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Calculus AB Syllabus

Course Philosophy

The Advanced Placement course in AP Calculus AB is taught over a full high school academic year and is comparable to Calculus I as taught in colleges and universities. Students are expected to take the AP test at the end of the year.

The course is organized into interrelated units as indicated on the course syllabus. Particular emphasis is placed on cumulated review, real life application problems and on teaching students the skills necessary to solve mathematic problems with and without the aid of technology. Concepts and problems are conveyed graphically, numerically, analytically, and verbally. Relevant real world applications involving calculus concepts are presented throughout the course. To accommodate those students with limited precursor knowledge, review topics from algebra, pre-calculus, SAT topics and trigonometry are woven into the curriculum as needed. In addiction, some time is devoted to the college application process. This course is about mathematics but it is also about gaining a greater awareness of self and how one fits in the world as well as an increased readiness for the rigors of college.

Course Details

In AP Calculus, students learn how to use the TI 84 and TI 89 calculators as a problem solving tool and as a tool to inductively discover calculus concepts and ideas. Students use the calculator on a daily basis to explore, discover and understand calculus concepts. Even though technology and the graphing calculator are integral to this calculus course, students are expected to “do” and to describe calculus concepts without the aid of a calculator as well as with a calculator.

Significant emphasis is placed on gaining an understanding of why mathematical concepts are true and on their real life relevance and applications. As a consequence, students make oral presentations and produce projects and mini lessons so that they have multiple opportunities to communicate mathematics verbally and in writing.

Students are encouraged to work in groups in class and outside of class. On a regular basis, student teams write their solutions to posed calculus problems on the board. This gives the students an opportunity to view alternative methods of solutions and to communicate the process they used with the rest of the class. Ironically, students often gain the most insight when viewing incorrect solutions presented by their peers. This method of multiple students working at the same time also diminishes the fear that some students have about trying new approaches. Students are usually assigned homework

daily. Upon completion of each homework assignment, students utilize teacher-generated solution keys and collaboratively assess their own performance and that of their peers. Students are encouraged to work cooperatively on assignments so as to maximize learning. To effectively gauge progress and growth, students take short weekly quizzes and take tests after completion of each unit. There are a significant number of timed speed drills/quizzes to provide preparation for the AP exam. As the AP exam allows the use of a calculator on only a portion of the exam, some tests will be calculator free. Thus, students are expected to sharpen their own mechanical skills and not become too dependent on the calculator. Some tests will be take-home exams. All exams contain AP style questions from both the free response and the multiple choice sections of the AP exam. In the spring semester, students begin taking memory quizzes in January. In January through April, students take a series of practice AP exams to improve their readiness for the AP Calculus exam. Their work is graded as it would be at an AP reading and, following each practice exam, students work cooperatively to gain greater understanding and clarity.

In addition to attending tutorial sessions, students are encouraged to form study groups on their own and to meet regularly with each other. Students should leave the course with an increased ability to share knowledge effectively with their peers and with the capacity to become math tutors (volunteer and paid) while in college.

Throughout the course, students create conjectures that “seem” true and test their conjectures using the graphing calculator and prior knowledge. For example, when learning the product rule, students test the conjecture, “is the derivative of a product the product of the derivatives” in a graphing calculator activity that gently guides them to knowledge of the product rule.

Students use the “define” feature of the TI 89 calculator to discover the chain rule. Some students also create “scripts” to facilitate understanding.

Students are encouraged to rewrite mathematical definitions in language that makes sense to them. With that in mind, all calculus concepts are defined mathematically, then reconstructed in metaphorical terms that make sense and simplified to what is referred to as the “kindergarten” definition. Students become aware that one must be able to express a concept in its simplest terms (i.e. the kindergarten definition) in order to fully understand it.

Students complete a Rieman sum and trapezoid rule activity using TI 89 calculator Rieman programs to gain an understanding of left, right, and midpoint Rieman and trapezoidal approximations for area under a curve. They discover that as the value of n increases, the value of the Rieman sum approaches the exact area under the curve. The use of the calculator greatly enhances students understanding of approximation techniques and their relationship to integration.

