Calc BC Work...5of 28 Calculus AB Syllabus Applications of Differentiation 3 weeks • Extrema on an interval and the Extreme Value Theorem AB26 • Rolle’s Theorem and the Mean

1 of 28 Calculus AB Syllabus

Calculus BCI teach Calculus as the culmination of all of the student's previous work in mathematics. This allows me to helpthe student organize their previous knowledge. This goal is met by, in addition to the presentation of calculustopics, but also by constant exposure to competition type questions covering the entire range of high schoolmath topics. This syllabus, shows all topics taught in the BC course.

BibliographyLarson, Ron, Robert P. Hostetler, and Bruce H. Edwards. Calculus with Analytic Geometry. 7th ed. Boston:Houghton Mifflin, 2002.

Hockett, Shirley 0., Barron's How To Prepare For The AP Calculus (7th Ed.)

COWculus on the Web: An online homework manage system sponsored by Temple University. Each studenthas an individual account and does homework problems online. The results are available to the teacher online.Good practice questions. http://www.math.temple.edu/~cow/

WebWork: Another homework management system sponsored by Rochester University. WebWork givesdifferent problems to each student. Students can work together, but must each do their own problems. Studentprogress is viewable online by the teacher and can be downloaded to the teachers gradebook.http://webwork.rochester.edu/

Teacher Website:http://teachers.dadeschools.net/akoskiA collection of programs, demonstrations, worksheets and other materials to enhance the learning ofmathematics.

Assessments:Chapter Tests and Quizzes from Larson TestBankMidterm Exam: Selected Questions from Released Exam 1985-1988Final Exam: Released Exam 2003Online Assignments from COWculusOnline Assignments from WebWorkMany individual worksheets developed (and borrowed) over the years.

Calculator Usage:Each student is expected to be comfortable with calculator usage. Much like graphing calculators, allCOWculus and WebWork assignments depend on calculator-like input. Like the TI-89 both systems willdisplay the "pretty" form of the mathematics entered if the student so desires. Since WebWork gives eachstudent a different form of the problem, it is common that problems will use numbers that are not easily donewithout a calculator. Student get a great deal of calculator practice this way.In addition, I have collected a vast number of calculator active worksheets to be used when I notice a studentwho needs more assistance. Finally, students work through many calculator active problems from releasedexams, both in class and for homework.

The graphing calculator and Geometer's Sketchpad are essential element in exploring abstract mathematics.With it the student is able to experiment, visualize and conjecture. Students become comfortable withcalculator use and are able to perform the basic tasks required by the AP curriculum. (Graphs, Solutions,Derivatives and Integrals)


Teaching StrategiesProjects

The course includes several major projects1. Cowculus and/or WebWork

a. Online homework and math practice. Provided in conjunction with Temple University andRochester University. See Homework Correlation at end of this document.

2. 16 Functionsa. Students create detailed and complete analysis of 16 basic functions. They must include ALL

information about roots, discontinuities, limits etc.3. Geometer's Sketchpad

a. A large collection of demonstrations and activities. A favorite is Dynagraphs which has beenmodified to match the 16 Functions activity.

4. Volume Projecta. Students create a volume model based on one of the volume integration techniques.

Accompanying paper work must show complete calculus solution, plus the actual value of theapproximation.

5. Daily Journal A collection of 1) assigned topics, 2) class impressions 3) independent research and 4)free writing. Students get daily practice in putting their mathematics ideas into words. Students will usedaily writing to explore calculus topics to develop an appreciation of calculus as a coherent body ofknowledge and as a human accomplishment.

6. Major Reviewa. Several "8-hour" review sessions are scheduled for struggling students. During these reviews a

complete review on basic topics is completed.7. Full Length practice exams

a. During the 3rd marking period, all students are required to take from 1-6 full length AP practiceexams. Exams are graded and returned during the sessions.

8. Mu Alpha Theta competitions and practicea. Students are encourage to participate in a myriad of mathematics competitions and practices.

Students can choose from as simple as ½ hour in class quizzes (Continental Math League) toweek-long major competitions.

b. Mu Alpha Theta, Florida Math League, Continental Math League , American Scholastic MathAssociation, AMC-8/10/12, AIME, USAMO

BC students, in many cases, are able to work independently. These students work through theCOWculus course as well as assignments from Larson. Progress is monitered through regularexaminations from the Larson Test Bank. In addition, these students spend a great deal of time workingthrough problems from mathematics competitions. Pacing for these students is self-directed.

