentages of each sex, women would outnumber men by more than 2 to 1. Jennifer Jennifer Delahunty Delahunty Delahunty Britz, the dean of admissions at Kenyon College Britz, the dean of admissions at Kenyon College in Ohio, a formerly all-male school, brought the matter to broad public attention in 2006 with an Op-Ed Op-Ed article article article for for for the the New York Times describing describing the the the dilemma dilemma dilemma of of of her her her admissions admissions office. "What "What messages messages messages are are are we we we sending sending sending young young young women women women that that that they they they must . . . must . . . be be even even more more accomplished accomplished accomplished than than than men men men to to to gain gain gain admission admission admission to to to the the the nation's nation's nation's top top top colleges?" colleges?" NewYork Times has long long favored allowing colleges to favored allowing colleges to use race as an admissions factor factor in in order to diversify student populations. She also wrote t hat exposure that exposure to people of different backgrounds and viewpoints better better educates educates educates all all all students students students –––– not not just just just those those those given given given a a a leg leg leg up. up. up. We We We are are are not not not in in in favor favor favor of of accepting accepting underqualified underqualified underqualified or or or clearly clearly clearly inferior inferior inferior students students students for for for the the the sake sake sake of of of diversity. diversity. diversity. But But most colleges are inundated with applications from students who more than meet their standards; the differences among many of them are slight. It makes sense for colleges to to pick pick pick a a a balanced balanced balanced population population population from from from within within within this this this group. group. group. At At At the the the same same same time, time, time, admissions admissions officers should avoid rigid notions of what constitutes enough men on campus. It's not harming harming UCLA, UCLA, UCLA, or or or destroying destroying destroying college college college social social social life, life, life, to to admit admit somewhat somewhat somewhat more more more women women than men. Even Even if if if the the the Civil Civil Civil Rights Rights Rights Commission Commission Commission finds finds finds pervasive pervasive pervasive gender gender gender discrimination discrimination discrimination in in admissions, there's little it could do about the situation. Such discrimination –––– though though not racial discrimination –––– is legal for undergraduate admissions at private, nonprofit is legal for undergraduate admissions at private, nonprofit colleges, colleges, even even even those those those that that that receive receive receive federal federal federal funding. funding. funding. Commission Commission Commission documents documents documents on on on the the inquiry suggest that colleges could find more "gender-neutral" ways of balancing their student student numbers, numbers, numbers, perhaps perhaps perhaps by by by offering offering offering programs programs programs and and and extracurricular extracurricular extracurricular activities activities activities that that attract men. Those Those might might might work work work for for for some some some schools schools schools but but but won't won't won't change change change the the the overall overall overall scenario. scenario. scenario. Not Not with with college college college populations populations populations composed composed composed of of of 57% 57% 57% women women women nationwide. nationwide. nationwide. The The The issue issue issue we'd we'd we'd like like the Commission on Civil Rights to investigate is: What's happening with the education education of of of U.S. U.S. U.S. boys? boys? boys? Why Why Why are are are so so so few few few of of of them them them