05-08真题

北京大学法律硕士复试历年真题汇总（04-09年）04年第一题很多律师在事实认定、证据运用、法律适用等方面求助于专家学者的论证意见书,并提交给法官。

这一现象在刘涌一案中达到极致。

对于这种“论证意见书”有两种观点。

反对者认为这干扰了司法公正;赞成者认为这有利于司法公正,请谈谈你的看法。

第二题可口可乐公司在其产品上用了中国篮球队队员姚明等三名队员的肖像。

但姚明的肖像权已经转让给百事可乐公司,并且可口可乐公司并未事先取得姚明的许可。

于是姚明将可口可乐公司告上法庭,要求赔偿精神损失1元。

但可口可乐公司辩称,其作为中国篮球队的唯一赞助商,与中国篮协等单位签定了相关合同。

合同约定可口可乐公司可以使用中国篮球队3名以上队员的集体肖像。

并且中国国家体育局也于1996年以文件的形式规定,国家级运动员的肖像权等无形资产归国家所有。

针对该案有如下看法:一,一般专家认为,肖像权只是每一个个体的人格权利,集体是不存在所谓的“集体肖像权”的。

所以可口可乐公司与中国篮协的协议违背法理;二,肖像权是人格权,不是财产。

《民法通则》也认为“公民有肖像权”。

中国国家体育局以文件的形式规定运动员的肖像权是无形资产,并归国家所有,违背了法律的规定,应该无效;三,国家为了培养运动员花费了大量的经费,从而要求运动员成名后,国家能利用其肖像权,获得一定的收益。

这并没有什么不可。

解决的办法在于,国家在运动员成名前就成名后的肖像权达成相关的协议,以减少成名后的纠纷;四,国家培养运动员的初衷在于提高国民身体素质,提倡运动并相应的要求运动员为国家挣得荣誉。

所以运动员的肖像权应该完全归运动员个人所有。

请就以上观点提出自己的看法。

05年第一题材料1:有媒体报道说,王朔新书《不想上床》5月即将出版。

王朔真要出新作了?昨天记者从业内了解到,此王朔非彼王朔。

在第十届长沙图书交易会上,长沙紫东阁华天大酒店进门处,大大的王朔要出新书的广告牌非常醒目。

走在楼层间,小幅的广告随处可见。

试卷名称：05-08年企业法令参谋考试真题解析——第三章合同实务--笔试试题试卷描述：在线考试、招聘笔试、微信考试试卷链接：试卷限时：50分钟一.单项选择题每题分值：2分是否标题问题乱序：是是否选项乱序：是是否可回溯：是难度：中1.[单项选择]甲公司与一公司拟买卖一检材，双方经屡次协商后，未能签订合同，由此甲公司承当缔约过失责任，缔约过失责任发生的根底是当事人违反_______。

A.履行合同义务B.先合同义务C.后合同义务D.不真正义务答案：B2.[单项选择]甲公司拟在与乙公司签订的购销合同中约定免责条款。

按照我国合同法对免责条款的规定，以下表述正确的选项是_______。

A.如果合同中有免责条款，此条款应有效B.允许以默示方式作出C.允许法官推定存在D.免责条款的提出必需是明示的答案：D3.[单项选择]甲公司向乙公司购置一布料，双方在合同中规定了履行日期。

乙公司欲提前履行合同。

按照我国合同法对提前履行的规定，以下表述正确的选项是_______。

A.债权人对提前履行均有拒绝权B.债权人的承受行为即暗示认可债务人的提前履行C.事后弗成主张债务人未适当履行合同债务D.法令规定了债务人无条件的提前履行权答案：B4.[单项选择]火车运行途中，车厢内灯管突然爆裂，击伤旅客张某左眼，张某有权请求承运人承当的责任是_______。

A.违约责任B.侵权责任C.违约责任或侵权责任D.违约责任和侵权责任答案：C5.[单项选择]甲贸易市场与乙公司签订合同，约定由乙公司以支援市场扶植为由向甲贸易市场捐赠2000万元，甲贸易市场将一栋大楼作价4000万元出售给乙公司。

但该大楼实际价值6000万元，按照该合同，双标的目的国家少缴纳土地增值税等税费达数百万元。

甲、乙之间的合同_______。

A.有效B.无效C.可撤销D.效力待定答案：B6.[单项选择]甲公司向乙公司购置木材，双方在丙市订立合同，约定在丁市履行，但对木材价格未作明确约定。

2008年考研小作文真题解析及参考范文一、考试真题Part A:Directions: You have just come back from Canada and found a music CD in your luggage that you forgot to return to Bob, your landlord there. Write him a letter to1）make an apology, and2）suggest a solutionYou should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use Li Ming instead.Do not write the address.二、命题解析今年小作文相对简单，预计全国平均分5－6分之间,略高于07年的4.93分。

