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MULTIV ARIABLE CALCULUSEXAM1F ALL2012Name:Honor Code Statement:Directions:Complete all problems.Justify all answers/solutions.Calculators are not permitted.Best of luck.(1)Find a unit vector that is perpendicular to both2i+j−3k and i+k.(2)If a·b=a·c and a=0,does it follow that b=c?Explain.Date:October11,2012.12MULTIV ARIABLE CALCULUS EXAM1F ALL2012(3)Give an equation for the plane containing the point(9,5,−1)and perpen-dicular to i−2k.Now give the set of parametric equations for this plane.MULTIV ARIABLE CALCULUS EXAM1F ALL20123 (4)State the Cauchy-Schwarz Inequality.(5)Is the following set closed?Give reason for your answer.X={(x,y,z)∈R3|0≤x≤1,0≤y≤1,0≤z<1}.(6)Is the function f(x,y)=xy−7x8y2+cos(x)differentiable at every pointin its domain?Why,or why not?(7)Given that f(x,y,z)=e ax sin(y)+x2sin(y)+x10y3−e bx cos(z).Note thatf(x,y,z)is class C∞(i.e it is smooth).Find f zxx.4MULTIV ARIABLE CALCULUS EXAM1F ALL2012(8)Determine several(say3with c≥0and3with c<0)level curves of thegiven function f(and make sure to indicate the height c of each curve).Use this information to describe the graph of f,be as specific as you can.(A sketch would be appropriate,but not required.)f(x,y)=xyMULTIV ARIABLE CALCULUS EXAM1F ALL20125 (9)Show that the following limit does not exist.lim (x,y)→(0,0)(x+y)2 x2+y26MULTIV ARIABLE CALCULUS EXAM1F ALL2012(10)Find a“good”linear approximation to the function f(x,y)=e x+2y at thepoint(0,0).Use this approximation to estimate the value of the function at(0.1,0.1)MULTIV ARIABLE CALCULUS EXAM1F ALL20127 (11)Find the gradient f(a),where f(x,y)=e xy+ln(x−y)and a=(2,1).(12)Find the matrix of partial derivatives of the function f(s,t)=(st,t sin(s),se t).8MULTIV ARIABLE CALCULUS EXAM1F ALL2012(13)A rectangular stick of butter(that is a right parallelepiped with squarebase)is placed in a microwave to melt.When the butter’s length is6 inches and its square cross-section measures1.5inches on a side,its length is decreasing at a rate of0.25inches per minute and its cross-sectional edge is decreasing at a rate of0.125inches per minute.How fast is the butter melting(i.e.at what rate is the solid volume of butter turning to liquid) at that instant?。
Math 231 Multivariable Calculus Fall 2008 Section 1 MWF 9:00 – 9:50 am King 239Section 2 MWF 10:00 – 10:50 am King 239Instructor:Susan Jane ColleyKing 222775-8388 (office) or -8380 (messages)775-3680 (home—please call before 10:00 pm)E-mail: *********************.edu(preferred)************************Web page: /~math/faculty/colley.htmlOffice Hours:Monday 11:00 am – noon, 3:30 – 4:30 pmTuesday 3:00 – 5:00 pmWednesday 3:30 – 5:00 pmFriday 11:00 am – noonAlso by appointmentText:S. J. Colley, Vector Calculus, 3rd ed.,Prentice Hall. This text is required and available at the Oberlin Bookstore. In addition, you should make sure that youhave easy access to a one-variable calculus text, in the event that you need toreview some topics.On Reserve:There are several copies of alternative texts on multivariable calculus placed on reserve for this course in Mudd Library, namely:J. Marsden, A. Tromba, and A. Weinstein, Basic Multivariable Calculus,W. H. Freeman / Springer Verlag.J. Marsden and A. Tromba, Vector Calculus, 3rd ed., W. H. Freeman.K. Pao and F. Soon, Study Guide for Vector Calculus, 3rd ed.J. Stewart, Multivariable Calculus, 3rd ed., Brooks/Cole.You are welcome, even encouraged, to consult these books (and any others) tosee additional examples and alternative approaches to the concepts. The onlytime you will be asked not to use these books is when you take certain exams. Goals:This course is devoted to the development of the calculus (differentiation and integration) of functions of several variables. Many of the ideas we will exploreare natural generalizations of concepts you have seen in one-variable calculus.The emphasis in this course will be on developing your mathematical intuition(especially your geometric intuition) as well as your technical prowess, so that yougain a meaningful understanding of the theory, computations, and applications thatcan be employed in a variety of contexts.Homework:The attached syllabus contains problems for you to work in order to gain some familiarity with the material. These problems are not to be turned in (unlessotherwise noted). You should do as many or as few of them as you need in orderto feel comfortable with the topics discussed in class. In addition, there will beseparately assigned, hand-in problem sets due weekly (usually Wednesdays). Nolate assignments will be accepted, but you may submit incomplete assignments.Solutions to the hand-in problem sets will be available online and in King 203. Exams:There will be one in-class, closed-book exam, two open-book, take-home exams, and a two-hour, closed-book final. Tentative dates for the midterm exams areOctober 3 (in-class), November 5 (take-home due), and December 3 (take-home due). Please let me know as soon as possible if there is a problem with anyof these dates. The final exam will take place on Thursday, December 18 from2:00 to 4:00 pm for Section 2 and Friday, December 19 from 2:00 to 4:00pm for Section 1.Participation:C lass attendance is not a formal part of your grade for the course. Therefore, you need not explain if you must miss a class, but you are responsible for finding outwhat material was discussed. It is certainly recommended that you attend asmany classes as possible, and that you are an active participant in them. Pleasetry to arrive on time; it can be quite disruptive to your classmates to havelatecomers and, moreover, it can be much more difficult for you to get what youneed from class if you are late.Grading:Midterm exams (100 points each) 300Final exam 200Homework 100TOTAL 600Deadlines:I will endeavor to be as clear as I can about the nature of assignments, and I will provide fair warning about when they are due. Late assignments normally willnot be accepted. At the same time, I do understand that emergencies arise, so ifunforeseen circumstances are interfering with your ability to complete some workin the course (e.g., significant illness, but not assignments for other classes), pleasecontact me immediately, preferably before the assignment is due.Online:Copies of assignments, handouts, etc. will be posted on the course Blackboard site. Go to (and your ―Academic Hub‖) toaccess these materials.Note:If you have a documented disability and wish to discuss academic accommodations, please contact me as soon as possible.Help:You should feel free to ask me questions about the material discussed in class, problems with the homework, life outside of vector calculus, etc. My office hoursappear above, but if they are inconvenient, you are welcome to arrange anothertime to meet with me. Besides me, you can also get help through StudentAcademic Services. This is mainly for more extensive help. To obtain this service,you need to get a card from Kay Knight in Peters 114 and