applying applying applying to to to and and and graduating graduating graduating from from college? Theories Theories and and and arguments arguments arguments abound. abound. abound. Some Some Some say say say that that that boys boys boys are are are more more more active active active and and and thus thus less able to sit still for long periods –––– and as a result, more likely to be categorized as and as a result, more likely to be categorized as having having attention deficit attention deficit / / hyperactivity disorder or needing special hyperactivity disorder or needing special education. A 2008 study by researchers at Northwestern University found that when girls are involved in a language-related task –––– such as reading such as reading –––– they show they show more activity in areas of the brain brain involved involved involved in in in encoding encoding encoding language. language. language. Boys Boys Boys use use use more more more sensory sensory sensory information information information to to to do do linguistic tasks. The study suggests boys might do better if they were taught language and arts in different ways. ways. Race Race Race is a is a factor as well. well. The The The gender gender gender gap gap gap is starker is starker among African American and Latino students. There There may be may be no one reason –––– or solution. But or solution. But figuring out ways ways to to to help boys help boys achieve in school is a better response to the gender gap than making it easier for them to get into college later. 1. As a result of the effort to raise the academic achievement of the girls for years, the girls girls have exceeded boys have exceeded boys t remendously tremendously tremendously in all courses in all courses in colleges except c alculus and calculus and other advanced-level science and math courses. 2. 2. Female Female Female students students students are are are facing facing facing the the the low low low admission admission admission rate rate rate because because because some some some colleges colleges colleges are are engaging engaging in in in discrimination discrimination discrimination against against against women women women to to to achieve achieve achieve the the the balance balance balance of of of their their their male male male and and female populations. 3. 3. Although Although Although the the the men men men were were were traditionally traditionally traditionally considered considered considered stronger stronger stronger candidates candidates candidates in in in areas areas areas of of engineering and science, t he admission the admission rate rate for for for men men men in these areas in these areas is still lower lower than than that for women. 4. Women have outnumbered men men in in in gaining gaining gaining admittance admittance admittance in in in UCLA UCLA UCLA’’s freshman class this this year year year because because because their their their admissions admissions admissions greatly greatly greatly rely rely rely on on on grades grades grades and and and test test test scores scores scores of of of their their applicants. 5. 5. Some Some Some college college leaders hold hold that that most most college college college students students students prefer prefer prefer their their their policy policy policy of of maintaining gender balance by admitting equal percentages of each sex. 6. The dilemma of the dean of admissions at Kenyon College is whether to use gender as as an an an admissions admissions factor in in order order order to to to achieve achieve gender gender balance balance balance or or use use race race as as an an admissions factor in order to diversify student populations. 7. 7. According According to to Jennifer Jennifer Jennifer Delahunty Delahunty Delahunty Britz, Britz, Britz, it it it is is is reasonable reasonable reasonable for for for colleges colleges colleges to to to pick pick pick a a balanced population from the candidates who more than meet their standards. 8. 