AP Calculus AB Syllabus

Course Overview and Objectives

This course covers all topics included in the Calculus AB outline as it appears in the AP Calculus Course Description. The objective of this course is to develop students’ understanding of calculus concepts, related mathematical skills and appropriate technology necessary for success on the Advanced Placement Exam and in subsequent college mathematics courses. The course emphasizes a multi-representational approach to calculus with concepts, results, and connections being expressed graphically, numerically, analytically, and verbally. The teacher will model how to communicate mathematics both verbally and in written sentences. The students will learn how to use graphing calculators to help solve problems, interpret results, and support conclusions.

Prerequisites

Before studying calculus, all students should complete the equivalence of four years of high school mathematics designed for college-bound students: courses in which they study algebra, geometry, trigonometry, and elementary functions.

Textbook and Calculator Resources

The textbook used for this course is: Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. Calculus: Graphical, Numerical, Algebraic. AP edition. Boston: Pearson Prentice Hall, 2007. The cost of replacing a lost or damaged textbook is approximately $100.

Each student must have a graphing calculator. The preferred calculator is a TI-84 or a TI-84 plus; however, other brands of graphing calculators may be used.

Course Outline By Topic and Lesson

Unit 1: Prerequisites for Calculus (2 to 3 weeks)

· 1.1 Lines

· 1.2 Functions and Graphs

· 1.3 Exponential Functions

· 1.5 Functions and Logarithms

· 1.6 Trigonometric Functions

Unit 2: Limits and Continuity (2 to 3 weeks)

· 2.1 Rates of Change and Limits

· 2.2 Limits Involving Infinity

· 2.3 Continuity

· 2.4 Rates of Change and Tangent Lines

Unit 3: Derivatives (5 weeks)

· 3.1 Derivative of a Function

· 3.2 Differentiability

· 3.3 Rules for Differentiation

· 3.4 Velocity and Other Rates of Change

· 3.5 Derivatives of Trigonometric Functions

· 3.6 Chain Rule

· 3.7 Implicit Differentiation

· 3.8 Derivatives of Inverse Trigonometric Functions

· 3.9 Derivatives of Exponential and Logarithmic Functions

Unit 4: Applications of Derivatives (5 weeks)

· 4.1 Extreme Values of Functions

· 4.2 Mean Value Theorem

· 4.3 Connecting f ' and f " with the Graph of f

· 4.4 Modeling and Optimization

· 4.5 Linearization

· 4.6 Related Rates

Unit 5: The Definite Integral (5 weeks)

· 5.1 Estimating with Finite Sums

· 5.2 Definite Integrals

· 5.3 Definite Integrals and Antiderivatives

· 5.4 Fundamental Theorem of Calculus

· 5.5 Trapezoidal Rule

Unit 6: Differential Equations and Mathematical Modeling (3 weeks)

· 6.1 Slope Fields

· 6.2 Antidifferentiation by Substitution

· 6.3 Antidifferentiation by Parts

· 6.4 Exponential Growth and Decay

· 6.5 Population Growth

Unit 7: Applications of Definite Integrals (4 weeks)

· 7.1 Integral as Net Change

· 7.2 Areas in the Plane

· 7.3 Volumes

Review/Practice for AP Exam (3 to 4 weeks)

· Multiple Choice and Free Response

· Independent and Small Group Practice

Assessment and Evaluation

Homework will be assigned each night. Quizzes will be given weekly and will be 15-20 minutes in length. Quizzes are designed to test a particular homework skill – some with calculator use and some without. A test will be given at the conclusion of each chapter in the text. These tests will have a calculator section and a non-calculator section. Each chapter test will have multiple choice questions as well as free response questions to serve as practice for the AP exam. All work that requires a written response or justification must be answered in complete sentences with no abbreviations. With the exception of quizzes and tests, students are encouraged and expected to collaborate with each other. Most of the learning will take place in paired, small group, and class discussions. Quizzes, chapter tests, and small group assignments will contribute 80% to each student’s semester average. A cumulative mid-term and cumulative year-end test will be given. If it will benefit the student, the mid-term or year-end test can replace one low test grade for the given semester. Homework and practice exam packets will account for the remaining 20% of a student’s average.

Student Expectations

· Homework is expected to be fully attempted.

· Each student must keep a 3-ring binder divided by chapters, practice exams, and labs. With extra attention given to organization, each student’s notebook will be a useful resource for future college mathematics courses.

· Students are strongly encouraged to seek help from each other outside of class.

· Students will frequently be asked to share ideas with the class and to show their work to the entire class. Emphasis will be placed on the justification of work and conclusions.

· Students should use proper vocabulary and terms when speaking or writing in class.

· Students should consult the textbook, notes from class, and study partners prior to consulting the teacher for extra help. This is to encourage responsibility for the material covered.

· Students are expected to bring materials, textbook, and homework to class daily.

· Disrespect and class interruptions will not be tolerated. Parents will be notified if behavior becomes a problem.

Feel free to contact me concerning your child’s progress. I can be reached by school phone: 770-537-2592 or by school e-mail: robin.campbell@bremencs.com.

You can access a weekly schedule for the class via our school website.

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