Rule of Four __________

The "Rule of Four" is a fundamental theme in all my math classes. I have the four domains: symbolic, numeric,analytic, and verbal permanently written on my board. During all presentations and discussions, students areexpected to present their work in as many of the domains as they can. I find that most of my students have littleexperience in transferring thinking from one domain to the other. During most discussions and presentations Iwill pose the question in one format and then ask students to reinterpret in one of the other domains. Extensiveuse of Geometer's sketchpad allows me to create graphic situations. Students are asked to describe that theythink will happen under certain conditions. Three particularly good sketches are Dynagraphs, Color Bars andPolar Plots. In addition, each student has a notebook in which they keep a daily journal. Students use thejournal to discuss their impressions of math and lessons. The course teaches students how to communicatemathematics and explain solutions to problems both verbally and in written sentences.


AP ReviewsI generally am able to finish all new material several weeks before the AP Exam. I use this time for review andpractice. During this time, students work on the sample questions in the AP Calculus Course Description and onmultiple-choice and free-response questions from AP Released Exams as well as problems from the Barron'sreview book. Some of these are assigned for homework, while others are given as a quiz or test.

Topic OutlineI have included a sample of typical assignments and correlated them to the topics in the Course Outline. I usedthe following codes. There is a more detailed description of some assignments at the end of the outline.

Partial Correlation to Class Assignments:Code Description

AB# or BC# COWculus online assignment

WW# WebWork online assignment

Prj# Class Project

Jrnl Journal Writing Assignment

GSP# Geometer's Sketchpad Demonstration

Lar# Larson page # exercises/discussion

Calc# Graphing Calculator exercise

WS# Work Sheet

FRQ AP Free Response Question

Prg# Teacher written Programs

Demo# Demonstrations, Models, hands on activities

Barrons Various Multiple Choice Sets to coverpractice and applications

Analysis of Graphs, Functions and Precalculus Review (summer or asneeded)

Students in BC should already be comfortable with these topics. Students work independently throughChapter 1 of the Barron's Calculus Book. Students are given a set of 16 functions to graph andcompletely describe. (See Graph Scoring guidelines at the end of this syllabus) At this time allfunctional transformations are discussed related to the graphs students are creating. GeometerSketchpad is use extensively to demonstrate the concepts of transformations. Students will be able towork with functions represented in a variety of ways: graphical, numerical, analytical

Barron's Chapter 1 16 Graphs ColorBar Program Dynagraphs ( ), ( ), , , , , , ,f ax af x f x a f x a f a f a f x f x etc WS4

I cover these topics in Calculus AB and Alebra 2. Many students are able to go directly to the BC curriculum.These students work independently using COWculus and assignments from Larson. Students who are able towork at an advanced pace,


Limits and Their Properties (2 Weeks)• An introduction to limits, including an intuitive understanding of the limitprocess

CAB11

• Using graphs and tables of data to determine limits Lar#48 Proj #1• Properties of limits GSP#1 Proj #1• Algebraic techniques for evaluating limits L#69 AB11• Comparing relative magnitudes of functions and their rates of change GSP#2• Continuity and one-sided limits AB12 AB13

• Geometric understanding of the graphs of continuous functions Calc#1• Intermediate Value Theorem Lar#75• Infinite limits AB13• Using limits to find the asymptotes of a function AB13Barron's Chapter 2 Multiple Choice Questions

Differentiation 2 Weeks• Zooming-in activity and local linearity Calc#2• Understanding of the derivative: graphically, numerically, and analytically WS1• Approximating rates of change from graphs and tables of data FRQ#9• The derivative as: the limit of the average rate of change, an instantaneousrate of change, limit of the difference quotient, and the slope of a curve at a point

variousFRQ

• The meaning of the derivative—translating verbal descriptions into equationsand vice versa

FRQ#7b

• The relationship between differentiability and continuity Lar#101• Functions that have a vertical tangent at a point 2

5y x• Functions that have a point on which there is no tangent y x• Differentiation rules for basic functions, including power functions andtrigonometric functions

AB21AB22

• Rules of differentiation for sums, differences, products, and quotients AB21• The chain rule Lars#133• Implicit differentiation Lars#142 AB22• Related rates Lars#149

BarronsAB17

Barron's Chapter 3 Multiple Choice Questions


Applications of Differentiation 3 weeks• Extrema on an interval and the Extreme Value Theorem AB26• Rolle’s Theorem and the Mean Value Theorem, and their geometricconsequences