Students gain an understanding of anti-differentiation by exploring slope fields in a variety of contexts. They begin with a pencil and paper activity using tables and a ruler to create slope fields for various simple differential equations. They gain additional understanding regarding initial conditions and anti-derivatives by exploring slope fields utilizing a java applet available at: http://www.math.lsa.umich.edu/courses/116/slopefields_no_navigation.html. In addition, the students learn how to use the differential equation setting on the TI 89 calculator to further explore differential equations, derivatives, and antiderivatives.

Students should expect to devote 12-20 hours per week, including the 4 hours of classroom instruction, toward their mastery of Calculus. This translates to total weekly hours = classroom hours times a multiplicative factor between 3 and 5.

Projects

1. Equation of a tangent line project : To help the students understand local linearity and how the derivative is, in fact, the slope of the tangent line at a point, each student zooms in on a chosen function and graphs it using available software, such as winplot, or graphs the “zoomed in” function by hand. Each student or student team creates a table of values and determines the equation of a tangent line at a designated point using the appropriate derivative rules and with the symmetric difference quotient. The student or team then compares the y intercepts of the two tangent lines and calculates the percent error between the two y intercepts. This project helps students gain an appreciation for the veracity of the derivative rules. It also provides a useful conceptual link between algebraic approximations of slope (symmetric difference quotient, what the students call the 9th grade way) and the calculus-based definition of slope. This project provides students with a powerful opportunity to utilize the rule of four-representing functions graphically, numerically, analytically, and verbally.

2. A Related Rates Project designed to foster creativity and a greater understanding of word problems. Students create their own related rates problems and solve them mathematically. Students also utilize the regression feature on the calculator to generate linear and non-linear equations which are then used in developing their related rates project(s).

3. A Missing Piece project (created by Marsha Hurwitz) developed to increase students understanding of continuity and differentiability. Students complete this two-pronged project by rewriting the children’s poem, “A Missing Piece” by Shel Silverstein as a mathematical essay/poem incorporating the criteria described below into their story. Students create a mathematical solution using the definitions of continuity and differentiability. Students use a TI 89 calculator and mathematical software (such as winplot) on this project.

a. Students must generate the piecewise function that defines “the circle” with a missing piece.

b. Identify a number of quadratics with the following criteria:

http://www.math.lsa.umich.edu/courses/116/slopefields_no_navigation.html

1) A quadratic that is not continuous at [-1,1]. Students need to address the consequences.

2) A quadratic that is continuous with the circle on [-1, 1] but results in points of non differentiability at x= 1 and x= -1. Students need to addresses the consequences.

3) A quadratic function that will fill the missing piece and results in continuity and differentiability at x= 1 and x= -1.

4) Also incorporate into the story plot a circle (this could be the main character or another character) that has an opening on [-3, 3]. What consequences does a parabola resulting in differentiability and continuity have on this circle’s ability to roll?

4. At the end of each chapter in the main text one or more “problem solving” exercises are assigned – these exercises are in fact mini-projects. The student or student team must share their results with the class.

GradingExams: 40%AP-Questions: 30%In-Class/HW: 30%

Calculus AB Syllabus

I. “Limits and Their Properties”. Chapter 1.A. Topics.

1. Epsilon-Delta Definition of Limit2. Limit Definitions: 9 main cases, including one sided limit definitions

and infinite limits.3. Linear Epsilon Delta Proofs 4. Evaluation of Limits: Substitution, Factoring, Rationalizing, and Limits

that do not exist.5. Properties of Limits6. The Squeeze Theorem7. Special Limits

;

;

8. Definition of Continuity9. Removable and Non-removable Discontinuities10. The Existence of a Limit11. Continuity on a Closed Interval12. Properties of Continuity13. Intermediate Value Theorem14. Vertical Asymptotes; Horizontal Asymptotes

B. Teaching Methods and Evaluations.1. Graphing Calculator Exploration of each topic above.

Of note:a. Definitions of limits presented theoretically, analytically, and

illustrated graphically by hand and with a graphing calculator.b. Special Limits explored with the graphing calculator and proved

algebraically.c. Evaluation of limits calculated algebraically and illustrated

graphically.d. Continuity explored graphically and with limits.e. Problems developed illustrating vertical and horizontal

asymptotes.