自2005年开考小作文以来，今年第四次考察了书信这一题型，再次印证了考研小作文的重点还是书信作文,而备忘录、摘要、报告、告示只需简单准备即可。

05年考察辞职信＋道歉信,06年考察请求信,07年考察建议信。

今年则再次考察了道歉信,充分表明真题是考研的根本,写作也不例外。

只要充分重视真题，,必将受益匪浅。

我们的写作教材中附有教育部公布的历年真题高分作文,历年经典句型均可借鉴。

需要注意的是,根据08年教育部最新大纲，考研小作文无需书写日期,使用缩进式,段间不空行，每段首行缩进4－5个字母。

称呼需要顶头写,由于题目中出现了人名，写成Dear + 人名即可。

正文中务必客气,礼多人不怪。

表示感谢的句型不可或缺,感谢房东对你的热情照顾。

同时表示道歉和提出解决方法两点提纲务必写到。

落款写在稿纸中间偏后的位置，Yours sincerely,或Sincerely yours，均可,注意大小写和逗号。

专题08 实验设计专题题型及解题技巧目录导航一、真题考法归纳考法01 实验变量分析考法02 正确写出实验目的考法03 准确写出实验原理考法04 完整写出实验思路与实验步骤考点05 实验结果与结论的预测与分析二、常考热点实验梳理三、实验热点专练1．（2023·山东·高考真题）当植物吸收的光能过多时，过剩的光能会对光反应阶段的PSⅡ复合体（PSⅡ）造成损伤，使PSⅡ活性降低，进而导致光合作用强度减弱。

细胞可通过非光化学淬灭（NPQ）将过剩的光能耗散，减少多余光能对PSⅡ的损伤。

已知拟南芥的H蛋白有2个功能：①修复损伤的PSⅡ；②参与NPQ的调节。

科研人员以拟南芥的野生型和H基因缺失突变体为材料进行了相关实验，结果如图所示。

实验中强光照射时对野生型和突变体光照的强度相同，且强光对二者的PSⅡ均造成了损伤。

(1)该实验的自变量为。

该实验的无关变量中，影响光合作用强度的主要环境因素有（答出2个因素即可）。

(2)根据本实验，（填“能”或“不能”）比较出强光照射下突变体与野生型的PSⅡ活性强弱，理由是。

(3)据图分析，与野生型相比，强光照射下突变体中流向光合作用的能量（填“多”或“少”）。

若测得突变体的暗反应强度高于野生型，根据本实验推测，原因是。

浓度、温度【答案】(1) 光、H蛋白 CO2(2)不能突变体PSⅡ系统光损伤小但不能修复，野生型光PSⅡ系统损伤大但能修复(3)少突变体PNQ高，PSⅡ系统损伤小，虽然损伤不能修复，但是PSⅡ活性高，光反应产物多【解析】（1）据题意拟南芥的野生型和H基因缺失突变体为材料进行了相关实验，实验中强光照射时对野生型和突变体光照的强度相同，结合题图分析实验的自变量有光照、H蛋白；影响浓度、温度、水分等。

光合作用强度的主要环境因素有CO2（2）据图分析，强光照射下突变体的NPQ/相对值比野生型的NPQ/相对值高，能减少强光对PSⅡ复合体造成损伤。

但是野生型含有H蛋白，能对损伤后的PSⅡ进行修复，故不能确定强光照射下突变体与野生型的PSⅡ活性强弱。

目录历年英一小作文概况分析 (2)2018年英语一小作文：（邀请信） (3)2017年英语一小作文：（推荐信） (4)2016年英语一小作文：（通知） (5)2015年英语一小作文：（建议信） (6)2014年英语一小作文：（建议信） (7)2013年英语一小作文：（邀请信） (8)2012年英语一小作文：（建议信） (8)2011年英语一小作文：（推荐信） (10)2010年英语一小作文：（通知） (11)2009年英语一小作文：（建议信） (12)2008年英语一小作文：（道歉信） (13)2007年英语一小作文：（建议信） (14)2006年英语一小作文：（咨询信） (15)2005年英语一小作文：（辞职信） (16)历年英一小作文概况分析考研英语是从1980年开始的；英语小作文是从2005年出现的；而英语二是从2010年出现的。