AB24

• Increasing and decreasing functions and the First Derivative Test Lar#181• Concavity and its relationship to the first and second derivatives AB27• Second Derivative Test Lar#189• Limits at infinity AB13• A summary of curve sketching—using geometric and analytic information aswell as calculus to predict the behavior of a function

AB24

• Relating the graphs of ,f, ,f’, and f''. WS1• Optimization including both relative and absolute extrema AB26• Tangent line to a curve and linear approximations AB16• Application problems including position, velocity, acceleration, andrectilinear motion

AB25AB26Barrons

AB17


Integration 4 Weeks• Antiderivatives and indefinite integration, including antiderivatives followingdirectly from derivatives of basic functions

AB30

• Basic properties of the definite integral Lar#271• Area under a curve FRQ#1a FRQ#8• Meaning of the definite integral Lar #269• Definite integral as a limit of Riemann sums Demo#1 AB32• Riemann sums, including left, right, and midpoint sums AB32• Trapezoidal sums Lar#301 AB32• Use of Riemann sums and trapezoidal sums to approximate definite integralsof functions that are represented analytically, graphically, and by tables of data

FRQ3a

• Use of the First Fundamental Theorem to evaluate definite integrals AB32• Use of substitution of variables to evaluate definite integrals Lar#297• Integration by substitution Lar#297• Discovery lesson on the Second Fundamental Theorem of Calculus Prog1• The Second Fundamental Theorem of Calculus and functions defined byintegrals

WS#2

• The Mean Value Theorem for Integrals and the average value of a function FRQ#3Select Multiple Choice Questions on Barron's Chapter 5,6,7, and 8


Logarithmic, Exponential, and Other Transcendental Functions 1weeks—

• The natural logarithmic function and differentiation AB35 AB36• The natural logarithmic function and integration AB37 Lar#347• Inverse functions Lar#335• Exponential functions: differentiation and integration — FRQ#8• Bases other than e and applications FRQ#8 Lar#357• Solving separable differential equations Lar#366

Journal:WS#5

FRQ#6

• Applications of differential equations in modeling, including exponential growth FRQ#11• Use of slope fields to interpret a differential equation geometrically WS#3• Drawing slope fields and solution curves for differential equations WS#3 FRQ#6• Euler’s method as a numerical solution of a differential equation Larson

AppendixA

FRQ#12

Barron's Multiple Choice Questions on Differential Equations Chapter 9

Logarithmic, Exponential, and Other Transcendental Functions 1week• Inverse trig functions and differentiation Lar#386• Inverse trig functions and integration Lar#393

Applications of Integration 3 weeks• The integral as an accumulator of rates of change AB34 FRQ#1• Area of a region between two curves FRQ#8a• Volume of a solid with known cross sections FRQ#10c• Volume of solids of revolution FRQ#8b• Applications of integration in problems involving a particle moving along a line,including the use of the definite integral with an initial condition and using the definiteintegral to find the distance traveled by a particle along a line

Barrons6


Integration Techniques, L’Hopital’s Rule, and Improper Integrals 1week• Review of basic integration rules• Integration by parts Lar#494• Trigonometric integrals Lar#512• Integration by partial fractions Barron's 5 BC#11• Solving logistic differential equations and using them in modeling Lar#523-58 Lar#409-12-15• L’Hopital’s Rule and its use in determining limits BC#12• Improper integrals and their convergence and divergence, includingthe use of L’Hopital’s Rule

Lar#547 AB#40


Infinite Series (6 weeks)• Convergence and divergence of sequences BC#01• Definition of a series as a sequence of partial sums BC#02• Convergence of a series defined in terms of the limit of the sequence ofpartial sumsof a series

BC#02

• Introduction to convergence and divergence of a series by using technologyon two examples to gain an intuitive understanding of the meaning ofconvergence

Calc#3

• Geometric series and applications Lar#569• The nth-Term Test for Divergence BC#03 Lar#571• The Integral Test and its relationship to improper integrals and areas ofrectangles

GSP#4BC#03-4

Lar#580

• Use of the Integral Test to introduce the test for p-series BC#03-4 Lar#577• Comparisons of series BC#05-6 Lar#587• Alternating series and the Alternating Series Remainder Lar#595• The Ratio and Root Tests BC#03-4 WS#6 Lar#603• Taylor polynomials and approximations: introduction using the graphingcalculator

Lar#613

• Power series and radius and interval of convergence BC#07 Lar#623• Taylor and Maclaurin series for a given function BC#08 Lar#638• Maclaurin series for sin x, cos x, xe and ln x

