Segment B will teach students that finding derivatives of functions can tell us many things about the functions including whether it is positive or negative, the rate of change at that point and the concavity of a function. Derivatives can be used to analyze curves and determine the local and global behavior of a function, as well as optimize quantities in real-world scenarios and relate rates of change.

PRE-REQUISITES: Pre-Calculus recommended

ESTIMATED COMPLETION TIME: 16-18 weeks or approximately 65 – 75 hours

MAJOR TOPICS AND CONCEPTS – SEGMENT B

The Definite Integral and Antiderivatives

  • How do we measure Distance Traveled?
  • The Definite Integral
  • The Fundamental Theorem and Interpretations
  • Theorems about Definite Integrals
  • Antiderivatives Graphically and Numerically
  • Constructing Antiderivatives Analytically
  • Differential Equations
  • Second Fundamental Theorem of Calculus
  • The Equations of Motion

Integration

  • Integration by Substitution
  • Integration by Parts
  • Tables of Integrals
  • Algebraic Identities and Trigonometric Substitutions
  • Approximating Definite Integrals
  • Improper Integrals

Definite Integral and Differential Equation

  • Areas and Volumes
  • Applications to Geometry
  • What is a Differential Equation?
  • Slope Fields
  • Separation of Variables

AP Exam Review

  • Format of AP Exam and test taking hints
  • Review of major topics in the course
  • Link to review sites
  • Section I Part A – Multiple Choice Questions – No Calculator
  • Section I Part B – Multiple Choice Questions – Calculator
  • Section II Part A – Free Response Questions – Calculator
  • Section II Part B – Free Response Questions – No Calculator

LINKS TO FULL COURSE CURRICULUM MAPS

SEGMENT B