本部分，学姐搜集了英语一05--18年的英语一小作文。

将小作文考题和范文都列了出来，并在范文中，将格式、固定句式、结构等关键部分均做了标记。

请学弟学妹们结合文档01 中提到的四大基本点认真去揣摩历年小作文的范文，对各种类型的小作文都要做到心里有数，然后再去针对性的练习。

历年小作文题材为：Directions:　Write an email to all international experts on campus, inviting them to attend the graduation ceremony. In your email, you should include the time, place and other relevant information about the ceremony.You should write about 100 words neatly on the ANWSER SHEET.Do not use your own name at the end of the email. U se “Li Ming” instead.Do not write the address .(10 points)Dear Sir or Madam, I am writing this letter in order to invite you to attend the forthcoming graduation ceremony. The ceremony will be hosted in the auditorium on our campus, at 10 o'clock in the morning on next Monday, January 15. It is advisable for you to dress formal. Please let us know your decision as soon as possible so that we could send you further details concerned. Since you are so popular among us that we sincerely hope you could accept this invitation and give the graduates a wonderful memory of our campus. If you are available, we request the honor of your company. It will be highly appreciated if you could give us an earliest favorable reply.Y ours sincerely,L i MingDirections:You are to write an email to James Cook, a newly-arrived Australian professor, recommending some tourist attractions in your city. Please give reasons for your recommendationYou should write neatly on the ANSWER SHEET.Do not sign your own name at the end of the email. Use “Li Ming” instead.Do not write the address.(10 points)Dear Professor,Welcome to Changchun, my hometown. I take great pleasure in recommending to you some terrific tourist attractions in Changbaishan, which is located in southern Jilin Province. The primary reasons of my recommendations are as follows.Changbaishan attracts millions of tourists every year for its exquisite natural beauty. For instance, “the Heavenly Lake” on the main peak of the Changbaishan, is the crater of a volcano, filled with clean and clear water all year around. Its extraordinary scenery brings people unforgettable experience. Furthermore, Changbaishan is also famous for a group of Hot Springs, in which people can relax themselves and release the pressure.Therefore, I don’t hesitate to recommend them to you. Hope you can really enjoy yourself and have fun.Yours sincerely,Li MingTo ensure students from oversea to be acquainted with the service of library in Beijing University, we write this notice to inform you of some relevant information about our library.To begin with , our library provides a large amount of books and materials covering not only most majors and subjects, but also many extra-curricular reading materials, thus satisfying all your reading requirements. Furthermore, the library opens during the week time, each day from 9:00 am to10:00pm. Last but not least, only students enrolled in this university and with a special Library Card are allowed to enter into our library.Anyone interested in studying or reading in our library should sign up their name with their monitor before August 31, and the Library Card will be issued within a week. Library of Beijing UniversityDirections:Suppose you are a librarian in your university. Write a notice of about 100 words, providing the newly-enrolled international students with relevant information about the library.You should write neatly on the ANWSER SHEET.Do not sign you own name at the end of the letter, use “Li Ming” instead. Do not write the address .(10 points) Notice August 20, 2015Directions:You are going to host a club reading session. Write an email of about 100 words recommending a book to the club members.You should state reasons for your recommendation.You should write neatly on the ANSWER SHEET.Do not sign your own name at the end of the letter. Use “Li Ming” instead.Do not write the address.（10 points）Dear members,I am writing to recommend you a great book, “Life Will Start from Tomorrow”, that I have just read recently, as I will hold a club reading session this weekend.The main reasons why I recommend this book are as follows.First and foremost, it is the story about two wheelchair girls, who are struggling, fighting against their destiny. We can learn perseverance from them. What’s more,its contents give us courage to face the difficulties we meet in our daily life.I really hope you will like it as I do and I am looking forward to discussing more with you.Sincerely yours,Li MingDirections:Write a letter of about 100 words to the president of your university, suggesting how to improve students’ physical condition.You should include the details you think necessary.You should write neatly on the ANSWER SHEET.Do not sign your own name at the end of the letter. Use “Li Ming” instead.Do not write the address.