Manipulation of series, including substitution, addition of series,multiplication of seriesby a constant and/or a variable, differentiation of series, integration ofseries, andforming a new series from a known series Taylor’s Theorem with theLagrange Form of the Remainder (Lagrange Error Bound)

LegrangeLar#611-612

Lar#630

Barron's Multiple Choice Questions: Chapter 10

Plane Curves, Parametric Equations, and Polar Curves (2 weeks)• Plane curves and parametric equations BC#13 Lar#672• Parametric equations and calculus Lar#681• Parametric equations and vectors: motion along a curve, position, velocity,acceleration, speed, distance traveled

BC#14

• Analysis of curves given in parametric and vector form BC#13• Polar coordinates and polar graphs Lar#685• Analysis of curves given in polar form Lar#691• Area of a region bounded by polar curves Lar#701Barron's Multiple Choice Questions: Chapter 8


Details for Sample Exercises/Assessments from Topic Outline

Geometer Sketchpad Sketches1. Teacher created sketch which shows dynamically the interaction between the delta neighborhood and theepsilon neighborhood. Examples for the 16 basic graphs demonstrate all types of discontinuities.

2. Dynagraphs. Dynagraphs dynamically demonstrate the relation between domain and range with two parallelreal lines. Dynaquiz- is a version where students must identify the function from unlabelled Dynagraphs.

3. Color Bars. Using the Dynagraph program as a base, a second line is colored to match the image of eachpoint based on student selected function. Students pick transformation and try to describe that they think willhappen.

4. Integral Test: Students had trouble understanding diagram on page 577 of Larson. Teacher created sketch tolet students dynamically move the rectangles. Students see that the translated rectangles now fit under thecurve.

Calculator Exercises1. Epsilon/Delta Discovery: Students must adjust the window of the x-variable and the y-variable to help

understand the epsilon-delta definition of limit.

2. Local Linearity: Students will zoom in on graphs of functions selected from the Basic 16 functions. Inparticular, students will compare the graphs of 2y x and y x .

3. Graphing partial sums to see convergence: Sample problem Larson pg 568 Firgure 8.5 also problems fromsection 8.2

Demonstrations

1. 2-dimensional and 3-dimensional models to illustrate the summation rules.

1

1

2

n

i

n ni

and

2

1

1 2 1

6

n

i

n n ni

.

Worksheets1. Given either f, f' or f", students will draw the graphs of the other two.

2. A collection of 2nd Fundamental Theorem Problems: ie. x

af t dt f x and

222

x

xf t dt f x f x

3. Slope Field Handout from AP Central by Nancy Stephenson4. Teacher made Transformation Worksheet. Students are given a sample function and 9 transformation todraw. i.e. ( ), ( ), , , , , , ,f ax af x f x a f x a f a f a f x f x etc

5. Solving Separable Differential Equations: Antidifferentiation and Domain Are Both Needed by DavidLomen (worksheet downloaded from AP Central)6. Summary of Tests for Series: See page 602 of Larson. Also teacher made worksheet that compares

Programs1. Color Bars – Program deforms a single copy of the real lines based on a transformation function. Studentspick transformation and try to describe that they think will happen.


Free Response QuestionsCalculus AB 2004 Form B

1. Question 1: a) Area under a curve b) volume between two curves c)2. Question 2 a) calculator eval y' b) cal eval y'' c) integral: accumulation of y' = y+C d)absolute maximum3. Question 3: a)Reimann b) MVT c) accel d) average value4. Question 4 graphic of f' a) find inflection b) abs max and min c) tangent line to f5. Question 5 slope field b) interpret data c) solve differential equation6. Question 6 a) area under curve b) area of triangle c) area of region between two graphs. Maximimze area.

Calculus AB 20047. Question 1: a) Accumulation b) interpret derivative verbally c) average value d) average rate of change

Calculus AB 20028. Question 1: a) Area between two curves (logs e^x) b) Volume between two curves c)abs max and min

Calculus AB 19989. Question 3: Graph of velocity a) find acceleration is positive b) average acc of car c) approx acc d) Reimansum explain the meaning of the integal.