bring it to me. After Isign the card, you shortly thereafter will be assigned a private undergraduate tutor. Note:Please note that the text, Vector Calculus, contains more material in places than you will be expected to master. When doing your reading, you should stressthose topics and examples that align most closely with class discussions, although,of course, you are certainly welcome (even encouraged) to read more thoroughly.I will be happy to discuss any subtleties or more advanced topics with youindividually.Outline of the CourseVectors (Chapter 1) 3.5 weeksDifferentiation in several variables (Chapter 2) 3 weeksVector-valued functions (Chapter 3) 1.5 weeksMaxima and minima (Chapter 4) 1.5 weeksMultiple integration (Chapter 5) 2 weeksLine integrals (Chapter 6) 1.5 weeksReadings and problems below are from Vector Calculus,2nd ed.Note that ―7/1‖ means problem 1 on page 7 of Vector Calculus. The problems assigned below are not to be turned in (unless otherwise noted); they are intended for your own practice. As a result, you should feel free to work together on these questions, ask me about them, etc.A strongly recommended routine is for you to do some relevant reading in the text before a topic is discussed in class, then to reread and work problems once that topic has been discussed. Also, please note that the dates indicated below are only approximations—please come to class to find out where we are!Date Topics Reading ProblemsVECTORSW 9/3 Introduction Preface (pp. xiii–xv)Vectors in R2 and R3 1.1 7/ 1,2,3,9,19,21,25F 9/5 Vectors (contd.) 1.2 16/ 1,3,5,9,10,11,13,17M 9/8 Vectors (contd.) 1.2 16/ 23,26,27,29,31,33W 9/10 Dot product 1.3 25/ 1,3,5,7F 9/12 Dot product (contd.) 1.3 25/ 11,17,21,23,26M 9/15 Cross product 1.4 37/ 1,3,5,7,8,11,13,15,18,20,25W 9/17 Flat stuff 1.5F 9/19 Flat stuff (contd.) 1.5 46/ 1,3,5,6,7,9,11,13,15,21,25Some n-dim’l geometry 1.6M 9/22 n-dim’l ge ometry (contd.) 1.6 57/ 1,3,5,7,13,17,19,24W 9/24 Cylindrical, spherical coords. 1.7 71/ 1,3,5,9,11,15,17F 9/26 Cylin., spherical coords. (contd.) 1.7 71/ 23,27,31,33DIFFERENTIATION IN SEVERAL VARIABLESM 9/29 Functions of several variables 2.1 92/ 1,5,7,8,11W 10/1 F’ns of sev’l vars. (contd.) 2.1 92/ 19,24,25,28,35,37,41 Limits 2.2F 10/3 Exam 1 (in class)M 10/6 Limits (contd.) 2.2 107/ 7,8,9,11,13,19,21,34,39W 10/8 Differentiation 2.3 124/ 1,3,5,11,15,17,21,2327,29,35,51F 10/10 Differentiation (contd.) 2.3, 2.4 (to p.130) 137/ 3,5,7,9,13,17,19,21M 10/13 Chain rule 2.5 150/ 1,2,3,5,11,17,19,23W 10/15 Directional derivatives 2.6 167/ 1,3,5,9,11,13,15F 10/17 Direct. derivs. (contd.) 2.6 (to p. 162) 168/ 17,19,23,29VECTOR-VALUED FUNCTIONSM 10/27 Parametrized curves 3.1 188/ 1,2,5,7,9,13,15,17,19,27W 10/29 Arclength 3.2 (to p. 194) 206/ 1,3,9,10,11F 10/31 Vector fieldsDivergence and curl 3.3 213/ 1,3,5,9,17,19,21M 11/3 Divergence and curl (contd.) 3.4 221/ 1,3,5,7,11,13,15,23,27MAXIMA AND MINIMAW 11/5 Taylor’s Theorem 4.1 244/ 1,5,7,8,13,15,19,23,25,27,31 Exam 2 due (take-home)F 11/7 Extrema of functions 4.2M 11/10 Extrema (contd.) 4.2 257/ 1,3,7,9,17,21,23,29,37,39 W 11/12 Lagrange multipliers 4.3 270/ 1,3,5,7,9,17,21,27,31F 11/14 Lagrange mults. (contd.) 4.3, 4.4 (skim)MULTIPLE INTEGRATIONM 11/17 Introduction: volumes 5.1 291/ 1,3,7,11,13Double integrals 5.2W 11/19 Double integrals (contd.) 5.2 307/ 1,3,7,11,13,15,17,28 Changing order of integration 5.3 311/ 1,3,7,15F 11/21 Triple integrals 5.4 321/ 1,5,8,11,17,23M 11/24 Change of variables theorem 5.5 341/ 1,3,7W 11/26 Change of variables (contd.) 5.5 342/ 9,13,17M 12/1 Applications 5.6 (to p. 353) 355/ 1,3,9,11,13,15,25LINE INTEGRALSW 12/3 Line integrals 6.1Exam 3 due (take-home)F 12/5 Line integrals (contd.) 6.1 (to p. 375) 379/ 1,3,7,11,17,21,25M 12/8 Green’s Theorem 6.2 388/ 1,3,7,9,15,19,25W 12/10 Conservative vector fields 6.3 399/ 1,3,5,11,17,21F 12/12 Review and a look aheadThursday, 12/18 2:00–4:00 pm FINAL EXAM for SECTION 2Friday, 12/19 2:00–4:00 pm FINAL EXAM for SECTION 1Honor Code PoliciesHomeworkYou are permitted, even encouraged, to collaborate on homework. For homework that is not graded, feel free to consult anyone at all: your classmates, me, other students, friends, relatives, Britney Spears, Stephen Colbert (these last two not really). For homework that is to be handed in and graded, I expect you to be somewhat more careful. Specifically, you should continue to ask questions of me regarding homework problems and you may collaborate with one or two of your classmates (per assignment). Please do not undertake significant collaboration with more than two students without permission. If you do collaborate, you are expected to write your own solution to problems (i.e., not to copy) and to indicate the name(s) of any student(s) with whom you worked.You may consult any written sources for hand-in homework, provided that you give appropriate citations. Please write your homework solutions with care.ExaminationsUnless specifically indicated otherwise, in-class tests are assumed to be closed-book. Collaboration of any sort (other than to ask me questions) will not be permitted. Take-home exams will have specific provisions for using books and notes, but, again, you are not to discuss the content of the exam with anyone other than me. Any time limits will be indicated with each test.Honor PledgeOn every assignment that you submit for credit, you are expected to sign the Oberlin College Honor Pledge:―I have adhered to the Honor Code on this assignment.‖If you need clarification of the policies above, please do not hesitate to ask. Should you require some variation in these rules, you must discuss the matter with me well in advance of any assignment. For general information about the Honor System at Oberlin, consult</students/links-life/rules-regs.html>.Guidelines for Written WorkMathematics is not only a means for understanding quantitative issues, but is also provides an effective and efficient notational and conceptual supplement to natural language. Good communication of mathematics requires thoughtful and precise prose writing, especially when trying to convey complex arguments and ideas.When you attempt any mathematical writing, you should bear the following in mind:∙Mathematical symbols provide an extremely compact and concise form of expression, so it is important that you surround your symbols with words, phrases, and sentences. It is expected that you will write your problem solutions in clear, grammatically correct prose consisting of complete sentences. Remember, you are providing a coherent solution, not just a list of answers. The reader should not have to guess about what you are thinking.∙―2 + 2 = 4‖ is a symbolic way of writing a sentence. In particular, the symbol ―=‖ means ―equals‖ and is a verb, equivalent to the verb ―to be‖.∙While we’re on the subject, you should have the greatest respect and reverence for the eq uals sign.Use it only to indicate that two quantities are actually equal (to the best of your knowledge), not as punctuation or to fill space on the page.∙You should expect to revise and rewrite your solutions before submission. Do not hand in your rough scratch work. If you cannot solve a problem completely, then write an honest, coherent attempt and indicate where you’ve had difficulties.∙Homework should be neatly and legibly written, the problems properly labeled (and in order), and the pages stapled. Final answers should be clearly marked as such. Presentation does make a difference and can even help you with your understanding.It takes time and practice to write mathematics well. If you make the effort, your written presentation is certain to improve.。
