数学专业英语第二版课后答案

2-A Why study geometry?Why do we study geometry? The student beginning the study of this text may well ask, "What is geometry? What can I expect to gain from this study?2-A为什么研究几何学？为什么我们研究几何学？刚开始学习这篇文章的学生会疑问，“几何是什么？研究几何我们能学到什么呢？Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools.许多居领导地位的学术机构承认，所有学习这个数学分支的人都将得到很好的收益。

事实是，他们需要学习几何作为学校入学考试的先决条件。

Geometry had its origin long ago in the measurements by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning "earth," and metron, meaning "measure." As early as 2000 B. C. we find the land surveyors of these people reestablishing vanishing landmarks and boundaries by utilizing the truths of geometry.很早以前，几何学源于测量被尼罗河的洪水淹没了的巴比伦人和埃及人的土地。

数学专业英语课后答案2.1数学、方程与比例词组翻译1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place汉译英（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。

2.12.比:ratio 比例:proportion 利率:interest rate 速率:speed 除:divide 除法:division 商:quotient 同类量:like quantity 项:term 线段:line segment 角:angle 长度:length 宽:width高度:height 维数:dimension 单位:unit 分数:fraction 百分数:percentage3.(1)一条线段和一个角的比没有意义,他们不是相同类型的量.(2)比较式通过说明一个量是另一个量的多少倍做出的,并且这两个量必须依据相同的单位.(5)为了解一个方程,我们必须移项,直到未知项独自处在方程的一边,这样就可以使它等于另一边的某量.4.(1)Measuring the length of a desk, is actually comparing the length of the desk to that of a ruler.(3)Ratio is different from the measurement, it has no units. The ratio of the length and the width of the same book does not vary when the measurement unit changes.(5)60 percent of students in a school are female students, which mean that 60 students out of every 100 students are female students.2.22.初等几何:elementary geometry 三角学:trigonometry 余弦定理:Law of cosines 勾股定理/毕达哥拉斯定理:Gou-Gu theorem/Pythagoras theorem 角:angle 锐角:acute angle 直角:right angle 同终边的角:conterminal angles 仰角:angle of elevation 俯角:angle of depression 全等:congruence 夹角:included angle 三角形:triangle 三角函数:trigonometric function直角边:leg 斜边:hypotenuse 对边:opposite side 临边:adjacent side 始边:initial side 解三角形:solve a triangle 互相依赖:mutually dependent 表示成:be denoted as 定义为:be defined as3.(1)Trigonometric function of the acute angle shows the mutually dependent relations between each sides and acute angle of the right triangle.(3)If two sides and the included angle of an oblique triangle areknown, then the unknown sides and angles can be found by using the law of cosines.(5)Knowing the length of two sides and the measure of the included angle can determine the shape and size of the triangle. In other words, the two triangles made by these data are congruent.4.(1)如果一个角的顶点在一个笛卡尔坐标系的原点并且它的始边沿着x轴正方向，这个角被称为处于标准位置.(3)仰角和俯角是以一条以水平线为参考位置来测量的,如果正被观测的物体在观测者的上方,那么由水平线和视线所形成的角叫做仰角.如果正被观测的物体在观测者的下方,那么由水平线和视线所形成的的角叫做俯角.(5)如果我们知道一个三角形的两条边的长度和对着其中一条边的角度,我们如何解这个三角形呢?这个问题有一点困难来回答,因为所给的信息可能确定两个三角形,一个三角形或者一个也确定不了.2.32.素数:prime 合数:composite 质因数:prime factor/prime divisor 公倍数:common multiple 正素因子: positive prime divisor 除法算式:division equation 最大公因数:greatest common divisor(G.C.D) 最小公倍数: lowest common multiple(L.C.M) 整除:divide by 整除性:divisibility 过程:process 证明:proof 分类:classification 剩余:remainder辗转相除法:Euclidean algorithm 有限集:finite set 无限的:infinitely 可数的countable 终止:terminate 与矛盾:contrary to3.(1)We need to study by which integers an integer is divisible, that is , what factor it has. Specially, it is sometime required that an integer is expressed as the product of its prime factors.(3)The number 1 is neither a prime nor a composite number;A composite number in addition to being divisible by 1 and itself, can also be divisible by some prime number.(5)The number of the primes bounded above by any given finite integer N can be found by using the method of the sieve Eratosthenes.4.(1)数论中一个重要的问题是哥德巴赫猜想,它是关于偶数作为两个奇素数和的表示.(3)一个数,形如2p-1的素数被称为梅森素数.求出5个这样的数.(5)任意给定的整数m和素数p,p的仅有的正因子是p和1,因此仅有的可能的p和m的正公因子是p和1.因此,我们有结论:如果p是一个素数,m是任意整数,那么p整除m,要么(p,m)=1.2.42.集:set 子集:subset 真子集:proper subset 全集:universe 补集:complement 抽象集:abstract set 并集:union 交集:intersection 元素:element/member 组成:comprise/constitute包含:contain 术语:terminology 概念:concept 上有界:bounded above 上界:upper bound 最小的上界:least upper bound 完备性公理:completeness axiom3.(1)Set theory has become one of the common theoretical foundation and the important tools in many branches of mathematics.(3)Set S itself is the improper subset of S; if set T is a subset of S but not S, then T is called a proper subset of S.(5)The subset T of set S can often be denoted by {x}, that is, T consists of those elements x for which P(x) holds.(7)This example makes the following question become clear, that is, why may two straight lines in the space neither intersect nor parallel.4.(1)设N是所有自然数的集合,如果S是所有偶数的集合,那么它在N中的补集是所有奇数的集合.(3)一个非空集合S称为由上界的,如果存在一个数c具有属性:x<=c对于所有S中的x.这样一个数字c被称为S的上界.(5)从任意两个对象x和y，我们可以形成序列（x，y），它被称为一个有序对，除非x=y，否则它当然不同于（y，x）.如果S和T是任意集合，我们用S*T表示所有有序对（x,y),其中x术语S，y属于T.在R.笛卡尔展示了如何通过实轴和它自己的笛卡尔积来描述平面的点之后，集合S*T被称为S和T的笛卡尔积.2.52.竖直线:vertical line 水平线:horizontal line 数对:pairs of numbers 有序对:ordered pairs 纵坐标:ordinate 横坐标:abscissas 一一对应:one-to-one 对应点:corresponding points圆锥曲线:conic sections 非空图形:non vacuous graph 直立圆锥:right circular cone 定值角:constant angle 母线:generating line 双曲线:hyperbola 抛物线:parabola 椭圆:ellipse退化的:degenerate 非退化的:nondegenerate任意的:arbitrarily 相容的:consistent 在几何上:geometrically 二次方程:quadratic equation 判别式:discriminant 行列式:determinant3.(1)In the planar rectangular coordinate system, one can set up aone-to-one correspondence between points and ordered pairs of numbers and also a one-to-one correspondence between conic sections and quadratic equation.(3)The symbol can be used to denote the set of ordered pairs（x，y）such that the ordinate is equal to the cube of the abscissa.（5）According to the values of the discriminate，the non-degenerate graph of Equation （iii） maybe known to be a parabola， a hyperbolaor an ellipse.4.（1）在例1，我们既用了图形，也用了代数的代入法解一个方程组（其中一个方程式二次的，另一个是线性的）。

1-A What is mathematics1-A 数学是什么？Mathematics comes from man' s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics.数学来源于人类的社会实践，例如，工农业生产，商业活动，军事行动和科学技术研究。

总之，数学服务于实践且在众多领域扮演重要角色。

没有数学的应用，现代科学技术分支也不会得到广泛地发展。

From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land, and trigonometry came from problems of surveying. To deal with some more complex practical problems, man established and then solved equation with unknown numbers, thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, i. e. geometry, trigonometry and algebra, in which only the constants were considered.早期数字的概念和形成源于人类的需要。

