AP Calculus BC - Weebly



AP Calculus BCWinter Packet4584701022262002014-2015~Happy Holidays!~Ms. SokoliWhat have we covered so far?Congratulations Mathematicians for completing the first two terms of this course! So far, we have covered the first five chapters of the Single Variable Calculus, 7th ed. textbook in our AP Calculus BC class. The following were the main topics covered: Concept of Limits and its relationship to the Derivatives of various functions, Differentiation and its application to real-life situations, and the concept of Integrals, as well as the connection between integral calculus and differential calculus. What is next? –> Winter PacketWe still have a lot of topics to cover for the AP Calculus Exam, May 5th, 2015, and time is flying by! In this course the best way to prepare for the AP exam is to make background reading and home assignments an integral part of your independent work & group activities and group projects part of the in class assignments. Your Winter statistics assignment is to study independently Chapter 6 on Application of Integration and Chapter 7 on Techniques of Integration + do the assigned homework.Due Dates, Grading Rubric & Submission GuidelinesThere are deadlines you have to meet during the break and I will help you manage the time well.Due datesStarting December 17, you will have a deadline EVERY Tuesday, Thursday and Sunday*there are only a couple of exceptions in the scheduleGrading Rubric(Tot 29% - term 3)1% per assignment submitted, graded on completion and effort. Total 9%At the beginning of Term 3: Chapter 6 Quiz- 10% & Chapter 7 Quiz – 10%Submission1%= follow submission instructionsMust submit before midnight of the due date at my e-mail asokoli@daltonschool.kr Upload it to Google drive and share it with me. I will confirm that I have received it. Save file as: “Ch. #.# _ Notes_StudentName” & “Ch. #.# _ Pg.#_Questions #s_StudentName”Example: Ch. 5.1_Notes_AnaSokoli and for the homework file Ch. #.# _ Pg.300_2,4,8,10,12_AnaSokoli** It goes without saying that cheating is not only unethical but it also won’t help you learn. In this case, cheating is anything where someone else is doing the thinking to the point that you don’t learn. Please, do the assigned work and make sure to spend as much as it takes on them to fully understand the concept.What to expect when we return in January 2015…Day 1: Review on Chapter 6 January 13, 2015Day 2: Chapter 6 QuizJanuary 15, 2015Day 3: Review on Chapter 7January 19, 2015Day 4: Chapter 7 QuizJanuary 20, 2015…And who knows? You may find these chapters entertaining!Chapter 6 Overview:In this chapter you will explore some of the applications of the definite integrals by using It to compute areas between curves, volumes of solids and the work done by a varying force. We will use a similar technique here like the one used to find the areas under a curve by finding the areas of smaller rectangles. Furthermore, we will use the Fundamental Theorem of Calculus and the Mid-point Rule to evaluate the integrals.Schedule: Chapter 6 Applications of IntegralsDue DateChapter 5 SectionsLearning ObjectivesHomework AssignmentDec 18, 20145.5 The Substitution RuleYou review/ learn how to replace a relatively complicated integral by a simpler integral using the Substitution Rule. <1 page notesPage 413 #3, 13, 21, 23, 39, 45, 59Extra: # 5, 11, 17, 33, 47, 53Dec 21, 20146.1 Areas Between CurvesYou learn how to establish the area between two curves as the limit of a Riemman sum and find such areas < 1 page notesPage 427 #1,3,5,11,13,,17,31Extra: #19,27,35,37,46Dec 23, 2014VolumesYou learn how to establish the volume of a solid of revolution as the limit of a Riemann sum using the method of discs or washers.< 1 page notesPage 438 #1,5,7,9,11,14,15Extra: #13,25, 28, 29, 49Dec 26, 20146.3 Volumes by Cylindrical Shells You learn how to establish the volume of a solid of revolution as the limit of a Riemann sum using the method of cylindrical shells.< 1 page notesPage 444 #1,5,7,9,15,37,45Extra: #7,17,21,39,47Optional Material (any time)6.4 WorkYou learn how to establish, using calculus, the definition of work done to move an object along a straight path if the force applied on the object varies.