超实用!ap微积分教材推荐正在进行ap微积分备考的同学们，你们使用的是哪些ap微积分教材呢?在今天的文章中，留学小编就为同学们推荐了6本极为实用的教材：Cracking the ap calculus AB&BC exams 2008 Edition、Barron''s ap Calculus with CD-ROM、Barron’s ap微积分2008、Kaplan ap Calculus AB & BC 2009、《高等数学》和《微积分》以及高中数学课本，希望大家能够重视!提前预祝各位考生能够在ap微积分考试取得满意成绩!ap微积分课程包括微积分AB (Calculus AB) 和微积分BC(Calculus BC)两门课。
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下面，小编就为大家推荐几本及其实用的ap微积分教材，希望可以同学们在ap微积分考试中取得满意成绩!1.Cracking the ap calculus AB&BC exams 2008 Edition作者：David S.Kahn 2.Barron''s ap Calculus with CD-ROM (Paperback)作者：Shirley O. Hockett，David Bock Barron''s Educational Series3.Barron’s ap微积分2008(附1张cd-rom)作者：张鑫(译)世界图书出版公司北京公司4.Kaplan ap Calculus AB & BC 2009(Kaplan ap Calculus Ab and Bc)作者:Ruby Kaplan Publishing5.中文参考书：高等教育出版社出版的《高等数学》和《微积分》以及高中数学课本。
Math1A,Calculus Final Exam Solutions Haiman,Fall2004 1.Evaluate the limit if it exists(possibly as an infinite limit).(a)limx→11(ln x)2(a)lim x→11/ln x does not exist,(b)lim x→11/(ln x)2=+∞.2.Differentiate the function y=sin(sin(sin x)).y =cos(sin(sin x))cos(sin x)cos x.3.Find(a)all local maxima and minima of the functionf(x)=x1−xe xy.6.Suppose we use Newton’s method to approximate the root r of the function whose graph is shown,using x1=1for thefirst approximation.1r2-11For the next approximation x2,decide whether x2<r or x2>r.Justify your answer.The tangent line at x=1crossess the x axis to the right of r,because the graph is concave downward.Therefore x2>r.7.Find the largest area of a rectangle with horizontal and vertical sides,lower-left corner at the origin (0,0),and upper-right corner on the curve y =e −x .We must maximize A =xe −x .We have dA/dx =(1−x )e −x =0at x =1.It’s a maximum by the first derviative test.The area is A =e −1.8.Find the limit.lim x →∞x 1/(1+ln x )We have lim x →∞x 1/(1+ln x )=lim x →∞e (ln x )/(1+ln x ).Now lim x →∞(ln x )/(1+ln x )=1,so lim x →∞x 1/(1+ln x )=e .9.If x a f (t )dt =x ln x for all x >0,find the function f (x )and the constant a .By the fundamental theorem of calculus,f (x )=d2 −40e u du =−12.11.Evaluate the indefinite integral.(x +1)(x +2)x 2dx = 1+3x −1+2x −2dx =x +3ln x −2/x +C.12.Sketch the region enclosed by the lines x =2,y =2and the curve xy =1,and find its area.1212The area is given by21/22−1/x dx =2x −ln x ]21/2=3−ln 2+ln(1/2)=3−2ln 2.13.Find the average value of the function f(x)=1/x on the interval[1,3].1x =ln x2.14.Find the volume of the circular cone obtained by rotating the triangle enclosed by the x and y axes and the line x+y=1about the y axis.10π(1−y)2dy=− 01πu2du=−πu3/3 01=π/3.15.Set up,but do not evaluate,an integral for the volume of the solid obtained by rotating the region enclosed by the x axis,the line x=2,and the curve y=xe−x about the y axis.202πx2e−x dx.。
AP® Calculus AB2011 Free-Response QuestionsForm BAbout the College BoardThe College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is made up of more than 5,900 of the world’s leading educational institutions and is dedicated to promoting excellence and equity in education. Each year, the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success — including the SAT® and the AdvancedPlacement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators and schools.© 2011 The College Board. College Board, Advanced Placement Program, AP, AP Central, SAT and the acorn logo are registered trademarks of the College Board. Admitted Class Evaluation Service and inspiring minds are trademarks owned by the College Board. All other products and services may be trademarks of their respective owners. Visit the College Board on the Web: . Permission to use copyrighted College Board materials may be requested online at:/inquiry/cbpermit.html.Visit the College Board on the Web: .AP Central is the official online home for the AP Program: .SECTION II, Part ATime—30 minutesNumber of problems—2A graphing calculator is required for these problems.1. A cylindrical can of radius 10 millimeters is used to measure rainfall in Stormville. The can is initially empty, and rain enters the can during a 60-day period. The height of water in the can is modeled by the function S , where ()S t is measured in millimeters and t is measured in days for 060.t ££ The rate at which the height of the water is rising in the can is given by ()()2sin 0.03 1.5.S t t =+¢(a) According to the model, what is the height of the water in the can at the end of the 60-day period?(b) According to the model, what is the average rate of change in the height of water in the can over the60-day period? Show the computations that lead to your answer. Indicate units of measure.(c) Assuming no evaporation occurs, at what rate is the volume of water in the can changing at time 7?t = Indicate units of measure.(d) During the same 60-day period, rain on Monsoon Mountain accumulates in a can identical to the one in Stormville. The height of the water in the can on Monsoon Mountain is modeled by the function M , where()()321330330.400M t t t t =-+ The height ()M t is measured in millimeters, and t is measured in days for 060.t ££ Let ()()().D t M t S t =-¢¢ Apply the Intermediate Value Theorem to the function D on the interval 060t ££ to justify that there exists a time t , 060,t << at which the heights of water in the two cans are changing at the same rate.2. A 12,000-liter tank of water is filled to capacity. At time 0,t = water begins to drain out of the tank at a rate modeled by (),r t measured in liters per hour, where r is given by the piecewise-defined function ()0.2600f or 051000for 5t t t r t e t -Ï££Ô=ÌÔ>Ó(a) Is r continuous at 5?t = Show the work that leads to your answer.(b) Find the average rate at which water is draining from the tank between time 0t = and time 8t = hours. (c) Find ()3.r ¢ Using correct units, explain the meaning of that value in the context of this problem.(d) Write, but do not solve, an equation involving an integral to find the time A when the amount of water in the tank is 9000 liters.WRITE ALL WORK IN THE EXAM BOOKLET.END OF PART A OF SECTION IISECTION II, Part BTime—60 minutesNumber of problems—4No calculator is allowed for these problems.3. The functions f and g are given by ()f x = and ()6.g x x =- Let R be the region bounded by the x -axis and the graphs of f and g , as shown in the figure above.(a) Find the area of R .