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Preparing for the AP* Calculus AB and BC Exams (Part 1 - Differential Calculus)

University of Houston System via Coursera

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Overview

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This course reviews the topics for the AP Calculus AB Exam. 

The course is divided into two parts.  Part 1 is Differential Calculus and incorporates mostly AB topics but does have some BC topics.  Part 2 is Integral Calculus, and again is mostly AB material.  The BC material that is not covered in either of these parts will be reviewed in an extension.

Each week of the six week review will include review videos for an important block of material, complete with videos of worked example problems and exam tips. There will also be an extensive online quiz given each week, with multiple problem versions that students can use to practice, along with practice tests to help students prepare for the AP* Calculus AB Exam.

* AP Calculus is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.





Syllabus

  • Week 1 - Limits and Continuity: limits of functions, asymptotic behavior, unbounded behavior, continuity properties of functions, the intermediate value theorem, limits of trigonometric functions and the extreme value theorem.

          Assessments: Practice Problems and Quizzes

  • Week 2 - Derivatives of Polynomials and Trigonometric Functions, Chain Rule, Higher Order Derivatives, and Implicit Differentiation: definition and concept of the derivative, derivative rules, higher order derivatives,interpretation of the derivative, chain rule, implicit differentiation.

         Assessments: Practice Problems and Quizzes

  • Week 3 - Applications of the Derivative: related rates, velocity/acceleration, Mean Value Theorem, intervals of increase/decrease, extreme values, concavity, points of Inflection and curve sketching.

          Assessments: Practice Problems and Quizzes

  • Week 4 - Transcendental Functions: inverse functions, exponential and natural logarithm functions, inverse trigonometric functions and hyperbolic functions.

          Assessments: Practice Problems and Quizzes

  • Week 5 - Further Applications of the Derivative: optimization, differentials L'Hospital's Rule.

          Assessments: Practice Problems and Quizzes

  • Week 6 - Practice AB Exam                                                                                  

          Assessments: Two exams






















Taught by

Jeffrey Morgan and Rebecca George

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