AP® Calculus BC Course Overview Everything in the Calculus BC topic outline as it appears in the AP® Calculus Course Description is covered in this course. The primary textbook is Calculus – Early Transcendentals 8th Edition by Howard Anton, Irl Bivens and Stephen Davis. The goal of this course is to prepare students for the AP Calculus BC exam in May. Throughout the course, the instruction and development of the AP Calculus concepts model the techniques (graphical, numerical, analytical and verbal) and emphasize the connections among all types of representations. These same techniques and connections are the focus of the AP examination and are reflected in assessment throughout the course. Students are given examples of AP Free Response as well as Multiple Choice questions in the form of in-class work, homework, quiz and test questions. Every test includes both Multiple Choice and Free Response questions. Students discuss Calculus orally through group work and in-class discussions. Students are expected to know the graphs of basic functions (basic trig functions, e x , ln x, simple polynomials) and use their familiarity of the graphs’ properties in order to applications. Students will be able to evaluate limits, differentiate, and integrate polynomial, trigonometric, exponential and logarithmic functions. Students are held accountable for the processes as well as the conceptual meaning behind limits, derivatives and integration. Technology The TI-83 Plus graphing calculator will be used for presentations. Students will use either a TI-83 or TI-84 graphing calculator. Students will use their calculators to graph, find zeros and points of intersection, evaluate derivatives at a point, and evaluate definite integrals. Student Evaluation Marking period grades are computed using homework, quizzes, and tests. All students are expected to take the AP exam. Tests include questions that are modeled after the AP Exam. Each test is comprised of a calculator and non-calculator part. Both parts contain multiple-choice questions as well as free response questions. Course Plan Below is the sequence of topics covered in the AP Calculus BC course. The following are covered extensively in Honors Analysis and are reviewed briefly via a summer packet and at the beginning of the school year. Review (Chapter 1) Real Numbers and the Coordinate Plane Lines and Linear Functions Polynomials and Rational Functions Algebra of Exponentials and Logarithms Parametric Functions Polar Functions (11.1) Graphs Trigonometric Functions Topic Outline for Calculus BC Limits and Continuity (Chapter 2) 6 days Computing Limits Limits at Infinity and End Behavior Continuity Continuity of Trigonometric and Inverse Functions The Derivative (Chapter 3) 16 days Rates of Change and Tangent Lines The Derivative Function Techniques of Differentiation Product and Quotient Rules Derivatives of Trigonometric Functions The Chain Rule Derivatives of Parametric Equations (11.2) Derivatives of Polar Equations (11.2) Derivatives of Logarithmic, Exponential and Inverse Trig Functions 8 days Implicit Differentiation Second Derivatives Derivatives of Logarithmic Functions Derivatives of Exponential and Inverse Trigonometric Functions L’Hopital’s Rule (Chapter 4) The Derivative in Graphing and Applications (Chapter 5) 20 days Related Rates (3.7) Local linearization (3.8) Analysis of Functions (Increase, Decrease, Concavity, Relative Extrema) Curve Sketching Absolute minima and maxima and applied problems Newton’s Method Mean-Value Theorem Integration (Chapter 6) 14 days Overview of Area Problem Indefinite Integral U-substitution Definition of Area as a Limit Definite Integral Fundamental Theorem of Calculus Principles of Integral Evaluation (Chapter 8) 11 days Integration by Parts Trigonometric Integrals and substitutions Partial Fractions Simpson’s Rule (numerical integration) Improper Integrals Applications of the Definite Integral (Chapter 7) 15 days Area between Two Curves Volumes by Slicing: Disks and Washers Volumes by Shells Average value of a function on an interval Lengths of Curves (7.4 and 11.2) Area in Polar Coordinates (11.3) Mathematical Modeling (Chapter 9) 6 days First-Order Differential Equations Slope Fields and solving equations graphically Euler’s Method and solving equation numerically Modeling – Population Growth and logistic equations Infinite Series (Chapter 10) 24 days Sequences Infinites Series Convergence Tests Comparison, Ratio and Root tests p series tests Conditional Convergence Taylor Series Power Series LaGrange remainder Review and preparation for AP Exam – Approximately 4 weeks Done both individually and in groups. Exams given and analyzed. Teacher Resources Primary Textbook Calculus – Early Transcendentals 8th Edition by Howard Anton, Irl Bivens and Stephen Davis Supplementary Texts: Calculus, 8th Edition, Houghton Mifflin Company, 2006 by Ron Larson, Robert P. Hostetler, and Bruce H. Edwards. Calculus: Graphical, Numerical, Algebraic, Prentice Hall, 2003 by Ross L Finney, Franklin D. Demana, Bert K. Waits and Daniel Kennedy. Additional Resources AP Calculus Course Description AP Released Exams Technology Resources Students are required to have a graphing calculator. The TI-83 or TI-84 is recommended for Calculus BC.