(b) The region R is the base of a solid. For each y , where 02,y ££ the cross section of the solid taken perpendicular to the y -axis is a rectangle whose base lies in R and whose height is 2y . Write, but do not evaluate, an integral expression that gives the volume of the solid.(c) There is a point P on the graph of f at which the line tangent to the graph of f is perpendicular to the graph of g . Find the coordinates of point P .4. Consider a differentiable function f having domain all positive real numbers, and for which it is known that()()34f x x x -=-¢ for 0.x >(a) Find the x -coordinate of the critical point of f . Determine whether the point is a relative maximum, a relativeminimum, or neither for the function f . Justify your answer.(b) Find all intervals on which the graph of f is concave down. Justify your answer.(c) Given that ()12,f = determine the function f .WRITE ALL WORK IN THE EXAM BOOKLET.t(seconds) 0 10 40 60()B t(meters)1001369 49 ()v t(meters per second) 2.0 2.3 2.5 4.65. Ben rides a unicycle back and forth along a straight east-west track. The twice-differentiable function B models Ben’s position on the track, measured in meters from the western end of the track, at time t , measured in seconds from the start of the ride. The table above gives values for ()B t and Ben’s velocity, (),v t measured in meters per second, at selected times t .(a) Use the data in the table to approximate Ben’s acceleration at time 5t = seconds. Indicate units of measure. (b) Using correct units, interpret the meaning of ()600v t dt Ú in the context of this problem. Approximate()600v t dt Ú using a left Riemann sum with the subintervals indicated by the data in the table.(c) For 4060,t ££ must there be a time t when Ben’s velocity is 2 meters per second? Justify your answer. (d) A light is directly above the western end of the track. Ben rides so that at time t , the distance ()L t betweenBen and the light satisfies ()()()()22212.L t B t =+ At what rate is the distance between Ben and the light changing at time 40?t =WRITE ALL WORK IN THE EXAM BOOKLET.6. Let g be the piecewise-linear function defined on []2,4p p - whose graph is given above, andlet ()()()cos .2x f x g x =- (a) Find ()42.f x dx p p -Ú Show the computations that lead to your answer.(b) Find all x -values in the open interval ()2,4p p - for which f has a critical point. (c) Let ()()30.x h x g t dt =Ú Find ().3h p -¢WRITE ALL WORK IN THE EXAM BOOKLET.END OF EXAM。
Unit 5 Nelson Mandela—a modern hero Ｉ．单元教学目标II．目标语言III. 教材分析和教材重组I. 教材分析本单元以Nelson Mandela —— a modern hero 为话题，目的在于使学生了解一个伟大的人应具备怎样的品质，学会表达自己的观点，并用所学的句型来描写一个伟人。
1.1 Warming Up列出一些形容词让学生判断一下哪些可以用来描述伟大的人，一个伟大的人应具备怎样的品质。
1.2 Pre-reading给学生提供了六个名人的图片，要求利用图片下面标注的人物的重要事迹以及学生对他们的了解，来判断这六个人谁是伟人，谁是重要的人但不是伟人。
1.3 Reading介绍Elias的生平，向学生展示Nelson Mandela是一个怎样的人。
这是一篇记叙文，让学生学会利用时间顺序描述一个人一生的主要活动。
1.4 Comprehending练习1和3帮助学生利用判断正误和时间顺序来整体理解课文。
练习2和4要求学生进一步了解课文细节。
1.5 Learning about Language分词汇和语法两部分。
其中Discovery useful words and expressions是根据课文语境在运用中掌握词汇，Grammar是有关关系副词where, when, why以及“介词＋关系代词”引导定语从句的用法，并通过练习加以巩固。
1.6 Using Language分为三部分，一是Listening，练习听力可配合P72的Listening Task进行。
二是Reading，这也是一篇精读文章，更详细地了解曼德拉。
三是Writing，要求利用时间顺序简要地描述一个人。
2. 教材重组2.1 因本教材重点强调的是阅读能力，故将Reading, Comprehending，Using Language 中的Reading合在一起设计成一节“阅读课”（一）（精读课）。
Final Examination DescriptionsExam Date: July 3, 2015Duration: 90 minutesSections:I.Define the following terms. Give examples to illustrate your answers. (15%) (每题3分, 共15分)e.g.1. morphemePlease refer to Appendix A for more information about this section.II.Identify the word-formation process involved in the creation of each of the underlined words below. Write your answer on the line provided. (10%) (每题1分，共10分)e.g.1. bitter, sw eet → bittersweet________(Based on Lectures 5, 6 and 7.)III.Fill in the blanks with words formed from the given stems. (15%) (每题1分，共15分)e.g.1. The local people were actually __________; they often spoke three, four, five languages.(lingual)(Based on Lectures 5, 6 and 8.)IV. Provide the meaning and an example word for each of the following roots below. (30%)(每题1.5分, 共30分)Please refer to Appendix B for more information about this section.V. For each sentence or sentence pair below, classify the meaning relation between the two words marked in bold into one of the following types of relation: homonymy, synonymy, antonymy, hyponymy, meronymy, portion-mass, or member-collection. (10%) (每题1分，共10分）e.g.1. It was a remark made in private, not in public.(Based on Lectures 12, 13 and 14.)VI. Each sentence below contains an incomplete collocation. Complete the collocation by filling in the blank with a suitable word from the words provided in the box. Use the words in their proper forms. Each word can only be used once. (20%) (每题1分，共20分）e.g.1.The Titanic sank on her __________ voyage.(Based on Lectures 14 and 15)Appendix ADefine the following terms. (You may want to use examples from the respective lectures or come up with your own examples to support your answer.)1.morphemeA morpheme is the smallest unit of language that has its own meaning, either a word or a part of a word. Inother words, it is a meaningful form that cannot be divided into smaller meaningful parts. (Lecture 4)2.morphologyMorphology is the study of the internal structure of words. In particular, it is the study of morphemes and their arrangements in forming words. (Lecture 4)3.free morphemeA free morpheme is a morpheme that can occur alone as an independent word. (Lecture 4)4.bound morphemeA bound morpheme is a morpheme that cannot occur as an independent word on its own but must becombined with other morphemes to form words. (Lecture 4)5.rootThe root of a word is the morpheme that conveys the main meaning of the word. (Lecture 4)6.affixAn affix is a bound morpheme added to the beginning (prefix) or end (suffix) of a stem. (Lecture 4)poundingCompounding is a word-formation process where two or more independent words are combined to form a new word. (Lecture 6)8.conversionConversion is a word-formation process by which a word of one part of speech is converted to another part of speech without any change of form, either in pronunciation or spelling. (Lecture 7)9.homonymyHomonymy refers to the relation between two words that are spelled or pronounced the same but differ in meaning. (Lecture 12)10.hyponymyHyponymy refers to the hierarchical relation that holds between a word with a more general meaning and a word with a more specific meaning. (Lecture 13)Appendix B。