< 1 page notesPage 449 # 1, 3, 7, 9, 11, 13, 15, 19, 21Optional Material (any time)6.5Average Value of a FunctionYou learn how to define the average value of a continuous function on an interval as the limit of a Riemann sum and to establish the Mean Value Theorem for Integrals in terms of the average of functions.< 1 page notesPage 453 # 1, 7, 11, 13, 17, 19, 21** Must take less than 1 page of notes: useful for studying later on. Make sure it is readable!** The Optional Material: sections of the book that you are not required knowing for the AP exam. I would highly recommend them if you have extra time and I would gladly be willing to check your work if you want to submit them.**Homework: must do the work independently. I will be grading for completion in faith that you will really try them out and do your best. EXTRA problems: for students that want to get more practice and challenge themselves. Hope all of you give them a try ~Happy Break!~Chapter 7 Overview:In Chapter 7 we develop techniques for using the basic integration formulas to obtain indefinite integrals of more complicated functions. We touched upon the Substitution Rule in Chapter 5.5 and here we will learn: integration by parts, method that are special to particular classes of functions such as trigonometric and rational functions.Schedule: Chapter 7 The Techniques of IntegrationDue DateChapter 6 SectionsLearning ObjectivesHomework AssignmentDec 28,, 20147.1 Integration by PartsYou learn how to obtain integration by parts as the rule corresponding to the Product Rule for differentiation and apply it to evaluate integrals.< 1 page notesPage 468 # 3, 11, 17, 19, 27, 37, 45, 55Extra # 25, 39, 45, 57, 65Dec 30, 20147.2 Trigonometric IntegralsYou learn how to evaluate integrals of the forms sinmx cosnx dx, tanmx secnx dx , sinmx cosnx dxsinmx sin nx dx, a cosmx cosnx dx <1 page notesPage 476 # 3, 9, 11, 21, 25, 32, 41Extra: # 23, 31, 56, 62~Happy New Year!~Jan 2, 20157.3 Trigonometric SubstitutionYou learn how to evaluate integrals of the forms a2- x2 dx, a2+ x2 dx , x2- a2 dx using trigonometric substitution< 1 page notesPage 483 # 5, 7, 9, 11, 23, 37Extra # 17, 29, 33Jan 4, 20157.4 Integration of Rational Functions by Partial FractionsYou learn how to recognize which technique or formula to use when given a particular integral to evaluate, and how to evaluate it.< 1 page notesPage 492 # 11, 15, 23, 29, 33, 43, 49, 57Extra #3, 17, 19, 39, 61Optional material(any time)7.5 Strategy for IntegrationYou learn how to recognize which technique or formula to use when given a particular integral to evaluate, and how to evaluate it.<1 page notesPage 499 # 1, 5, 9, 13, 23, 25, 27, 35, 39, 41, 49, 51, 61, 63, 75Optional material(any time)7.6 Integration Using Tables and Computer Algebra SystemsYou learn how to use tables and computer algebra systems to integrate functions that have elementary antiderivatives.< 1 page notesPage 504 # 3, 7, 9, 11, 15, 17, 19, 23, 29, 31, 35, 41Optional material(any time)7.7 Approximate IntegrationYou learn how to find approximate values of definite integrals that are difficult to evaluate, using the Midpoint Rule, the Trapezoidal Rule, and Simpson’s Rule.< 1 page notesPage 516 # 1, 3, 5, 7, 11, 13, 19, 21, 31, 35Jan 6, 20157.8 Improper Integrals(Vertical Asymptotes are Optional)You learn how to evaluate the definite integral abfxdx where the interval is infinite or where f has an infinite discontinuity on [a, b]< 1 page notesPage 527 # 1, 5, 7, 13, 27, 31, 43, 49, 51, 55Extra: # 9, 15, 23, 33, 53, , 57REVIEW: so we can have questions for the first Review Day on Jan 13,2015** Must take less than 1 page of notes: useful for studying later on. Make sure it is readable!** The Optional Material: sections of the book that you are not required knowing for the AP exam. I would highly recommend them if you have extra time and I would gladly be willing to check your work if you want to submit them.**Homework: must do the work independently. I will be grading for completion in faith that you will really try them out and do your best. EXTRA problems: for students that want to get more practice and challenge yourselves. Hope all of you give them a try **You can hand in the assignments any time BEFORE the due date ................
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