最全的全新版大学英语第二版综合教程2答案课后练习答案Unit1 Ways of LearningPart II Reading TaskComprehensionContent QuestionPair Work1. They were studying arts education in Chinese kindergartens and elementary schools in Nanjing.2. Their 18-month-old son Benjamin was fond of trying to place the key into the slot of the key box during their stay at the Jinling Hotel.3. They would come over to watch Benjamin and then try to teach him how to do it properly.4. Because he realized that this anecdote was directly relevant to their assigned tasks in China: to investigate early childhood education and to throw light on Chinese attitudes toward creativity.5. Most of them displayed the same attitude as the staff at the Jinling Hotel.6. He emphasized that the most important thing is to teach the child that on can solve a problem effectively byoneself.7. He means that this incident pointed to important differences in educational and artistic practices between China and the USA.8. The manner in which the Chinese staff saw the need to teach the child by guiding his hand in the characteristic of a broader attitude to education, one that stands in contrast to the Western preference for leaving the child to explore and learn unaided.9. One example is of children at the age of 5 or 6 painting flowers, fish and animals skillfully and confidently; in a second example, calligraphers 9 and 10 yearsold were producing works; and in a third, young artists work on perfecting their craft for several hours a day.10. Americans think that unless creativity has been acquired early, it may never emerge, and skills can be picked up later. Chinese think that if skills are not acquired early, they may never be acquired, and there is no hurry to promote creativity.11. This is mainly due to the difference in their way of thinking.12. The author makes the suggestion that we should strikea better balance between the poles of creativity and basic skills.Text OrganizationWorking On Your Own1) The text begins with an anecdote.2) His thoughts are mainly about different approaches to learning in China and the West.3) He winds up the text with a suggestion in the form of a question.2. Chinese1) Show a child how to do something, or tech by holding the hand2) Give greater priority to developing skills at an early age, believing that creativity can be promoted over time Americans1) Teach children that they should rely on themselves for solutions to problems2) Put more emphasis on fostering creativity in young children, thinking skills can be picked up laterLanguage Sense Enhancement(1) Summarizing(2) value originality and independence(3) contrast between(4) in terms of(5) harbor(6) fearful(7) comparable(8) promote creativity(9) emerge(10) picked up Language Focus VocabularyI1) insert2) on occasion3) investigate4) In retrospect5) initial6) phenomena7) attached8) make up for9) is awaiting10) not; in the least11) promote12) emerged1) a striking contrast between the standards of living in the north of the country and the south.2) is said to be superior to synthetic fiber.3) as a financial center has evolved slowly.4) is not relevant to whether he is a good lawyer.5) by a little-known sixteen-century Italian poet have found their way into some English magazines.1) be picked up; can’t accomplish; am exaggerating2) somewhat; the performance; have neglected; they apply to3) assist; On the other hand; are valid; a superior II1) continual2) continuous3) continual4) continuous1) principal2) principal3) principle4) principles5) principalIII1. themselves2. himself/herself3. herself/by herself/on her own4. itself5. ourselves6. yourself/by yourself/on your own Comprehensive ExercisesI. cloze(1) contrast(2) exaggerating(3) priority(4) on the other hand(5) promoting(6) pick up(7) assist(8) accomplish(9) occasion(10) neglecting(11) worthwhile(12) superior0-(2) perform(3) facing(4) competent(5) equipped(6) designed(7) approach(8) rest(9) definitely(10) qualityII. translation(1) It takes an enormous amount of courage to make a departure from the tradition.(2) Tom used to be very shy, but this time he was boldenough to give a performance in front of a large audience.(3) Many educators think it desirable to foster the creative spirit in the child at an early age.(4) Assuming this painting really is a masterpiece, do you think it’s worthwhile to buy it?(5) If the data is statistically valid, it will throw light on the problem we are investigating.To improve our English, it is critical to do more reading, writing, listening and speaking. Besides, learning by heart as many well-written essays as possible is also very important. Without an enormous store of good English writing in your head you cannot express yourself freely in English. It is also helpful to summarize our experience as we go along, for in so doing, we can figure out which way of learning is more effective and will produce the most desirable result. As long as we keep working hard on it, we will in due course accomplish the task of mastering English.Unit2 ValuesPart II Reading TaskComprehensionContent QuestionPair Work1. The Salvation Army is a religious charitable organization. A Salvation Army bell ringer is a volunteer who help it collect donations.2. The boy asked him: Are you poor? He did it simply out of confusion and curiosity. Obviously he knew nothing about the Salvation Army bell ringer.3. He said, “I have more than some people, but not as much as others.” This means that he was neither poor nor rich.4. The boy’s mother scolded him because the question was social inappropriate, especially to a person who looked poor.5. Yes, economically he is poor. He lives in a small basement apartment. He doesn’t even have a color TV. He falls into the lowest income category. And so on.6. No, the writer does not feel poor. This is because he has enjoyed good health and creativity which he thinks are much more important than material goods.7. He feels out of place among people who are primarily interested in material things.8. She told him that she was interested in what’s on the inside. but after he took her to his poorly furnishedapartment, she changed her mind completely.9. It only shows that to her the most important thing was still material goods rather than what she had claimed before.10. Commercial can put people under pressure to purchase more than is really necessary.11. Because December is the time for to work for the Salvation Army as a bell ringer, which gives him a genuine sense of belonging and brings him happiness in helping others.12. The boy’s question has helped the writer realize that, despite his lack of expensive possessions, he is rich in many other ways and should be thankful for that.Text OrganizationWorking On Your Own1) a.√2) the essay is meant to explain something that is, the author’s view of life.3) That one can live a life full of riches without being rich financially.Part One: The writer’s encounter with a boy who raised thequestion “are you poor?”Part Two: In search of an answer the writer finds that not having expensive possessions doesn’t make him feel poor mainly because he enjoys life in many other ways.Part Three: In conclusion, the writer thinks he’s grown to understand more about himself because of the boy’s question. Language Sense Enhancement(1) attain(2) wear and tear(3) dependable(4) modest(5) primarily(6) minimal(7) exceptionally(8) illness-free(9) spirited(10) energizingLanguage FocusVocabularyI1) abrupt2) emotional3) bless4) wear and tear5) dated6) consequences7) seemingly8) in contrast to9) Curiosity10) genuine11) primarily12) sentiments1) confronted with more than one problem, try to solve the easiest one first.2) vital to the existence of all forms of life.3) some confusion among the students about what to do after class to follow up on the subject.4) nothing more than a job and an apartment to be happy.5) tickled him to think that she’d come to ask his advice1) a lingering; fabricating; sentiments2) fill out; every item; vital; consequences3) be denied; tangible; cherish; attainII1. It is a long trip and will take us five hours by bus.2. She arrived early and took a front row seat.3. Don’t take me for a fool.4. It takes a lot of imagination to fabricate such a story.5. My uncle will take me (along on his trip) to the Arctic this summer.6. He took the dinner plate I passed to him.7. Kevin took second prize in the weight-lifting competition.8. If you don’t take my advice, you will regret it. III1. hanging2. to give3. to return4. being praised5. not having written6. to say7. to open8. being helped Comprehensive ExercisesI. cloze(1) well-off/affluent(2) dated(3) falling into(4) bracket(5) deny(6) tangible(7) pursuit(8) cherishes(9) out of place(10) abrupt(11) focus(12) donations(1) consume(2) fueled(3) annual(4) plain(5) physically(6) security(7) indicates(8) equally(9) traditional(10) followsIII. Translation1) The company denied that its donations had a commercial purpose.2) Whenever he was angry, he would begin to stammer slightly.3) Education is the most cherished tradition in our family. That’s why my parents never took me to dinner at expensive restaurants, but sent me to the best private school.4) Shortly after he recovered from the surgery, he lost his job and thus had to go through another difficult phase of his life.5) In contrast to our affluent neighbors, my parents are rather poor, but they have always tried to meet our minimal needs.With more and more donations coming in, our university will be much better off financially next year. We will thus be able to focus on the most important task that we, educators, must take on: to encourage students to attain their scholarly/academic goals, to train them to be dependable and responsible individuals, to prepare them for the life ahead, and to guide them in their pursuit of spiritual as well as material satisfaction.Unit3 The Generation GapPart II Reading TaskComprehensionContent QuestionPair Work1. There are seven characters---Father, Mother, Heidi, Diane, Sean, Restaurant Manager, and Mrs. Higgins.2. No. Because what he does usually ends up embarrassing them.3. To buy a guitar.4. To check if Sean was going to embarrass him.5. He knew his father was going to embarrass him.6. It was unnecessary and embarrassing.7. He wanted Dan to pressure his son into asking Diane to the senior prom.8. He would speak to his son and insist that the latter give Diane a call.9. She felt humiliated.10. Because the Thompson had just moved.11. He tried to let her know how exceptionally talented a young woman Heidi was.12. Because she couldn’t bear being embarrassed by her father.Text OrganizationWorking On Your Own1. A fast-food restaurant2. The Thompson family dining room3. An office at a high schoolScene One: Father embarrassed Sean by talking too proudly to the restaurant manager.Scene Two: Father embarrassed Diane by persuading a colleague into pressing his son to ask her to the senior prom. Scene Three: Father embarrassed Heidi by boating to an officialat her new school about how talented she was. Language Sense Enhancement(1) once in a while(2) for(3) the problem(4) he thinks(5) humiliated(6) class president(7) have(8) Actually(9) stop to think(10) interferenceLanguage FocusVocabularyI1) typical2) dumb3) junior4) glorious5) welfare6) came over7) interference8) fading9) narrowed down10) frank11) schemes12) at any rate1) consists of five generals and four police officers.2) will be in a location overlooking the lake.3) was humiliated by her comments about my family background in front of so many people.4) have any proof that it was Henry who stole the computer?5) was exhausted after the long cycle ride.1) hysterical; was handed down by; should have known better than2) twisted; over and over; talented son3) patience; not to keep him in suspense; assured; repeatedlyII. Collocation1. adequate2. anxious3. certain4. content5. crazy6. likely7. fortunate8. keenIII. Usage1. be admitted2. live3. be postponed4. buy5. be banned6. be Comprehensive ExercisesI. cloze(1) typical(2) welfare(3) constant(4) frank5) talent(6) dumb(7) know better than that(8) repeatedly(9) dread(10) interference(11) bet(12) assure(1) despite(2) really(3) same(4) contact(5) admitted(6) attempt(7) not(8) tend(9) different(10) mannerII. Translation(1) Have scientists found proof of water on Mars?(2) The planning committee has narrowed down the possible locations for the nuclear power plant to two coastal towns.(3) Sam not only lost his job but also both legs; he had to live on welfare for the rest of his life.(4) A jury consisting of 12 members voted in unison that Mary was guilty.(5) Sean felt humiliated to hear his talent being questioned.George, the son of Mr. Johnson, liked listening to heavy metal music in the evenings, which made it hard for other residents in the community to fall asleep. Eventually the exhausted neighbors lost their patience and decided on direct interference. They called Mr. Johnson to tell him in a frank manner what they were thinking. Mr. Johnson assured them that he would certainly settle the issue. As soon as he put down the phone he scolded his son, “What has come over you? You should know better than to disturb others for your own amusement.” In the end George traded his CD’s for computer games software from his classmates.Unit4 The Virtual WorldPart II Reading TaskComprehensionContent QuestionPair Work1. She used to be a television producer, but now she is a writer.2. She writes and edits articles online, submits them via email, and communicates with colleagues via the Internet, too.3. She could stay computer-assisted at home for weeks, going out only t get mail, newspapers and groceries.4. They feel as if they had become one with the computer, and life seems to be unreal.5. That people who grew used to a virtual life would feel an aversion to outside forms of socializing.6. She gets overexcited, speaks too much, and interrupts others.7. She is bad-tempered, easily angered, and attacks everyone in sight, all because she has long become separated from others and lacks emotional face-to-face exchanges with people.8. She fights her boyfriend, misinterpreting his intentions because of the lack of emotional cues given by theirtyped dialogue.9. Because we rely on co-works for company.10. She calls people, arrangers to meet the few friends remaining in the City, gets to the gym, arranges interviews for stories, doctor’s appointments---anything to get her out of the house and connected with others.11. No, she doesn’t feel happy. She feels being face to face is intolerable.12. She makes her excuses and flees, re-enters her apartment, runs to the computer, clicks on the modem, and disappears into the virtual world again.Text OrganizationWorking On Your Own1. 2-32. 1,4-10,133. 114. 12The first paragraph describes the consequences of living a virtual life and the last tells of the author’s escape back into it. Together, they bring out the dilemma people at presentare in: Because of modern technology, we have a choice between a virtual life and real life, but find both unsatisfactory. Language Sense Enhancement(1) routine(2) for company(3) unemployment(4) externally(5) drug abuse(6) restore(7) fled(8) gym(9) set apart(10) appointmentsVocabularyI1) conversely2) but then3) symptom4) spitting5) abusing6) tone7) took; in8) editing9) have arranged10) in sight11) stretched12) data1) smoking cigarettes jars on me.2) find themselves getting sucked in.3) has arranged for a technician from the computer store to check and repair it.4) fled their country to avoid military service/fled to other countries to avoidmilitary service.5) restore people’s confidence in it.1) the virtual; on line; via2) nightmare; routine; any appointment; arrange for3) cue; remarks; his tuneII. Collocation1. We came here all the way on foot.2. Private cars are not allowed on campus.3. They are on vacation in Florida.4. Mary has been talking to her friend on the phone for an hour.5. Don’t worry, Lucy is always on time.6. Industrial demand on fuel is on the rise.III. Usage1. hard2. difficult3. impossible4. tough5. hard6. easyComprehensive ExercisesI. cloze(1) Internet(3) virtual(4) routines(5) arrange(6) nightmare(7) annoying(8) connection(9) crawls(10) take in(11) spit(12) data(13) sucked into(14) At times(15) flee(16) on line(1) companion(2) deliver(3) access(4) enables(5) customers(6) delights(7) provides(9) remote(10) information II. Translation 1.1) Research shows that laughter can bring a lot of health benefits.2) A show Internet connection speed is really annoying.3) As the law stands, helping someone commit suicide is a crime.4) In her report, Mary tries to interpret the data froma completely different angle.5) Sue is a girl of great talent. Her amazing memory sets her apart from her classmates.Perhaps you envy me for being able to work from home on the computer. I agree that the Internet has made my job a lot easier.I can write, submit and edit articles via email, chat with my colleagues on line and discuss work with my boss. With a click of the mouse, I can get all the data I need and keep up with the latest news. But then, communicating through the Net can be frustrating at times. The system may crash. Worse still, without the emotional cues of face-to-face communication, the typed words sometimes seem difficult to interpret.Unit5 Overcoming ObstaclesPart II Reading TaskComprehensionContent QuestionPair Work1. Because the pole was set at 17 feet which was three inches higher than his personal best.2. Because pole-vaulting combines the grace of a gymnast with the strength ofa body builder.3. His childhood dream was to fly. His mother read him numerous stories about flying when he was growing up.4. Because he believed in hard work and sweat. His motto: If you want something, work for it!5. Michael's mother wished he could relax a bit more and be that "free dreaming" little boy. On one occasion she attempted to talk to him and his father about this, but his dad quickly interrupted, smiled and said, "You want something, work for it!"6. He began a very careful training program.7. He seemed unaware of the fact that he had just beaten his personal best by three inches. He was very calm.8. He began to feel nervous when the bar was set at nine inches higher than his personal best.9. What his mother had taught him about how to deal with tension or anxiety helped him overcome his nervousness.10. The singing of some distant birds in flight made him associate his final jump with his childhood dream.11. He could imagine the smile on his mother’s face. He thought his father was probably smiling too, even laughing. However, in fact, his father hugged his wife and cried likea baby in her arms.12. Because he was blind.Text OrganizationWorking On Your OwnPart One: Michael faced the most challenging competition in his pole-vaulting career.Part Two: Michael’s childhood was marked with dreams and tough training.Part Three: Michael topped his personal best, won the championship and set a new world record.(1) It also has the element of flying, and the thought of flying as high as a two-story building is a mere fantasy to anyone watching such an event.As long as Michael could remember he had always dreamed of flying.(2) All of Michael’s vaults today seemed to be the reward for his hard work.Language Sense Enhancement(1) startled(2) bale of hay(3) off(4) intensity(5) shaking the tension(6) tense(7) description(8) out of nowhere(9) pictured(10) scaredVocabularyI1) startled2) mere3) motion4) sweating5) stretched out6) vain7) On the occasion8) anxiety9) emotions10) ashamed of11) In my mind’s eye12) recurring1) coincides with her husband’s.2) sends the prices soaring/results in the soaring of prices.3) of alternate sunshine and rain.4) have been his lifelong passions, although he studied economics at university.5) Tension came over her1) media; dedication to; grace2) his competitors; in excitement; hug him; congratulate him on3) emotions; numerous; intensity; passion forII. CollocationMike, a Green, made the suggestion that a large parkbe built near the community.2. In a letter to his daughter, Mr. Smith expressed his wish that she (should) continue her education to acquire still another degree.3. There is no reason to hold the belief that humans have no direct moral responsibility to safeguard the welfare of animals.4. Children need to feel safe about the world they grow up in, and it is unwise to give them the idea that everything they come into contact with might be a threat.5. Anxiety can result from the notion that life has not treated us fairly.6. Nobody believed his claim that he was innocent. III. Words with Multiple Meanings1. I work out in the gym for one hour every morning.2. Florence has worked as a cleaner at the factory for five years.3. The wounded man worked his way across the field on his hands and knees.4. The safe load for a truck of this type works out at about twenty-five tons.5. It is difficult to understand how human minds work.6. To my disappointment, the manager’s plan of promoting the new products doesn’t work at all.7. The teacher has a lot of experience of working with children who don’t know how to learn.8. The medicine was like magic, and it worked instantly after you took it.Comprehensive ExercisesI. cloze(1) In my mind’s eye(2) groan(3) competitor(4) intensity(5) anxiety(6) tense(7) sweat(8) tension(9) soaring(10) recurring(11) brought me back to earth(12) fantasy(13) sweat(14) congratulate(15) number(16) media(1) engineer(2) forget(3) convinced(4) how(5) build(6) accident(7) thought(8) only(9) sharp(10) touched(11) instructions(12) finallyII. Translation1) It is the creativity and dedication of the workers and executives that turned the company into a profitable business.2) The prices of food and medicine have soared in thepast three months.3) We plan to repaint the upper floors of the office building.4) His success shows that popularity and artistic merit sometimes coincide.5) I don’t want to see my beloved grandmother lying in a hospital bed and groaning painfully.Numerous facts bear out the argument/statement/claim that in order to recover speedily from negative emotion, you should allow yourself to cry. You needn’t/don’t have to be ashamed of crying. Anxiety and sorrow can flow out of the body along with tears.Consider the case of/Take Donna. Her son unfortunately died in a car accident. The intensity of the blow made her unable to cry. She said, “It was not until two weeks later that I began to cry. And then I felt as if a big stone had been lifted from my shoulders. It was the tears that brought me back to earth and helped me survive the crisis.”Unit6 Women, Half the SkyPart II Reading TaskComprehensionContent QuestionPair Work1. They liked girly toys such as a miniature kitchen, and Barbies.2. To convert a gas-guzzling SUV into a hybrid electric vehicle.3. Because she didn’t know anything about cars and was afraid of being cheated by the mechanic.4. She was craving independence and wanted to live away from home for some time.5. It helped her earn six engineering credits, which of course made it easier for her to become an engineering major.6. Five years.7. In her view, if you find a subject is difficult to learn, it does not mean you’re not good at it. It just means you have to set your mind and work harder to get good at it.8. Because he had confidence in her abilities believing she could have done better if she had studied more.9. No, she wasn’t always confident. She had moments of panic, worried that asa woman she would be unable to understand thermodynamics.10. She considers it wrong because it is based on a faultypremise.11. It is flexible and more powerful than we imagine.12. What she means is not to accept others’ opinions blindly but to use one’s own judgment.Text OrganizationWorking On Your OwnPart One: The author describes how she stumbled into engineering.Part Two: The author writes about how she has overcome obstacles, including the bias against women, on her way to success.Part Three: The author draws the conclusion that women can do anything men can so long as they believe in their own abilities.1) she was not a tomboy.not to an engineering department.she didn’t know the first thing about engineering. because she craved independence from her parents.already earned her six credits in engineering.2) math and design.she participated in a national competition to convert an SUVnto a hybrid electric vehicle.work harder at it.that she should study more.had to work hard at courses she found difficult, which encouraged her to keep going.Language Sense Enhancement(1) limit(2) denying(3) favor(4) others(5) relevant(6) translating(7) hard and fast conclusions(8) focus(9) incredibly flexible(10) consider the possibilityVocabularyI1) cultural/culture2) indication3) miniature4) ironic5) stumbled into6) decent7) buzzing8) abnormal9) mechanical10) Shuddering11) implied12) leap1) convert RMB into US dollars in the foreign exchange office at the airport.2) didn’t know the first thing about cooking as she looked puzzled as to how to cook rice with the rice cooker.3) their faulty equipment the team had accomplished some very useful work.4) allowing me to work flexible hours as long as I work eight hours a day.5) couldn’t help thinking the book must be quitefascinating.1) will not panic/feel panic; ’ll be at a disadvantage2) hybrid; transmissions3) crave; One indication; to distinguishII. Synonyms in Context1. also2. as well/too3. too。

数学专业英语课后答案1、He kept walking up and down, which was a sure（）that he was very worried. [单选题] *A. sign(正确答案)B. characterC. natureD. end2、20．Jerry is hard-working. It’s not ______ that he can pass the exam easily. [单选题] * A．surpriseB．surprising (正确答案)C．surprisedD．surprises3、--What’s the weather like today?--It’s _______. [单选题] *A. rainB. windy(正确答案)C. sunD. wind4、Many of my classmates are working _______volunteers. [单选题] *A. as(正确答案)B. toC. atD. like5、Mary is interested ______ hiking. [单选题] *A. onB. byC. in(正确答案)D. at6、We need a _______ when we travel around a new place. [单选题] *A. guide(正确答案)B. touristC. painterD. teacher7、While they were in discussion, their manager came in by chance. [单选题] *A. 抓住时机C. 碰巧(正确答案)D. 及时8、Our campus is _____ big that we need a bike to make it. [单选题] *A. veryB. so(正确答案)C. suchD. much9、57．Next week will be Lisa's birthday. I will send her a birthday present ________ post. [单选题] *A．withB．forC．by(正确答案)D．in10、The manager demanded that all employees _____ on time. [单选题] *A. be(正确答案)B. areC. to be11、He has two sisters but I have not _____. [单选题] *A. noneB. someC. onesD. any(正确答案)12、______! It’s not the end of the world. Let’s try it again.（）[单选题] *A. Put upB. Set upC. Cheer up(正确答案)D. Pick up13、My brother usually _______ his room after school. But now he _______ soccer. [单选题] *A. cleans; playsB. cleaning; playingC. cleans; is playing(正确答案)D. cleans; is playing the14、The museum is _______ in the northeast of Changsha. [单选题] *A. sitB. located(正确答案)C. liesD. stand15、______ my great joy, I met an old friend I haven' t seen for years ______ my way ______ town. [单选题] *A. To, in, forB. To, on, to(正确答案)C. With, in, toD. For, in, for16、In the closet（）a pair of trousers his parents bought for his birthday. [单选题] *A. lyingB. lies(正确答案)c. lieD. is lain17、44．—Hi, Lucy. You ________ very beautiful in the new dress today.—Thank you very much. [单选题] *A．look(正确答案)B．watchC．look atD．see18、They all choose me ______ our class monitor.（）[单选题] *A. as(正确答案)B. inC. withD. on19、My mother’s birthday is coming. I want to buy a new shirt ______ her.（）[单选题] *A. atB. for(正确答案)C. toD. with20、--Could you please tell me _______ to get to the nearest supermarket?--Sorry, I am a stranger here. [单选题] *A. whatB. how(正确答案)C. whenD. why21、?I am good at schoolwork. I often help my classmates _______ English. [单选题] *A. atB. toC. inD. with(正确答案)22、He was very excited to read the news _____ Mo Yan had won the Nobel Prize for literature [单选题] *A. whichB. whatC. howD. that(正确答案)23、Becky is having a great time ______ her aunt in Shanghai. （）[单选题] *A. to visitB. visitedC. visitsD. visiting(正确答案)24、In the future, people ______ a new kind of clothes that will be warm when they are cold, and cool when they’re hot.（）[单选题] *A. wearB. woreC. are wearingD. will wear(正确答案)25、This message is _______. We are all _______ at it. [单选题] *A. surprising; surprisingB. surprised; surprisedC. surprising; surprised(正确答案)D. surprised; surprising26、Your homework must_______ tomorrow. [单选题] *A. hand inB. is handed inC. hands inD. be handed in(正确答案)27、Since the war their country has taken many important steps to improve its economic situation. [单选题] *A. 制定B. 提出C. 讨论D. 采取(正确答案)28、How _______ Grace grows! She’s almost as tall as her mother now. [单选题] *A. cuteB. strongC. fast(正确答案)D. clever29、_____ is not known yet. [单选题] *A. Although he is serious about itB. No matter how we will do the taskC. Whether we will go outing or not(正确答案)D. Unless they come to see us30、You cannot see the doctor _____ you have made an appointment with him. [单选题] *A. exceptB.evenC. howeverD.unless(正确答案)。