18th EditionCalculusVisit our website at /clep for the most up-to-date information.The materials in these fi les are intended for personal use by students preparing for aCollege-Level Examination Program (CLEP®) examination. These materials are ownedand copyrighted by the College Board. All copyright notices must rem ain intact.Violations of this policy may be subject to legal action, including but not limited to,payment for each guide that is disseminated unlawfully and associated damages.© 2006 The College Board. All rights reserved. College Board, College-Level Examination Program, CLEP,CalculusDescription of the ExaminationThe Calculus examination covers skills and concepts that are usually taught in a one-semester college course in calculus. The content of each examination is approximately 60% limits and differential calculus and 40% integral calculus. Algebraic, trigonometric, exponential, logarithmic, and general functions are included. The exam is primarily concerned with an intuitive understanding of calculus and experience with its methods and applications. Knowledge of preparatory mathematics, including algebra, plane and solid geometry, trigonometry, and analytic geometry is assumed.Students are not permitted to use a calculator during the CLEP Calculus exam.The examination contains 45 questions to be answered in 90 minutes. Any time candidates spend on tutorials and providing personal information is in addition to the actual testing time.Knowledge and Skills RequiredQuestions on the exam require candidates to demon-strate the following abilities:• Solving routine problems involving the techniques of calculus (about 50% of the examination)• Solving nonroutine problems involving an understanding of the concepts and applications of calculus (about 50% of the examination)The subject matter of the calculus examination is drawn from the following topics. The percentages next to the main topics indicate the approximate percentages of exam questions on those topics. 5%Limits• Statement of properties, e.g., limit of a constant, sum, product, or quotient• Limits that involve infi nity, e.g., lim x x →01is nonexistent and lim sin x xx→∞=0• Continuity55% Differential CalculusThe Derivative • Defi nitions of the derivative,e.g., ′=−−→f a f x f a x ax a ()lim ()()and ′=+−→f x f x h f x hh ()lim()()0• Derivatives of elementary functions• Derivatives of sum, product, and quotient (including tan x and cot x )• Derivative of a composite function (chain rule), e.g., sin ,,ln()ax b ae kx kx +()• Derivative of an implicitly defi ned function • Derivative of the inverse of a function (including Arcsin x and Arctan x )• Derivatives of higher order• Corresponding characteristics of graphs of f f f ,,′′′and • Statement (without proof) of the Mean Value Theorem; applications and graphical illustrations• Relation between differentiability and continuity • Use of L ’Hôpital’s rule (quotient and indeterminate forms)Applications of the Derivative • Slope at a point• Tangent lines and linear approximation • Curve sketching: increasing and decreasing functions; relative andabsolute maximum and minimum points; concavity; points of infl ection • Extreme value problems• Velocity and acceleration of a particle moving along a line• Average and instantaneous rates of change • Related rates of change40% Integral CalculusAntiderivatives and Techniques of Integration • Concept of antiderivatives • Basic integration formulas• Integration by substitution (use of identi-ties, change of variable)The following sample questions do not appear on an actual CLEP examination. They are intendedto give potential test-takers an indication of the format and diffi culty level of the examination, and to provide content for practice and review. Knowing the correct answers to all of the sample questionsis not a guarantee of satisfactory performance on the exam.C A L C U L U S1. C2. E3. B4. D5. C6. D7. A8. D9. B10. D11. D12. D13. B14. D15. D16. B17. E18. B19. C20. E21. E22. C23. C 24. B25. D26. E27. B28. D29. C30. A31. B32. C33. D34. D35. B36. D37. C38. D39. C40. B41. B42. A43. B44. A45. AStudy ResourcesTo prepare for the Calculus exam, you shouldstudy the contents of at least one introductorycollege-level calculus textbook, which you can fi ndin most college bookstores. Y ou would do well toconsult several textbooks, because the approaches tocertain topics may vary. When selecting a textbook,check the table of contents against the “Knowledgeand Skills Required” for this exam.Additional suggestions for preparing for CLEP examsare given in “Preparing to Take CLEP Examinations.”Answer KeyI. Preparing to Take CLEP ExaminationsHaving made the decision to take one or more CLEP exams, most people then want to know how to prepare for them—how much, how long, when, and how should they go about it? The precise answers to these questions vary greatly from individual to individual. However, most candidates fi nd that some type of test preparation is helpful.Most people who take CLEP exams do so to show that they have already learned the key material taught in a college course. Many of them need only a quick review to assure themselves that they have not forgotten what they once studied, and to fi ll in some of the gaps in their knowledge of the subject. Others feel that they need a thorough review and spend several weeks studying for an exam. Some people take a CLEP exam as a kind of “fi nal exam” for independent study of a subject. This last group requires signifi cantly more study than do those who only need to review, and they may need some guidance from professors of the subjects they are s tudying.The key to how you prepare for CLEP exams often lies in locating those skills and areas of prior learning in which you are strong and deciding where to focus your energies. Some people may know a great deal about a certain subject area but may not test well. These individuals would probably be just as concerned about strengthening their test-taking skills as they would about studying for a specifi c test. Many mental and physical skills are used in preparing for a test. It is important not only to review or study for the exams but also to make certain that you are alert, relatively free of anxiety, and aware of how to approach standardized tests. Suggestions about developing test-taking skills and preparing psychologically and physically for a test are given in this chapter. The following section suggests ways of assessing your knowledge of the content of an exam and then reviewing and studying the material.Using the Examination GuidesWhether you are using the latest edition of this Study Guide, or you have downloaded an individual examination guide from the CLEP Web site, you will fi nd the same information. Each exam guide includes an outline of the knowledge and skills covered by the test, sample questions similar to those that appear on the exam, and tips for preparing to take the exam.You may also choose to contact a college in your area that offers a course with content comparable to that on the CLEP exam you want to take. If possible, use the textbook required for that course to help you prepare. To get this information, check the college’s catalog for a list of courses offered. Then call the admissions offi ce, e xplain what subject you’re interested in, and ask who in that academic department you can contact for specifi c information on textbooks and other study resources to use. Be sure that the college you’re interested in gives credit for the CLEP exam for which you’re