(10 points)Dear my president,I am writing to express my suggestions with regard to improve our students’ physical condition, and I will try to make some conductive suggestions here.In my personal level, I find no better suggestions other than the following two: In the first place, we should be offered more time to take physical exercise between lessons, even if in the cold winter. What’s more, if possible, our school can establish more sports activities in the afternoon to enhance our constitution, meanwhile it also can enrich our life.I hope you will find these proposals useful, and I hope that you take my suggestions into serious consideration.Yours sincerely,Li MingDirections:Write an e-mail of about 100 words to a foreign teacher in your college, invitinghim/her to be a judge for the upcoming English speech contest.You should include the details you think necessary.You should write neatly on the ANSWER SHEET.Do not sign your own name at the end of the e-mail, Use "Li Ming" instead.Do not write the address.(10 points)Dear Professor Wang,I am writing on behalf of our college to invite you to be a judge for the English speech contest which will be held next week.We know that you are admired by all the students. As college students, we would like to improve our abilities in spoken English as well as written English. We would be grateful if you could be the judge for this contest to be held in Room 102, the Teaching Building on Saturday, June 4th, at 7p.m.We trust you will be disengaged and able to give us the pleasure of your company. We are looking forward to seeing you.Yours sincerely,Li MingDirections:Some internationals students are coming to your university. Write them an email in the name of the Students’ Union to1)extend your welcome and2)provide some suggestions for their campus life here.You should write about 100 words on ANSWER SHEET2.Do not sign your name at the end of the letter. Use Li Ming instead.Do not write the address (10 points)Dear All,I am writing on behalf of our Student’s Association to send our warm welcome. And in order to make you adjust life in China, I am making some constructive advices with regard to the life in our university.To begin with, you’d better grasp the basic communicating vocabulary as much as possible so as to freely express yourself. In addition, you can read some books on Chinese customs and daily life style in case you feel uneasy once join a completely strange context. Finally, relax yourself and feel confident toward your future life.I hope you will find these proposals useful, and I would be ready to discuss this matter with you to further details.Yours sincerely,Li MingDirections:Write a letter to a friend of yours to1)recommend one of your favorite movies and2)give reasons for your recommendationYour should write about 100 words on ANSWER SHEET 2Do not sign your own name at the end of the letter. Use “LI MING” instead.Do not writer the address.(10 points)Dear friend,I am writing, without hesitation, to share one of my favorite movies, Forest Gump, with you, which is not only conducive to your study, but also beneficial to your life.For one thing, the beautiful language in this original English movie may contribute to your study of English in listening, speaking, reading and writing. For another thing, the profound cultural elements implicit in the scene will equip you with foreign cultural background and, above all, enrich your daily life.Would you like to see this movie after my recommendation? Remember to tell me your opinion about the movie. I am looking forward to your early reply.Yours,Li Ming2010年英语一小作文：（通知）Directions:You are supposed to write for the postgraduate association a notice to recruit volunteers for an international conference on globalization, you should conclude the basic qualification of applicant and the other information you think relative.You should write about 100 words.Do not sign your own name at the end of the letter. Use "postgraduate association" ins tead.NoticeNext month there will be an international meeting about global integration in our city. Forty volunteers are needed for the preparing work and service as desk clerks and guides. Any one who want to be one of the volunteers should have an interview.There are some requests below. First, fluent English is required. Both desk clerks and guides must communicate foreigners with English expertly. Second, patience is indispensable. You may face not only much important things, but also much trifle, and you should settle all down, especially the desk clerks. Third, enough time must be ensured because of train. If you are up to the mustard below, give us a call, and then you can have an interview for the chance of being a lucky volunteer. This notice is available until next Sunday.Postgraduates’ AssociationJan.9.2010Directions:Restrictions on the use of plastic bags have not been so successful in some regions. “White pollution” is still going on.Write a letter to the editor(s) of your local newspaper to1)give your opinions briefly, and2)make two or three suggestions.You should write about 100 words. Do not sign your own name at the end of the letter. Use "Li Ming" instead.Do not write the address. (10 points)Dear Editor,I am