最全的全新版大学英语第二版综合教程2答案课后练习答案Unit1 Ways of LearningPart II Reading TaskComprehensionContent QuestionPair Work1. They were studying arts education in Chinese kindergartens and elementary schools in Nanjing.2. Their 18-month-old son Benjamin was fond of trying to place the key into the slot of the key box during their stay at the Jinling Hotel.3. They would come over to watch Benjamin and then try to teach him how to do it properly.4. Because he realized that this anecdote was directly relevant to their assigned tasks in China: to investigate early childhood education and to throw light on Chinese attitudes toward creativity.5. Most of them displayed the same attitude as the staff at the Jinling Hotel.6. He emphasized that the most important thing is to teach the child that on can solve a problem effectively byoneself.7. He means that this incident pointed to important differences in educational and artistic practices between China and the USA.8. The manner in which the Chinese staff saw the need to teach the child by guiding his hand in the characteristic of a broader attitude to education, one that stands in contrast to the Western preference for leaving the child to explore and learn unaided.9. One example is of children at the age of 5 or 6 painting flowers, fish and animals skillfully and confidently; in a second example, calligraphers 9 and 10 years old were producing works; and in a third, young artists work on perfecting their craft for several hours a day.10. Americans think that unless creativity has been acquired early, it may never emerge, and skills can be picked up later. Chinese think that if skills are not acquired early, they may never be acquired, and there is no hurry to promote creativity.11. This is mainly due to the difference in their way of thinking.12. The author makes the suggestion that we shouldstrike a better balance between the poles of creativity and basic skills.Text OrganizationWorking On Your Own1.1) The text begins with an anecdote.2) His thoughts are mainly about different approaches to learning in China and the West.3) He winds up the text with a suggestion in the form of a question.2. Chinese1) Show a child how to do something, or tech by holding the hand2) Give greater priority to developing skills at an early age, believing that creativity can be promoted over timeAmericans1) Teach children that they should rely on themselves for solutions to problems2) Put more emphasis on fostering creativity in young children, thinking skills can be picked up later Language Sense Enhancement(2) value originality and independence(3) contrast between(4) in terms of(5) harbor(6) fearful(7) comparable(8) promote creativity(9) emerge(10) picked upLanguage FocusVocabularyI1.1) insert2) on occasion3) investigate4) In retrospect5) initial6) phenomena7) attached8) make up for10) not; in the least11) promote12) emerged2.1) a striking contrast between the standards of living in the north of the country and the south.2) is said to be superior to synthetic fiber.3) as a financial center has evolved slowly.4) is not relevant to whether he is a good lawyer.5) by a little-known sixteen-century Italian poet have found their way into some English magazines.3.1) be picked up; can’t accomplish; am exaggerating2) somewhat; the performance; have neglected; they apply to3) assist; On the other hand; are valid; a superiorII1.1) continual2) continuous3) continual2.1) principal2) principal3) principle4) principles5) principalIII1. themselves2. himself/herself3. herself/by herself/on her own4. itself5. ourselves6. yourself/by yourself/on your own Comprehensive ExercisesI. cloze1.(1) contrast(2) exaggerating(3) priority(4) on the other hand(5) promoting(6) pick up(7) assist(8) accomplish(9) occasion(10) neglecting(11) worthwhile(12) superior2.0-(2) perform(3) facing(4) competent(5) equipped(6) designed(7) approach(8) rest(9) definitely(10) qualityII. translation1.(1) It takes an enormous amount of courage to make a departure from the tradition.(2) Tom used to be very shy, but this time he was bold enough to give a performance in front of a large audience.(3) Many educators think it desirable to foster the creative spirit in the child at an early age.(4) Assuming this painting really is a masterpiece, do you think it’s worthwhile to buy it?(5) If the data is statistically valid, it will throw light on the problem we are investigating.2.To improve our English, it is critical to do more reading, writing, listening and speaking. Besides, learning by heart as many well-written essays as possible is also very important. Without an enormous store of good English writing in your head you cannot express yourself freely in English. It is also helpful to summarize our experience as we go along, for in so doing, we can figure out which way of learning is more effective and will produce the most desirable result. As long as we keep working hard on it, we will in due course accomplish the task of mastering English.Unit2 ValuesPart II Reading TaskComprehensionContent QuestionPair Work1. The Salvation Army is a religious charitable organization. A Salvation Army bell ringer is a volunteer who help it collect donations.2. The boy asked him: Are you poor? He did it simply out of confusion and curiosity. Obviously he knew nothing about the Salvation Army bell ringer.3. He said, “I have more than some people, but not as much as others.”This means that he was neither poor nor rich.4. The boy’s mother scolded him because the question was social inappropriate, especially to a person who looked poor.5. Yes, economically he is poor. He lives in a small basement apartment. He doesn’t even have a color TV. He falls into the lowest income category. And so on.6. No, the writer does not feel poor. This is because he has enjoyed good health and creativity which he thinks are much more important than material goods.7. He feels out of place among people who are primarily interested in material things.8. She told him that she was interested in what’s on the inside. but after he took her to his poorly furnished apartment, she changed her mind completely.9. It only shows that to her the most important thing was still material goods rather than what she had claimed before.10. Commercial can put people under pressure to purchase more than is really necessary.11. Because December is the time for to work for the Salvation Army as a bell ringer, which gives him a genuine sense of belonging and brings him happiness in helping others.12. The boy’s question has helped the writer realize that, despite his lack of expensive possessions, he is rich in many other ways and should be thankful for that.Text OrganizationWorking On Your Own1.1) a.√2) the essay is meant to explain something that is, the author’s view of life.3) That one can live a life full of riches withoutbeing rich financially.2.Part One: The writer’s encounter with a boy who raised the question “are you poor?”Part Two: In search of an answer the writer finds that not having expensive possessions doesn’t make him feel poor mainly because he enjoys life in many other ways.Part Three: In conclusion, the writer thinks he’s grown to understand more about himself because of the boy’s question.Language Sense Enhancement1.(1) attain(2) wear and tear(3) dependable(4) modest(5) primarily(6) minimal(7) exceptionally(8) illness-free(9) spirited(10) energizingLanguage FocusVocabularyI1.1) abrupt2) emotional3) bless4) wear and tear5) dated6) consequences7) seemingly8) in contrast to9) Curiosity10) genuine11) primarily12) sentiments2.1) confronted with more than one problem, try to solve the easiest one first.2) vital to the existence of all forms of life.3) some confusion among the students about what to do after class to follow up on the subject.4) nothing more than a job and an apartment to be happy.5) tickled him to think that she’d come to ask his advice3.1) a lingering; fabricating; sentiments2) fill out; every item; vital; consequences3) be denied; tangible; cherish; attainII1. It is a long trip and will take us five hours by bus.2. She arrived early and took a front row seat.3. Don’t take me for a fool.4. It takes a lot of imagination to fabricate such a story.5. My uncle will take me (along on his trip) to the Arctic this summer.6. He took the dinner plate I passed to him.7. Kevin took second prize in the weight-lifting competition.8. If you don’t take my advice, you will regret it. III1. hanging2. to give3. to return4. being praised5. not having written6. to say7. to open8. being helped Comprehensive ExercisesI. cloze1.(1) well-off/affluent(2) dated(3) falling into(4) bracket(5) deny(6) tangible(7) pursuit(8) cherishes(9) out of place(10) abrupt(11) focus(12) donations2.(1) consume(2) fueled(3) annual(4) plain(5) physically(6) security(7) indicates(8) equally(9) traditional(10) followsIII. Translation1.1) The company denied that its donations had a commercial purpose.2) Whenever he was angry, he would begin to stammer slightly.3) Education is the most cherished tradition in our family. That’s why my parents never took me to dinner at expensive restaurants, but sent me to the best private school.4) Shortly after he recovered from the surgery, helost his job and thus had to go through another difficult phase of his life.5) In contrast to our affluent neighbors, my parents are rather poor, but they have always tried to meet our minimal needs.2.With more and more donations coming in, our university will be much better off financially next year. We will thus be able to focus on the most important task that we, educators, must take on: to encourage students to attain their scholarly/academic goals, to train them to be dependable and responsible individuals, to prepare them for the life ahead, and to guide them in their pursuit of spiritual as well as material satisfaction.Unit3 The Generation GapPart II Reading TaskComprehensionContent QuestionPair Work1. There are seven characters---Father, Mother, Heidi, Diane, Sean, Restaurant Manager, and Mrs. Higgins.2. No. Because what he does usually ends upembarrassing them.3. To buy a guitar.4. To check if Sean was going to embarrass him.5. He knew his father was going to embarrass him.6. It was unnecessary and embarrassing.7. He wanted Dan to pressure his son into asking Diane to the senior prom.8. He would speak to his son and insist that the latter give Diane a call.9. She felt humiliated.10. Because the Thompson had just moved.11. He tried to let her know how exceptionally talenteda young woman Heidi was.12. Because she couldn’t bear being embarrassed by her father.Text OrganizationWorking On Your Own1.1. A fast-food restaurant2. The Thompson family dining room3. An office at a high school2.Scene One: Father embarrassed Sean by talking too proudly to the restaurant manager.Scene Two: Father embarrassed Diane by persuading a colleague into pressing his son to ask her to the senior prom.Scene Three: Father embarrassed Heidi by boating to an official at her new school about how talented she was. Language Sense Enhancement1.(1) once in a while(2) for(3) the problem(4) he thinks(5) humiliated(6) class president(7) have(8) Actually(9) stop to think(10) interferenceLanguage FocusVocabularyI1.1) typical2) dumb3) junior4) glorious5) welfare6) came over7) interference8) fading9) narrowed down10) frank11) schemes12) at any rate2.1) consists of five generals and four police officers.2) will be in a location overlooking the lake.3) was humiliated by her comments about my family background in front of so many people.4) have any proof that it was Henry who stole the computer?5) was exhausted after the long cycle ride.3.1) hysterical; was handed down by; should have known better than2) twisted; over and over; talented son3) patience; not to keep him in suspense; assured; repeatedlyII. Collocation1. adequate2. anxious3. certain4. content5. crazy6. likely7. fortunate8. keenIII. Usage1. be admitted2. live3. be postponed4. buy5. be banned6. beComprehensive ExercisesI. cloze1.(1) typical(2) welfare(3) constant(4) frank(5) talent(6) dumb(7) know better than that(8) repeatedly(9) dread(10) interference(11) bet(12) assure2.(1) despite(2) really(3) same(4) contact(5) admitted(6) attempt(7) not(8) tend(9) different(10) mannerII. Translation1.(1) Have scientists found proof of water on Mars?(2) The planning committee has narrowed down the possible locations for the nuclear power plant to two coastal towns.(3) Sam not only lost his job but also both legs; he had to live on welfare for the rest of his life.(4) A jury consisting of 12 members voted in unison that Mary was guilty.(5) Sean felt humiliated to hear his talent being questioned.2.George, the son of Mr. Johnson, liked listening to heavy metal music in the evenings, which made it hard for other residents in the community to fall asleep. Eventually the exhausted neighbors lost their patience and decided on direct interference. They called Mr. Johnson to tell him in a frank manner what they were thinking. Mr. Johnsonassured them that he would certainly settle the issue. As soon as he put down the phone he scolded his son, “What has come over you? You should know better than to disturb others for your own amusement.”In the end George traded his CD’s for computer games software from his classmates.Unit4 The Virtual WorldPart II Reading TaskComprehensionContent QuestionPair Work1. She used to be a television producer, but now she is a writer.2. She writes and edits articles online, submits them via email, and communicates with colleagues via the Internet, too.3. She could stay computer-assisted at home for weeks, going out only t get mail, newspapers and groceries.4. They feel as if they had become one with the computer, and life seems to be unreal.5. That people who grew used to a virtual life wouldfeel an aversion to outside forms of socializing.6. She gets overexcited, speaks too much, and interrupts others.7. She is bad-tempered, easily angered, and attacks everyone in sight, all because she has long become separated from others and lacks emotional face-to-face exchanges with people.8. She fights her boyfriend, misinterpreting his intentions because of the lack of emotional cues given by their typed dialogue.9. Because we rely on co-works for company.10. She calls people, arrangers to meet the few friends remaining in the City, gets to the gym, arranges interviews for stories, doctor’s appointments---anything to get her out of the house and connected with others.11. No, she doesn’t feel happy. She feels being face to face is intolerable.12. She makes her excuses and flees, re-enters her apartment, runs to the computer, clicks on the modem, and disappears into the virtual world again.Text OrganizationWorking On Your Own1.1. 2-32. 1,4-10,133. 114. 122.The first paragraph describes the consequences of living a virtual life and the last tells of the author’s escape back into it. Together, they bring out the dilemma people at present are in: Because of modern technology, we have a choice between a virtual life and real life, but find both unsatisfactory.Language Sense Enhancement1.(1) routine(2) for company(3) unemployment(4) externally(5) drug abuse(6) restore(7) fled(8) gym(9) set apart(10) appointmentsVocabularyI1.1) conversely2) but then3) symptom4) spitting5) abusing6) tone7) took; in8) editing9) have arranged10) in sight11) stretched12) data2.1) smoking cigarettes jars on me.2) find themselves getting sucked in.3) has arranged for a technician from the computer store to check and repair it.4) fled their country to avoid military service/fled to other countries to avoid military service.5) restore people’s confidence in it.3.1) the virtual; on line; via2) nightmare; routine; any appointment; arrange for3) cue; remarks; his tuneII. Collocation1. We came here all the way on foot.2. Private cars are not allowed on campus.3. They are on vacation in Florida.4. Mary has been talking to her friend on the phone for an hour.5. Don’t worry, Lucy is always on time.6. Industrial demand on fuel is on the rise.III. Usage1. hard2. difficult3. impossible4. tough5. hard6. easy Comprehensive ExercisesI. cloze1.(1) Internet(2) click(3) virtual(4) routines(5) arrange(6) nightmare(7) annoying(8) connection(9) crawls(10) take in(11) spit(12) data(13) sucked into(14) At times(15) flee(16) on line2.(1) companion(2) deliver(3) access(4) enables(5) customers(6) delights(7) provides(8) small(9) remote(10) informationII. Translation1.1) Research shows that laughter can bring a lot of health benefits.2) A show Internet connection speed is really annoying.3) As the law stands, helping someone commit suicide is a crime.4) In her report, Mary tries to interpret the data from a completely different angle.5) Sue is a girl of great talent. Her amazing memory sets her apart from her classmates.2.Perhaps you envy me for being able to work from home on the computer. I agree that the Internet has made my job a lot easier. I can write, submit and edit articles via email, chat with my colleagues on line and discuss work with my boss. With a click of the mouse, I can get all the data I need and keep up with the latest news. But then, communicating through the Net can be frustrating at times. The system may crash. Worse still, without the emotional cues of face-to-face communication, the typed words sometimes seem difficult to interpret.Unit5 Overcoming ObstaclesPart II Reading TaskComprehensionContent QuestionPair Work1. Because the pole was set at 17 feet which was three inches higher than his personal best.2. Because pole-vaulting combines the grace of a gymnast with the strength of a body builder.3. His childhood dream was to fly. His mother read him numerous stories about flying when he was growing up.4. Because he believed in hard work and sweat. His motto: If you want something, work for it!5. Michael's mother wished he could relax a bit more and be that "free dreaming" little boy. On one occasion she attempted to talk to him and his father about this, but his dad quickly interrupted, smiled and said, "You want something, work for it!"6. He began a very careful training program.7. He seemed unaware of the fact that he had just beaten his personal best by three inches. He was very calm.8. He began to feel nervous when the bar was set at nine inches higher than his personal best.9. What his mother had taught him about how to deal with tension or anxiety helped him overcome his nervousness.10. The singing of some distant birds in flight made him associate his final jump with his childhood dream.11. He could imagine the smile on his mother’s face. He thought his father was probably smiling too, even laughing. However, in fact, his father hugged his wife and cried like a baby in her arms.12. Because he was blind.Text OrganizationWorking On Your Own1.Part One: Michael faced the most challenging competition in his pole-vaulting career.Part Two: Michael’s childhood was marked with dreams and tough training.Part Three: Michael topped his personal best, won the championship and set a new world record.2.(1) It also has the element of flying, and the thought of flying as high as a two-story building is a mere fantasy to anyone watching such an event.As long as Michael could remember he had always dreamed of flying.(2) All of Michael’s vaults today seemed to be the reward for his hard work.Language Sense Enhancement1.(1) startled(2) bale of hay(3) off(4) intensity(5) shaking the tension(6) tense(7) description(8) out of nowhere(9) pictured(10) scaredVocabularyI1.1) startled2) mere3) motion4) sweating5) stretched out6) vain7) On the occasion8) anxiety9) emotions10) ashamed of11) In my mind’s eye12) recurring2.1) coincides with her husband’s.2) sends the prices soaring/results in the soaring of prices.3) of alternate sunshine and rain.4) have been his lifelong passions, although he studied economics at university.5) Tension came over her3.1) media; dedication to; grace2) his competitors; in excitement; hug him; congratulate him on3) emotions; numerous; intensity; passion forII. Collocation1. Mike, a Green, made the suggestion that a large park be built near the community.2. In a letter to his daughter, Mr. Smith expressed his wish that she (should) continue her education to acquire still another degree.3. There is no reason to hold the belief that humans have no direct moral responsibility to safeguard the welfare of animals.4. Children need to feel safe about the world they grow up in, and it is unwise to give them the idea that everything they come into contact with might be a threat.5. Anxiety can result from the notion that life has not treated us fairly.6. Nobody believed his claim that he was innocent. III. Words with Multiple Meanings1. I work out in the gym for one hour every morning.2. Florence has worked as a cleaner at the factory for five years.3. The wounded man worked his way across the field on his hands and knees.4. The safe load for a truck of this type works out at about twenty-five tons.5. It is difficult to understand how human minds work.6. To my disappointment, the manager’s plan of promoting the new products doesn’t work at all.7. The teacher has a lot of experience of working with children who don’t know how to learn.8. The medicine was like magic, and it workedinstantly after you took it. Comprehensive ExercisesI. cloze1.(1) In my mind’s eye(2) groan(3) competitor(4) intensity(5) anxiety(6) tense(7) sweat(8) tension(9) soaring(10) recurring(11) brought me back to earth(12) fantasy(13) sweat(14) congratulate(15) number(16) media2.(1) engineer(2) forget(3) convinced(4) how(5) build(6) accident(7) thought(8) only(9) sharp(10) touched(11) instructions(12) finallyII. Translation1.1) It is the creativity and dedication of the workers and executives that turned the company into a profitable business.2) The prices of food and medicine have soared in the past three months.3) We plan to repaint the upper floors of the office building.4) His success shows that popularity and artistic merit sometimes coincide.5) I don’t want to see my beloved grandmother lying in a hospital bed and groaning painfully.2.Numerous facts bear out the argument/statement/claim that in order to recover speedily from negative emotion, you should allow yourself to cry. You needn’t/don’t have to be ashamed of crying. Anxiety and sorrow can flow out of the body along with tears.Consider the case of/Take Donna. Her son unfortunately died in a car accident. The intensity of the blow made her unable to cry. She said, “It was not until two weeks later that I began to cry. And then I felt as if a big stone had been lifted from my shoulders. It was the tears that brought me back to earth and helped me survive the crisis.”Unit6 Women, Half the SkyPart II Reading TaskComprehensionContent QuestionPair Work1. They liked girly toys such as a miniature kitchen, and Barbies.2. To convert a gas-guzzling SUV into a hybridelectric vehicle.3. Because she didn’t know anything about cars and was afraid of being cheated by the mechanic.4. She was craving independence and wanted to live away from home for some time.5. It helped her earn six engineering credits, which of course made it easier for her to become an engineering major.6. Five years.7. In her view, if you find a subject is difficult to learn, it does not mean you’re not good at it. It just means you have to set your mind and work harder to get good at it.8. Because he had confidence in her abilities believing she could have done better if she had studied more.9. No, she wasn’t always confident. She had moments of panic, worried that as a woman she would be unable to understand thermodynamics.10. She considers it wrong because it is based on a faulty premise.11. It is flexible and more powerful than we imagine.12. What she means is not to accept others’opinions blindly but to use one’s own judgment.Text OrganizationWorking On Your Own1.Part One: The author describes how she stumbled into engineering.Part Two: The author writes about how she has overcome obstacles, including the bias against women, on her way to success.Part Three: The author draws the conclusion that women can do anything men can so long as they believe in their own abilities.2.1) she was not a tomboy.not to an engineering department.she didn’t know the first thing about engineering. because she craved independence from her parents. already earned her six credits in engineering.2) math and design.she participated in a national competition to convert an SUV into a hybrid electric vehicle.work harder at it.that she should study more.had to work hard at courses she found difficult, which encouraged her to keep going.Language Sense Enhancement1.(1) limit(2) denying(3) favor(4) others(5) relevant(6) translating(7) hard and fast conclusions(8) focus(9) incredibly flexible(10) consider the possibilityVocabularyI1.1) cultural/culture2) indication3) miniature4) ironic5) stumbled into6) decent7) buzzing8) abnormal9) mechanical10) Shuddering11) implied12) leap2.1) convert RMB into US dollars in the foreign exchange office at the airport.2) didn’t know the first thing about cooking as she looked puzzled as to how to cook rice with the rice cooker.3) their faulty equipment the team had accomplished some very useful work.4) allowing me to work flexible hours as long as I work eight hours a day.5) couldn’t help thinking the book must be quite fascinating.3.1) will not panic/feel panic; ’ll be at a disadvantage。

数学专业英语【第二版】1- A 什么是数学数学来自于人的社会实践，例如，工业和农业生产、商业活动、军事行动和科研工作。

与数学反过来，为实践服务和所有字段中的伟大作用。

没有现代的科学和技术分支机构可以定期制定中的数学，应用无早有需要的人来了数字和形式的概念。

然后，开发出的几何土地和三角测量的问题来自测量的问题。

若要对付一些更复杂的实际问题，男子成立，然后解决方程未知号码，因此代数发生。

17 世纪前, 男子向自己限于小学数学，即几何、三角和代数，只有常量被认为在其中。

17 世纪产业的快速发展促进了经济和技术的进展和所需变量的数量、处理从常量到带来两个分支的数学-解析几何和微积分，属于高等数学，现在有很多分支机构，其中有数学分析、高等代数、微分方程的高等数学中的可变数量的飞跃函数理论等。