preparing.Begin by carefully reading the test description and outline of knowledge and skills required for the exam in the exam guide. As you read through the topics listed, ask yourself how much you know about each one. Also note the terms, names, and symbols that are mentioned, and ask yourself whether you are familiar with them. This will give you a quick overview of how much you know about the subject. If you arefamiliar with nearly all the material, you will probably need a minimum of review; however, if topics and terms are unfamiliar, you will probably require substantial study to do well on the exam.If, after reviewing the test description provided in the exam guide, you fi nd that you need extensive review, put off answering the sample questions until you have done some reading in the subject. If you complete them before reviewing the material, you will probably look for the answers as you study, and they will not be a good assessment of your ability at a later date. Do not refer to the sample questions as you prepare for the exam. None of the sample questions appear on the CLEP exam, so concentrating on them without broader study of the subject won’t help you.If you think you are familiar with most of the test material, try to answer the sample questions, checking your responses against the answer key. Use the test-taking strategies described in the next chapter.Assessing Your Readiness for a CLEP ExaminationSuggestions for StudyingThe following suggestions have been gathered from people who have prepared for CLEP exams or other college-level tests.e CLEP tutorials.Make sure you are familiar with the computer-based format of the CLEP exams. Use the CLEPSampler, which can be downloaded from the CLEP Web site, to familiarize yourself with CLEP CBT exams before taking the test; it’s also the only offi cial CLEP tutorial program for computer-based testing. You can fi nd the Sampler on the Web at /clep. If you are not comfortable using a computer, you can practice the necessary pointing, clicking, and scrolling skills by working with the Sampler. You’ll also be able to practice using the testing tools that will help you navigate throughout the test, and you’ll see the types of questions you’ll be required to answer.If you don’t have access to a computer, check with the library or test center at the school where you’ll be testing. Many CLEP test centers and college libraries will have the Sampler installed on computers in public areas, so you’ll be able to practice and review before your test date. The tutorials are also part of the testing software, and you’ll be able to work through them before you begin your test.Check with the test center to see how much time will be allotted for your testing appointment; then you can determine how much time you might need to spend on the tutorials.Remember, if you want to review content covered by each examination, the exam description includes a content outline, a description of the knowledge and skills required to do well, and sample questions. An answer key is also included. However, th is exam guide is not intended to replace a textbook. Additional study may be required.2.Defi ne your goals and locate study materials.First, determine your study goals. Set aside a block of time to review the exam guide andthen decide which exam(s) you will take. Using the guidelines for knowledge and skillsrequired, locate suitable resource materials. If a preparation course is offered by an adult school or college in your area, you might fi nd it helpful to enroll. (You should be aware, however, that such courses are not authorized or sponsored by the College Board. The College Board has no responsibility for the content of these courses; nor are they responsible for books on preparing for CLEP exams that have been published by other organizations.) If you know others who have taken CLEP exams, ask them how they prepared.You may want to get a copy of a syllabus for the college course that is comparable to the CLEP exam(s) you plan to take. Some colleges, like MIT and Carnegie Mellon, offer their course materials for free online; these can be an excellent resource. You can also ask the appropriate professor at the school you’ll be attending, or check his or her Web site, for a reading list. Use the syllabus, course materials and/or reading list as your guide for selecting textbooks and study materials. You may purchase these or check them out of your local library. Educational Web sites, like those offered by PBS or the National Geographic Society, can be helpful as well.Check with your librarian about locating study aids relevant to the exams you plan to take. These supplementary materials may include, for example, videos or DVDs made by education-oriented companies and organizations; language tapes; and computer software. And don’t forget that what you do with your leisure time can be very educational, whether it’s surfi ng current-events Web sites,watching a PBS series, reading a fi nancial newsletter, or attending a play.3.Find a good place to study.To determine what kind of place you need for studying, ask yourself these questions: Do I need a quiet place? Does the telephone distract me? Do objects I see in this place remind me of things I should do?Is it too warm? Is it well lit? Am I too comfortable here? Do I have space to spread out my materials?You may fi nd the library more conducive to studying than your home. If you decide to study at home or in your dorm, you might prevent interruptions by other household members by putting a sign on the door of your study room to indicate when you will be available.4.Schedule time to study.To help you determine where studying best fi ts into your schedule, try this exercise: Make a list of your daily activities (for example, sleeping, working, eating, attending class, sports, or exercise) and estimate how many hours a day you spend on each activity. Now, rate all the activities on your list in order of their importance and evaluate your use of time. Often people are astonished at how an average day appears from this perspective. You may discover that your time can be scheduled in alternative ways.For example, you could remove the least important activities from your day and devote that time to studying or to another important activity.5.Establish a study routine and a set of goals.To study effectively, you should establish specifi c goals and a schedule for accomplishing them. Some people fi nd it helpful to write out a weekly schedule and cross out each study period when it iscompleted. Others maintain their concentration better by writing down the time when they expect to complete a study task. Most people fi nd short periods of intense study more productive than long stretches of time. For example, they may follow a regular schedule of several 20- or 30-minute study periods with short breaks between them. Some people like to allow themselves rewards as theycomplete each study goal. It is