8. Actually Actually the the Civil Civil Civil Rights Rights Rights Commission Commission Commission can can can do do do little little little to to to change change change the the the situation situation situation of of discrimination in college admission because such discrimination is ____________________________________________________________________. 9. The study shows that in doing linguistic tasks the boys use more sensory information, the girls show more _________________________________________. 10. 10. Despite Despite Despite various various various theories theories theories and and and arguments arguments arguments about about about why why why so so so few few few boys boys boys apply apply apply to to to and and We form many of our opinions 1_____ our our favorite books. favorite books. The author whom we prefer is our most potent teacher; we look at at the the the world world world 2______ 2______ his eyes. If we habitually read books that are elevating in tone, pure in style, 3______ i n reasoning, in reasoning, and and keen keen keen in in in insight, insight, insight, our our our minds minds minds 4______ 4______ the the same same same characteristics. characteristics. characteristics. If, If, If, 5_________, 5_________, we read weak or vicious books, our minds contract the f aults and faults and vices of the books. We cannot escape the influence of what we read any more 6_______ we can escape escape the the the influence influence influence of of of the the the air air air that that that we we breathe. The best books are 7______ which which stir stir us up most and make us the most 8______ to do something and be something something ourselves. ourselves. ourselves. The The The best best best books books books lift lift us us to a to a higher plane 9_____ w e breathe a we breathe a purer atmosphere. As we should associate with people who can inspire inspire us us us to to to nobler nobler deeds, 10______ we should only read those books which have an uplifting power, power, and and and 11______ 11______ 11______ stir stir stir us us us to to to make make make the the most of ourselves and our opportunities. … Good books elevate the character, 12_______ the taste, take the attractiveness attractiveness out out out of of of low low low pleasures, pleasures, pleasures, and and lift us upon a higher plane of thinking and living. It is not easy to be 13______ directly after reading a noble and 1. A) by B) with C) from D) in 2. A) with B) through C) in D) inside 3. A) sound B) good C) beautiful D) hard 4. A) have B) with C) being D) develop 5. A) on the contrary B) however C) on the other hand D) anyway 6. A) however B) than C) as D) but 7. A) them B) they C) theirs D) those 8. A) determining B) determine C) determined D) being determined 9. A) which B) where C) while D) when 10. A) as B) and C) so D) also 11.A) they B) books C) those D) which 12. A) pure B) purify C) pore D) pear 13. A) mean B) meaningful C) meanwhile D) meaning inspiring book. The conversation of a man who reads for improvement or pleasure pleasure will will will be be be flavored flavored flavored 14______ 14______ 14______ his his reading; but it will not be about his reading. 15_______ you read, read with enthusiasm, enthusiasm, with with with energy energy energy, , , read read with with the the whole whole mind, mind, mind, if if if you you you would would would increase increase increase your your mental stature. Learn to absorb the mental mental and and and the the the moral moral moral life life life of of of a a a book, book, book, and and assimilate 16______ into your life. 17_____ is the best reader who consumes the most knowledge and converts it 18______ 18______ character. character. character. Mechanical Mechanical Mechanical readers readers remember words, the h usks of husks of things, but digest 19_______. They cram their brains but starve their 20______. If you are getting getting the the the most most most out out out of of of a a a book, book, book, you you you will will feel feel a a a capacity capacity for for doing doing doing things things things which which you never felt before. 14. A) with B) of C) by D) after 15.A) What B) That C) Books D) Whatever 16. A) them B) it C) which D) life 17. A) It B) He C) None D) Everyone 18. A) by B) with C) in D) into 19. A) things B) something C) nothing D) anything 20. A) hearts B) stomachs C) minds D) tastes 。