数学家研究理念和主张。

所有命题公理、假设、定义和定理都。

符号是一种特殊和功能强大的数学工具，用于表示很多时候的理念和主张。

公式、数字和图表是阿拉伯数字1,2,3,4,5,6,7,8,9,0 与另外的符号"+"、减法"-"，乘"*"，除"\"和平等"="。

数学中的结论得到主要由逻辑推理和计算。

长期的数学史上，以中心地点的数学方法被占领逻辑扣除。

现在，由于电子计算机是迅速发展和广泛应用，计算的作用变得越来越多重要。

在我们这个时代计算不只用于处理大量的信息和数据，而且还进行一些只是可以做的工作较早前的逻辑推理，例如，大部分的几何定理的证明。

1--B 方程方程是平等的语句的两个相等的数字或数字符号之间。

因此(a-5）= 一5a 和x 3 = 5 是方程。

方程的两种——身份和方程的条件。

方程的算术或代数的身份。

这种方程中两名成员是相似的或成为相似的指示操作的性能。

因此12-2=2+8,(m+n)(m-n) = m n 是身份。

1—c 比与测量今天的思想沟通往往根据编号和数量的比较。

全新版大学英语第二版综合教程课后练习答案详解精编W O R D版 IBM system office room 【A0816H-A0912AAAHH-GX8Q8-GNTHHJ8】Key to Exercises of College English Book 2全新版大学英语(第二版)综合教程2课后练习答案Unit 1★ Text AVocabularyI.1.1) insert 2) on occasion 3) investigate 4) In retrospect 5) initial 6) phenomena7) attached 8) make up for 9) is awaiting 10) not…in the least 11) promote 12) emerged2. 1) There is a striking contrast between the standards of living in the north of the country and thesouth.2) Natural fiber is said to be superior to synthetic fiber.3) The city’s importance as a financial center has evolved slowly.4) His nationality is not relevant to whether he is a good lawyer.5) The poems by a little-known sixteenth-century Italian poet have found their way into someEnglish magazines.3. 1) be picked up, can’t accomplish, am exaggerating2) somewhat, performance, have neglected, they apply to3) assist, On the other hand, are valid, a superiorII.1. 1) continual 2) continuous 3) continual 4) continuous2. 1) principal 2) principal 3) principle 4) principles 5) principalIII.1. themselves2. himself/herself3. herself/by herself/on her own4. itself5. ourselves6. yourself/ by yourself/on your ownComprehensive ExerciseI. Cloze1. 1) contrast 2) exaggerating 3) priority 4) on the other hand 5) promoting 6) pick up 7) assist 8) accomplish 9) on occasion 10) neglecting11) worthwhile 12) superior2. 1) end 2) perform 3) facing 4) competent 5) equipped6) designed 7) approach 8) rest 9) definitely 10) quality1.1) It takes an enormous amount of courage to make a departure from the tradition.2) Tom used to be very shy, but this time he was bold enough to give a performance in front ofa large audience.3) Many educators think it desirable to foster the creative spirit in the child at an early age.4) Assuming (that) this painting really is a masterpiece, do you think it’s worthwhile tobuy/purchase it?5) If the data is statistically valid, it will throw light on the problem we are investigating.2. To improve our English, it is critical to do more reading, writing, listening and speaking.Besides, learning by heart as many well-written essays as possible is also very important.Without an enormous store of good English writing in your head you cannot express yourself freely in English. It is also helpful to summarize our experience as we go along, for in so doing, we can figure out which way of learning is more effective and will produce the most desirable result. As long as we keep working hard on it, we will in due course accomplish the task of mastering English.★ Text BComprehension check: c c d a c b1.g h e c f a b d2.1) adopt 2) account 3) from your point of view 4) ended up 5) furthermore 6) fund 7) annual8) keeping track of 9) pace 10) intends11) perspective 12) deviseUnit 2★ Text AVocabularyI. 1. 1) abrupt 2) emotional 3) bless 4) wear and tear 5) dated6）consequences 7）seemingly 8) in contrast to 9) Curiosity 10) genuine 11) primarily 12) sentiments2. 1) When you are confronted with more than one problem, try to solve the easiest one first.2) Water is vital to the existence of all forms of life.3) There is still some confusion among the students about what to do after class to follow upon the subject.4) As a person of simple living habits, he needs nothing more than a job and an apartment tobe happy.5) It tickled him to think that she’d come to as his advice.3. 1) a lingering, fabricating, sentiments2) fill out, every item, vital, consequences3) be denied, tangible, cherish, attainII.1.It’s a long trip and will take us five hours by bus.2.She arrived early and took a front row seat.3.Don’t take me for a fool.4.It takes a lot of imagination to fabricate such a story.5.My uncle will take me (along on his trip) to the Arctic this summer.6.He took the dinner plate I passed to him.7.Kevin took second prize in the weight-lifting competition.8.If you don’t take my advice, you will regret it.III.1.hanging2. to give3. to return4. being praised5. not having written6. to say7. to open8. being helpedComprehensive ExerciseI.1. 1) well-off/affluent 2) dated 3) falling into 4) bracket 5) deny6) tangible 7) pursuit 8) cherishes 9) out of place 10) abrupt11) focus 12) donations2. 1) consume 2) fueled 3) annual 4) plain 5) physically 6) security7) indicates 8) equally 9) traditional 10) followsII. Translation1.1) The company denied that its donations had a commercial purpose.2) Whenever he was angry, he would begin to stammer slightly.3) Education is the most cherished tradition in our family. That’s why my parents never tookme to dinner at expensive restaurants, but sent me to the best private school.4) Shortly after he recovered from the surgery, he lost his job and thus had to go throughanother difficult phase of his life.5) In contrast to our affluent neighbors, my parents are rather poor, but they have always triedhard to meet our minimal needs.2. With more and more donations coming in, our university will be much better off financiallynext year. We will thus be able to focus on the most important task that we, educators, must take on: to encourage students to attain their scholarly/academic goals, to train them to bedependable and responsible individuals, to prepare them for the life ahead, and to guide them in their pursuit of spiritual as well as material satisfaction.★ Text BComprehension Check: b b d c d dLanguage Practice1.f c g e b a h d2.1) stunned 2) hold (fast) to 3) folks 4) generosity 5) discount 6) liable7) ranks 8) on the run 9) make up 10) blends in 11) by all accounts 12) comes intocontact withUnit 3★ Text AVocabularyI.1．1) typical 2)dumb 3) junior 4) glorious 5) welfare 6)came over 7) interference 8)fading 9) narrowed down 10) frank 11)schemes 12) at any rate2. 1) The Security council consists of five generals and four police officers.2) The new hotel will be in a location overlooking the lake.3) I was humiliated by her comments about my family background in front of so many people.4) Do you have any proof that it was Henry who stole the computer?5) the boy was exhausted after the long cycle ride.3. 1) hysterical; was handed down; should have known better than2) twisted, over and over, talented son3) patience, not to keep him in suspense, assured, repeatedlyII.1.adequate2. anxious3. certain4. content5. crazy6. likely7. fortunate8. keenIII.1.be admitted2. live3. be postponed4. buy5. be banned6. beComprehensive ExerciseI. 1. 1) typical 2) welfare 3) constant 4) frank 5) talent 6) dumb7) know better than that 8) repeatedly 9) dread 10) interference 11) bet 12) assure2. 1) despite 2) really 3) same 4) contact 5) admitted 6) attempt7) not 8) tend 9) different 10) mannerII. Translation1. 1) Have scientists found proof of water on Mars?2) The planning committee has narrowed down the possible locations for the nuclear power plantto two coastal towns.3) Sam not only lost his job but also both legs; he had to live on welfare for the rest of his life.4) A jury consisting of 12 members voted in unison that Mary was guilty.5) Sean felt humiliated ti hear his talent being questioned.2. George, the son of Mr. Johnson, liked listening to heavy metal music in the evenings, whichmade it hard for other residents in the community to fall asleep. Eventually the exhaustedneighbors lost their patience and decided on direct interference. They called Mr. Johnson to tell him in a frank manner what they were thinking. Mr. Johnson assured them that he wouldcertainly settle the issue. As soon as he put down the phone he scolded his son, “What has come over youYou should know better than to disturb others for your own amusement.” In the end George traded his CD’s for computer games software from his classmates.★ Text BComprehension Check: b a b c d aLanguage Practice1. d e f g a b h c2. 1) and he like 2) popularity 3) had been kept in the dark 4) define 5) was aware of 6)relate 7)were up to 8) trend 9)opportunity 10)mobile 11)comments12) interviewedUnit 4★ Text AVocabularyI.1. 1) conversely 2). but then 3) symptom 4) spitting 5) abusing 6) tone7) took…in 8) editing 9) have arranged 10) in sight 11) stretched 12) data2. 1) The sight of teenagers smoking cigarettes jars on me.2) A lot of American teenagers don’t like street gangs, but they find themselves gettingsucked in.3) Jeffrey’s computer crashed again this morning. The manager has arranged for a technicianfrom the computer store to check and repair it.4) During the Vietnam War, many young Americans fled their country to avoid militaryservice/fled to other countries to avoid military service.5) The new government is planning an anti-corruption campaign so as to restore people’sconfidence in it.3. 1) the virtual, on line, via 2) nightmare, routine, any appointment, arrange for3) cue, remarks, his tuneII. 1. We came here all the way on foot.2. Private cars are not allowed on campus.3. They are on vocation in Florida.4. Mary has been talking to her friend on the phone for an hour.5. Don’t worry, Lucy is always on time.6. Industrial demand on fuel is on the rise.III. 1. hard 2. difficult 3. impossible 4. tough 5. hard 6. easyComprehensive ExerciseI.1. 1) internet 2) click 3) virtual 4) routines 5) arrange 6) nightmare 7) annoying 8) connection 9)crawls 10) take in 11) spit 12) data 13) sucked into 14) At times 15) flee 16) on line2. 1) companion 2) deliver 3) access 4) enables 5) customers 6) delights 7) provides 8) small 9)remote 10) informationII. Translation1. 1) Research shows that laughter can bring a lot of health benefits.2) A slow Internet connecting speed is really annoying.3) As the law stands, helping someone commit suicide is a crime.4) In her report, Mary tries to interpret the data from a completely different angle.5) Sue is a girl of great talent. Her amazing memory sets her apart from her classmates.2. Perhaps you envy me for being able to work from home on the computer. I agree that theInternet has made my job a lot easier. I can write，submit and edit articles via email, chat with my colleagues on line and discuss work with my boss. With a click of the mouse, I can get all thedata I need and keep up with the latest news. But then, communicating through the Net can be frustrating at times. The system may crash. Worse still, without the emotional cues of face-to-face communication, the typed words sometimes seem difficult to interpret.★ Text BComprehension Check: c a a b d cLanguage Practice1．d e a c b f g h2．1) vehicle 2) hooked on 3)intense 4)worldwide 5)overnight 6)slipped7) on the whole 8) called forth 9) outwards 10)Needless to say 11) to my knowledge 12)On top of thatUnit 5★ Text AVocabularyI.1. 1) startled 2) mere 3) motion 4) sweating 5) stretched 6) vain 7) On one occasion8) anxiety 9) emotions 10) ashamed 11) In my mind’s eye 12) recurring2. 1) Mrs. White’s birthday coincides with her husband’s.2) They make big profits on the stuff they sell by creating an artificial shortage, which send s theprices soaring/results in the soaring of prices.3) It has been a week of alternate sunshine and rain.4) Politics and philosophy have been his lifelong passions, although he studied economics atuniversity.5) Tension came over her, as she waited for her first TV interview.3. 1) media, dedication to, grace 2) his competitors, in excitement, hug him, congratulate him on 3) emotions, numerous, intensity, passion forII.1.Mike, a Green, made the suggestion that a large park be built near the community.2.In a letter to his daughter, Mr. Smith expressed his wish that she (should) continue her educationto acquire still another degree.3.There is no reason to hold the belief that humans have no direct moral responsibility to safeguardthe welfare of animals.4.Children need to feel safe about the world they grow up in, and it is unwise to give them the ideathat everything they come into contact with might be a threat.5.Anxiety can result from the notion that life has not treated us fairly.6.Nobody believed his claim that he was innocent.III.1.I work out in the gym for one hour every morning.2.Florence has worked as cleaner at the factory for five years.3.The wounded man worked his way across the field on his hands and knees.4.The safe load for a truck of this type works out at about twenty-five tons.5.It is difficult to understand how human minds work.6.To my disappointment, the manager’s plan of promoting the new products doesn’t work atall.7.The teacher has a lot of experience of working with children who don’t know how to learn.8.The medicine was like magic, and it worked instantly after you took it.Comprehensive ExerciseI.1. 1) In my mind’s eye 2) groan 3) competitor 4) intensity 5) anxiety 6) tense7) sweat 8) tension 9) soaring 10) recurring 11) brought me back to earth12) fantasy 13) sweat 14) congratulate 15) numerous 16) media2. 1) engineer 2) forget 3) convinced 4) how 5) build 6) accident7) thought 8)only 9) sharp 10) touched 11) instructions 12) finallyII. Translation1. 1) It is the creativity and dedication of the workers and executives that turned the company into aprofitable business.2) The prices of food and medicine have soared in the past three months.3) We plan to repaint the upper floors of he office building.4) His success shows that popularity and artistic merit sometimes coincide.5) I don’t want to see my beloved grandmother lying in a hospital bed and groaning painfully. 2. Numerous facts bear out the argument/statement/claim that in order to recover speedily fromnegative emotion, you should allow yourself to cry. You needn’t/don’t have to be ashamed of crying. Anxiety and sorrow can flow out of the body along with tears.Consider the case of/Take Donna, Her son unfortunately died in a car accident. The intensity of the blow made her unable to cry. She said, “It was not until two weeks later that I began to cry.And then I felt as if a big stone had been lifted from my shoulders. It was the tears that brought me back to earth and helped me survive the crisis.”★ Text BComprehension Check: b c b b c aLanguage Practice1. a e d c b h f g2.1) aid 2) inclined 3) in good health 4) shortcomings 5) penetrated6) dismiss 7)has suffered from 8)progressive 9)optimistic 10)to a degree 11)hold on to12)installUnit 6★ Text AVocabularyI.1. 1) culture/cultural 2) indication 3) miniature 4) ironic 5) stumbled into 6) decent7) buzzing 8) abnormal 9) mechanical 10) Shuddering 11) implied 12) leap2. 1) You can convert RMB into US dollars in the foreign exchange office a the airport.2) I figured she didn’t know the first thing about cooking as she looked puzzled as to how tocook rice with the rice cooker.3) The manager glowed with pleasure upon hearing that in spite of their faulty equipment the teamhad accomplished some very useful work.4) I’m grateful to my company for allowing me to work flexible hours as long as I work eighthours a day.5) On seeing the comments made in the margins by previous readers, Tom couldn’t help thinkingthe book must be quite fascinating.3. 1) will not panic/feel panic, ’ll be at a disadvantage 2) hybrid, transmission3) crave, One indication, to distinguishII. 1. also 2. as well/too 3. too 4. also 5. as well/too 6. too 7. also 8. AlsoIII. 1. I’ve had enough 2. When I was old enough to work and earn money3. can’t get enough sleep at night4. has so far collected enough of them5. have strong enough arms6. have just enough money to live onComprehensive ExerciseI.1. 1) stumbled into 2) not know the first thing about 3) mechanical 4) when it comes to5) hybrid 6) gritted her teeth 7) premise 8) at a disadvantage 9) panic 10) cultural11) flexible 12) imply2. 1) chair 2) force 3) secrets 4) painstaking 5) recognized 6) steered 7) essentially8) observation 9) women 10) tutor 11) inspired 12) unlessII. Translation1. 1) He is a man of few words, but when it comes to playing a computer games, he is far too cleverfor his classmates.2) Children who don’t know any better may think these animals are pretty cute and startplaying with them.3) There is no way to obtain a loan, so to buy the new equipment, I will just have to grit my teethand sell my hybrid car.4) The hunter would not have fired the shots if he hadn’t seen a herd of elephants comingtowards his campsite.5) I find it ironic that Tom has a selective memory --- he does not seem to remember painfulexperiences in the past, particularly those of his own doing.2. Nancy Hopkins is a biology professor at MIT. She craves knowledge and works hard. However,as a scientist, she could not help noticing all kinds of indications of gender inequality on campus.Men and women professors did the same work, but when it came to promotion theadministrators were rather selective. It was ironic that after so much cultural progress, womenwere still at a disadvantage in institutions of higher education. When her request for more lab space was refused, she knew she had to fight. So she gritted her teeth and complained to the President. The fight ended in victory and Nancy was converted into a gender-equality advocate. ★ Text BComprehension Check: b a d b d c aLanguage Practice1. b d a e g c f h2.1) crisis 2) weighed down 3) supportive 4) takes all the credit 5) pleaded6) in control of 7) party 8) expense 9) lives for 10) semester11) at every opportunity 12) stirUnit 7★ Text AVocabularyI.1. 1) Strictly speaking 2) drifted 3) resembles 4) invaded 5) is conquered 6) fascinating 7) snack 8) put…into practice 9) source 10) climate 11) surrendered 12) were aroused2. 1) an absolute necessity rather than a luxury 2) is a valuable addition to the football team.3) will get out of control, if the firemen do not arrive within ten minutes.4) alternative but to g via Vancouver to get to Seattle5) declared all beef imports will be banned for the next six months as an emergency measure tostop the spread of mad cow disease.3. 1) systematic, have invented, to a very real extent, mysteries2) to establish, to be modifies/ modifying 3) tolerance towards, strike out, enrichII. 1. a) wish b) wish c) want d) want/wish 2. a) skin b) hide/skin c) hide d) skin3. a) raise/rear b) raise c) rear/raise d) raise4. a) royal b) kingly/royal c) sovereign d)royal/kinglyIII. 1. Indeed 2. though 3. Frankly 4. Moreover 5. To my knowledge6. however7. nevertheless8. Yet9. instead 10) in other wordsComprehensive ExerciseI.1. 1) fascinating 2) tolerance 3) invented 4) addition 5) ban 6) corrupt7) out of control 8) influenced 9) elite 10)came up with 11) establishing12) Massive 13）sources 14）enrich2. 1) early 2) similar 3) source 4) observation 5) examine6) features 7) declared 8) stronger 9) accident 10) sprungII. Translation1. 1) Many small businesses have sprung up in the city since the new policy went into effect.2) On hearing the news, she smiled briefly, and then returned to her habitual frown.3) He paused for effect, then said:“We can reach/enter these markets through new channels.”4) The addition of a concert hall to the school will help it nourish young musical talents.5) We have no way to protect our personal liberties until we have established a sovereign state,/Wecan’t protect our personal liberties unless we, first of all, establish a sovereign state.2. Though how the English language came into existence remains a mystery to many people，linguists believe that English and most other European languages have descended from acommon source: the Indo-European parent language. English was first spoken by the Anglo-Saxons who invaded England in the fifth century. They passed onto us the basic vocabulary of English. In over fifteen centuries of its development, English has enriched itself by massive borrowing. As British immigrants landed in America and established the United States as an independent nation, a new variety was added to the English language : American English.Though some people worry that the language is running out of control, many native speakers of English take pride in the tolerance of their language.★ Text BComprehension Check: c c c d b dLanguage Practice1. g e d c b h f a2. 1) give way to 2) predict 3) substantial 4) integrate 5) in transition 6) aspect7) to name a few 8) authority 9) dominate 10) had contributed to 11) unique12) rid yourself ofUnit 8VocabularyI. 1) barking 2) evil 3) brooding, hatched 4) migrant 5) tragedies 6) counterpart7) are complaining/complain 8) grim 9) flocks, fed on 10) vegetation11) patches 12) Scores of2. 1) was lined with people who came to welcome the distinguished foreign guests2) the boss silenced all lively conversation in the office3) wearing a pair of sun glasses, the famous movie star passed the crowded unnoticed.4) looked deserted 5) were stricken by it3. 1) patches, came into full bloom, were puzzled, mysterious2) throbbed with, sickened, migrant, a chorus 3) had crept into. Flickered, the starkII. 1. age-old, air force, daughter-in-law, first-rate, greenhouse, half brother, ice-cream, lifelike, light year, salesperson, self-centered, threefold, overuse, stone-still, worldwide2.1) poverty-stricken people 2) heart-breaking news 3) newly-built 4) well-fed kids5) successful spacewalk 6) peace-loving 7) need-based scholarships 8) color-blind people III. 1. lying 2. laid 3. lay 4. lain 5. lie 6. lay 7. lie 8. lay 9. lay 10. liesComprehensive ExerciseI.1. 1) spell 2) stricken 3) misfortunes 4) surroundings 5) blossom/bloom 6) migrant7)deserted 8) silence 9) sickened 10) hatch 11) puzzled 12) in harmony with2. 1) rate 2) publication 3) dangerous 4) banned 5) export6) profit 7) accept 8)comprehend 9) boundaries 10) ultimatelyII. Translation1.1) This is a prosperous town, but there is still poverty in the midst of wealth and abundance.2) The Brown family was stricken with one misfortune after another, but their children nevercomplained.3) The museum is designed in such a way that it stands in perfect harmony with its surroundings.4) It was a miracle that these flowers did not wither at all in the blazing sun.5) Flocks of sheep feed on the patches of vegetation that rise above the winter snow.2. This village was once famous for its beautiful natural surroundings. All the year round, the treeswere green and the flowers in bloom. Clear streams flowed out of the hills through acheckerboard of rice fields. Birds sang all day, and deer came and went in a leisurely manner.However, with the coming of DDT and other pesticides, an evil spell seemed to have settled over the village. Misfortunes came one after another. Chicken died suddenly, cattle and sheep were stricken by mysterious maladies, and farmers complained about a sickening feeling that puzzled the village doctor. The village square, once throbbing with life, was now deserted.★ Text BComprehension Check: b d a b b cLanguage Practice1.c d g a h b e f2.1) adapt 2) injured 3) immune 4) hostile 5) gives out 6) slight 7) take up8) significance 9) for the most part 10) deliberate 11)span 12) get caught up in。

