2007 - 2008 AP Calculus AB Syllabus

Office Hours:
Tuesday - Thursday
After school 3:15 pm to 4:45 pm
(Subject to change without notice.)

Students can earn extra credit towards their grade (up to a grade of 89.9%) 

AP Calculus AB Syllabus

Fall 2007 – Spring 2008, 3º  (MTuThF 9:50-10:40, W 9:50-10:25)

Mr. D. Weston

Thurgood Marshall Academic High School, Rm. 219

Phone: 415-695-5612, x.3219

Email: WestonDarth@gmail.com

Course Overview

AP^® Calculus AB course is intended for students with mathematical ability and a desire to be challenged.  It will cover basic topics in differential and integral calculus.  The student will pursue these topics in a variety of ways including presentation to the class by groups of students, projects and self-study.  At the end of the course, students will be able to compute and/or analyze mathematical problems in the following subject areas: analysis of graphs, limits of functions (including one-sided limits), asymptotes, continuity, derivatives, concept of a derivative, derivative at a point, derivative as a function, second derivatives, applications of derivatives, computation of derivatives, power functions, exponential functions, logarithmic functions, trigonometric functions, inverse trigonometric functions, sum rule, product rule, quotient rule, chain rule, implicit and explicit differentiation, techniques of anti-differentiation / indefinite integrals, definite integrals, the fundamental theorem of Calculus, application of anti-differentiation, numerical approximation such as Riemann sum, the trapezoid method and Simpson’s Rule. 

This course is taught in a style much like a college course: it requires significantly more work than a non-Advanced Placement class and expects the students to take the responsibility for their successes and failures.  It is intended to extend the mathematical skills and knowledge of students strong in high school math who are ready to have their limits expanded.  In addition to mathematics, the course includes study skills, calculator skills, test-taking strategies and skills, and activities to make the students more effective communicators.

Textbook

Foerster, Paul A. (1998). Calculus:  Concepts and Applications.  Key Curriculum Press:  Berkeley, CA.  ISBN: 1-55953-117-7.  Replacement cost is $66.00.

Required Materials

Graphing Calculator [C5]:  Students are expected to bring a graphing calculator to class everyday.  In order that you know how to use the calculator you will need to practice using it before using it on the test.  You should check the College Board website (http://www.collegeboard.com/student/testing/ap/calculus_ab/calc.html?calcab) to see which calculators are acceptable and not acceptable.  For those of you planning to go to college (everyone I hope) you will most likely need to have a calculator on your own for your college math and science courses.  If the cost of a graphing calculator is a burden, the school has some TI-83Plus calculators which can be checked out.

Graph Paper:  Needed for weekly homework assignments

Computer access and an email account:  The presentations and projects require you to use the computer to prepare.  Some communication for the course will be via e-mail.  If you do not have access to a computer there are computers at school available for your use.  If you do not have an email account, a free account can be set up either though the school district or an online provider like gmail, yahoo or hotmail.

Course Planner [C2]

Summer Assignment

Review of Important concepts in PreCalculus

(Due the first week of school)

Limits, Derivatives, Integrals, and Integrals (Chapter 1)

(2 Weeks)

1. The Concept of Instantaneous Rate
2. Rate of Change by Equation, Graph, or Table
3. One Type of Integral of a Function
4. Definite Integrals by Trapezoids, from Equations and Data
5. Limits of a Function
6. Graphing different types of functions with a graphing calculator [C5]

Activities / Assessments

• Quiz 1
• Chapter 1 Test

Properties of Limits (Chapter 2)

(2 Weeks)

1. Numerical Approach to the Definition of Limits
2. Graphical and Algebraic Approaches to the Definition of Limits
3. The Limit Theorems
4. Continuity
5. Limits Involving Infinity
6. Intermediate Value Theorem
7. Using a graphical calculator’s lists features to approximate the limit [C5]

Activities / Assessments

• Quiz 2

• Project 1 – Limits
• Problem Set 1 given to students – topic: limits
• Chapter 2 Test

Derivatives, Antiderivatives, and Indefinite Integrals (Chapter 3)

(3 weeks)

1. Graphical Interpretation of Derivative
2. Difference Quotients and One Definition of Derivative (x®c)
3. Derivative Functions, Numerically and Graphically
4. Derivative of the Power Function and Another Definition of the of Derivative (Dx®0) or (h®0)
5. Displacement, Velocity, and Acceleration
6. Introduction to Sine, Cosine, and Composite Functions
7. Derivatives of Composite Functions – Chain Rule
8. Proof and Application of Sine and Cosine Derivatives
9. Antiderivatives and Indefinite Integrals

8. Graphing calculator parametric mode [C5]

Activities / Assessments

• Student presentations 1 - about Graphing Calculator functions [C5]
• Quiz 3
• Quiz 4

• Chapter 3 Test

Products, Quotients, and Parametric Functions (Chapter 4)

(3 weeks)