上海上海交通大学研究生入学考试英语真题
上海上海交通大学研究生入学考试英语真题上海交通大学研究生入学考试英语真题上海交通大学是中国一所著名的综合性高等学府，其研究生教育一直备受瞩目。
每年，上海交通大学都会组织研究生入学考试，而英语是其中一门必考科目。
本文将模拟一篇上海交通大学研究生入学考试英语真题，帮助考生熟悉考试题型，提升备考效果。
Section A: Vocabulary and Structure（词汇与结构）Directions: There are 20 incomplete sentences in this section. For each sentence, there are four choices marked A, B, C, and D. Choose the one that best completes the sentence. Mark your answer on the ANSWER SHEET with a single line through the center.1. Many parents are willing to make great _____ for the education of their children.A. decreasesB. contributionsC. increasesD. consultations2. A large-scale earthquake can cause immeasurable _____, destroying countless homes and taking many lives.A. devastationB. designationC. destinationD. demonstration3. The government has implemented a series of _____ to stimulate economic growth.A. measuresB. pressureC. expensesD. judgmentsSection B: Reading Comprehension（阅读理解）Directions: There are 4 passages in this section. 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. Mark your answer on the ANSWER SHEET with a single line through the center.Passage 1Air pollution is a major concern for many cities around the world. A new study conducted by researchers at Shanghai Jiao Tong University investigated the impact of air pollution on children's health. The study focused on respiratory disease rates among children living in heavily polluted areas compared to those in cleaner areas.The researchers collected data from over 10,000 children between the ages of 6 and 12 years old. They found that children living in polluted areas were significantly more likely to develop respiratory diseases, such as asthma and bronchitis, than those in cleaner areas. Furthermore, the severity of their symptoms and the frequency of hospital visits were also higher among the children living in polluted areas.These findings highlight the urgent need for effective measures to combat air pollution and protect the health of children. The researchers suggest that reducing emissions from factories and vehicles, as well as promoting the use of clean energy sources, are crucial steps in improving air quality and reducing respiratory disease rates.4. What is the focus of the study conducted by researchers at Shanghai Jiao Tong University?A. The impact of air pollution on children's health.B. The effectiveness of reducing emissions from factories.C. The severity of asthma and bronchitis symptoms.D. The importance of clean energy sources.5. According to the study, what was found among children living in polluted areas?A. They were less likely to develop respiratory diseases.B. They experienced fewer symptoms of asthma and bronchitis.C. They had lower hospital visit rates.D. They were more likely to develop respiratory diseases.6. What measures do the researchers suggest to combat air pollution?A. Promoting the use of clean energy sources.B. Encouraging more hospital visits for children.C. Increasing emissions from factories.D. Closing down factories in polluted areas.Section C: Translation（翻译）Directions: Translate the following passage into English and write your translation on the ANSWER SHEET.近年来，随着科技的快速发展与普及，人们对人工智能的关注与热情持续升温。
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上海交通大学试卷电磁场与波期终试卷(A 卷)姓名____________班级_____________学号_____________得分____________ 一. 填空问答题（每小题5分，共30分）1. 已知222sin y x y z A x y a z ya xe a =++K K K K ，求A ∇×=K ____________________________。
2. 已知r r A A a A a ϕϕ=+KK K ，,r A A ϕ分别为常数，,r a a ϕK K为圆柱坐标系的单位矢量，则为（填“是”或“不是”）常矢量。
A K3. 一平面波的电场为()()3323j kx j kx z y E ea e ππ−−−+=+K a K K ，该平面波的传播方向为；极化方式为。