2. Each topic presented through combinations of lecture, student and group interaction, graphing calculator usage, supplements, Power Point presentations and assignments.

3. Limits presented in relation to their role in the definition of a derivative.4. Supplements of Chapter 1:

a. Linear Epsilon Delta Proofs.b. Limit Evaluations – algebraically, graphically, and from tables.

Includes limits involving infinity and one-sided limits.c. Proofs of Special Limits.d. Continuity –algebraic, graphical, and with limits.e. “Functions Modeling Change”—pg. 123-124: # 20-34

5. Teacher created individual and group tests, graphing projects, and other evaluations. Multiple Choice and Free Response questions listed in VIII of the syllabus.

C. Assignments. Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.1. 1.1: A Brief Preview of Calculus; Tangent lines and the Length of

a Curve. 1-9o, 23, 25. 2. 1.2: The Concept of Limit. 9-25o, Supplement-Limit epsilon – delta

proofs. 3. 1.3: Computation of Limits. 1, 5, 9, 11, 13, 17, 19, 25, 39, 41, 43, 49, 51,

63, 65. Supplement-Evaluation of Limits. 4. 1.4: Continuity and Its Consequences. 5, 7, 9, 13, 25, 37, 41-49o. Supplement-

Continuity. 5. 1.5: Limits Involving Infinity; Asymptotes. 1-9o, 10, 11-37o, 57, 59.

Supplement-Evaluation of Limits. 6. 1.6: Formal Definition of the Limit. 9-15o, 25, 26, 35.7. Review Exercises. 1, 11, 12, 19, 25, 29, 31, 38, 39, 51, EE # 1.8. Larson Problem Solving. 5, 9, 12 Chapter 1.

II. “Derivatives”. Chapter 2.A. Topics.

1. Difference Quotient2. Definition of Tangent Line with Slope m3. Definition of the Derivative4. Alternate form of the Derivative5. Derivative Notation6. Differentiability and Continuity7. The Constant Rule8. The Power Rule; the Constant Multiple Rule; Sum and Difference Rules;

Derivatives of Sine and Cosine9. Average Velocity; Average Rate of Change10. Instantaneous Rate of Change11. Position Function; Velocity; Speed; Acceleration12. Product Rule, Quotient Rule13. Derivatives of the Tangent, Cotangent, Secant, and Cosecant Trig

Functions.14. Higher Order Derivatives15. The Chain Rule

16. The General Power Rule17. Derivatives of Trig Functions w/Chain Rule18. Implicit Differentiation/Implicit Function Theorem19. Linear Approximations20. Motion on a Line21. Differential of Logarithmic Functions22. The Number e23. The Natural Logarithmic Function – Differentiation 24. Exponential Functions: Differentiation 25. Inverse Functions 26. Differentiation of Inverse Functions27. Solving Exponential Equations

B. Teaching Methods and Evaluations.1. Graphing Calculator Exploration of each topic.

Of note:a. Use of the graphing calculator with the tangent line problem.b. Explore the definition of the derivative using the graphing

calculator to graph the function and the definition of its derivative with delta equal to .01 in the same viewing window.

c. Exploration of Differentiability vs. Continuity.d. Graphical exploration of the relation of a function and its first

and second derivatives - graphical, numerical, and analytical.e. Graphical illustration of average rate of change and

instantaneous rate of change.f. Graphical project with Linear Approximations.g. Graphical Regression Analysis to find a model for the data

given. Graph and interpret its derivative.h. Graph the function, the tangent line, and the normal line.

2. Each topic presented through lecture, student and group interaction, graphing calculator usage, supplements, Power Point presentations and assignments.