writing this letter to draw your attention to the deteriorating situation of "white pollution" in some regions despite the implementation of restrictions on the use of plastic bags.In order to put an effective stop to the wide spread of "white pollution", I would like to make the following suggestions. Firstly，the price of plastic bags should be further raised; Secondly,special government departments should be established to supervise the making and using of plastic bags to ensure they are used when really needed.I hope my suggestions would be of help and thank you for your attention.Sincerely Yours,Li MingDirections:You have just come back from Canada and found a music CD in your luggage that you forgot to return to Bob, your landlord there. Write him a letter to1)make an apology, and2)suggest a solution.You should write about 100 words on ANSWER SHEET 2.Do not sign your own name at the end of the letter. Use "Li Ming" instead.Do not write the address. (10 points)Dear Bob,I am writing the letter to inform you that I wish to extend my sincere apology to you. I am a tenant from China who had been living in your house in Canada for two weeks.First and foremost, I take this opportunity show my heartfelt appreciation to the kind assistance you render me during my stay in Canada. In addition, I borrowed one CD of Beethoven’s symphonies from you in Canada. Unfortunately, when I returned home, I found to my surprise that CD in my personal baggage due to my carelessness.To solve the problem, I would like to send this CD to you by Express Mail Service. Once again, please accept my sincere apology for any inconveniences I have caused. I hope the settlement of the matter will meet your wishes.Sincerely yours,Li MingDirections:Write a letter to your university library, making suggestions for improving its service.You should write about 100 words on ANSWER SHEET2.Do not sign your own name at the end of the letter. Use “Li Ming” instead.Do not write the address. (10 points)Dear Sir or Madam,I’m a student in the university and a loyal reader of this library. I’m writing to tell some of my ideas, which I hope to be helpful for you.I notice that many magazines in our library are out of date. It would be beneficial to us students if they could be updated in time. And I suggest introducing some new journals so as to bring new fresh air to the library. Furthermore, since we have a huge number of books, it is not easy to find the right one easily. However,if we can introduce some new searching means, such as implementing new information management system that would be useful.Thank you for taking time reading this letter and I’m looking forward to seeing some new changes soon.Sincerely Yours,Li MingDirections:You want to contribute to Project Hope by offering financial aid to a child in a remote area. Write a letter to the department concerned, asking them to help find a candidate. You should specify what kind of child you want to help and how you will carry out your plan.Write your letter in no less than 100 words. Write it neatly on ANSWER SHEET 2.Do not sign your own name at the end of the letter; use “Li Ming” instead.Do not write the address. (10 points)Dear Sir/Madam,I’m a teacher of Renmin University of China and I’d like to contribute to Project Hope by offering financial aid to a child in a remote part of your province. Therefore, I would be most grateful if you could send me information regarding such a child who has met the following requirements:First, he must be very poor and truly in need of help. Second, he must have the strong desire to improve things around him.Third,he must be healthy, happy and optimistic. Last but not the least is that he must be willing to return to his hometown to do something for it after graduation from university.I would send him money every year from this year on until he finishes his higher education. Your prompt reply to this letter would be highly appreciated. I’m looking forward to hearing from you soon.Sincerely Yours,Li MingDirections:Two months ago you got a job as an editor for the magazine Designs & fashions. But now you find that the work is not what you expected. You decide to quit. Write a letter to your boss, Mr. Wang, telling him your decision stating your reason(s), and making an apology.Write your letter with no less than 100 words.Write it neatly on ANSWER SHEET2.Do not sign your own name at the end of the letter, use “Li Ming” instead.You do not need to write the address. (10 points)Dear Mr. Wang,First of all, please allow me to express my deep sorry to you for my resignation.I do know that this will bring about much trouble to you so that I write to you for my explanation.I decided to quit for some reasons as follows. To begin with, the job as an editor for the magazine Designs & Fashions is not suitable to me. What’ s more,I am preparing for another degree and I prefer to further my study. Again, I apologize for my resignation to you!I am looking forward to your early reply.Sincerely yours,Li Ming。