1. Combinations of Two Functions
2. Derivative of a Product of Two Functions
3. Derivative of a Quotient of Two Functions
4. Derivatives of the Other Trigonometric Functions
5. Derivatives of Inverse Trigonometric Functions
6. Differentiability and Continuity
7. Derivative of a Parametric Function
8. Graphs and Derivatives of Implicit Relations
9. Using a graphing calculator to graph the derivative of a function [C5]

Activities / Assessments

• Student Presentations 2
• Problem set 2 given to students derivatives and simple integrals
• Quiz 5
• Quiz 6
• Chapter 4 Test

Definite and Indefinite Integrals (Chapter 5)

(3 weeks)

1. A Definite Integral Problem
2. Review of Antiderivatives
3. Linear Approximations and Differentials
4. Formal Definition of Antiderivative and Indefinite Integral
5. Riemann Sums and the Definition of Definite Integral
6. The Mean Value Theorem and Rolle’s Theorem
7. Some Very Special Riemann Sums
8. The Fundamental Theorem of Calculus
9. Definite Integral Properties and Practice
10. A Way to Apply Definite Integrals
11. Numerical Integration by Simpson’s Rule and a Grapher
12. Graphing calculator functions and programs to approximate the definite integral [C5]

Activities / Assessments

• Project 2 – Finding the value of pi (π) using approximations of the definite integral
• Quiz 7
• Chapter 5 Test

The Calculus of Exponential and Logarithmic Functions (Chapter 6)

(3 weeks)

1. Integral of the Reciprocal Function: A Population Growth Problem
2. Antiderivative of the Reciprocal Function
3. Natural Logarithms, and Another Form of the Fundamental Theorem
4. In x Really Is a Logarithmic Function
5. Derivatives of Exponential Functions – Logarithmic Differentiation
6. The Number e, and the Derivative of Base b Logarithm Functions
7. The Natural Exponential Function: The Inverse of ln
8. Limits of Indeterminate Forms: l’Hospital’s Rule
9. Derivative and Integral Practice for Transcendental Functions

Activities / Assessments

• Project 3 – Visual soundbite of a topic – poster with media literacy 1-page paper
• Quiz 8
• Quiz 9
• Chapter 6 Test

Cumulative Review: (Chapters 1-6)

(1.5 weeks)

Activities / Assessments

• Student Presentations 3
• Fall Semester Final

The Calculus of Growth and Decay (Chapter 7)

(3 weeks)

1. Direct Proportion Property of Exponential Functions
2. Exponential Growth and Decay
3. Other Differential Equations for Real-World Applications
4. Graphical Solution of Differential Equations by Using Slope Field
5. Numerical Solution of Differential Equations by Using Euler’s Method
6. Predator-Prey Population Problems

Activities / Assessments

• Project 4 – Leaky cistern in a rainstorm
• Quiz 10
• Quiz 11
• Chapter 7 Test

The Calculus of Plane and Solid Figures (Chapter 8)

(3 weeks)

1. Cubic Functions and Their Derivatives
2. Critical Points and Points of Inflection
3. Maxima and Minima in Plane and Solid Figures
4. Area of a Plane Region
5. Volume of a Solid by Plane Slicing
6. Volume of a Solid of Revolution by Cylindrical Shells
7. Length of a Plane Curve – Arc Length
8. Area of a Surface of Revolution
9. Lengths and Areas for Polar Coordinates
10. Graphing calculator’s polar modes

Activities / Assessments

• Student presentations 4 – Groups present topics from Chapter 8
• Quiz 12
• Chapter 8 Test

Algebraic Calculus Techniques for the Elementary Functions (Chapter 9)

(3 weeks)

Introduction to the Integral of a Product of Two Functions

1. Integration by Parts – A Way to Integrate Products
2. Rapid Repeated Integration by Parts
3. Reduction Formulas and Computer Software
4. Integrating Special Powers of Trigonometric Functions
5. Integration by Trigonometric Substitution
6. Integration of Rational Functions by Partial Fractions
7. Integrals of the Inverse Trigonometric Functions
8. Calculus of the Hyperbolic and Inverse Hyperbolic Functions
9. Improper Integrals
10. Miscellaneous Integrals and Derivatives

Activities / Assessments

• Project 5 – Volume of solid of rotation using plane slicing and cylindrical shells

• Quiz 13

• Quiz 14
• Chapter 9 Test

The Calculus of Motion – Averages, Extremes, and Vectors (Chapter 10)

(2 weeks)

Introduction to Distance and Displacement for Motion Along a Line

1. Distance, Displacement, and Acceleration for Linear Motion
2. Average Value Problems in Motion and Elsewhere
3. Related Rates
4. Minimal Path Problems
5. Maximum and Minimum Problems in Motion and Elsewhere
6. Vector Functions for Motion in a Plane

Activities / Assessments

• Project 6 – Freeway problems
• Quiz 15
• Chapter 10 Test

Cumulative Review (Chapter 5 to 10)