3. Supplements of Chapter 2:a. The Derivative: The limit of the Difference Quotient.b. Proofs of theorems of Chapter 2.c. Definition of the Derivative and Differentiability.d. Symmetric Difference Quotient, estimation of the rate of change

(derivative) from graphs and tables, and the alternate form of the derivative.

e. Derivative Group Challenge In-Class Warf. Chain Rule and Implicit Differentiation (Implicit Function Theorem).g. Equation of a Tangent Line Project # 1. h. AP Test and the Calculator.i. Local Linear Approximations. j. Motion on a Line. k. Velocity and Acceleration Applications

4. Evaluations:a. Teacher created individual and group tests, graphing projects,

and other evaluations.

b. Multiple Choice and Free Response questions listed in VIII of the syllabus.

C. Assignments. Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 2.1: Tangent Lines and Velocity. 1-25o, 35, 37, 39, EE # 1. 2. 2.2 : The Derivative. 5-13o, 14-24, 31, 33, 35, 49, 64, EE # 1.

Supplements. Proofs. 3. 2.3: Computation of the Derivatives; The Power Rule. 1-37o, 38, 39, 40,

45, 55, 59-62, EE # 1. Supplements. Proofs.4. 2.4: The Product and Quotient Rules. 1-15o, 19, 29, 31, 49-52.

Supplements. Proofs. 5. 2.5: The Chain Rule. 1-27o, 29-34, 35-39o, 41-44, EE # 1. 6. 2.6: Derivatives of Trigonometric Functions. 3-19o, 25-31o, 33-36, 42.

Supplements.

7. 2.7: Derivatives of Exponential and Log Functions. 1-45o, 49-52, 61, 65.8. 2.8: Implicit Differentiation and Inverse Trigonometric Functions. 1-23o,

29-37o, 45, 57, EE # 1. Supplement: Implicit Function Theorem pg. 979.9. 2.9: The Mean Value Theorem 1, 3, 5, 9, 11, 13, 15, 29-34. Supplement.

Larson hand-out pgs 172-178; 1-4, 5, 7, 9, 10, 11-31o, 37-41, 43, 45-52. 10. Review Exercises. 1, 2, 3-19o, 23-59o, 60-68, 71, 73, 75, 77, 78, 83-86.11. Larson Problem Solving. 10, 14 Chapter 2.

III. “Applications of Differentiation”. Chapter 3.A. Topics.

1. Definition of Extrema on an Interval2. Relative Extrema and Critical Numbers3. The Extreme Value Theorem4. Increasing and Decreasing Functions5. The First Derivative Line Test6. Rolle’s Theorem; The Mean Value Theorem7. Concavity8. The Second Derivative Test; The Second Derivative Line Test9. Inflection Points10. Monotonic Functions11. Horizontal Asymptote Test

12. L’Hopital’s Rule of the form .

13. Curve Sketching 14. Optimization15. Newton’s Method16. Differentials17. Related Rates


Of note:

a. First Derivative Test project - discussion of the sign of the first derivative and the increasing or decreasing behavior of the function.

b. Second Derivative Test project - discussion of the sign of the second derivative and the concavity of the function.

c. Function vs. its first and second derivative to discuss rate of change.

d. Intermediate Value Theorem and Extreme Value Theorem illustrated graphically with discussion of continuity.

e. Critical points and Inflection points.f. Regression Analysis to develop a model of the data, then graph

its first and/or second derivatives to discuss trends and make conclusions.

g. Horizontal and Vertical Asymptotes.h. Curve Sketching.i. Optimization-problems related to engineering and business.j. Newton’s Method project.

2. Each topic presented through lecture, student and group interaction, graphing calculator usage, supplements, Power Point presentations, and various assignments.

3. Supplements of Chapter 3:a. Review of solving Trigonometric Equations.b. Curve Sketching outline with theorems and definitions. c. Curve Sketching project. Curve Sketching without the use of a

graphing calculator. Use all the techniques of curve sketching. Continuous and Discontinuous functions, horizontal asymptotes, vertical asymptotes, oblique asymptotes, and points where the function is not differentiable are included. Graphing calculator used as reinforcement.

d. Optimization Project – use first or second derivative test to prove optimization.

e. Newton’s Method Project.f. Differentials.g. Related Rates Project # 2h. Use of AP Test Preparation questions of section VIII to provide:

1. Problems of distance, displacement, average velocity, and instantaneous velocity,

2. Reading graphs and tables to answer questions concerning extrema, inflection, and concavity.

3. Graphs of the first or second derivative, answer questions concerning the function, f(x).

4. Tables to answer questions concerning average rate of change and instantaneous rate of change.

5. Questions using the alternate form of the derivative, first derivative test, and the equation of the line tangent to the graph.


