## AP Calculus AB Online Exam Review

This review focuses on key perspectives that connect the topics of limits, the derivative and its application, the integral and its application, and the Fundamental Theorem of Calculus in order for students to be prepared to take the AP Calculus AB Exam in May of 2016. This review serves as exam preparation and is not recommended as a replacement for a year-long AP Calculus AB course.

**Topics to be addressed:**

Module One: Limits and Differentiation; Applications

- Average Rate of Change
- Limit Definition of the Derivative
- Particle Motion
- Writing Sentences
- Module One Objectives
- After completing module one, students will be able to:
- Identify when to use average rate of change to estimate a derivative value at a specified point and when to find a derivative value at a specified point
- Apply the mean value theorem
- Create strategies to identify when limit problems on the AP Calculus AB Exam are hinting toward the limit definition of the derivative
- Find derivatives to do limit definition of the derivative problems instead of using manipulation skills to find the limit
- Find the velocity, acceleration and speed of a particle in motion using calculus
- Analyze a position function of a particle and determine key characteristics about the motion of the particle

- After completing module one, students will be able to:

Module Two: Applications of Integration and the Fundamental Theorem of Calculus

- Applying the Fundamental Theorem of Calculus
- Applications of the Definite Integral
- Approximations Involving the Integral
- Volumes of Revolution
- Volumes by Known Cross Sections
- Using the Graphing Calculator
- Module Two Objectives
- After completing module two, students will be able to:
- Employ Part I of the FTC to continuous functions
- Employ Part I of the FTC to particle motion problems
- Apply Part II of the FTC with emphasis on using the Chain Rule
- Review left, right, midpoint, Reimann Sums, as well as trapezoidal sum approximations
- Use definite integrals to represent the volume of 3D figures of revolution by the disk method and washer methods
- Use definite integrals to represent the volume of 3D figures formed by cross sections
- Plot the graph of a function to solve calculus problems

- After completing module two, students will be able to:

**Instructor
Melissa Burkhead** teaches Pre-AP Geometry, Pre-AP Pre-Calculus and BC Calculus at Trinity Valley School in Fort Worth, Texas. She has been teaching secondary students for 23 years, including schools in Mexico City, the El Paso public schools, Austin’s magnet school program and the Episcopal school system. Ms. Burkhead moderates the online courses:

*Teaching Geometry with the Geometer’s Sketchpad*and

*Teaching Algebra with the Geometer’s Sketchpad for Key Curriculum Press*. She has presented at numerous AP conferences and most recently represented The College Board with a special focus in AP Calculus in Abu Dhabi, U.A.E. and Bogotá, Colombia. She is also a reader for the AP Calculus exam. She holds a bachelor’s in mathematics and political science from Georgetown College and a master’s in education (mathematics specialty) from The University of Texas at El Paso.