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AP Calculus AB

About This Course

Course Description: This course prepares high school students planning to take the Calculus AB Advanced Placement exam. For more information about this exam please click here.  Students will study the main ideas found in differential calculus: limits, derivatives, and basic integration. By the end of the course, students will be able to demonstrate an adequate understanding of these topics. 

To be successful in this course students must be proficient in precalculus. Students may forgo enrolling in a precalculus course provided they have a strong background in algebra 2  and trigonometry. Please review the prerequisite before enrolling in this course. Students will not be able to complete the course without having a strong background in these subjects. 

The topics discussed in AP Calculus AB are equivalent to those found in a semester college-level calculus 1 course. Consequently, those who score at a 3 on the exam may qualify for college credit whereas some colleges require at least a 4 on the exam. 

Course Information

Course Topics

  • The idea of a limit
  • Calculating limits
  • Squeeze Theorem
  • Infinite Limits
  • Indeterminate Forms
  • L’Hospital’s Rule
  • Continuity
  • Average Rate of Change
  • Instantaneous Rate of Change
  • Properties of Derivatives
  • Derivatives of Special Functions
    • Trigonometric Functions
    • Exponential Functions
    • Logarithmic Functions
  • The Power Rule
  • The Product Rule
  • The Quotient Rule
  • The Chain Rule
  • Implicit Differentiation
  • Logarithmic Differentiation
  • Inverse Trigonometric Functions
  • Optimization
  • Related Rates, I
  • Related Rates, II
  • Motion
    • Position
    • Velocity
    • Acceleration
  • Linear Approximation
  • Critical Points
  • Monotonicity of Functions
    • Increasing, Decreasing 
  • Inflection Points
  • Concavity
  • Relative and Absolute Extrema
    • First Derivative Test
    • Second Derivative Test
  • Graphing Functions
  • Interpreting Graphs 
  • Antiderivatives
    • Indefinite Integrals
  • Fundamental Theorem of Calculus
    • Definite Integrals 
  • Basic Properties of Integrals
  • Integrals of Basic Functions
  • Integration by substitution
  • Numerical Integration
    • Left-Hand Rule
    • Right-Hand Rule
    • Midpoint Rule
    • Trapezoidal Rule
    • Simpson’s Rule
  • The Area of an Enclosed Region
    • Vertical Simple Regions
    • Horizontal Simple Regions
  • The Average Value of a Function
  • Volumes
    • Disk/Washer Method
    • Shell Method
    • Non-rotational Symmetries
      • Cross-sections
  • Separable Differential Equations
  • Graphing and Understanding Slope Fields
  • Growth and Decay Problems

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