C. Assignments.

Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 3.1: Linear Approximations and Newton’s Method. 13, 15. 2. 3.2: Indeterminate Forms and L’Hopital’s Rule. 3, 7, 17, 25, 33, 35.

3. 3.3: Maximum and Minimum Values. 5-27o, 31-37o, 57, 65, 66, 69, 70, EE # 2 & 3.

4. 3.4: Increasing and Decreasing Functions. 1-33o, 63.5. 3.5: Concavity and the Second derivative Test. 1-35o, 36, 53-55. 6. 3.6: Overview of Curve Sketching. 19, 25, 27, 28, 32, 39. 7. 3.7: Optimization. 2-12, 15-19, 22, 24, 27, 31, 33-35, 39-43o, EE # 1. 8. 3.8: Related Rates. 1-13o, 19-27o, 31, 32-34, 37; Supplement: Larson

hand-out pgs 149-153.9. 3.9: Rates of Change in Economics and the Sciences. 1-15o, 16, 17, 21,

22, 25, 26, 28, 30, 36-39, 41-49o, 54-56, 59, 60.10. Review Exercises. 1, 5, 11, 17, 21, 25, 29, 33, 47, 49-52, 55-60, EE # 4.

11. L’Hopital’s Rule of the form .

12. AP Test Preparation of section VIII.13. Larson Problem Solving. 10, 14 Chapter 2.14. Larson Problem Solving. 9, 10 Chapter 3.

IV. “Integration”. Chapter 4.A. Topics

1. Anti-Derivative2. Constant of Integration, General Solution3. Differential Equation4. Antidifferentiation5. Indefinite Integration, Integrand, Variable of Integration, Indefinite

Integral6. Integration Rules7. General Solutions8. Initial Condition, Particular Solution9. Integration using u-substitution/Integration Tables 10. General Power Rule for Integration11. Sigma Notation, Index of Summation12. Area—Upper Sums, Lower Sums

Circumscribed Rectangle, Inscribed Rectangle13. Limit of the Lower and Upper Sums14. Definition of the Area of a Region in the Plane15. Riemann Sums – left, right, and midpoint sums16. Definite Integrals and Riemann Sums17. Continuity and Integration18. The Definite Integral as the Area of a Region19. Properties of Definite Integrals20. The Fundamental Theorem of Calculus21. U Substitution and the Change of the Variables and the Intervals of

Integration22. The Mean Value Theorem for Integrals

23. Average Value of a Function24. The Definite Integral of the rate of change of a quantity over an interval

interpreted as the change of the quantity over the interval25. The Second Fundamental Theorem of Calculus26. Integration of Even and Odd Functions27. Trapezoidal Rule, Simpson’s Rule28. Accumulation of Rate of Changes 29. Numerical Approximation of the Definite Integrals30. Integral applications to finding distance31. Integration of Logarithmic Functions32. The Number e33. The Natural Logarithmic Function--Integration34. Exponential Functions: Integration35. Inverse Functions 36. Integration of Inverse Functions


Of note:a. Integration.b. Summation.c. Definite Integration.d. Area.e. Trapezoidal and Simpson’s Rule.f. Distance Applications.

2. Each topic presented through lecture, student and group interaction, graphing calculator usage, Project # 3, supplements, Power Point presentations, assignments, and other projects where applicable.