not essential that you accomplish every goal exactly within yourschedule; the point is to be committed to your task.6.Learn how to take an active role in studying.If you have not done much studying for some time, you may fi nd it diffi cult to concentrate at fi rst. Trya method of studying, such as the one outlined below, that will help you concentrate on and rememberwhat you read.a.First, read the chapter summary and the introduction so you will know what to look for inyour reading.b.Next, convert the section or paragraph headlines into questions. For example, if you are reading asection entitled “The Causes of the American Revolution,” ask yourself, “What were the causes of the American Revolution?” Compose the answer as you read the paragraph. Reading and answering questions aloud will help you understand and remember the material.c. Take notes on key ideas or concepts as you read. Writing will also help you fi x concepts more fi rmlyin your mind. Underlining key ideas or writing notes in your book can be helpful and will be useful for review. Underline only important points. If you underline more than a third of each paragraph, you are probably underlining too much.d.If there are questions or problems at the end of a chapter, answer or solve them on paper as if youwere asked to do them for homework. Mathematics textbooks (and some other books) sometimes include answers to some or all of the exercises. If you have such a book, write your answers before looking at the ones given. When problem solving is involved, work enough problems to master the required methods and concepts. If you have diffi culty with problems, review any sample problems or explanations in the chapter.e.To retain knowledge, most people have to review the material periodically. If you are preparing foran exam over an extended period of time, review key concepts and notes each week or so. Do not wait for weeks to review the material or you will need to relearn much of it.Psychological and Physical PreparationMost people feel at least some nervousness before taking a test. Adults who are returning to college may not have taken tests in many years, or they may have had little experience with standardized tests. Some younger students, as well, are uncomfortable with testing situations. People who received their education in countries outside the United States may fi nd that many tests given in this country are quite different from the ones they are accustomed to taking.Not only might candidates fi nd the types of tests and questions unfamiliar, but other aspects of the testing environment may be strange as well. The physical and mental stress that results from meeting this new experience can hinder a candidate’s ability to demonstrate his or her true degree of knowledge in the subject area being tested. For this reason, it is important to go to the test center well prepared, both mentally and physically, for taking the test. You may fi nd the following suggestions helpful.1.Familiarize yourself as much as possible with the test and the test situation before the day of the exam.It will be helpful for you to know ahead of time:a.How much time will be allowed for the test and whether there are timed subsections. (Thisinformation is included in the examination guides and in the CLEP Sampler.)b.What types of questions and directions appear on the exam. (See the examination guides and theCLEP Sampler.)c.How your test score will be computed.d. In which building and room the exam will be administered. If you don’t know where the building is,get directions ahead of time.e.The time of the test administration. You may wish to confi rm this information a day or two before theexam and fi nd out what time the building and room will be open so that you can plan to arrive early.f. Where to park your car and whether you will need a parking permit or, if you will be taking publictransportation, which bus or train to take and the location of the nearest stop.g.Whether there will be a break between exams (if you will be taking more than one on the same day),and whether there is a place nearby where you can get something to eat or drink.2.Be relaxed and alert while you are taking the exam:a.Get a good night’s sleep. Last-minute cramming, particularly late the night before, is usuallycounterproductive.b.Eat normally. It is usually not wise to skip breakfast or lunch on the day you take the exam or to eat abig meal just before testing.c.Avoid tranquilizers and stimulants. If you follow the other directions in this book, you won’t needartifi cial aids. It’s better to be a little tense than to be drowsy, but stimulants such as coffee and cola can make you nervous and interfere with your concentration.d.Don’t drink a lot of liquids before taking the exam. Leaving to use the restroom during testing willdisturb your concentration and reduce the time you have to complete the exam.e.If you are inclined to be nervous or tense, learn some relaxation exercises and use them to preparefor the exam.3. Be sure to:a.Arrive early enough so that you can fi nd a parking place, locate the test center, and get settledcomfortably before testing begins. Allow some extra time in case you are delayed unexpectedly.b.Take the following with you:●Any registration forms or printouts required by the test center. Make sure you have fi lled out allnecessary paperwork in advance of your testing date.●Your driver’s license, passport, or other government-issued identifi cation that includes yourphotograph and signature, as well as a secondary form of ID that includes a photo and/or yoursignature, such as a student ID, military ID, social security card, or credit card. You will be asked to show this identifi cation to be admitted to the testing area.● A valid credit card to pay the $60 examination fee. (This fee is subject to change.) Although acredit card is the preferred method of payment, you can also pay by check or money order(payable to the College-Level Examination Program). Your test center may require an additionaladministration fee. Contact the test center to determine the amount and the method of payment.●Two pencils with good erasers. You may need a pencil for writing an outline or fi guring out mathproblems. Mechanical pencils are prohibited in the testing room.