数学专业英语第二版1-A 什么是数学数学来自于人(de)社会实践,例如,工业和农业生产、商业活动、军事行动和科研工作.与数学反过来,为实践服务和所有字段中(de)伟大作用.没有现代(de)科学和技术分支机构可以定期制定中(de)数学,应用无早有需要(de)人来了数字和形式(de)概念.然后,开发出(de)几何土地和三角测量(de)问题来自测量(de)问题.若要对付一些更复杂(de)实际问题,男子成立,然后解决方程未知号码,因此代数发生.17 世纪前, 男子向自己限于小学数学,即几何、三角和代数,只有常量被认为在其中.17 世纪产业(de)快速发展促进了经济和技术(de)进展和所需变量(de)数量、处理从常量到带来两个分支(de)数学-解析几何和微积分,属于高等数学,现在有很多分支机构,其中有数学分析、高等代数、微分方程(de)高等数学中(de)可变数量(de)飞跃函数理论等.数学家研究理念和主张.所有命题公理、假设、定义和定理都.符号是一种特殊和功能强大(de)数学工具,用于表示很多时候(de)理念和主张.公式、数字和图表是阿拉伯数字 1,2,3,4,5,6,7,8,9,0 与另外(de)符号"+"、减法"-",乘"",除"\"和平等"=".数学中(de)结论得到主要由逻辑推理和计算.长期(de)数学史上,以中心地点(de)数学方法被占领逻辑扣除.现在,由于电子计算机是迅速发展和广泛应用,计算(de)作用变得越来越多重要.在我们这个时代计算不只用于处理大量(de)信息和数据,而且还进行一些只是可以做(de)工作较早前(de)逻辑推理,例如,大部分(de)几何定理(de)证明.1--B 方程方程是平等(de)语句(de)两个相等(de)数字或数字符号之间.因此(a-5） = 一 5a 和 x 3 = 5 是方程.方程(de)两种——身份和方程(de)条件.方程(de)算术或代数(de)身份.这种方程中两名成员是相似(de)或成为相似(de)指示操作(de)性能.因此 12-2=2+8,(m+n)(m-n) = m n 是身份.1—c 比与测量今天(de)思想沟通往往根据编号和数量(de)比较.当你描述为 6 英尺高(de)人时,你比较他更小(de)单位,称为脚(de)高度.当一个人描述为昂贵(de)商品时,他指相对于其他相似或不同(de)商品这种商品(de)海岸.如果你说你(de)起居室(de)尺寸由 24 18 英尺,一个人可以判断房间(de)一般形式比较尺寸.当纳税人说他(de)城市政府支出 42%(de)税一美元作教学用途(de)时他知道 42 美分(de)每 100 美分用于此目(de).化学家和物理学家不断比较测量(de)数量在实验室里.家庭主妇比较时测量数量(de)烤(de)成分.与他规模图纸建筑师和他工作绘图(de)机器草拟比较成品中相应实际长度在绘图中(de)行(de)长度.定义.一个数量为另一种像数量是第一次(de)商(de)比例除以第二个.比率是一个分数,而关于一小部分(de)所有规则都适用于比.我们写(de)比率与分数线、斜线号、司标志,或符号"："（这读"是"）.因此,3 到 4 is3/ 3 和 4,被称为比例(de)条款(de)比率.很重要(de)了解比像数量(de)商学生.以某个角度向一条线段(de)比率已没有意义；他们不是同一种(de)数量.我们找到一条线段,第二个线段(de)比例或一个角,第二个角度(de)比例.这是我们做(de)测量它们并寻找他们(de)测量(de)商.测量必须表达相同(de)单位.S 比始终是一个抽象(de)数字；即,它有没有单位.它是一个数字,认为除了它所来自(de)测量单位.除非有相反是一个重要(de)原因,应最简单(de)形式表示(de)比率.在前面(de)示例(de)客厅尺寸在哪里由 24 18 英尺,最终和长度(de)比率是宽度(de) 3:4.但不是 18:24.第二章：几何与三角2.2 A 为什么要研究几何我们为什么研究几何开始此文本研究(de)学生也许会问,"什么是几何.什么可以预料从这项研究获得"许多高校领导已经认识到正面(de)好处可以获得所有人学习数学(de)这个分支.这种明显(de)从这一事实它们需要(de)几何研究作为这些院校预科(de)先决条件.几何巴比伦和埃及(de)尼罗河流域洪水淹没土地测量中很久以前了它(de)起源.希腊单词几何被从土力工程处、地球"意义"和美唐、意义"度量值".早作为公元前 2000 年,我们发现(de)这些土地测量师人家重建消失(de)地标和边界(de)利用几何(de)真理.几何是一门科学,由线条(de)形式处理.几何(de)研究是培养成功(de)工程师、科学家建筑师和草拟(de)重要组成部分.木匠、钳工、石匠、艺术家和设计师所有应用几何在他们(de)行业中(de)事实.在本课程学生将学到很多关于几何数字如线条、角度、三角形、圆和设计和多种模式.所得(de)几何研究(de)最重要(de)目标之一使学生在他(de)听力、阅读和思维更重要.学习几何他远离盲目接受语句和思想(de)实践领导和教想清楚与批判前形成(de)结论.有几何(de)学生可以获得许多其他不太直接(de)利益.这些人当中必须包括训练在英语语言(de)精确使用和分析(de)能力一种新形势或成基本部件,以及利用毅力、创意和解决问题(de)逻辑论证(de)问题.欣赏大自然(de)创作将几何研究(de)副产品.学生还应制定数学和数学家,我们(de)文化和文明(de)贡献(de)认识.一些几何术语1.固体和飞机.固是三维图.固体(de)常见示例是多维数据集、球、圆柱、圆锥和金字塔.多维数据集有六个面光滑、平整(de).这些面孔被称为平面曲面,或只是飞机、平面有两个方面.长度和宽度.表面(de)黑板或桌面是平面曲面(de)一个例子.2、线条和线段.我们都很熟悉,但很难词(de)定义.一线可由在一张纸上移动(de)钢笔或铅笔标记(de)代表.一条线,可被视为有只有一维,长度.虽然当我们绘制一条直线,我们给它(de)宽度和厚度,我们认为只(de)跟踪(de)长度,考虑行时.点有没有长度、没有宽度和没有厚度,但标记(de)位置.我们都熟悉用这种表达式作为铅笔点和针点.我们点表示一个小点,并将其命名(de)旁边,打印为大写字母 A 点 ' 图 2-2-1.在行(de)标记上它(de)两个点,用大写字母或附近(de)一个小字母命名.图 2-2-2 (de)直线是读"AB 线"行 l".直线延伸到无穷远(de)两个方向并没有结束.线上(de)两个点之间(de)部分称为行被称为一条线段.一条线段两个端点(de)命名.因此,图 2-2-2,我们称为 AB 线 l (de)一条线段.当不会混淆可能导致,表达"线段 AB 通常由 AB 段或更换,简单地说,行 AB.有三种线路：直线、断(de)线和曲线.弯曲(de)线条或,简单地说,曲线不是其中(de)任何部分是直行.断(de)线联接、直线线段组成为能得到一个唯一(de)图 2-2-3.3.部分(de)一个圆.圆是封闭(de)躺在一个平面,其中(de)所有点都都距离称为中心一个固定(de)点.一个圆(de)符号.图 2-2-4,O 是 ABC 中心,或简单(de) 圆点从圆(de)中心绘制(de)线段是圆(de)半径（复数,半径）.OA、转播,业主立案法团是中华民国(de)半径圆(de)直径是通过中心圆圈圈上(de)终结点(de)一条线段.一个直径等于两个半径.弦是任何加入圆上(de)两个点(de)线段.教育署是图 2-2-4 圈(de)弦.从这个定义很明显直径是弦.一条弧线,如弧 AE,其中由 AE 表示圆(de)任何部分.A、 E 点圆分为轻微弧 AE 和主要弧安倍.直径分为两个弧形称为半圆(de)一个圆.如 AB 和 BCD.周围是一圈(de)长度.涉及字母标识是数值(de)真正(de)任何一组字母它.因此身份 (+ 2) x = ax + 2 x 成为 3 (7++ 2) = 21++ 6 或 27 = 27,时,例如,x = 3,和= 7.这是事实,只有某些值(de)一封信中,或某些集(de)方程相关(de)值(de)两个或更多(de)信,是方程(de)条件或简单(de)方程.Thus3x-5 = 7 是真正为 x = 4 只；和 2 x-y = 10 是真正为 x = 6和 y = 2 和许多其他值对 x 和 y.任何数字或数字符号,满足这个方程(de)方程根.要获取(de)根或方程根(de)称为方程(de)求解.有很多种(de)方程.他们是线性方程组,二次 .解方程就发现未知词(de)价值.要做到这一点,我们必须,当然,改变条款有关直到未知(de)词单独一侧(de)方程,从而使它等于东西(de)另一边.然后,我们获得(de)价值与未知(de)问题(de)答案.若要求解方程,因此,移动和更改有关(de)条款,不做公式不真实,直到未知(de)数量只是意味着提起一侧,无论哪一方.方程(de)很大(de)使用.我们可以使用许多数学问题中(de)方程.我们可能会发现几乎每一个问题给我们一个或多个语句什么是等于什么等于某事；这给了我们方程,与我们可能工作如果我们需要.2.2 C 三角函数和直角三角形(de)解决方案相互依存(de)边和角(de)三角形.我们知道这从几何.三角开始通过显示这种依赖性之间(de)边和角(de)三角形(de)确切性质.为此目(de)三角雇佣双方(de)比率.这些比率称为三角函数.6 三角函数(de)直角三角形,为 A,任何急性角表示,如下所示；这些函数（比率) 是极为重要(de)三角学(de)研究.他们必须载入史册.最重要(de)应用程序之一是三角(de)三角形(de)解决方案.让我们现在占用(de)直角三角形(de)解决方案.一个三角形组成(de)六个部分、三边和三个角度.若要解决一个三角形是找到不给予(de)部分.直角三角形有一个角度,以正确(de)角度,总是给予.因此当双方或一方和急性角度来看,有一个直角三角形可以得到解决.解直角三角形(de)一般指示提供如下.第三章3—A 符号指示集一组(de)概念如此广泛利用整个现代数学(de)认识是所需(de)所有大学生.集是通过集合中一种抽象方式(de)东西(de)数学家谈(de)一种手段.集,通常用大写字母： A、 B、 C、进程运行·、 X、 Y、 Z ；由小写字母指定元素： a、 b (de) c、进程运行·,若 x、 y z.我们用特殊符号 x∈S 意味着 x 是 S (de)一个元素或属于美国(de) x如果 x 不属于 S,我们写xS.≠当方便时,我们应指定集(de)元素显示在括号内；例如,由符号表示(de)积极甚至整数小于 10 集 {2,468} {2,,进程运行·} 作为显示(de)所有积极甚至整数集,而三个点等(de)发生.点(de)和等等(de)意思是清楚时,才使用.上市(de)大括号内(de)一组成员方法有时称为名册符号.涉及到另一组(de)第一次基本概念是平等(de)集.DEFINITIONOFSETEQUALITY.两组 A 和 B,据说是平等(de) （或相同(de)）如果它们包含完全相同(de)元素,在这种情况下,我们写 A = B.如果其中一套包含在另一个元素,我们说这些集是不平等,我们写 A = B.EXAMPLE1.根据对这一定义,由于他们都是由构成(de)这四个整数 2, 和 8 两套 {2,468} 和 {2,864} 一律平等.因此,当我们用来描述一组(de)名册符号,元素(de)显示(de)顺序无关.动作.集 {2,468} 和 {2,2,4,4,6,8} 是平等(de)即使在第二组,每个元素 2 和 4 两次列出.这两组包含(de)四个要素 2,468 和无他人；因此,定义要求我们称之为这些集平等. 此示例显示了我们也不坚持名册符号中列出(de)对象是不同.类似(de)例子是一组在密西西比州,其值等于{M、我、 s、 p} 一组单词中(de)字母,组成四个不同字母 M、我、 s 和体育3—B 子集S.从给定(de)集 S,我们可能会形成新集,称为.(de)子集例如,组成(d e)那些正整数小于 10 整除 4 （集合{8 毫米}） (de)一组一般是(de)所有甚至小于 10.整数集(de)一个子集,我们有以下(de)定义. 子集(de)定义.A一组据说是B,集(de)一个子集,我们写A B每当A(de)每个元素也属于B.我们还说包含B A或B包含. 关系称为集.A和B(de)声明并不排除可能性,B.事实上,我们可能B A和B A,但只有当A和B都具有相同(de)元素发生这种情况.换句话说,A = B当且仅当B和B A.这一命题是上述定义(d e)平等和包容(de)直接后果.如果A和B,但A≠B,然后我们说(de)就是你(de)真子集我们表明这通过编写B.在所有(de)应用程序集理论,我们有一套固定事先,S,我们只关心这给定组(de)子集.底层(de)设置(de)不同而有所不同从一个应用程序,到另一台；它将转交作为每个特定(de)话语(de)通用组.符号{X∣X∈S和X满足P},将指定(de)所有元素X在S中满足该属性集体育当通用设置为我们所指(de)id(de)理解,我们省略参照以S,我们只需写{X∣X满足P}.这读取 '"集(de)所有这种x满足p.' "在此方法中指定(de)设置说笔下定义(de)属性,例如,所有正实数(de)一组可以被指定为{X∣X大于 0} ；通用集S,在这种情况下理解为所有实数集.当然,这封信x是个笨蛋,并可由任何其他方便(de)符号替换.因此,我们可以写{x∣x大于0} = {y∣y大于0} = {t∣t大于 0} 等等.它有可能设置为不包含任何元素.这套被称为空集或无效设置,并将由symbolφ表示.我们会考虑φto是每一集(de)一个子集.有些人觉得很有用(de)一套类似于一个容器（例如,一个袋子或框）包含某些对象,其元素.空集则类似于一个空(de)容器.为了避免逻辑(de)困难,我们必须区分元素x和集{x}(de)唯一元素是x,(A box with a hat in it is conceptually distinct from t he hat itself.)尤其是,空(de)setφis集合{φ}不相同.事实上,空设置φcontains没有元素而集{φ}有一个元素φ（一个框,其中包含一个空框不是空(de)）.组成一个元素(de)集合,有时也称为一个元素集.3— C在讨论任何分支(de)数学,它分析、代数、几何,最好使用符号和集理论(de)术语.这一问题,在世纪后期开发(de)布尔和康,已对 19 20世纪数学发展(de)深远(de)影响.它具有统一许多看似已断开连接(de)想法,并有助减少许多数学概念(de)逻辑基础,优雅和有系统(de)方式.集理论彻底治疗需要长时间(de)讨论,我们认为这本书(de)范围.幸运(de)是,基本(de) noticns 是几号中,并有可能发展(de)非正式讨论通过集理论思想工作知识(de)方法.实际上,我们将讨论不是一个新(de)理论作为协议有关(de)精确(de)术语,我们要将应用到更多或更少(de)熟悉(de)想法.在数学中,'"集'"一词用于表示作为单个实体(de)集合称为想查看(de)对象(de)集合,作为'"群'",这类名词(de)'"'"部落,'人群'"'",团队',是所有示例(de)集合,集合中(de)各个对象称为元素或一组(de)成员他们都说属于或载于一组.反过来,集包含或由其元素(de)表示.我们须主要兴趣(de)数学对象集：集数字、集(de)曲线、集(de)几何图形,等等.在许多应用程序,它是方便快捷(de)处理中,没有什么特别(de)集假定在集合中(de)各个对象(de)性质有关.这些称为抽象集.抽象集理论已经发展到处理(de)任意对象,这种集合,并从这种普遍性理论派生其权力.第四章4-A存在某些子集(de) R (de)区分,因为他们不共享(de)所有实数(de)特殊属性.在本节中,我们将讨论两个这样(de)子集、整数、有理数.若要引进(de)正整数,我们开始数字 1,在其存在(de)公理 4 保证.2、 2++ 3 1 (de)数由表示数字 1++ 1,依此类推.数字 1 2、 3,… …,以这种方式获得(de)重复加 1 (de)是积极(de)而他们则称为正整数.严格地说,这说明(de)正整数还没有完全完成因为我们已经没有详细解释我们"等等",什么意思表达或者"重复加 1".虽然直观(de)表达意义上去很清晰,实数系统精心治疗有必要给(de)正整数更精确(de)定义.有许多方法来执行此操作.一种方便(de)方法是先介绍一个感应集(de)概念.感应集(de)定义.实数集称为感应集,如果它具有以下两个属性：(a) 1 号是集.(b) 在一组,每个 x 数字 x + 1 是还在一组.例如,R 是归纳(de)组.所以是 R + 一组.现在我们将定义为那些属于每个感应集(de)实数(de)正整数.Definition (de)正整数.实数称为一个正整数,如果它属于每一个感应集.让 P 表示这个集合(de)所有(de)正整数.然后,P 是本身感应集因为 (a) 它包含 1,并且 (b) 它包含 x + 1,每当它包含 x.由于 P 成员属于每个感应集,我们称之为 P (de)最小(de)感应集.此属性(de)设置 P 形成一种类型(de)推理逻辑基础诱导,详细(de)讨论,其中有 4 部这个介绍数学家调用证明(de).消极(de)正整数称为负(de)整数.正整数,连同负整数和0(zero),从我们称之为简单(de)整数集设置 Z.实数系统彻底治疗,它会有必要在此阶段,证明某些定理(de)整数.例如,sum、差异,或产品(de)两个整数,但两个整数(de)商不需要是一个整数.然而,我们不应进入该等债权证明表(de)详细信息.整数(de)商 / b （其中 b 0) 被称为有理数.有理数,由 Q,表示(de)一组包含 Z 为子集.读者应意识到由 Q 满足所有字段公理和顺序公理.为此,我们说(de)有理数集是一个有序(de)字段.不在 Q (de)实数称为非理性.4-B读者是无疑熟悉实数(de)一条直线上(de)点(de)几何表示形式.代表0,有权代表 1,在图 2-4-1 所示(de) 0 及另一人,选择一个点.此选项确定规模.如果一个采用一套合适(de)欧几里德几何公理,然后每个真实(de)数字对应于这条线上(de)一个点,相反,在行上(de)每个点对应于一个且仅一个实数.为此线通常称为真正(de)直线或实轴,而且很习惯使用单词实际数量和互换点.因此我们经常讲点(de) x,而不是点对应(de)实数.实数(de)订购关系有一个简单(de)几何解释.如果 x < y、点 x 位于左侧(de)点(de) y,如图 2-4-1 所示.正数躺到左侧(de) 0 0,负数(de)权利.如果 < b、点 x 满足不等式 < x < b 当且仅当 x 是之间和 b.此设备(de)几何表示实数是非常有价值(de)工具,有助我们去发现和更好地了解实数(de)某些属性.然而,读者应意识到必须将所有属性都被视为定理(de)实数(de)推断出从不涉及任何几何公理.这并不意味着人不应该让几何研究(de)实数属性中(de)使用.相反,几何往往表明特定(de)定理证明(de)方法和有时几何参数是比纯粹(de)解析证明（一个完全取决于公理(de)实数）更加出色.在这本书中,几何参数用于很大程度上有助于激励或澄清特定(de)讨论.不过,所有(de)重要定理(de)证明以解析(de)窗体.4 C首先,让我们把注意力转移到分数.你肯定见过表达式"一半"和"季度",分母等于 2 或 4 时使用它们.1/3 是读"三分之一".其他分数是以相同(de)方式读取(de).因此,我们读 1/5,1/6,1/7,1/10,1/25,1/100 为五分之一,六分之一,六分之一、七分之一,十分之一,1:25 上午和百分之一.这些表达式被视为名词,因此可能产生(de)复数形式.因此,我们作为三分之二；读了 2/3同样 5 6,9 105/100 是读取六分之五、九十分之五百分之一.但是,如果分母(de)最后一位是 1 或 2,然后我们不要读分数以上述方式.例如,我们宣布 5/21 作为"五个超过 21".此方法还在其它情况下使用.如果分数不是一项共同 .,1/1089年或 501/1205年）,然后我们说"一对千和 89 个"或"五一百以上十二百和五".下一步,让我们检查小数.他们是很简单(de)发音.只读取数(de)整数部分普通(de)方式,然后说"点"（代表"小数点"）,然后后另读取一个小数位.因此读取十二-点-六-五；Π正确,6 位小数,等于three-point-one-four-one-five-nine-two,正确(de)五个重要(de)数字,等于 three-point-one-four-one-six.小于一个小数部分时,一般不写了,例如,,但仅限于英格兰.56）.56 读"点-5-6",.0007 读"点-团团转-团团转-团团转-七"或通常更-三-0 (de)七.现在代数表达式,分数再次读取"指针经过".（2a-1)/(ax+b) 对 ax + b 读取 2a-1 和括号表示"到"一词如（a+b)(a-b) 读"加进减号 b b".权力指数或指数由表示."平方"和 3"桂鱼",或"到第三个"指数(de)读取索引 2.其它指数",第四,第五,减号第二部分,第 n,以"读取.身份 ^3++ b ^3 = (+ b)(a^2-ab+b^2) 读取"多次元(de)罗宋汤(de)脓 b 到平方(de) ab 加 b 平方等于 a + b".或与方程 x^(-2/3) + √^2 = 0 读取"x,减号(de)三分之二,加上第五根(de)平方等于零".。