3. Supplements of Chapter 4:a. Limit of a Riemann Sum as a definite integral.b. Riemann sum using left, right, and midpoint evaluations.c. Proofs related to Integration topics of Chapter 4.d. Indefinite and Definite Integration.e. Integration Overview.f. Selected problems of AP Test Preparation questions of section

VIII to provide:1. Integral of a rate of change to give accumulated change.2. Integration to find the area of a region.3. Integration to find total distance or displacement.4. Use of antiderivatives to discuss motion along a line.5. Using tables or graphs of velocity to answer questions

concerning distance, accumulation, or lower and upper estimate of total accumulations.

6. Problems concerning area, Second Fundamental Theorem of Calculus, and average rate of change.

7. Using graphs to find definite integrals given the graph of the derivative

g. Trapezoidal and Rieman Sum Activity (algebraically, graphically, tables).


C. Assignments. Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 4.1: Antiderivatives. 1-33o, 39-52, 57-68, EE # 1. Supplement Larson Hand-Out Pgs. 251 & 255; Larson Pg 255 # 1-14.

2. 4.2: Sums and Sigma Notation. 5-15o, 19, 21, 27-31o, 32, 35, 37; EE # 1. 3. 4.3: Area. 17-26. 4. 4.4: The Definite Integral. 1, 5-23o, 33-38, 49. 5. 4.5: The Fundamental Theorem of Calculus. 1-37o, 38, 39-43o, 47-57o,

63-64. 6. 4.6: Integration by Substitution. 1-39o, 66. Supplement–Proofs.7. 4.7: Numerical Integration. 29-36. 8. 4.8: The Natural Log as an Integral. 1-4, 9-12, 13-29o, 45.9. Review Exercises. 1-23o, 35, 36, 41-61o.10. Selected problems of Section VIII of AP Test Preparation.11. Larson Problem Solving. 7, 9 & 10 Chapter 4.

END OF FIRST SEMESTER

V. “First Order Differential Equations”. Chapter 7. A. Topics.

1. Differential Equations – Separation of Variables 2. Slope Fields 3. Differential Equations - Growth and Decay 4. Differential Equations – Newton’s Law of Cooling (Heating) 5. Logistic Growth 6. Euler’s Method 7. First Order Linear Differential Equations


Of note:a. Exponential and Logarithmic Functions.b. Differentiation and Integration of Exponential and Logarithmic

Functions.c. Exponential, Logarithmic, and Polynomial function comparison

graphically to compare rate of change.d. Differential Equations.e. Slope Fields.f. Functions and their Inverses.

2. Each topic presented through lecture, student and group interaction, graphing calculator usage, supplements, Power Point presentations, assignments, and other projects where applicable.

3. Supplements of Chapter 5:

a. Proofs of Logarithmic and Exponential Functions/Logarithms and Their Properties (Chapter 4: “Functions Modeling Change”—pg. 144-180).

b. au and logau.c. Selected problems to provide mastery:

1. Relationship of the slope field and the differential equation - general and particular solution.

2. Graphing slope fields.3. Solving Differential Equations – general and particular

solution.4. Calculator and non-calculator applications.5. Differential Equations – Growth and Decay.6. Differential Equations – Newton’s Law of Cooling

(Heating).d. Slope Fields.e. Logistic Growth.f. Euler’s Method.g. Proofs of the Derivatives of Inverse Trig Functions.


C. Assignments.Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 7.1: Modeling with Differential Equations. 1-39o, 45, 60.2. 7.2: Separable Differential Equations. 1-15o, 19-35o, 53. 3. 7.3: Direction Fields and Euler’s Method. 7-12.4. Larson hand-out pgs. 404-412. 1-27o, 31-47o, 48-60. 5. Review Exercises. 1-17o, 23-26, 31.6. Selected problems of Section VIII of AP Test Preparation7. Larson Problem Solving: Chapter 5 # 1 & Chapter 6 # 2, 6 & 9.

VI. “Applications of the Definite Integral”. Chapter 5.A. Topics.

1. Area between two curves2. Volume: disk method3. Volume: shell method4. Volume: solids with known cross sections5. Enrichment Topics

a. Arc Lengthb. Surface of Revolutionc. Workd. Moments, Centers of Mass, and Centroidse. Fluid Pressure and Fluid Force

B. Teaching Methods and Evaluations.1. Graphing Calculator Exploration of each topic.2. Each topic presented through lecture, student and group

interaction, graphing calculator usage, supplements, Power Point

presentations, and other assignments where applicable.