●Your glasses if you need them for reading or seeing the chalkboard or wall clock.c.Leave all books, papers, and notes outside the test center. You will not be permitted to use your ownscratch paper; it will be provided by the test center.d.Do not take a calculator to the exam. If a calculator is required, it will be built into the testingsoftware and available to you on the computer. The CLEP Sampler and the pretest tutorials willshow you how to use that feature.e.Do not bring a cell phone or other electronic devices into the testing room.f.Be prepared to adjust to an uncomfortable temperature in the testing room. Wear layers of clothingthat can be removed if the room is too hot but that will keep you warm if it is too cold.4.When you enter the test room:a.Although you will be assigned to a computer testing station, the test center administrator can usuallyaccommodate special needs. Be sure to communicate your needs before the day you test.b. Read directions carefully and listen to all instructions given by the test administrator. If you don’tunderstand the directions, ask for help before test timing begins. If you must ask a question aftertesting has begun, raise your hand and a proctor will assist you. The proctor can answer certain kinds of questions but cannot help you with the exam.c.Know your rights as a test-taker. You can expect to be given the full working time allowed for takingthe exam and a reasonably quiet and comfortable place in which to work. If a poor testing situation is preventing you from doing your best, ask whether the situation can be remedied. If bad testingconditions cannot be remedied, ask the person in charge to report the problem on an ElectronicIrregularity Report that will be submitted with your test results. You may also wish to immediately write a letter to CLEP, P.O. Box 6656, Princeton, NJ 08541-6656. Describe the exact circumstances as completely as you can. Be sure to include the name of the test center, the test date, and the name(s) of the exam(s) you took. The problem will be investigated to make sure it does not happen again, and, if the problem is serious enough, arrangements will be made for you to retake the exam without charge.Arrangements for Students with DisabilitiesCLEP is committed to working with test-takers with disabilities. If you have a learning or physical disability that would prevent you from taking a CLEP exam under standard conditions, you may request special accommodations and arrangements to take it on a regularly scheduled test date or at a special administration. Contact a CLEP test center prior to registration about testing accommodations and to ensure the accommodation you are requesting is available. Each test center sets its own guidelines in terms of deadlines for submission of documentation and approval of accommodations. Only students with documented hearing, learning, physical, or visual disabilities are eligible to receive testing accommodations. Also, it is important to ensure that you are taking the exam(s) with accommodations that are approved by your score recipient institution.Testing accommodations that may be provided with appropriate disability documentation include:●ZoomText (screen magnifi cation)● Modifi able screen colors●Use of a reader or amanuensis or sign language interpreter● Extended time● Untimed rest breaksII. Taking the ExaminationsA person may know a great deal about the subject being tested but not be able to demonstrate it on the exam. Knowing how to approach an exam is an important part of the testing process. While a command of test-taking skills cannot substitute for knowledge of the subject matter, it can be a signifi cant factor in successful testing.Test-taking skills enable a person to use all available information to earn a score that truly refl ects her or his ability. There are different strategies for approaching different kinds of exam questions. For example, free-response and multiple-choice questions require very different approaches. Other factors, such as how the exam will be graded, may also infl uence your approach to the exam and your use of test time. Thus, your preparation for an exam should include fi nding out all you can about the exam so you can use the most effective test-taking strategies.Taking CLEP Exams1.Listen carefully to any instructions given by the test administrator and read the on-screen instructionsbefore you begin to answer the questions.2.Keep an eye on the clock and the timing that is built into the testing software. You have the optionof turning the clock on or off at any time. As you proceed, make sure that you are not working too slowly. You should have answered at least half the questions in a section when half the time forthat section has passed. If you have not reached that point in the section, speed up your pace on the remaining questions.3.Before answering a question, read the entire question, including all the answer choices. Don’t thinkthat because the fi rst or second answer choice looks good to you, it isn’t necessary to read ther emaining options. Instructions usually tell you to select the “best’’ answer. Sometimes one answer choice is partially correct but a nother option is better; therefore, it’s usually a good idea to read all the answers before you choose one.4.Read and consider every question. Questions that look complicated at fi rst glance may not actually beso diffi cult once you have read them carefully.5.Do not puzzle too long over any one question. If you don’t know the answer after you’ve considered itbriefl y, go on to the next question. Mark that question using the mark tool at the bottom of the screen, and go back to review the question later, if you have time.6.Watch for the following key words in test questions:all generally never perhapsalways however none rarelybut may not seldomexcept must often sometimesevery necessary only usuallyWhen a question or answer option contains words such as ‘‘always,’’ ‘‘every,’’ ‘‘only,’’ ‘‘never,’’ and “none,” there can be no exceptions to the answer you choose. Use of words such as ‘‘often,’’ “rarely,”‘‘sometimes,’’ and ‘‘generally’’ indicates that there may be some exceptions to the answer.7.Make educated guesses. There is no penalty for incorrect answers. It is to your benefi t to guess if youdo not know an answer since CLEP CBT uses “rights-only” scoring. (An explanation of theprocedures used for scoring CLEP exams is given in the next chapter.) If you are not sure of thecorrect answer but have some knowledge of the question and are able to eliminate one or more of the answer choices as wrong, your chance of getting the right answer is improved.8.Do not waste your time looking for clues to right answers based on fl aws in question wording orpatterns in correct answers. CLEP puts a great deal of effort into developing valid, reliable, and fair exams. CLEP test development committees are composed of college faculty who are experts in the subjects covered by the exams and are appointed by the College Board to write test questions and to scrutinize each question that is included on a CLEP exam. Faculty committee members make every effort to ensure that the questions are not ambiguous, that they have only one correct answer, and that they cover college-level topics. These committees do not intentionally include ‘‘trick’’ questions. If you think a question is fl awed, ask the test administrator to report it, or write immediately to CLEP Test Development, P.O. Box 6600, Princeton, NJ 08541-6600. Include the name of the exam and test center, the exam date, and the number of the exam question. All such inquiries are investigated by testdevelopment professionals.。