(2 weeks)

• Review of material and discussion of what makes a solution complete
• Student Presentations 5 - released free-response questions from the AP Calculus AB test
• AP Calculus Test (Wed., May 7, 2008, 8:00 am)

The Calculus of Variable-Factor Products (Chapter 11)

(1.5 weeks)

1. Review of Work – Force Times Displacement
2. Work Done by a Variable Force
3. Mass of a Variable-Density Object
4. Moments, Cancroids, Center of Mass, and the Theorem of Pappus
5. Force Exerted by a Variable Pressure – Center of Pressure
6. Other Variable-Factor Products

Activities / Assessments

• Quiz 16
• Chapter 11 Test

The Calculus of Functions Defined by Power Series (Chapter 12)

(1.5 weeks)

Introduction to Power Series

1. Geometric Sequences and Series as Mathematical Models
2. Power Series for an Exponential Function
3. Power Series for Other Elementary Functions
4. Taylor and Maclaurin Series, and Operations on These Series
5. Interval of Convergence for a Series – The Ratio Technique
6. Convergence of Series at the Ends of the Convergence Interval
7. Error Analysis for Series
8. Cumulative Reviews

Activities / Assessments

• Student Presentations 6
• Quiz 17
• Chapter 12 Test
• Spring Semester Final

Activities / Assessments

Tests / Quizzes

• Test/quiz content:  Tests and quizzes are based on the material in the textbook, covered in class, assigned to students to solve, learn, review prior to the test/quiz.  Students will receive collections of problems similar to the free-response questions on the AP Calculus AB test.  They are expected to solve the problems on their own or in small groups.  Some of these problems will appear in later tests and/or quizzes.
• Test Structure:  Tests will be divided into different parts that will include multiple-choice questions, short answer questions, and free-response questions.  Approximately half of each chapter test will not allow the use of graphing calculators and approximately half will require use of graphing calculators.  Test are worth a maximum of 100 points each, except the final exam that will be worth 200 pts.  Quizzes are worth 20 points each.
• Students are expected to pass all tests and quizzes with 70% or higher.  Students not meeting this expectation are expected to review the material covered by the test or quiz, complete a test review assignment and take a different version of the test in a timely manner (before the next test).  Only one make-up test will be given for each chapter test or quiz.
• Make-up testing will be done at lunch and after school and students receive the average of the scores of the different versions taken.  It is in the student’s best interest to pass the quizzes and tests and quizzes the first time the take them.

Homework

• Homework will be assigned approximately every week and is due at the beginning of class on the day it is due!  Messy and illegible homework will be returned ungraded.
• Late homework will be accepted, but will be penalized 10% of maximum possible score for being late.
• Homework will be assigned a grade based on its completeness and accuracy.  Each assignment will be worth 10 points.  Acceptable homework with a score of 6 or higher.  Homework assignments with scores of 5 points or less will be returned for revision.  The student will receive an average of the original grade and the revised grade.

Projects

• Once each marking period, students will be given a topic to research and create a carefully designed and product explaining.  Topics will be drawn from the material covered just prior to the project assignment.
• The projects are intended to extend to student conceptual understanding of the topics and allow an opportunity to connect different topics and skills.
• Students are expected to explain the background of the topic, the assigned problem and its relationship to recently covered topics, then present the solution completely with graphs, diagrams and equations.  Further projects must include sources used listed using the APA style.
• Each project will be worth 60 points.  The projects are formal presentations of the solution and as such must meet a level of content and formatting considerably higher than a homework assignment.  (See examples of acceptable work and the scoring rubric given with each project.)  Projects that do not meet minimum standards will be returned for revision.  Students revising their projects will receive an average of the original grade and the revised grade.

Presentations

• All students are required to given three presentations each semester.  Each student will work in groups of students.
• Presentations are intended to build students’ ability to speak in front of their peers and to completely create an organized presentation. 
• The rubric includes points for cooperation, content, organization, design of the PowerPoint document and public speaking skills.  The first presentation is worth 40 points, the second and third presentation are worth 60 points each.
• Each group will be responsible for creating a researched and informative PowerPoint presentation about a topic assigned to / picked by the group.  The presentation should include background knowledge; a clear explanation of the topic; a demonstration problem with graphs, equations and diagrams; discussion about which calculator tools can be used to investigate the problem; what should be included when answering a problem involving the topic, and a list of sources presented in the APA style.  Students will be expected to produce a handout for their classmates and turn in an electric copy of their presentation.

Technology

• A graphing calculator is a valuable tool in the study of mathematics.  The capabilities of the TI-84Plus will be taught and used though the entire duration of this course. [C5]
• Equation Editor is important for presenting readable equations in computer-formatted presentations and papers.  Students will be trained to use Equation Editor and will expected to use it to prepare their presentations.
• Students will use Microsoft PowerPoint, Word and Excel (or freeware equivalents) to prepare presentations and projects.

Grades and distribution of assignments