C. Assignments.Text: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 5.1: Area between Curves. 1-25o, 29, 31, 37, 41, 42.2. 5.2: Volume; Slicing, Disks and Washers. 1-7o, 17-20, 22b, 23a, 24-28,

EE # 2.3. 5.3: Volume by Cylindrical Shells. 1-9o, 17a, 17d, 19a, 19d, 21, 23a,

23b, 23c, 25, 35, 37 37. 4. Selected problems of Section VIII of AP Test Preparation5. Enrichment Topics:

a. 5.4: Arc Length and Surface Area.b. 5.5: Projectile Motion. c. 5.6: Applications of Integration to Physics and Engineering.

d. 5.7: Probability.

VII. “Integration Techniques, L’Hopital’s Rule…”. Chapter 6 (Enrichment).A. Topics.

1. Integration by Parts

2. L’Hopital’s Rule of the form

3. Additional Topics:a. Trigonometric Integrationb. Trigonometric Substitutionc. Partial Fractionsd. Integration by Tablese. Indeterminate Formsf. Improper Integrals

B. Teaching Methods and Evaluations.1. Graphing Calculator Exploration of each topic.2. Each topic presented through lecture, student and group

interaction, graphing calculator usage, supplements, assignments, and Power Point presentations where applicable.

3. Teacher created individual and group tests, and other evaluations. Multiple Choice and Free Response questions listed in VIII of the syllabus.

C. Assignments.Text Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

1. 6.1: Review of Formulas and Techniques. 2. 6.2: Integration by Parts. 3. 6.3: Trigonometric Integrals and Trigonometric Substitution.

4. 6.4: Integration of Rational Functions Using Partial Fractions.5. 6.5: Integration by Tables 6. 6.6: Improper Integrals.

VIII. AP Test Preparation.A. Selected test questions from:

1. “Released Exams”—1998-2007 AP Calculus AB; The College Board.2. “Released Exams”—1998-2007 AP Calculus BC; The College Board.3. Other Resources (e. g: Kaplan AP Calculus AB & BC 2007; Barron’s

How to Prepare for AP Calculus Advanced Placement Examination).

Resources

Major Textbook: Smith, Robert T; Minton, Roland B. Calculus Early Transcendental Functions 3 rd Edition . Boston: McGraw-Hill, 2007.

Supplemental materials include previous AP exams, teacher generated PowerPoint presentations, AP Institute materials and a variety of calculus resources available on the Internet including the College Board’s AP Central website. In addition, problems and projects from the other textbooks and support materials (as listed below) are utilized through the year. The school provides a TI-89 calculator for each student to use in the course.

Additional reference textbooks and materials for sampling purposes: Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy.

Calculus- Graphical, Numerical, Algebraic, 3rd ed. Menlo Park: Scott Foresman Addison-Wesley, 2007.

Foerster, Paul. Calculus: Concepts and Applications, 2nd ed. Key Curriculum Press, 2005.

Hughes-Hallett, Gleason, & McCallum. Calculus, of a Single Variable, 4th ed. New York: Wiley & Sons, 2005.

Stewart, James. Calculus, 5th ed. Pacific Grove, Calif.: Brook/Cole Publishing Company, 2005.

Fischbeck, Sally E. The TI-89, A Graphing Calculator with computer Algebra, Tips for TI-83 Users. Texas Interments. education.ti.com/us/product/tech/89/down/tips.html

Advanced Placement Summer Institute 2006—AP AB-Calculus

Anton, Howard; Bivens, Irl and Davis, Stephen.Calculus – 8th ed. Anton Textbooks, Inc 2005

Connally, Hughes-Hallett, Gleason, ET AL. Functions Modeling Change—A Preparation For Calculus Texas Edition 2e. John Wiley & Sons 2007.

Larson, Hostetler & Edwards. Calculus of a Single Variable, 8th ed. Houghton Mifflin co, 2006

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