Calculus AB 199610. Question 2: a) Area under curve b) divide region in half c) volume by cross-sections

Calculus BC 199111. Question 6: Rate of Rumor a) max rumor speed b) solve differential equations c)

Calculus BC 200


Graph Scoring Guidelines

1. Axes labeled.2. Equal scales.3. Graph labeled with function name.4. Graph is neat.5. Graph is accurate.6. Reference line (y=x) is drawn.7. Good interval. (Shows important function values)8. Good interval. (Shows all symmetries)9. Good interval. (Shows periodic behavior)10. Good interval. (Shows discontinuities including assymptotes)11. Table of values (Shows interesting examples of above)12. Mapping13. Colorbars (see 7)14. Colorbars (see 8)15. Colorbars (see 9)16. Colorbars (see 10)17. Domain is stated

a. Identify and Discuss all discontinuities18. Range is stated.19. Roots and intercepts are listed.20. Symmetries are stated

a. X-axisb. Y-axisc. Y = Xd. Origin

21. Odd-Even Analysis22. Function Analysis

a. Well-Definedb. One-to-Onec. Ontod. Periodic

23. Identify and state all special limit valuesa. x b. x c. x ad. x ae. x a


Cowculus- AB Online homework Assignments 2468 Problems

Complete COWculus Online Assignment ListAB 00 First Assignment

Precalculus Book

o Functions

Linear Functions

Equation of a line: problems: 1-20

Normal lines: problems: 1-27

Parallel lines: problems: 1-28

Slope of a line: problems: 1-20

AB 02 Sequences

Precalculus Book

o Numbers

Sequences

Arithmetic and geometric sequences: problems: 1-16

Linearly recursive sequences: problems: 1-31

AB 03 Linear Equations

Precalculus Book

o Equations

Linear Equations

Fractional linear equations: problems: 1-16

Linear equations with parameters: problems: 1-8

Solving linear equations: problems: 1-10

AB 04 Plotting

Precalculus Book

o Plotting, Graphs

Lines

Intersecting two lines: problems: 1-13

Lines, point-slope: problems: 2,4,6,8,10,12,14,16


Sketching lines: problems: 1-10

Three collinear points: problems: 2,4,6,8,10,12,14,16,18,20,22

Plotting

Locating Points on Curves: problems: 2,4,6,8,10

Plotting points on a line: problems: 2,4,6,8,10,12

Points and midpoints in the plane: problems: 2,4,6,8,10,12,14,16

Points and midpoints on a line: problems: 2,4,6,8,10,12,14

AB 05 Polynomials

Precalculus Book

o Polynomials

Factoring, Roots

Factoring quadratic polynomials: problems: 2-24

Finding rational roots: problems: 1-19

Polynomial Algebra

Linear combinations: problems: 2,4,6,8,10,12,14,16,18,20

Polynomial addition: problems: 5,10,15,20,25,30,35,40

Polynomial division: problems: 1-25

Polynomial multiplication: problems: 15-43

AB 06 Algebra Basics

Calculus Book I

o Functions and Geometry

Distance

A point and a line: problems: 11-20

Circles I: problems: 5-11

Circles II: problems: 4-8

Circles III: problems: 6-21

Circles IV: problems: 4-10

Distance: problems: 10-20

Lines


Equation of a line: problems: 14-20

Normal lines: problems: 1-27

Parallel lines: problems: 20-28

Slope of a line: problems: 10-20

AB 07 Inequalities

Calculus Book I


Inequalities

Absolute value inequalities: problems: 1-24

Inequalities and intervals: problems: 1-18

Simple inequalities: problems: 2-22

AB 08 Functions

Calculus Book I


Functions

Composition of Functions: problems: 1-25

Roots: problems: 3-21

AB 09 Plotting

Calculus Book I


Plotting in the Plane

Plotting points: problems: 1-11

Sketching curves: problems: 1-12

AB 10 Trigonometry

Calculus Book I


Trigonometry

Recognizing the trigonometric functions: problems: 10-30,40-52

Trigonometric Identities: problems: 5-19


AB 11 Limits

Calculus Book I

o Limits and Continuity

Ordinary Limits