Sets of points in the planeWe have already shown that there is a one-to-one correspondence be tween points in a plane and pairs of numbers (x,y) . Certain sets of points in the plane may be of special interest. For example , we may wish to exa mine the set of point comprising the circumference of a certain circle , or the set of points constituting the interior of a certain triangle . One may w onder if such sets of points may be succinctly described in compact mathe matical notation.We may write{(x,y)|y=2x} （1）to describe the set of ordered pairs (x,y) , or corresponding points , such that the ordinate is equal to twice the abscissas. In effect ,then, the vertical line in (1) is read “such that” . By “the graph of the set of ordered pair s” is meant the set of all points of the plane corresponding to the set of ordered pairs. The student will readily infer that the set of points constituting the graph lies on a straight line.Consistent the set{(x,y)|y=x^2}Consistent with our previous interpretation , this symbol represents the se t of ordered pairs (x,y) such that the ordinate is equal to the square of the abscissa. Here ,the total graph comprises a simple recognizable geometric al figure , a curve known as a parabola.on the basis of these two example ,one may be tempted to believe that an y ar-bitrarily drawn curve , which of course determines a set of points ord ered pairs, could be described succinctly by a simple equation. Unfortunat ely ,this is not the case. For example , the broken line in figure 2-2-3 is on e of such curves.Consider now the set{(x,y)|y>2x} （2）to describe the set of points (x,y) whose ordinate is greater than twice its abscissa. In this case ,our set of point constitutes not a curve , but a region of the coordinate plane.建立点在平面上我们已经表明,在平面之间存在一一对应点和坐标(x,y)。

2.2 几何与三角词组翻译1.学会institution，建筑师 architect, 机械师 machinist, 制图员draftsman, 测量者surveyor, 木匠carpenter2.点point, 端点endpoint, 线line, 直线straight line, 线段 line segment, 曲线curved line, 折线 broken line, 射线ray , 平面 plane,曲面 curved surface3.立体solid, 柱体cylinder, 立方体cube,球 sphere, 棱锥pyramid,圆锥 cone ,4.圆circle,圆心 center, 直径diameter, 半径radius, 半圆semicircle, 弦chord, 弧arc, 优弧major arc, 劣弧minor arc5.角angle, 边side, 三角形triangle, 直角三角形right triangle,斜边 hypotenuse, 直角边right-angle side6.长度length,宽度 breadth/width,厚度 thickness, 位置position7.几何的geometrical,立体的 three-dimensional , 弯曲的curved,等距离的equidistant ,无限的 infinite8.培养创造力train originality,必须的毅力 necessary perseverance , 提高鉴赏力raise/improve the appreciation ability9.消失了的边界vanishing boundaries/landmarks,有序性和优美感 orderliness and sense of beauty, 几何图形大量存在geometric forms abound in , 定理成立的先决条件a prerequisite to a theorem 汉译英1.许多专家都认为数学是学习其他科学技术的必备基础和先决条件。

2.1 数学、方程与比例（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。

Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.（2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。

No modern scientific and technological branches could be regularly developed without the application of mathematics.（3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。

Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often.（4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。

Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered.（5）方程与算数的等式不同在于它含有可以参加运算的未知量。

Equation is different from arithmetic identity in that it contains unknown quantity which can join operations.6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。