专题05北京高考三角函数选填真题1.【2024年北京卷06】已知()()sin 0f x x ωω=>，()11f x =−，()21f x =，12min π||2x x −=，则ω=（ ） A. 1 B. 2 C. 3 D. 4【答案】B 2.【2024年北京卷12】已知ππ,63α⎡⎤∈⎢⎥⎣⎦，且α与β的终边关于原点对称，则cos β的最大值为________．由题意π2π,Z k k βα=++∈，从而()cos cos π2πcos k βαα=++=−，3.【2023年北京卷13】已知命题p:若α,β为第一象限角，且α>β，则tanα>tanβ．能说明p 为假命题的一组α,β的值为α= ，β= ． 【答案】 9π4π3单位圆因为f (x )=tanx 在(0,π2)上单调递增，若0<α0<β0<π2，则tanα0<tanβ0， 取α=2k 1π+α0,β=2k 2π+β0,k 1,k 2∈Z ，则tanα=tan (2k 1π+α0)=tanα0,tanβ=tan (2k 2π+β0)=tanβ0，即tanα<tanβ， 令k 1>k 2，则α−β=(2k 1π+α0)−(2k 2π+β0)=2(k 1−k 2)π+(α0−β0)， 因为2(k 1−k 2)π≥2π,−π2<α0−β0<0，则α−β=2(k 1−k 2)π+(α0−β0)>3π2>0，即k 1>k 2，则α>β.不妨取k 1=1,k 2=0,α0=π4,β0=π3，即α=9π4,β=π3满足题意.故答案为：9π4;π3. 4.【2022年北京卷05】已知函数f(x)=cos 2x −sin 2x ，则（ ）A ．f(x)在(−π2,−π6)上单调递减B ．f(x)在(−π4,π12)上单调递增C ．f(x)在(0,π3)上单调递减D ．f(x)在(π4,7π12)上单调递增【答案】C 5.【2022年北京卷13】若函数f(x)=Asinx −√3cosx 的一个零点为π3，则A =________；f(π12)=________． 【答案】 1 −√2 【解析】 ∵f(π3)=√32A −√32=0，∴A =1∴f(x)=sinx −√3cosx =2sin(x −π3) f(π12)=2sin(π12−π3)=−2sin π4=−√2 【三角函数性质灵活考查】（2022北京卷改编）若()sin f x A x x =关于3x π=对称，则A =________．【答案】3− 【解析】对称性运用 ∵f(2π3)=f(0)，∴A =−36. 【2021年北京07】函数f(x)=cosx −cos2x ，试判断函数的奇偶性及最大值（ ） A ．奇函数，最大值为2 B ．偶函数，最大值为2 C ．奇函数，最大值为98D ．偶函数，最大值为98【答案】D由题意，f(−x)=cos(−x)−cos(−2x)=cosx −cos2x =f(x)，所以该函数为偶函数， 又f(x)=cosx −cos2x =−2cos 2x +cosx +1=−2(cosx −14)2+98， 所以当cosx =14时，f(x)取最大值98. 7.【2021年北京13】若点P(cosθ,sinθ)与点Q(cos(θ+π6),sin(θ+π6))关于y 轴对称，写出一个符合题意的θ=___． 【答案】5π12（满足θ=5π12+kπ,k ∈Z 即可）8. 【2020年北京卷10】2020年3月14日是全球首个国际圆周率日（π Day ）．历史上，求圆周率π的方法有多种，与中国传统数学中的“割圆术”相似．数学家阿尔·卡西的方法是：当正整数n 充分大时，计算单位圆的内接正6n 边形的周长和外切正6n 边形（各边均与圆相切的正6n 边形）的周长，将它们的算术平均数作为2π的近似值．按照阿尔·卡西的方法，π的近似值的表达式是（ ）． A ．3n (sin 30°n +tan 30°n ) B ．6n (sin 30°n +tan 30°n) C ．3n (sin60°n+tan60°n)D ．6n (sin60°n+tan60°n)【答案】A单位圆内接正6n 边形的每条边所对应的圆周角为360°n×6=60°n，每条边长为2sin30°n，所以，单位圆的内接正6n 边形的周长为12nsin 30°n，单位圆的外切正6n 边形的每条边长为2tan 30°n，其周长为12ntan 30°n，∴2π=12nsin30°n +12ntan 30°n2=6n (sin 30°n+tan30°n)，则π=3n (sin 30°n+tan30°n).9.【2020年北京卷12】若函数f(x)=sin(x +φ)+cosx 的最大值为2，则常数φ的一个取值为________． 【答案】π2（2kπ+π2,k ∈Z 均可）【解析】因为f (x )=cosφsinx +(sinφ+1)cosx =√cos 2φ+(sinφ+1)2sin (x +θ)， 所以√cos 2φ+(sinφ+1)2=2，解得sinφ=1，故可取φ=π2.故答案为：π2（2kπ+π2,k ∈Z 均可）. 10. 【2019年北京文科06】设函数f (x )=cosx +bsinx （b 为常数），则“b =0”是“f (x )为偶函数”的（ ） A ．充分而不必要条件 B ．