4. 真空中，已知一电磁波的电场强度为()(00cos sin x z E a E t y a E t y )ωβω=−+β−G G G，则此电磁波的磁场强度的瞬时表达式为__________________________________________。
5. 磁通连续性原理的方程是___________________________________（微分形式），其物理意义是6. 矩形波导中的面电流分布的特点是10T E二． 计算题（第3题10分，其余3题各1. 一同轴线内导体的半径为，外导体的半径为b 。
内外导体间填充电导率分别为a 1ε和2ε的两种不同的理想电介质，如图所示。
设同轴线内外导体间施加电压为U ，且已知其外导体接地。
求：① 同轴线中内外导体间各介质中的0E K 和D K；② 各介质中的束缚体电荷密度和面电荷密度的表达式。
3. 自由空间中，一正弦电磁波的磁场强度的复矢量为2()(a a )e j x y x y z H π−+=−++K G G A/m① 求该电磁波的波长；② 求电磁波传播方向上的单位矢量；③ 导出磁场强度的瞬时矢量和电场强度的瞬时矢量()H t K ()E t K的表达式；④ 求出此平面波的瞬时坡印亭矢量和平均能流密度矢量()S t K av S K；⑤ 求其平均电磁场能量密度。
av w 3. 真空中，两半径均为的半圆环与两条相互平行的长为的直导线构成如图所示的载流回路，回路中载直流a 2a I 。
求坐标原点O 处的磁感应强度B G 。
4. 如题图所示，一载均匀电流00j I I e=D的正方形导电环处于xoy 平面，环心处于坐标原点，各边长为l λ<<。
① 详细导出该正方形电流环在远区场点()ϕθ,,R p 处的矢量磁位及电磁场分量的表达式；② 写出该正方形电流环在远区的平均功率密度的表达式；③ 导出其辐射电阻的表达式。
上海交通大学试卷电磁场与波期终试卷(A 卷)姓名____________班级_____________学号_____________得分____________一. 填空题（每小题3分，共30分）1. 真空中，已知一电磁波的电场强度为()(x t E x t E E y z β−ω+β−ω=sin a cos a 00)GG G ，则此电磁波的磁场强度的瞬时表达式为__________________________________________。
2. 已知圆柱坐标系中， 11sin cos r z 2A a A a A a A ϕϕϕ=++K G G G（其中为常数），此矢量______（填“是”或“不是”）常矢量，因为________。
12,A A 3. 旋度定理的数学表达式为_______，它可利用公式______和公式________导出。
4. 若静电场中填充线性、各向同性、介电常数为ε的非均匀电介质，且电介质中没有自由体电荷存在，则束缚体电荷_______（填“可存在”或“也不存在”）。
若束缚体电荷存在，则束缚体电荷密度p ρ=_______；若束缚体电荷不存在，原因是_______。
5. 为在垂直于基本电振子（电流元）轴线方向上，距离基本电振子10处得到电场强度的有效值大于km 1mV m ，则基本电振子的辐射功率为_______。
6. 若一空气矩形波导中导波的工作频率3GHz f =，相速8p 3.7510m s v =×，导波的电场分量j 40sin()e V m ,0z y xE aβx z E E π−===b ，则该波导管上纵向面电流的最大值为______；若取波导管的宽、窄边的尺寸满足关系：2a =，则波导管的尺寸为______。
7. 两种磁介质的分界面的方程是321m x y z ++=，已知包含坐标原点一侧的区域①的相对导磁率r1 3.0μ=，其磁通量密度125x z T B a a =+KK K，又知区域②中填充相对导磁率r2 6.0μ=的磁介质，其区域②中磁通量密度2B =K_______。
8. 理想媒质中传播的和导电媒质中传播的平面波的传播特点的异同处是_________________________________________________________________________________________。
9. 恒定电场的基本方程是___________________________________（微分形式），其物理意义是_________________________________________________________________________。
10. 矩形波导不能传输与模式，因为_________________________________。
0m TM n 0M T 二．计算题（前1小题20分，后2小题各25分，共7０分）1. 有一均匀平面电磁波由空气斜入射到0z =处的理想导体平面上，其电场强度的复矢量为 j(6+8)5eV m x z y E a −=KK第1页 共2页① 求此平面波的工作频率和波长；② 写出入射波的电场强度和磁场强度的瞬时表达式；③求入射角i θ；④ 写出合成波的电场强度以及磁场强度的复数表达式；⑤ 求出合成波传播方向上的相速和波长；⑥ 写出导体平面上的面电流密度的表达式；⑦ 简述合成波的特点。
2. 如题图所示，在无限大的理想接地导电平面上有一半径为的半球形导体凸部，半球a 的球心在导体平面上，若在半球形导体凸部附近平行于x 轴放一长度为的均匀直线电荷（中心在处，线电荷密度为l y h a =>l ρ）。
① 求镜像电荷的分布以及各镜像电荷的所受到的作用力。
第2页 共2页3. 已知一内充空气的矩形波导的横截面尺寸为，其中传输的TM 2mm 1023×=×b a 11模的两个磁场分量为zj x b y a x E b k j H βπππωε−=e cos sin 02c zj y by a x E a k j H βπππωε−−=e sin cos 02c ①．求模的截止频率；②．当信号源频率为截止频率的两倍时，求此模式的传播常数11M T c f 0f c f γ、波导波长g λ及波阻抗；③．设信号源频率TM Z 2c 0f f =′，再求此模式的传播常数γ及波阻抗；④．导出波导壁上的面电流密度表达式（自选并画出坐标）。
TM Z上海交通大学试卷电磁场与波期终试卷(A 卷)姓名____________班级_____________学号_____________得分____________ 一．填空题（每小题3分，共30分）1．已知一静止电荷位于圆柱坐标系中的点q ()⎟⎠⎞⎜⎝⎛−=a a p z r p ,3,,,00πϕ处，则此点电荷在直角坐标系中的点()()a a a p z y x p ,,,,11=处产生的电场强度E G的y 向分量____________________；电场强度=y E E G在圆球坐标系中的θ向分量=____________________。
θE 2. 矢量场的唯一性定理为_______________________________________________________ _____________________________________________________________________________。
3． 真空中，已知一电磁波的电场强度为()(x t E a x t E a E y z βωβω−+−=sin cos 00)GG G ，则此电磁波的磁场强度的瞬时表达式为_____________________________________________。
4． 时变场中，有机玻璃和水的交界面处的边界条件为__________________________ ________________________________。
5．在一无限大的理想接地导电平面（xoy 平面）上方（媒质为空气）距离为处有一正电荷，并位于均匀电场中。
当z q z a E G0=z ________________时，电荷受力为零。
6．真空中，载直流为I 的两根半无限长直导线（垂直于xoy 平面）和一半径为a 的有缺口圆环形导线（处于xoy 平面内）构成回路。
设缺口的张角为α2，则环心点的磁感应强度p =B G__________________________________。
（注：电流方向及坐标自取，并画出坐标系）7．一均匀平面波从空气垂直入射到理想导体表面（=z ０）上，已知其反射波的电场强度为，则其入射波为_____________极化波；理想导体表面（０）上的面电流密度________________________________。
(z j y x r e a j a E E βG GG 20+−=)=z =S JG 8． 一尺寸为的矩形波导工作于TE b a ×10波，当工作频率25.9=f GHz 时，波导波长95.4=g λcm ；当GHz 时，其波导波长8.9=′f =′gλ________________。
9．尺寸为的空气矩形波导（其轴线沿向）中TE b a ×z 10波的平均功率密度的表达式_______________________；功率容量的表达式=av SG =br P __________________________。
10．三个沿x 轴排列，间距为2λ的半波对称振子（轴线沿轴）用于自由空间中远区辐射电磁波，各电流元激励电流的相位相同，振幅比为１：２：１，则该天线阵的归一化方向图函数y ()=ϕθ,F _______________________________________。