最全的全新版大学英语第二版综合教程2答案课后练习答案Unit1 Ways of LearningPart II Reading TaskComprehensionContent QuestionPair Work1. They were studying arts education in Chinese kindergartens and elementary schools in Nanjing.2. Their 18-month-old son Benjamin was fond of trying to place the key into the slot of the key box during their stay at the Jinling Hotel.3. They would come over to watch Benjamin and then try to teach him how to do it properly.4. Because he realized that this anecdote was directly relevant to their assigned tasks in China: to investigate early childhood education andto throw light on Chinese attitudes toward creativity.5. Most of them displayed the same attitude as the staff at the Jinling Hotel.6. He emphasized that the most important thing is to teach the child that on can solve a problem effectively by oneself.7. He means that this incident pointed to important differences in educational and artistic practices between China and the USA.8. The manner in which the Chinese staff saw the need to teach the child by guiding his hand in the characteristic of a broader attitude to education, one that stands in contrast to the Western preference for leaving the child to explore and learn unaided.9. One example is of children at the age of 5 or 6 painting flowers, fish and animals skillfully and confidently; in a second example, calligraphers 9 and 10 years old were producing works; and in a third, young artists work on perfecting their craft for several hours a day.10. Americans think that unless creativity has been acquired early, it may never emerge, and skills can be picked up later. Chinese think that if skills are not acquired early, they may never be acquired, and there is no hurry to promote creativity.11. This is mainly due to the difference in their way of thinking.12. The author makes the suggestion that we should strike a better balance between the poles of creativity and basic skills.Text OrganizationWorking On Your Own1.1) The text begins with an anecdote.2) His thoughts are mainly about different approaches to learning in China and the West.3) He winds up the text with a suggestion in the form of a question.2. Chinese1) Show a child how to do something, or tech by holding the hand2) Give greater priority to developing skills at an early age, believing that creativity can be promoted over timeAmericans1) Teach children that they should rely on themselves for solutions to problems2) Put more emphasis on fostering creativity in young children, thinking skills can be picked up laterLanguage Sense Enhancement(1) Summarizing(2) value originality and independence(3) contrast between(4) in terms of(5) harbor(6) fearful(7) comparable(8) promote creativity(9) emerge(10) picked upLanguage FocusVocabularyI1.1) insert2) on occasion3) investigate4) In retrospect5) initial6) phenomena7) attached8) make up for9) is awaiting10) not; in the least11) promote12) emerged2.1) a striking contrast between the standards of living in the north of the country and the south.2) is said to be superior to synthetic fiber.3) as a financial center has evolved slowly.4) is not relevant to whether he is a good lawyer.5) by a little-known sixteen-century Italianpoet have found their way into some English magazines.3.1) be picked up; can’t accomplish; am exaggerating2) somewhat; the performance; have neglected; they apply to3) assist; On the other hand; are valid; a superiorII1.1) continual2) continuous3) continual4) continuous2.1) principal2) principal3) principle4) principles5) principalIII1. themselves2. himself/herself3. herself/by herself/on her own4. itself5. ourselves6. yourself/by yourself/on your own Comprehensive ExercisesI. cloze1.(1) contrast(2) exaggerating(3) priority(4) on the other hand(5) promoting(6) pick up(7) assist(8) accomplish(9) occasion(10) neglecting(11) worthwhile(12) superior2.0-(2) perform(3) facing(4) competent(5) equipped(6) designed(7) approach(8) rest(9) definitely(10) qualityII. translation1.(1) It takes an enormous amount of courage to make a departure from the tradition.(2) Tom used to be very shy, but this time he was bold enough to give a performance in front of a large audience.(3) Many educators think it desirable to foster the creative spirit in the child at an early age. (4) Assuming this painting really is a masterpiece, do you think it’s worthwhile to buy it?(5) If the data is statistically valid, it will throw light on the problem we are investigating. 2.To improve our English, it is critical to do more reading, writing, listening and speaking. Besides, learning by heart as many well-written essays as possible is also very important. Without an enormous store of good English writing in your head you cannot express yourself freely in English. It is also helpful to summarize our experience as we go along, for in so doing, we can figure out which way of learning is more effective and will produce the most desirable result. As long as we keep working hard on it, we will in due course accomplish the task of mastering English.Unit2 ValuesPart II Reading TaskComprehensionContent QuestionPair Work1. The Salvation Army is a religious charitable organization. A Salvation Army bellringer is a volunteer who help it collect donations.2. The boy asked him: Are you poor? He did it simply out of confusion and curiosity. Obviously he knew nothing about the Salvation Army bell ringer.3. He said, “I have more than some people, but not as much as others.” This means that he was neither poor nor rich.4. The boy’s mother scolded him because the question was social inappropriate, especially to a person who looked poor.5. Yes, economically he is poor. He lives ina small basement apartment. He doesn’t even have a color TV. He falls into the lowest income category. And so on.6. No, the writer does not feel poor. This is because he has enjoyed good health and creativity which he thinks are much more important than material goods.7. He feels out of place among people who are primarily interested in material things.8. She told him that she was interested inwhat’s on the inside. but after he took her to his poorly furnished apartment, she changed her mind completely.9. It only shows that to her the most important thing was still material goods rather than what she had claimed before.10. Commercial can put people under pressure to purchase more than is really necessary.11. Because December is the time for to work for the Salvation Army as a bell ringer, which gives him a genuine sense of belonging and brings him happiness in helping others.12. The boy’s question has helped the writer realize that, despite his lack of expensive possessions, he is rich in many other ways and should be thankful for that.Text OrganizationWorking On Your Own1.1) a.√2) the essay is meant to explain something that is, the author’s view of life.3) That one can live a life full of riches without being rich financially.2.Part One: The writer’s encounter with a boy who raised the question “are you poor?”Part Two: In search of an answer the writer finds that not having expensive possessions doesn’t make him feel poor mainly because he enjoys life in many other ways.Part Three: In conclusion, the writer thinks he’s grown to understand more about himself because of the boy’s question.Language Sense Enhancement1.(1) attain(2) wear and tear(3) dependable(4) modest(5) primarily(6) minimal(7) exceptionally(8) illness-free(9) spirited(10) energizingLanguage FocusVocabularyI1.1) abrupt2) emotional3) bless4) wear and tear5) dated6) consequences7) seemingly8) in contrast to9) Curiosity10) genuine11) primarily12) sentiments2.1) confronted with more than one problem, try to solve the easiest one first.2) vital to the existence of all forms oflife.3) some confusion among the students about what to do after class to follow up on the subject.4) nothing more than a job and an apartment to be happy.5) tickled him to think that she’d come to ask his advice3.1) a lingering; fabricating; sentiments2) fill out; every item; vital; consequences3) be denied; tangible; cherish; attainII1. It is a long trip and will take us five hours by bus.2. She arrived early and took a front row seat.3. Don’t take me for a fool.4. It takes a lot of imagination to fabricate such a story.5. My uncle will take me (along on his trip) to the Arctic this summer.6. He took the dinner plate I passed to him.7. Kevin took second prize in the weight-lifting competition.8. If you don’t take my advice, you will regret it.III1. hanging2. to give3. to return4. being praised5. not having written6. to say7. to open8. being helpedComprehensive ExercisesI. cloze1.(1) well-off/affluent(2) dated(3) falling into(4) bracket(5) deny(6) tangible(7) pursuit(8) cherishes(9) out of place(10) abrupt(11) focus(12) donations2.(1) consume(2) fueled(3) annual(4) plain(5) physically(6) security(7) indicates(8) equally(9) traditional(10) followsIII. Translation1.1) The company denied that its donations hada commercial purpose.2) Whenever he was angry, he would begin tostammer slightly.3) Education is the most cherished tradition in our family. That’s why my parents never took me to dinner at expensive restaurants, but sent me to the best private school.4) Shortly after he recovered from the surgery, he lost his job and thus had to go through another difficult phase of his life.5) In contrast to our affluent neighbors, my parents are rather poor, but they have always tried to meet our minimal needs.2.With more and more donations coming in, our university will be much better off financially next year. We will thus be able to focus on the most important task that we, educators, must take on: to encourage students to attain their scholarly/academic goals, to train them to be dependable and responsible individuals, to prepare them for the life ahead, and to guide them in their pursuit of spiritual as well as material satisfaction.Unit3 The Generation GapPart II Reading TaskComprehensionContent QuestionPair Work1. There are seven characters---Father, Mother, Heidi, Diane, Sean, Restaurant Manager, and Mrs. Higgins.2. No. Because what he does usually ends up embarrassing them.3. To buy a guitar.4. To check if Sean was going to embarrass him.5. He knew his father was going to embarrass him.6. It was unnecessary and embarrassing.7. He wanted Dan to pressure his son into asking Diane to the senior prom.8. He would speak to his son and insist that the latter give Diane a call.9. She felt humiliated.10. Because the Thompson had just moved.11. He tried to let her know how exceptionally talented a young woman Heidi was.12. Because she couldn’t bear being embarrassed by her father.Text OrganizationWorking On Your Own1.1. A fast-food restaurant2. The Thompson family dining room3. An office at a high school2.Scene One: Father embarrassed Sean by talking too proudly to the restaurant manager.Scene Two: Father embarrassed Diane by persuading a colleague into pressing his son to ask her to the senior prom.Scene Three: Father embarrassed Heidi by boating to an official at her new school about how talented she was.Language Sense Enhancement1.(1) once in a while(2) for(3) the problem(4) he thinks(5) humiliated(6) class president(7) have(8) Actually(9) stop to think(10) interference Language Focus VocabularyI1.1) typical2) dumb3) junior4) glorious5) welfare6) came over7) interference8) fading9) narrowed down10) frank11) schemes12) at any rate2.1) consists of five generals and four police officers.2) will be in a location overlooking the lake.3) was humiliated by her comments about my family background in front of so many people.4) have any proof that it was Henry who stole the computer?5) was exhausted after the long cycle ride.3.1) hysterical; was handed down by; should have known better than2) twisted; over and over; talented son3) patience; not to keep him in suspense; assured; repeatedlyII. Collocation1. adequate2. anxious3. certain4. content5. crazy6. likely7. fortunate8. keenIII. Usage1. be admitted2. live3. be postponed4. buy5. be banned6. be Comprehensive ExercisesI. cloze1.(1) typical(2) welfare(3) constant(4) frank(5) talent(6) dumb(7) know better than that(8) repeatedly(9) dread(10) interference(11) bet(12) assure2.(1) despite(2) really(3) same(4) contact(5) admitted(6) attempt(7) not(8) tend(9) different(10) mannerII. Translation1.(1) Have scientists found proof of water on Mars?(2) The planning committee has narrowed downthe possible locations for the nuclear power plant to two coastal towns.(3) Sam not only lost his job but also both legs; he had to live on welfare for the rest of his life.(4) A jury consisting of 12 members voted in unison that Mary was guilty.(5) Sean felt humiliated to hear his talent being questioned.2.George, the son of Mr. Johnson, liked listening to heavy metal music in the evenings, which made it hard for other residents in the community to fall asleep. Eventually the exhausted neighbors lost their patience and decided on direct interference. They called Mr. Johnson to tell him in a frank manner what they were thinking. Mr. Johnson assured them that he would certainly settle the issue. As soon as he put down the phone he scolded his son, “What has come over you? You should know better than to disturb others for your own amusement.” In the end George traded his CD’s for computer gamessoftware from his classmates.Unit4 The Virtual WorldPart II Reading TaskComprehensionContent QuestionPair Work1. She used to be a television producer, but now she is a writer.2. She writes and edits articles online, submits them via email, and communicates with colleagues via the Internet, too.3. She could stay computer-assisted at home for weeks, going out only t get mail, newspapers and groceries.4. They feel as if they had become one with the computer, and life seems to be unreal.5. That people who grew used to a virtual life would feel an aversion to outside forms of socializing.6. She gets overexcited, speaks too much, and interrupts others.7. She is bad-tempered, easily angered, andattacks everyone in sight, all because she has long become separated from others and lacks emotional face-to-face exchanges with people.8. She fights her boyfriend, misinterpreting his intentions because of the lack of emotional cues given by their typed dialogue.9. Because we rely on co-works for company.10. She calls people, arrangers to meet the few friends remaining in the City, gets to the gym, arranges interviews for stories, doctor’s appointments---anything to get her out of the house and connected with others.11. No, she doesn’t feel happy. She feels being face to face is intolerable.12. She makes her excuses and flees, re-enters her apartment, runs to the computer, clicks on the modem, and disappears into the virtual world again. Text OrganizationWorking On Your Own1.1. 2-32. 1,4-10,133. 114. 122.The first paragraph describes the consequences of living a virtual life and the last tells of the author’s escape back into it. Together, they bring out the dilemma people at present are in: Because of modern technology, we have a choice between a virtual life and real life, but find both unsatisfactory.Language Sense Enhancement1.(1) routine(2) for company(3) unemployment(4) externally(5) drug abuse(6) restore(7) fled(8) gym(9) set apart(10) appointmentsVocabularyI1.1) conversely2) but then3) symptom4) spitting5) abusing6) tone7) took; in8) editing9) have arranged10) in sight11) stretched12) data2.1) smoking cigarettes jars on me.2) find themselves getting sucked in.3) has arranged for a technician from the computer store to check and repair it.4) fled their country to avoid military service/fled to other countries to avoid militaryservice.5) restore people’s confidence in it.3.1) the virtual; on line; via2) nightmare; routine; any appointment; arrange for3) cue; remarks; his tuneII. Collocation1. We came here all the way on foot.2. Private cars are not allowed on campus.3. They are on vacation in Florida.4. Mary has been talking to her friend on the phone for an hour.5. Don’t worry, Lucy is always on time.6. Industrial demand on fuel is on the rise. III. Usage1. hard2. difficult3. impossible4. tough5. hard6. easyComprehensive ExercisesI. cloze1.(1) Internet(2) click(3) virtual(4) routines(5) arrange(6) nightmare(7) annoying(8) connection(9) crawls(10) take in(11) spit(12) data(13) sucked into(14) At times(15) flee(16) on line2.(1) companion(2) deliver(3) access(4) enables(5) customers(6) delights(7) provides(8) small(9) remote(10) informationII. Translation1.1) Research shows that laughter can bring a lot of health benefits.2) A show Internet connection speed is really annoying.3) As the law stands, helping someone commit suicide is a crime.4) In her report, Mary tries to interpret the data from a completely different angle.5) Sue is a girl of great talent. Her amazing memory sets her apart from her classmates.2.Perhaps you envy me for being able to work fromhome on the computer. I agree that the Internet has made my job a lot easier. I can write, submit and edit articles via email, chat with my colleagues on line and discuss work with my boss. With a click of the mouse, I can get all the data I need and keep up with the latest news. But then, communicating through the Net can be frustrating at times. The system may crash. Worse still, without the emotional cues of face-to-face communication, the typed words sometimes seem difficult to interpret.Unit5 Overcoming ObstaclesPart II Reading TaskComprehensionContent QuestionPair Work1. Because the pole was set at 17 feet which was three inches higher than his personal best.2. Because pole-vaulting combines the grace of a gymnast with the strength of a body builder.3. His childhood dream was to fly. His mother read him numerous stories about flying when he was growing up.4. Because he believed in hard work and sweat. His motto: If you want something, work for it!5. Michael's mother wished he could relax a bit more and be that "free dreaming" little boy. On one occasion she attempted to talk to him and his father about this, but his dad quickly interrupted, smiled and said, "You want something, work for it!"6. He began a very careful training program.7. He seemed unaware of the fact that he had just beaten his personal best by three inches. He was very calm.8. He began to feel nervous when the bar was set at nine inches higher than his personal best. 9. What his mother had taught him about how to deal with tension or anxiety helped him overcome his nervousness.10. The singing of some distant birds in flight made him associate his final jump with his childhood dream.11. He could imagine the smile on his mother’s face. He thought his father was probably smilingtoo, even laughing. However, in fact, his father hugged his wife and cried like a baby in her arms.12. Because he was blind.Text OrganizationWorking On Your Own1.Part One: Michael faced the most challenging competition in his pole-vaulting career.Part Two: Michael’s childhood was marked with dreams and tough training.Part Three: Michael topped his personal best, won the championship and set a new world record.2.(1) It also has the element of flying, and the thought of flying as high as a two-story building is a mere fantasy to anyone watching such an event. As long as Michael could remember he had always dreamed of flying.(2) All of Michael’s vaults today seemed to be the reward for his hard work.Language Sense Enhancement1.(1) startled(2) bale of hay(3) off(4) intensity(5) shaking the tension(6) tense(7) description(8) out of nowhere(9) pictured(10) scaredVocabularyI1.1) startled2) mere3) motion4) sweating5) stretched out6) vain7) On the occasion8) anxiety9) emotions10) ashamed of11) In my mind’s eye12) recurring2.1) coincides with her husband’s.2) sends the prices soaring/results in the soaring of prices.3) of alternate sunshine and rain.4) have been his lifelong passions, although he studied economics at university.5) Tension came over her3.1) media; dedication to; grace2) his competitors; in excitement; hug him; congratulate him on3) emotions; numerous; intensity; passion forII. Collocation1. Mike, a Green, made the suggestion that a large park be built near the community.2. In a letter to his daughter, Mr. Smith expressed his wish that she (should) continue hereducation to acquire still another degree.3. There is no reason to hold the belief that humans have no direct moral responsibility to safeguard the welfare of animals.4. Children need to feel safe about the world they grow up in, and it is unwise to give them the idea that everything they come into contact with might be a threat.5. Anxiety can result from the notion that life has not treated us fairly.6. Nobody believed his claim that he was innocent.III. Words with Multiple Meanings1. I work out in the gym for one hour every morning.2. Florence has worked as a cleaner at the factory for five years.3. The wounded man worked his way across the field on his hands and knees.4. The safe load for a truck of this type works out at about twenty-five tons.5. It is difficult to understand how humanminds work.6. To my disappointment, the manager’s plan of promoting the new products doesn’t work at all.7. The teacher has a lot of experience of working with children who don’t know how to learn.8. The medicine was like magic, and it worked instantly after you took it.Comprehensive ExercisesI. cloze1.(1) In my mind’s eye(2) groan(3) competitor(4) intensity(5) anxiety(6) tense(7) sweat(8) tension(9) soaring(10) recurring(11) brought me back to earth(12) fantasy(13) sweat(14) congratulate(15) number(16) media2.(1) engineer(2) forget(3) convinced(4) how(5) build(6) accident(7) thought(8) only(9) sharp(10) touched(11) instructions(12) finallyII. Translation1.1) It is the creativity and dedication of the workers and executives that turned the company into a profitable business.2) The prices of food and medicine have soared in the past three months.3) We plan to repaint the upper floors of the office building.4) His success shows that popularity and artistic merit sometimes coincide.5) I don’t want to see my beloved grandmother lying in a hospital bed and groaning painfully.2.Numerous facts bear out the argument/statement/claim that in order to recover speedily from negative emotion, you should allow yourself to cry. You needn’t/don’t have to be ashamed of crying. Anxiety and sorrow can flow out of the body along with tears.Consider the case of/Take Donna. Her son unfortunately died in a car accident. The intensity of the blow made her unable to cry. She said, “It was not until two weeks later that I began to cry. And then I felt as if a big stone had been lifted from my shoulders. It was the tears that brought meback to earth and helped me survive the crisis.”Unit6 Women, Half the SkyPart II Reading TaskComprehensionContent QuestionPair Work1. They liked girly toys such as a miniature kitchen, and Barbies.2. To convert a gas-guzzling SUV into a hybrid electric vehicle.3. Because she didn’t know anything about cars and was afraid of being cheated by the mechanic.4. She was craving independence and wanted to live away from home for some time.5. It helped her earn six engineering credits, which of course made it easier for her to become an engineering major.6. Five years.7. In her view, if you find a subject is difficult to learn, it does not mean you’re not good at it. It just means you have to set your mindand work harder to get good at it.8. Because he had confidence in her abilities believing she could have done better if she had studied more.9. No, she wasn’t always confident. She had moments of panic, worried that as a woman she would be unable to understand thermodynamics.10. She considers it wrong because it is based on a faulty premise.11. It is flexible and more powerful than we imagine.12. What she means is not to accept others’opinions blindly but to use one’s own judgment. Text OrganizationWorking On Your Own1.Part One: The author describes how she stumbled into engineering.Part Two: The author writes about how she has overcome obstacles, including the bias against women, on her way to success.Part Three: The author draws the conclusion thatwomen can do anything men can so long as they believe in their own abilities.2.1) she was not a tomboy.not to an engineering department.she didn’t know the first thing about engineering. because she craved independence from her parents. already earned her six credits in engineering.2) math and design.she participated in a national competition to convert an SUV into a hybrid electric vehicle.work harder at it.that she should study more.had to work hard at courses she found difficult, which encouraged her to keep going.Language Sense Enhancement1.(1) limit(2) denying(3) favor(4) others(5) relevant(6) translating(7) hard and fast conclusions(8) focus(9) incredibly flexible(10) consider the possibilityVocabularyI1.1) cultural/culture2) indication3) miniature4) ironic5) stumbled into6) decent7) buzzing8) abnormal9) mechanical10) Shuddering11) implied12) leap2.1) convert RMB into US dollars in theforeign exchange office at the airport.2) didn’t know the first thing about cooking as she looked puzzled as to how to cook rice with the rice cooker.3) their faulty equipment the team had accomplished some very useful work.4) allowing me to work flexible hours as long as I work eight hours a day.5) couldn’t help thinking the book must be quite fascinating.3.1) will not panic/feel panic; ’ll be at a disadvantage2) hybrid; transmissions3) crave; One indication; to distinguishII. Synonyms in Context1. also2. as well/too3. too4. also5. as well/too6. too。

2023数学专业英语试题及参考答案数学专业英语试题一、词汇及短语1. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions “在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or number symbols.equation ：“方程”“等式”等式是关于两个数或数的符号相等的'一种陈述3. In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。

注“two members”表等号的两端alike 相同的一样的On the performance of …中的“on”引导一个介词短语做状语Either…or…4. is true “成立”5. to more and change the terms移次和变形without making the equation untrue 保持方程同解数学专业英语试题二、句型及典型翻译1. change the terms about 变形2. full of ：有许多的充满的例 The streets are full of people as on a holiday(像假日一样，街上行人川流不息)3. in groups of ten…4. match something against sb. “匹配”例 Long ago ,when people had to count many things ,they matched them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。

