2 days. 2 days. 3.6 Chain Rule 2 days Cumulative. 3 days Review and Quiz

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Jerome Garrett
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1 AP Calculus AB Syllabus Course Overview: Students will study all topics covered on the Calculus AB exam as outlined by the AP Calculus Course Description through a combination of lecture, guided practice, cooperative learning, and technology exploration. As a pre-requisite, students taking AP Calculus AB will have taken a pre-calculus class. This pre-calculus course includes the study of limits and continuity. For this reason, our study of limits will be brief and will allow for a slower pace on some of the more difficult calculus concepts. Course Planner: ased on a semester course 180 minutes each Section Number Topics Covered Timeline 2.1 Rates of Change and Limits 2.2 Limits Involving Infinity 2.3 Continuity 2.4 Rates of Change and Tangent Lines 4 days and 3.1 Derivative of a Function 4 days 3.2 Differentiability 4 days 3.3 Rules for Differentiation 4 days 3.4 Velocity and Other Rates of Change 4 days 3.5 Derivatives of Trigonometric Functions 3.6 Chain Rule Practice derivative rules. Review points at which a derivative does not exist. 3.7 Implicit Differentiation 4 days 3.8 Derivatives of Inverse Trigonometric Functions 3.9 Derivatives of Exponential and 4 days Logarithmic Functions and 4 days 4.1 Extreme Values of Functions 6 days 4.2 Mean Value Theorem 4.3 Connecting f' and f" with the Graph 4 days off

2 Practice connecting graphs of functions and their derivatives. Practice finding extreme values, and inflection points. 4.4 Modeling and Optimization 8 days 1 day Practice solving optimization problems. 4.5 Linearization and Newton's Method 4 days 4.6 Related Rates 8 days I day and Practice solving related rate problems. 5.1 Estimating with Finite Sums 4 days 5.2 Definite Integrals 4 days 5.3 Definite Integrals and 4 days Antiderivatives 5.4 Fundamental Theorem of Calculus 6 days 5.5 Trapezoidal Rule and 6.1 Slope Fields 4 days 6.2 Antidifferentiation by Substitution 4 days 6.4 Exponential Growth and Decay 4 days involving slope fields. Practice solving growth and decay problems. 7.1 Integral As Net Change 6 days 7.2 Areas in the Plane 4 days 7.3 Volumes 6 days involving areas of regions bounded by curves

3 involving solids of revolution or cross-sections. 7.5 Applications from Science and Statistics and Course Review and Preparation,for Final Exam Final Exam involving applications of the definite integral. Major topics of the course will be reviewed and students will prepare for the final exam. Assess student comprehension of course material 8 days 6 days 1 day Teaching Strategies: Concepts will be introduced in a traditional lecture format, but students will apply and practice their learning in a variety of cooperative structures and guided practice activities. Students will regularly participate in a competitive group contest in which groups solve free response problems from previous AP exams. The groups will do a problem per day applicable directly to a topic being covered in class. The AP problems not only serve as practice and reinforcement of the class activities, but also as a challenge and extension for high-achieving students. In addition, students will participate in a variety of other activities including but not limited to exercises requiring matching graphs of a derivative to a graph of the original function, drawing slope fields and matching differential equations to the graph of the corresponding function using these slope fields, finding regression equations for data and drawing tangent lines to these graphs, and completing "writing to learn" textbook activities and including these in a portfolio. At the conclusion of the course, students are given the option to attend evening review sessions to further prepare for the AP exam. Technology and Computer Software: The graphing calculator is used on a regular basis to illustrate key concepts, add depth to student understanding, and perform complex calculations allowing the class to explore more challenging problems without having to perform the calculus operations by hand. All students are provided with a TI-83 or TI-84 graphing calculator. Power point presentations provided by the textbook are used on a regular basis to add to the lectures and review key ideas.

4 Student Evaluation: Marking period grades are calculated using zes, tests, and student portfolios. The portfolios may contain any combination of tests, zes, bonus problems, extra-credit research assignments, "writing to learn" textbook activities, and math contest exams. s are designed in a similar fashion to the AP exam including both multiple-choice and free-response style questions. Calculators are required for some parts of the tests and zes, while they are not allowed on other portions. Each marking period grade is 40% of the student's final average with the final exam making up the remaining 20%. Teacher Resources Primary Textbook: Finney, Ross L. Franldin D. Demana, Burt K. Waits, Daniel Kennedy. Calculus Graphical Numerical Algebraic 3 rd edition New York: Pearson Prentice Hall, Secondary Textbook: Swokowski, Earl W., Michael Olinick, Dennis Pence, Jeffery A. Cole Calculus of a Single Variable. 2nd edition. Boston: PWS Publishing Company, Student Activities: Homework assignments daily; students review these problems the next class period by putting them on the board and explaining their process and thinking to the class. Portfolio assignments the majority of these are "writing to learn" activities provided in the primary text. Other assignments may include bonus problems or brief research projects. s and zes 1 test and lor 2 zes per chapter Guided practice and student board work daily Cooperative group contests involving free-response questions from released AP exams (students are grouped and remain with these groups for approximately 2 weeks) 3 to 4 problems per week. Many of these problems require that the students justify their results by explaining their approach in complete sentences. Calculus Match Game (grouping graphs into "families" of three which represent f", f', and f ) Chapter 3 Calculator activities involving slope fields, tangent lines and linear approximations, regression equations, rectangle approximations, and solids of revolution (provided by textbook or teacher generated) 1 or 2 group activities per chapter. (These activities are more complicated and may take

5 half a class period to complete. The graphing calculator however is used on a daily basis and is integrated into almost every topic in the course. These activities go above and beyond calculations and normal calculus uses of the graphing calculator. See next page for an example of one of these activities.) Summary Students will master the AB Calculus curriculum through a combination of lecture, exploration, discovery, guided practice, and independent practice. Students will learn calculus concepts with a combination of a traditional "pencil and paper" approach as well as a technology approach to solve complex problems and add depth to their understanding. All students will demonstrate the ability to explain their understanding through a combination of daily oral explanations of homework assignments, portfolio writing assignments, and competitive group activities. In this manner, a complete appreciation of the application of calculus as well as calculus theory is achieved.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only.

AP Calculus AB. Nevada Academic Standards that are assessable at the local level only. Calculus AB Priority Keys Aligned with Nevada Standards MA I MI L S MA represents a Major content area. Any concept labeled MA is something of central importance to the entire class/curriculum; it is a