Basic Limits: problems: 1-28

Basic limits, more examples: problems: 1-17

Finding delta: problems: 2-23

AB 12 Continuity

Calculus Book I


Continuity

A missing value: problems: 2-26

Discontinuities of simple piecewise defined functions: problems: 1-13

Epsilon and delta: problems: 2-13

AB 13 One Sided Limits

Calculus Book I


One-sided Limits and Asymptotes

Asymptotes: problems: 2,4,6,8,10,12,14,16,18

Asymptotes of oscillating functions: problems: 6,8,10,12,14,16,18

Limits at infinity: problems: 2,4,6,8,10,12,14,16,18,20,22,24

More asymptotes: problems: 4,6,8,10,12,14,16,18,20

One-sided limits: problems: 2,4,6,8,10,12,14,16,18,20

AB 14 Special Limits

Calculus Book I


Special Limits

More trigonometric limits: problems: 1-20

Piecewise limits: problems: 1-20


Trigonometric limits: problems: 1-20

AB 15 Slope

Calculus Book I

o The Derivative

Slope and Tangents

Differentiability: problems: 2,4,6,8,10,12,14,16

Tangent line equation: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30

Tangent line slope: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30

AB 16 Linearization

Calculus Book I

o The Derivative

Linearization

Linear approximation: problems: 2,4,6,8,10,12,14,16,18,20,22

Linearization: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26

AB 17 related rates

Calculus Book I

o Applications of the Derivative

Related Rates

A sliding ladder: problems: 1-7

Man and streetlight: problems: 1-10

Rates of change: problems: 1-12

AB 18 Algebra and Geometry

Calculus Book I


Distance

A point and a line: problems: 5,10,15,20

Circles I: problems: 5,10

Circles II: problems: 5,8

Circles III: problems: 5,10,15,20


Circles IV: problems: 5,10

Distance: problems: 5,10,15,20

Functions

Composition of Functions: problems: 3,6,9,12,15,18,21

Roots: problems: 3,6,9,12,15,18,21

Inequalities

Absolute value inequalities: problems: 3,6,9,12,15,18,21

Inequalities and intervals: problems: 3,6,9,12,15,18

Simple inequalities: problems: 3,6,9,12,15,18,21

Lines

Equation of a line: problems: 5,10,15,20

Normal lines: problems: 5,10,15,20,25

Parallel lines: problems: 5,10,15,20

Slope of a line: problems: 5,10,15,20

Plotting in the Plane

Plotting points: problems: 3,6,9

Sketching curves: problems: 3,6,9

AB 19 Trigonometry

Calculus Book I


Trigonometry

Recognizing the trigonometric functions: problems: 17-24,30,35,40,45,50

Trigonometric Identities: problems: 5-19

************ 1|10 ******************

Abstract Algebra

o Groups

Matrix Groups

General linear group: problems: 1

AB 20 Derivatives #1


Calculus Book I

o Techniques and Theory of Differentiation

Powers, Products, Quotients

Polynomials: problems: 3,6,9,12,15,18,21

Power Rule: problems: 3,6,9,12,15,18,21

Product Rule: problems: 3,6,9,12,15,18,21

Quotient Rule: problems: 3,6,9,12,15,18,21

Trigonometric Functions

Simple trigonometric examples: problems: 3,6,9,12,15

Trigonometric functions: problems: 3,6,9,12,15,18,21


Calculus Book I


Chain Rule

Advanced Chain Rule: problems: 3,6,9,12,15,18,21

Chain Rule: problems: 3,6,9,12,15,18,21

Fractional powers: problems: 3,6,9,12,15,18,21

More Chain Rule: problems: 3,6,9,12,15,18,21

More examples: problems: 3,6,9,12,15,18

Powers of functions: problems: 3,6,9,12,15,18

Products of powers: problems: 3,6,9,12,15,18,21

Trigonometric examples: problems: 3,6,9,12,15,18,21


Calculus Book I


Implicit Differentiation

Implicit derivatives: problems: 3,6,9,12,15,18

Normal lines: problems: 3,6,9,12,15,18,21

Slope of implicit curves: problems: 3,6,9,12,15,18


Tangent lines: problems: 3,6,9,12,15,18,21

AB 23 Normal Lines

Calculus Book I


