AP CALCULUS AB Course Syllabus Course Overview AP Calculus AB is designed to be a college-level introduction to the Calculus concepts. At the end of the course, students will have the option of taking the College Board AP Calculus AB test for college credit. The AP Calculus AB course aims to help students develop an understanding of the concepts of calculus, experience the use of calculus methods, and discover how these methods may be applied to practical, real-world situations. The course, while maintaining strict, traditional mathematical content, incorporates technology to study limits, derivatives, integrals, as well as their applications. It covers everything in the Calculus AB topic outline as it appears in the AP Calculus Course Description. The primary textbook for the course is the Calculus Graphical, Numerical, Algebraic by Finney, Demana, Waits, and Kennedy. Course Goals and Major Student Outcomes A student completing this course should at the minimum be able to: Work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal Understand the connections among these representations Understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems Understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems Understand the relationship between the derivative and the definite integral as expressed in both parts of the fundamental theorem of calculus Use technology to help solve problems, experiments interpret results, and verify conclusions Course Objectives The objectives of this course are: To cultivate students’ basic understanding of the concepts of calculus To provide students an experience in the use of calculus methods To show students that calculus methods may be applied to real-world, practical applications Course Planner (1st Quarter) Unit 1: Pre-Calculus Review A. Lines 1. Slope as Rate of Change 2. Parallel & Perpendicular Lines 3. Equations of Lines B. Functions and Graphs 1. Functions 2. Domain & Range 3. Families of Functions 4. Piecewise Functions 5. Composition of Functions C. Exponential and Logarithmic Functions 1. Exponential Growth & Decay 2. Inverse Functions 3. Logarithmic Functions 4. Properties of Logarithms D. Trigonometric Functions 1. Graphs of Basic Trigonometric Functions I. Domain & Range II. Transformations III. Inverse Trigonometric Functions 2. Applications Unit 2: Limits and Continuity A. Limits at a Point 1. Properties of Limits 2. Two-sided 3. One-sided B. Limits Involving Infinity 1. Asymptotic Behavior 2. End Behavior 3. Properties of Limits 4. Visualizing Limits C. Continuity 1. Continuous Functions 2. Discontinuous Functions I. Removable Discontinuity II. Jump Discontinuity III. Infinite Discontinuity D. Rates of Change, Tangent Lines, & Normal Lines Unit 3: Derivatives A. Derivatives of a Function B. Differentiability 1. Local Linearity 2. Numeric Derivatives Using the Calculator 3. Differentiability and Continuity C. Rules for Differentiation D. Velocity and Other Rates of Change E. Derivatives of Trigonometric Functions (2nd Quarter) Unit 3: Derivatives (continued) A. Chain Rule B. Implicit Differentiation C. Derivatives of Inverse Trigonometric Functions D. Derivatives of Logarithmic and Exponential Functions Unit 4: Applications of Derivatives A. Extreme Values of Functions 1. Local (Relative) Extrema 2. Global (Absolute) Extrema B. Using the Derivative 1. Mean Value Theorem 2. Rolle’s Theorem 3. Increasing & Decreasing Functions C. Analysis of Graphs Using the First and Second Derivatives 1. Critical values 2. 1st Derivative Test for Extrema 3. Concavity and Points of Inflection 4. 2nd Derivative Test for Extrema D. Optimization Problems E. Linearization Models F. Related Rate Problems Unit 5: The Definite Integral A. Approximating Areas 1. Reimann Sums 2. Trapezoidal Rule 3. Definite Integrals B. The Fundamental Theorem of Calculus C. Definite Integrals and Antiderivatives 1. The Average Value Theorem (3rd Quarter) Unit 6: Differential Equations and Mathematical Modeling A. Antiderivatives B. Integration by Parts C. Integration by Substitution D. Separable Differential Equations 1. Growth & Decay 2. Slope Fields 3. General Differential Equations E. Numerical Methods Unit 7: Applications of Definite Integrals A. Integrals as Net Change B. Areas in the Plane C. Volumes 1. Solids with known cross-sections 2. Solids of revolution I. Disk Method II. Shell Method Unit 8: L’Hopital’s Rule, Improper Integrals and Partial Fractions A. L’Hopital’s Rule B. Relative Rates of Growth C. Improper Integrals D. Partial Fraction (4th Quarter) Unit 9: Review for the Advance Placement Examination A. Multiple Choice Questions B. Free-Response Questions C. Practice Drills D. Mock AP Examination E. Formula Quizzes Instructional Methods and Strategies Throughout the duration of this course: Broad concepts and applications shall be emphasized Various technological means shall be used to aid in learning and reinforce concepts The course as a whole shall be unified through the use of cohesive themes (e.g., derivatives, integrals, limits, etc…..) Topics shall be presented in a challenging format Technology and Computer Software The teacher shall be using Powerpoint presentations which has been developed to aid in teaching various calculus concepts. TI-83, TI-84, or TI-89 shall be used to model calculator steps as an aid to solve selected Calculus problem. Student Evaluation AP Calculus AB is an honors course patterned after a college level course. As such, the grading will be much heavily dependent on major tests and the final exam. Because of the cumulative nature of the AP exam, most major tests will also be cumulative in nature. Students can expect quizzes and tests to be 50% of their grade. Classworks and homeworks/warmups will be 30% and 20% of their final grade, respectively. Participation in classroom discussions, oral presentations, as well as written responses to mathematical problems are EXPECTED and will also count toward the final grade.