最全的全新版大学英语第二版综合教程2答案课后练习答案Unit1 Ways of LearningPart II Reading TaskComprehensionContent QuestionPair Work1. They were studying arts education in Chinese kindergartens and elementary schools in Nanjing.2. Their 18-month-old son Benjamin was fond of trying to place the key into the slot of the key box during their stay at the Jinling Hotel.3. They would come over to watch Benjamin and then try to teach him how to do it properly.4. Because he realized that this anecdote was directly relevant to their assigned tasks in China: to investigate early childhood education and to throw light on Chinese attitudes toward creativity.5. Most of them displayed the same attitude as the staff at the Jinling Hotel.6. He emphasized that the most important thing is to teach the child that on can solve a problem effectively by oneself.7. He means that this incident pointed to important differences in educational and artistic practices between China and the USA.8. The manner in which the Chinese staff saw the need to teach the child by guiding his hand in the characteristic of a broader attitude to education, one that stands in contrast to the Western preference for leaving the child to explore and learn unaided. 9. One example is of children at the age of 5 or 6 painting flowers, fish and animals skillfully and confidently; in a second example, calligraphers 9 and 10 years old were producing works; and in a third, young artists work on perfecting their craft for several hours a day.10. Americans think that unless creativity has been acquired early, it may never emerge, and skills can be picked up later. Chinese think that if skills are not acquired early, they may never be acquired, and there is no hurry to promote creativity.11. This is mainly due to the difference in their way of thinking.12. The author makes the suggestion that we should strike a better balance between the poles of creativity and basic skills.Text OrganizationWorking On Your Own1.1) The text begins with an anecdote.2) His thoughts are mainly about different approaches to learning in China and the West.3) He winds up the text with a suggestion in the form of a question.2. Chinese1) Show a child how to do something, or tech by holding the hand2) Give greater priority to developing skills at an early age, believing that creativity can be promoted over timeAmericans1) Teach children that they should rely on themselves for solutions to problems2) Put more emphasis on fostering creativity in young children, thinking skills can be picked up laterLanguage Sense Enhancement(1) Summarizing(2) value originality and independence(3) contrast between(4) in terms of(5) harbor(6) fearful(7) comparable(8) promote creativity(9) emerge(10) picked upLanguage FocusVocabularyI1.1) insert2) on occasion3) investigate4) In retrospect5) initial6) phenomena7) attached8) make up for9) is awaiting10) not; in the least11) promote12) emerged2.1) a striking contrast between the standards of living in thenorth of the country and the south.2) is said to be superior to synthetic fiber.3) as a financial center has evolved slowly.4) is not relevant to whether he is a good lawyer.5) by a little-known sixteen-century Italian poet have found their way into some English magazines.3.1) be picked up; can’t accomplish; am exaggerating2) somewhat; the performance; have neglected; they apply to3) assist; On the other hand; are valid; a superiorII1.1) continual2) continuous3) continual4) continuous2.1) principal2) principal3) principle4) principles5) principalIII1. themselves2. himself/herself3. herself/by herself/on her own4. itself5. ourselves6. yourself/by yourself/on your own Comprehensive ExercisesI. cloze1.(1) contrast(2) exaggerating(3) priority(4) on the other hand(5) promoting(6) pick up(7) assist(8) accomplish(9) occasion(10) neglecting(11) worthwhile(12) superior2.0-(2) perform(3) facing(4) competent(5) equipped(6) designed(7) approach(8) rest(9) definitely(10) qualityII. translation1.(1) It takes an enormous amount of courage to make a departure from the tradition.(2) Tom used to be very shy, but this time he was bold enough to give a performance in front of a large audience.(3) Many educators think it desirable to foster the creative spirit in the child at an early age.(4) Assuming this painting really is a masterpiece, do you think it’s worthwhile to buy it?(5) If the data is statistically valid, it will throw light onthe problem we are investigating.2.To improve our English, it is critical to do more reading, writing, listening and speaking. Besides, learning by heart as many well-written essays as possible is also very important. Without an enormous store of good English writing in your head you cannot express yourself freely in English. It is also helpful to summarize our experience as we go along, for in so doing, we can figure out which way of learning is more effective and will produce the most desirable result. As long as we keep working hard on it, we will in due course accomplish the task of mastering English.Unit2 ValuesPart II Reading TaskComprehensionContent QuestionPair Work1. The Salvation Army is a religious charitable organization.A Salvation Army bell ringer is a volunteer who help it collect donations.2. The boy asked him: Are you poor? He did it simply out of confusion and curiosity. Obviously he knew nothing about the Salvation Army bell ringer.3. He said, “I have more than some people, but not as much as others.” This means that he was neither poor nor rich.4. The boy’s mother scolded him because the question was social inappropriate, especially to a person who looked poor.5. Yes, economically he is poor. He lives in a small basement apartment. He doesn’t even have a color TV. He falls into the lowest income category. And so on.6. No, the writer does not feel poor. This is because he has enjoyed good health and creativity which he thinks are much more important than material goods.7. He feels out of place among people who are primarily interested in material things.8. She told him that she was interested in what’s on the inside. but after he took her to his poorly furnished apartment, she changed her mind completely.9. It only shows that to her the most important thing was still material goods rather than what she had claimed before.10. Commercial can put people under pressure to purchase more than is really necessary.11. Because December is the time for to work for the Salvation Army as a bell ringer, which gives him a genuine sense of belonging and brings him happiness in helping others.12. The boy’s question has helped the writer realize that, despite his lack of expensive possessions, he is rich in many other ways and should be thankful for that.Text OrganizationWorking On Your Own1.1) a.√2) the essay is meant to explain something that is, the author’s view of life.3) That one can live a life full of riches without being rich financially.2.Part One: The writer’s encounter with a boy who raised the question “are you poor?”Part Two: In search of an answer the writer finds that not having expensive possessions doesn’t make him feel poor mainly because he enjoys life in many other ways.Part Three: In conclusion, the writer thinks he’s grown to understand more about himself because of the boy’s question.Language Sense Enhancement1.(1) attain(2) wear and tear(3) dependable(4) modest(5) primarily(6) minimal(7) exceptionally(8) illness-free(9) spirited(10) energizing Language Focus VocabularyI1.1) abrupt2) emotional3) bless4) wear and tear5) dated6) consequences7) seemingly8) in contrast to9) Curiosity10) genuine11) primarily12) sentiments2.1) confronted with more than one problem, try to solve the easiest one first.2) vital to the existence of all forms of life.3) some confusion among the students about what to do after class to follow up on the subject.4) nothing more than a job and an apartment to be happy.5) tickled him to think that she’d come to ask his advice 3.1) a lingering; fabricating; sentiments2) fill out; every item; vital; consequences3) be denied; tangible; cherish; attainII1. It is a long trip and will take us five hours by bus.2. She arrived early and took a front row seat.3. Don’t take me for a fool.4. It takes a lot of imagination to fabricate such a story.5. My uncle will take me (along on his trip) to the Arctic this summer.6. He took the dinner plate I passed to him.7. Kevin took second prize in the weight-lifting competition.8. If you don’t take my advice, you will regret it.III1. hanging2. to give3. to return4. being praised5. not having written6. to say7. to open8. being helpedComprehensive ExercisesI. cloze1.(1) well-off/affluent(2) dated(3) falling into(4) bracket(5) deny(6) tangible(7) pursuit(8) cherishes(9) out of place(10) abrupt(11) focus(12) donations2.(1) consume(2) fueled(3) annual(4) plain(5) physically(6) security(7) indicates(8) equally(9) traditional(10) followsIII. Translation1.1) The company denied that its donations had a commercial purpose.2) Whenever he was angry, he would begin to stammer slightly.3) Education is the most cherished tradition in our family.That’s why my parents never took me to dinner at expensive restaurants, but sent me to the best private school.4) Shortly after he recovered from the surgery, he lost his job and thus had to go through another difficult phase of his life.5) In contrast to our affluent neighbors, my parents are rather poor, but they have always tried to meet our minimal needs.2.With more and more donations coming in, our university will be much better off financially next year. We will thus be able to focus on the most important task that we, educators, must take on: to encourage students to attain their scholarly/academic goals, to train them to be dependable and responsible individuals, to prepare them for the life ahead, and to guide them in their pursuit of spiritual as well as material satisfaction.Unit3 The Generation GapPart II Reading TaskComprehensionContent QuestionPair Work1. There are seven characters---Father, Mother, Heidi, Diane, Sean, Restaurant Manager, and Mrs. Higgins.2. No. Because what he does usually ends up embarrassing them.3. To buy a guitar.4. To check if Sean was going to embarrass him.5. He knew his father was going to embarrass him.6. It was unnecessary and embarrassing.7. He wanted Dan to pressure his son into asking Diane to the senior prom.8. He would speak to his son and insist that the latter give Diane a call.9. She felt humiliated.10. Because the Thompson had just moved.11. He tried to let her know how exceptionally talented a young woman Heidi was.12. Because she couldn’t bear being embarrassed by her father. Text OrganizationWorking On Your Own1.1. A fast-food restaurant2. The Thompson family dining room3. An office at a high school2.Scene One: Father embarrassed Sean by talking too proudly to the restaurant manager.Scene Two: Father embarrassed Diane by persuading a colleague into pressing his son to ask her to the senior prom.Scene Three: Father embarrassed Heidi by boating to an official at her new school about how talented she was.Language Sense Enhancement1.(1) once in a while(2) for(3) the problem(4) he thinks(5) humiliated(6) class president(7) have(8) Actually(9) stop to think(10) interferenceLanguage FocusVocabularyI1.1) typical2) dumb3) junior4) glorious5) welfare6) came over7) interference8) fading9) narrowed down10) frank11) schemes12) at any rate2.1) consists of five generals and four police officers.2) will be in a location overlooking the lake.3) was humiliated by her comments about my family background in front of so many people.4) have any proof that it was Henry who stole the computer?5) was exhausted after the long cycle ride.3.1) hysterical; was handed down by; should have known better than2) twisted; over and over; talented son3) patience; not to keep him in suspense; assured; repeatedlyII. Collocation1. adequate2. anxious3. certain4. content5. crazy6. likely7. fortunate8. keenIII. Usage1. be admitted2. live3. be postponed4. buy5. be banned6. be Comprehensive ExercisesI. cloze1.(1) typical(2) welfare(3) constant(4) frank(5) talent(6) dumb(7) know better than that(8) repeatedly(9) dread(10) interference(11) bet(12) assure2.(1) despite(2) really(3) same(4) contact(5) admitted(6) attempt(7) not(8) tend(9) different(10) mannerII. Translation1.(1) Have scientists found proof of water on Mars?(2) The planning committee has narrowed down the possible locations for the nuclear power plant to two coastal towns.(3) Sam not only lost his job but also both legs; he had to live on welfare for the rest of his life.(4) A jury consisting of 12 members voted in unison that Mary was guilty.(5) Sean felt humiliated to hear his talent being questioned.2.George, the son of Mr. Johnson, liked listening to heavy metal music in the evenings, which made it hard for other residents in the community to fall asleep. Eventually the exhausted neighbors lost their patience and decided on direct interference. They called Mr. Johnson to tell him in a frank manner what they were thinking. Mr. Johnson assured them that he would certainly settle the issue. As soon as he put down the phone he scolded his son, “What has come over you? You should know better than to disturb others for your own amusement.”In the end George traded his CD’s for computer games software from his classmates.Unit4 The Virtual WorldPart II Reading TaskComprehensionContent QuestionPair Work1. She used to be a television producer, but now she is a writer.2. She writes and edits articles online, submits them via email, and communicates with colleagues via the Internet, too.3. She could stay computer-assisted at home for weeks, going out only t get mail, newspapers and groceries.4. They feel as if they had become one with the computer, and life seems to be unreal.5. That people who grew used to a virtual life would feel an aversion to outside forms of socializing.6. She gets overexcited, speaks too much, and interrupts others.7. She is bad-tempered, easily angered, and attacks everyone in sight, all because she has long become separated from others and lacks emotional face-to-face exchanges with people.8. She fights her boyfriend, misinterpreting his intentions because of the lack of emotional cues given by their typed dialogue.9. Because we rely on co-works for company.10. She calls people, arrangers to meet the few friends remaining in the City, gets to the gym, arranges interviews for stories, doctor’s appointments---anything to get her out of the house and connected with others.11. No, she doesn’t feel happy. She feels being face to face is intolerable.12. She makes her excuses and flees, re-enters her apartment, runs to the computer, clicks on the modem, and disappears into the virtual world again.Text OrganizationWorking On Your Own1.1. 2-32. 1,4-10,133. 114. 122.The first paragraph describes the consequences of living a virtual life and the last tells of the author’s escape back into it. Together, they bring out the dilemma people at present are in: Because of modern technology, we have a choice between a virtual life and real life, but find both unsatisfactory.Language Sense Enhancement1.(2) for company(3) unemployment(4) externally(5) drug abuse(6) restore(7) fled(8) gym(9) set apart(10) appointments VocabularyI1.1) conversely2) but then3) symptom4) spitting5) abusing6) tone7) took; in8) editing9) have arranged11) stretched12) data2.1) smoking cigarettes jars on me.2) find themselves getting sucked in.3) has arranged for a technician from the computer store to check and repair it.4) fled their country to avoid military service/fled to other countries to avoid military service.5) restore people’s confidence in it.3.1) the virtual; on line; via2) nightmare; routine; any appointment; arrange for3) cue; remarks; his tuneII. Collocation1. We came here all the way on foot.2. Private cars are not allowed on campus.3. They are on vacation in Florida.4. Mary has been talking to her friend on the phone for an hour.5. Don’t worry, Lucy is always on time.6. Industrial demand on fuel is on the rise.III. Usage1. hard2. difficult3. impossible4. tough5. hard6. easy Comprehensive ExercisesI. cloze1.(1) Internet(2) click(3) virtual(4) routines(5) arrange(6) nightmare(7) annoying(8) connection(9) crawls(10) take in(11) spit(12) data(13) sucked into(14) At times(15) flee(16) on line2.(1) companion(2) deliver(3) access(4) enables(5) customers(6) delights(7) provides(8) small(9) remote(10) informationII. Translation1.1) Research shows that laughter can bring a lot of health benefits.2) A show Internet connection speed is really annoying.3) As the law stands, helping someone commit suicide is a crime.4) In her report, Mary tries to interpret the data from a completely different angle.5) Sue is a girl of great talent. Her amazing memory sets her apart from her classmates.2.Perhaps you envy me for being able to work from home on the computer.I agree that the Internet has made my job a lot easier. I can write, submit and edit articles via email, chat with my colleagues on line and discuss work with my boss. With a click of the mouse, I can get all the data I need and keep up with the latest news. But then, communicating through the Net can be frustrating at times. The system may crash. Worse still, without the emotional cues of face-to-face communication, the typed words sometimes seem difficult to interpret.Unit5 Overcoming ObstaclesPart II Reading TaskComprehensionContent QuestionPair Work1. Because the pole was set at 17 feet which was three inches higher than his personal best.2. Because pole-vaulting combines the grace of a gymnast with the strength of a body builder.3. His childhood dream was to fly. His mother read him numerous stories about flying when he was growing up.4. Because he believed in hard work and sweat. His motto: If you want something, work for it!5. Michael's mother wished he could relax a bit more and be that "free dreaming" little boy. On one occasion she attempted to talk to him and his father about this, but his dad quickly interrupted, smiled and said, "You want something, work for it!"6. He began a very careful training program.7. He seemed unaware of the fact that he had just beaten his personal best by three inches. He was very calm.8. He began to feel nervous when the bar was set at nine inches higher than his personal best.9. What his mother had taught him about how to deal with tension or anxiety helped him overcome his nervousness.10. The singing of some distant birds in flight made him associate his final jump with his childhood dream.11. He could imagine the smile on his mother’s face. He thought his father was probably smiling too, even laughing. However, in fact, his father hugged his wife and cried like a baby in her arms. 12. Because he was blind.Text OrganizationWorking On Your Own1.Part One: Michael faced the most challenging competition in his pole-vaulting career.Part Two: Michael’s childhood was marked with dreams and tough training.Part Three: Michael topped his personal best, won the championship and set a new world record.2.(1) It also has the element of flying, and the thought of flying as high as a two-story building is a mere fantasy to anyone watching such an event.As long as Michael could remember he had always dreamed of flying.(2) All of Michael’s vaults today seemed to be the reward for his hard work.Language Sense Enhancement1.(1) startled(2) bale of hay(3) off(4) intensity(5) shaking the tension(6) tense(7) description(8) out of nowhere(9) pictured(10) scaredVocabularyI1.1) startled2) mere3) motion4) sweating5) stretched out6) vain7) On the occasion8) anxiety9) emotions10) ashamed of11) In my mind’s eye12) recurring2.1) coincides with her husband’s.2) sends the prices soaring/results in the soaring of prices.3) of alternate sunshine and rain.4) have been his lifelong passions, although he studied economics at university.5) Tension came over her3.1) media; dedication to; grace2) his competitors; in excitement; hug him; congratulate him on3) emotions; numerous; intensity; passion forII. Collocation1. Mike, a Green, made the suggestion that a large park be built near the community.2. In a letter to his daughter, Mr. Smith expressed his wish that she (should) continue her education to acquire still another degree.3. There is no reason to hold the belief that humans have no direct moral responsibility to safeguard the welfare of animals.4. Children need to feel safe about the world they grow up in, and it is unwise to give them the idea that everything they come into contact with might be a threat.5. Anxiety can result from the notion that life has not treatedus fairly.6. Nobody believed his claim that he was innocent.III. Words with Multiple Meanings1. I work out in the gym for one hour every morning.2. Florence has worked as a cleaner at the factory for five years.3. The wounded man worked his way across the field on his hands and knees.4. The safe load for a truck of this type works out at about twenty-five tons.5. It is difficult to understand how human minds work.6. To my disappointment, the manager’s plan of promoting the new products doesn’t work at all.7. The teacher has a lot of experience of working with children who don’t know how to learn.8. The medicine was like magic, and it worked instantly after you took it.Comprehensive ExercisesI. cloze1.(1) In my mind’s eye(2) groan(3) competitor(4) intensity(5) anxiety(6) tense(7) sweat(8) tension(9) soaring(10) recurring(11) brought me back to earth(12) fantasy(13) sweat(14) congratulate(15) number(16) media2.(1) engineer(2) forget(3) convinced(4) how(5) build(6) accident(7) thought(8) only(9) sharp(10) touched(11) instructions(12) finallyII. Translation1.1) It is the creativity and dedication of the workers and executives that turned the company into a profitable business. 2) The prices of food and medicine have soared in the past three months.3) We plan to repaint the upper floors of the office building.4) His success shows that popularity and artistic merit sometimes coincide.5) I don’t want to see my beloved grandmother lying in a hospital bed and groaning painfully.2.Numerous facts bear out the argument/statement/claim that in order to recover speedily from negative emotion, you should allow yourself to cry. You needn’t/don’t have to be ashamed of crying. Anxiety and sorrow can flow out of the body along with tears.Consider the case of/Take Donna. Her son unfortunately died in a caraccident. The intensity of the blow made her unable to cry. She said, “It was not until two weeks later that I began to cry. And then I felt as if a big stone had been lifted from my shoulders. It was the tears that brought me back to earth and helped me survive the crisis.”Unit6 Women, Half the SkyPart II Reading TaskComprehensionContent QuestionPair Work1. They liked girly toys such as a miniature kitchen, and Barbies.2. To convert a gas-guzzling SUV into a hybrid electric vehicle.3. Because she didn’t know anything about cars and was afraid of being cheated by the mechanic.4. She was craving independence and wanted to live away from home for some time.5. It helped her earn six engineering credits, which of course made it easier for her to become an engineering major.6. Five years.7. In her view, if you find a subject is difficult to learn, it does not mean you’re not good at it. It just means you have toset your mind and work harder to get good at it.8. Because he had confidence in her abilities believing she could have done better if she had studied more.9. No, she wasn’t always confident. She had moments of panic, worried that as a woman she would be unable to understand thermodynamics.10. She considers it wrong because it is based on a faulty premise.11. It is flexible and more powerful than we imagine.12. What she means is not to accept others’ opinions blindly but to use one’s own judgment.Text OrganizationWorking On Your Own1.Part One: The author describes how she stumbled into engineering. Part Two: The author writes about how she has overcome obstacles, including the bias against women, on her way to success.Part Three: The author draws the conclusion that women can do anything men can so long as they believe in their own abilities.2.1) she was not a tomboy.not to an engineering department.she didn’t know the first thing about engineering.because she craved independence from her parents.already earned her six credits in engineering.2) math and design.she participated in a national competition to convert an SUV into a hybrid electric vehicle.work harder at it.that she should study more.had to work hard at courses she found difficult, which encouraged her to keep going.Language Sense Enhancement1.(1) limit(2) denying(3) favor(4) others(5) relevant(6) translating(7) hard and fast conclusions(8) focus(9) incredibly flexible(10) consider the possibilityVocabularyI1.1) cultural/culture2) indication3) miniature4) ironic5) stumbled into6) decent7) buzzing8) abnormal9) mechanical10) Shuddering11) implied12) leap2.1) convert RMB into US dollars in the foreign exchange office at the airport.2) didn’t know the first thing about cooking as she looked puzzled as to how to cook rice with the rice cooker.3) their faulty equipment the team had accomplished some very useful work.4) allowing me to work flexible hours as long as I work eight。

2.3集合论的基本概念单词、词组1.1集set，子集subset，真子集proper subset，全集universal subset，空集void/ empty set，基地集the underlying set 1.2正数positive number，偶数even integer，图形diagram，文氏图V enn diagram，哑标dummy index，大括号brace 1.3可以被整除的be divisible by，两两不同的distinct from each other，确定的definite，无关紧要的irrelevant/inessential 1.4一样的结论the same conclusion，等同的效果equivalent effect，用大括号表示集sets are designated by braces，把这个图形记作A：this diagram is designated by letter A，区别对象to distinguish between objects，证明定理to prove theorems，把结论可视化to visualize conclusions/consequences汉译英2.1由于小于10且能被3整除的正整数组成的集是整数集的子集。

The set consisting of those positive integers less than 10 which are divisible by 3 is a subset of the set of all integers.2.2如果方便，我们通过在括号中列举元素的办法来表示集。

When convenient，we shall designate sets by displaying the elements in braces.2.3用符号￠表示集的包含关系，也就是说，式子A￠B表示A包含于B。