Implicit Differentiation

Normal lines: problems: 3,6,9,12,15,18,21,24

AB 24 Theory and Fractions

Calculus Book I


Exponential Functions

Basic exponentials: problems: 1-20

Theory

Inverse Functions: problems: 1-26

Mean Value Theorem: problems: 1-15

Visual Mean Value Theorem: problems: 1-13

AB 25 Related Rates

Calculus Book I


Rate of Change

Displacement: problems: 2,4,6,8,10

Marginal cost: problems: 1-10

Velocity: problems: 2,4,6,8,10

Related Rates

A sliding ladder: problems: 1-7

Man and streetlight: problems: 2,4,6,8,10

Rates of change: problems: 2,4,6,8,10

AB 26 Max|Min #1

Calculus Book I



Maxima, Minima

Maximum value: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26

More on relative extrema: problems: 2,4,6,8,10,12,14,16,18,20,22,24

Relative extrema: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26

Optimization

A Maximal Product: problems: 2,4,6,8,10,12

An Efficient Poster: problems: 2,4,6,8,10

Closest point on a curve: problems: 2,4,6,8,10,12

Folding a Box: problems: 2,4,6,8,10

Maximal rectangles under curves: problems: 1,4,7,9,12

More rectangles under curves: problems: 2,4,6,8,10,12

Well designed gardens: problems: 2,4,6,8,10,12

AB 27 Graphing

Calculus Book I


Graphing

Concavity: problems: 2,4,6,8,10,12

Graphing: problems: 2,4,6,8,10,12

Inflection points: problems: 2,4,6,8,10,12

Monotonicity: problems: 2,4,6,8,10,12

Monotonicity and singularities: problems: 2,4,6,8,10,12

AB 28 Approximations 1

Calculus Book I


Approximations

Differentials: problems: 1-10

Linear approximation: problems: 1-10

Linearization: problems: 1-23

Tangent line equation: problems: 1-20


Trigonometric examples: problems: 1-20

AB 29 Newton's method

Calculus Book I


Newton's Method

Newton solver: problems: 1-18

AB 30 Sums and Antidif

Calculus Book II

o Integration

Indefinite Integrals

Indefinite integrals: problems: 2,4,6,8,10,12,14,16,18,20

Integration by substitution: problems: 1-27

Substitution - change of variables: problems: 1-14

Substitution, additional problems: problems: 1-16

Sums

Geometric series: problems: 2,4,6,8

Repeating decimals: problems: 2,4,6,8

Summation: problems: 2,4,6,8

AB 31 Definite Integrals

Calculus Book II

o Integration

Definite Integrals

Definite integrals: problems: 1-23

More substitutions: problems: 1-21

Substitution methods: problems: 2-21

AB 32 Approximations 2

Calculus Book II

o Integration

Definite Integrals


Midpoint rule: problems: 1-15

Trapezoid rule: problems: 1-17

AB 33 FTC

Calculus Book II

o Integration

Fundamental Theorem

Differentiation and the Fundamental Theorem: problems: 1-20

AB 34 Application of Integration

Calculus Book II

o Applications of Integration

Area

Area between curves I: problems: 1-22

Area between curves II: problems: 1-21

Area under a curve: problems: 1-21

Assorted Applications

Average value: problems: 1-16

Differential equations: problems: 1-10

Volume

Solids of revolution - shells: problems: 1-22

Solids of revolution - washers: problems: 1-31

AB 35 Logs

Calculus Book II

o Transcendental Functions

The Natural Logarithm

Derivative of natural log: problems: 2-18

Differentiating logarithmic functions I: problems: 2-14

Differentiating logarithmic functions II: problems: 2-22

Logarithm, definite integrals: problems: 1-24

Logarithm, indefinite integrals: problems: 1-25


Logarithmic Equations: problems: 2-18

Logarithmic curves and tangents I: problems: 1-20

Logarithmic curves and tangents II: problems: 1-20

Simplifying logarithms of algebraic expressions: problems: 1-12

Simplifying logarithms of numbers: problems: 1-16

AB 36 E (exponential)