必要而不充分条件C ．充分必要条件D ．既不充分也不必要条件【答案】C解：设函数f (x )=cosx +bsinx （b 为常数）， 则“b ＝0”⇒“f (x )=cosx 为偶函数”，“f （x ）为偶函数”⇒()()f x f x =− ，cos sin cos sin x b x x b x ∴+=−，cos sin cos sin x b x x b x ∴+=−sin sin b x b x ∴=−，2sin 0b x ∴=对任意x 成立；∴0b =11. 【2019年北京文科08】如图，A ，B 是半径为2的圆周上的定点，P 为圆周上的动点，∠APB 是锐角，大小为β，图中阴影区域的面积的最大值为（ ）A.44cos ββ+B.44sin ββ+C.22cos ββ+D.22sin ββ+【答案】B解：由题意可得22AOB APB β∠=∠=，要求阴影区域的面积的最大值，即为直线QO ⊥AB ，即有QO ＝2，Q 到线段AB 的距离为22cos β+，224AB sin sin ββ==，扇形AOB 的面积为12•2β•4=4β，△ABQ 的面积为12(2+2cosβ)•4sinβ=4sinβ+4sinβcosβ=4sinβ+2sin2β，即有阴影区域的面积的最大值为4β+4sin β． 12. 【2019年北京理科09】函数2()2f x sin x =的最小正周期是 ． 【答案】π213. 【2018年北京理科07】在平面直角坐标系中，记d 为点P(cosθ.sinθ)到直线x −my −2=0的距离．当θ、m 变化时，d 的最大值为（ ）A ．1B ．2C ．3D ．4【答案】C 解：法一：由题意d =|cosθ−msinθ−2|√12+m 2=|√m 2+1sin(θ+α)−2|√m 2+1，tan α=1m =yx ，∴当sin (θ+α)=−1时，d max ＝1+2√m 2+1≤3．∴d 的最大值为3．法二： P 点在单位圆221x y +=上动，圆心到直线距离的最大值（圆心到过定点的距离）+半径 14. 【2018年北京理科11】设函数π()cos()6f x x ω=−(0)ω>．若π()()4f x f ≤对任意的实数x 都成立，则ω的最小值为___________.ω⋅π4−π6=2kπ，k ∈Z ，解得ω=8k +23 15. 【2018年北京文科07】在平面直角坐标系中，AB ̂，CD ̂，EF ̂，GH ̂是圆221x y +=上的四段弧（如图），点P 其中一段上，角α以Ox 为始边，OP 为终边．若tan cos sin ααα<<，则P 所在的圆弧是（ ）A ．AB ̂ B ．CD ̂C ．EF ̂D ．GH ̂ 【答案】C解：A ．在AB 段，正弦线小于余弦线，即cos α＜sin α不成立，故A 不满足条件． B ．在CD 段正切线最大，则cos α＜sin α＜tan α，故B 不满足条件． C ．在EF 段，正切线，余弦线为负值，正弦线为正， 满足tan α＜cos α＜sin α，D ．在GH 段，正切线为正值，正弦线和余弦线为负值， 满足cos α＜sin α＜tan α不满足tan α＜cos α＜sin α． 16. 【2017年北京理科12】在平面直角坐标系xOy 中，角α与角β均以Ox 为始边，它们的终边关于y 轴对称，若sinα=13，则cos (α−β)= ．解：方法一：∵角α与角β均以Ox 为始边，它们的终边关于y 轴对称，方法二：∵sinα=13，当α在第一象限时，cosα=2√23， ∵α，β角的终边关于y 轴对称，∴β在第二象限时，sinβ=sinα=13，cosβ=−cosα=−2√23， ∴cos (α−β)=cosαcosβ+sinαsinβ=−2√23×2√23+13×13=−7917. 【2016年北京理科07】将函数sin(2)3y x π=−图象上的点(,)4t π向左平移s (0)s >个单位长度得到点'P .若'P 位于函数sin 2y x =的图象上，则A.12t =,s 的最小值为6πB.t =,s 的最小值为6πC.12t =,s 的最小值为3π D.t =,s 的最小值为3π【答案】A将x =π4代入得：t =sin π6=12，将函数y =sin (2x −π3)图象上的点P 向左平移s 个单位， 得到P ′（π4−s ，12）点，若P ′位于函数y =sin2x 的图象上， 则sin （π2−2s ）=cos2s =12，则2s =±π3+2k π，k ∈Z ， 则s =±π6+k π，k ∈Z ，由s ＞0得：当k ＝0时，s 的最小值为π618. 【2014年北京理科14】设函数()sin()(,,f x A x A ωϕωϕ=+是常数,0,0A ω>>).若()f x 在区间ππ[,]62上具有单调性,且π2ππ()()()236f f f ==−,则()f x 的最小正周期为 . 【答案】π．则x =π2离最近对称轴距离为7π12−π2=π12．又f （π2）＝﹣f （π6），则f （x ）有对称中心（π3，0）， 由于f （x ）在区间[π6，π2]上具有单调性，则π2−π6≤12T ⇒T ≥2π3，从而7π12−π3=T 4⇒T ＝π．。