Calculus Book II


The Exponential Function

Definite integrals of exponentials: problems: 1-24

Derivatives of exponentials I: problems: 1-16

Derivatives of exponentials II: problems: 1-26

Exponential Equations: problems: 1-15

Exponential curves and tangents: problems: 1-15

Indefinite integrals of exponentials: problems: 1-25

AB 37 Logs|Exp Applications

Calculus Book II


Logarithms and Exponentials, Applications

Area and volume, log and exp functions: problems: 1-20

Differential equation of proportional growth: problems: 1-18

Newton's Law of Cooling: problems: 1-10

Population growth: problems: 1-12

AB 38 Log differentiation

Calculus Book II


Logarithmic Differentiation

Logarithmic differentiation 1: problems: 1-10





AB 39 Inverse Functions

Calculus Book II


Inverse Trigonometric Functions

Differentiation and i.t.f.s: problems: 1-14

Evaluating inverse trig functions: problems: 1-30

Integration and i.t.f's: problems: 1-17

Inverse functions - review: problems: 1-21

More differentiation and i.t.f.s: problems: 1-14

Recognizing trigonometric and inverse trigonometric functions: problems: 1-38

AB 40 Improper Integrals

Calculus Book II

o Methods of Integration

Improper Integrals

Improper integrals of unbounded functions: problems: 1-16

Improper integrals over unbounded intervals: problems: 1-20


BC TopicsBC01 Sequences1

Calculus Book III

o Sequences and series

Sequences

Limits of sequences: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34

Limits using L'Hospital's rule: problems: 2,4,6,8,10,12,14,16,18,20

Sequences with exponential terms: problems: 1-15

BC02 Sequences2

Calculus Book III


Sequences

Limits of sequences: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34

Limits using L'Hospital's rule: problems: 2,4,6,8,10,12,14,16,18,20

Sequences with exponential terms: problems: 1-15

BC03 Div, Int, Ratio

Calculus Book III


Series

The divergence test: problems: 2,4,6,8,10,12,14,16,18,20

The integral test: problems: 2,4,6,8,10,12,14,16,18,20

The n-th root test: problems: 6-10,12,14,16,17

The ratio test: problems: 2,4,6,8,10,12,14-17

BC04 Div, Int, Ratio

Calculus Book III


Series

The divergence test: problems: 2,4,6,8,10,12,14,16,18,20

The integral test: problems: 2,4,6,8,10,12,14,16,18,20


The n-th root test: problems: 6-10,12,14,16,17

The ratio test: problems: 2,4,6,8,10,12,14-17

BC05 Limit Comparison

Calculus Book III


Series

The limit comparison test: problems: 1-19

BC06 Limit Comparison

Calculus Book III


Series

The limit comparison test: problems: 1-19

BC07 Power Series

Calculus Book III


Power and Taylor series

Power series: problems: 1-18

BC08 Power Series

Calculus Book III



Power series: problems: 1-18

BC09 Taylor Series

Calculus Book III



Taylor series: problems: 2,4,6,8,10,12,14,16,18,20,22,24,26

BC10 Taylor Series

Calculus Book III




Taylor series: problems: 1-26

BC11 Partial Fractions

Calculus Book II

o Methods of Integration

Partial Fractions

Denominators with simple linear factors: problems: 1-15

Multiple linear factors: problems: 2,4,6,8,10,12,14,16,18

Simple linear and irreducible quadratic factors: problems:2,4,6,8,10,12,14,16,18,20

BC12 Lhopitals Rule

Calculus Book I


L'Hopital's Rule

L'Hopital 1: problems: 1-21



L'Hopital's Rule 1: problems: 1-20



BC13 Speed|Velocity|Tangents

Calculus Book III

o Curves

Acceleration

Acceleration of a curve: problems: 1-20

Length

Length of a curve: problems: 1-10

Speed and Velocity


Speed: problems: 1-20

Velocity: problems: 1-20

Vectors Tangent to Curves

Unit vector tangent to a curve: problems: 1-20

Vector tangent to a curve: problems: 1-20

BC14 Parametric

Calculus Book III

o Curves

Parametrizations

Parametrizations of paths I: problems: 1-33

Parametrizations of paths II: problems: 1-33

Parametrizations of paths III: problems: 4-19

BC15 Conics

Calculus Book II

o Geometry, Curves and Polar Coordinates

Conic Sections

Ellipses I: problems: 2-12

Ellipses II: problems: 2-12

Geometry of conics: problems: 2-16

Hyperbolas I: problems: 2-13

Hyperbolas II: problems: 2-16

Parabolas I: problems: 1-12

Parabolas II: problems: 1-17

BC16 Polar

Calculus Book II

o Geometry, Curves and Polar Coordinates

Polar Coordinates

Plotting points in polar coordinates: problems: 1-11

Polar-Cartesian coordinate conversion: problems: 1-13


WebWork Assignments1. 100_Limits_01

2. 100_Limits_02

3. 200_Derive_01

4. 200_Derive_02_TL

5. 200_Derive_03_PQ6. 200_Derive_04_PQ27. 200_Derive_05_CR

8. 200_Derive_06_DR

9. 200_Derive_07_IM

10. 200_Derive_08_TR

11. 200_Derive_09_RR12. 200_Derive_10_RR0213. 200_Derive_AP_01_MM

14. 200_Derive_AP_02_MM

15. 200_Derive_AP_03_MM

16. 200_Derive_AP_04_GR

17. 200_Derive_MVT_01

18. 300_Integrate_DFQ19. 300_Integrate_FTC20. 300_Integrate_Sub

21. Differential_Equations_-_Euler_Slope

22. Differential_Equations_-_Growth_and_Decay

23. Differential_Equations_-_Linear

24. Differential_Equations_-_Logistic

25. Differential_Equations_-_Modeling26. Differential_Equations_-_Separable

27. Logs_and_Exponents

28. Logs_and_Exponents_2



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