一、名词解释1.临界荷载：指允许地基产生一定范围塑性变形区所对应的荷载。

（02、07、09、11、13）2.临塑荷载：是指基础边缘地基中刚要出现塑性变形时基底单位面积上所承受的荷载，是相当于地基土中应力状态从压密阶段过度到剪切阶段的界限荷载。

（03、04、05、06、08、10）3.最佳含水量：在一定击实功作用下，土被击实至最大干重度，达到最大压实效果时土样的含水量。

（02-13）4.临界水头梯度：土开始发生流沙现象时的水力梯度。

（02、03、04、06、08、10、11）i cr=5.砂流现象：土体在向上渗流力的作用下，颗粒间有效应力为零，颗粒发生悬浮移动的现象。

（05、07、09、13）6.灵敏度：以原状土的无侧限抗压强度与同一土经过重塑后（完全扰动，含水量不变）的无侧限抗压强度之比。

（02）S t=7.地基土的容许承载力：保证地基稳定的条件下，建筑物基础或者土工建筑物路基的沉降量不超过允许值（考虑一定安全储备后的）的地基承载力。

（03）8.主动土压力：当挡土墙向离开土体方向偏移至土体达到极限平衡状态时，作用在墙上的土压力。

（04、10）9.有效应力原理：1 土的有效应力σ′总是等于总应力σ减去孔隙水压力U2 土的有效应力控制了土的变形及强度性质。

（05-13）10.先期固结压力：土层历史上曾经承受的最大固结压力，也就是土体在固结过程中所承受的最大有效应力。

（03）11.正常固结土：土的自重应力（P0）等于土层先期固结压力(Pc)。

也就是说，土自重应力就是该土层历史上受过的最大有效应力。

（ORC=1）（04、07、09、11、13）12.超固结土：土的自重应力小于先期固结压力。

也就是说，该土层历史上受过的最大有效应力大于土自重应力。

(ORC>1)（05、08）13.欠固结土：土层的先期固结压力小于土层的自重应力。

也就是说该土层在自重作用下的固结尚未完成。

(ORC<1)（02、06、10）14.土层的固结度：在某一深度z处，有效应力σzt’与总应力p的比值，也即超静空隙水压力的消散部分与起始超空隙水压力的比值。

南京工业大学810化工原理真题1、(08考题)精馏操作时，增大回流比R，其他操作条件不变，则精馏段液气比L/V将( ) [单选题] *A.增大(正确答案)B.不变C.不确定D.减小2、(07考题)某精馏操作的进料状况由饱和液体变为冷液体时，其他条件不变，理论塔板数的变化是( ) [单选题] *A.增多B. 不变C.不确定D. 减小(正确答案)3、(05考题)精馏操作中，回流比从最小回流比逐渐增大时，精馏总费用的变化情况是( ) [单选题] *A.减小B.增大C.先减小后增大(正确答案)D.先增大后减小4、(09考题)精馏段操作线和提馏段操作线的交点恰好落在平衡线上时，精馏操作的( ) [单选题] *A.回流比无穷大，所需塔板数无限多B.回流比无穷小，所需塔板数无限小C.回流比最小，所需塔板数无穷多(正确答案)D. 回流比最小，所需踏板数最少5、(04考题)某连续精馏塔，F不变而xF减小欲保持xD和xW不变，则D将( ) [单选题] *A.增多B.减小(正确答案)C.不变D.无法确定6、(09考题)某连续精馏塔，若F不变而XF减小，欲保持XD和Xw不变，则回流比R需要( ) [单选题] *A.增大(正确答案)B.减小C.不变D.先增大后减小7、双组分连续精馏计算中，q的变化将引起( )的变化。

[单选题] *A.平衡线与q线B.平衡线与精馏段操作线C.平衡线与提馏段操作线D.q线与提馏段操作线(正确答案)8、某二元混合物，α=3，全回流条件下xn=0.3，yn+1=( )。

[单选题] *A、0.9；B、0.3；(正确答案)C、0.854；D、0.794。

9、其他条件不变的情况下，增大回流比能( )。

[单选题] *A、减少操作费用；B、增大设备费用；C、提高产品纯度；(正确答案)D、增大塔的生产能力。

10、加大回流比，塔顶轻组分组成将( )。

[单选题] *A、不变；B、变小；C、变大；(正确答案)D、忽大忽小。