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Syllabus Title: 
AP Calculus AB
Syllabus Description: 

What do electrical engineers, economists, and business managers have in common? All use calculus to answer big questions on the job. In this course, you’ll explore the basics of calculus including functions, graphs, integrals, and more, all while gaining valuable problem solving skills. Prerequisites: Successful completion of Math through Algebra II and/or Pre-Calculus or equivalent.

Collection Semester: 
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Unit 1: Functions and Graphs
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  • Functions and Function Notation
  • Absolute Value and Piecewise Defined Functions
  • Inequalities
  • Composition and Combination of Functions
  • Exponential and Logarithmic Functions
  • Transformation of Functions
  • Trigonometric Functions
  • Power, Polynomial, and Rational Functions
  • Vectors and Vector-Valued Functions
  • Polar Coordinates and Graphs
  • Parametric Equations and Conic Sections
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Unit 2: Limits and Continuity
New Unit Content: 
  • Intuitive Definition of a Limit
  • Algebraic Techniques for Finding the Limits
  • One-Sided Limits
  • Infinite Limits
  • Limits at Infinity
  • Limits of Special Trigonometric Functions
  • Continuity
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Unit 3: Derivatives
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  • Definition of the Derivative
  • Differentiation Rules
  • The Chain Rule
  • Derivatives of Exponential Functions
  • Derivative of Logarithmic Functions
  • Derivatives of Inverse Functions
  • Differentiability and Continuity
  • Implicit Differentiation
  • Logarithmic Differentiation
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Unit 4: Application of the Derivative
New Unit Content: 
  • Tangent and Normal Lines
  • Position, Velocity, and Acceleration
  • Related Rates
  • Relative Extrema and the First Derivative Test
  • Concavity and the Second Derivative Test
  • Absolute Extrema and Optimization
  • Rolle’s Rule and the Mean Value Theorem
  • Differentials
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Unit 5: Antiderivatives and Definite Integrals
New Unit Content: 
  • Differential Equations and Slope Fields
  • Antiderivatives
  • The Chain Rule for Antiderivatives
  • Antiderivatives of Exponentials
  • Antiderivatives of Logarithms
  • Antiderivatives and Inverse Trigonometric Functions
  • Fundamental Theorem of Calculus
  • The Definite Integral
  • Fundamental Theorem of Calculus
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Unit 6: Application of Antiderivatives and Definite Integrals
New Unit Content: 
  • Analyzing Curves with Antiderivatives
  • Volume
  • Separable Differential Equations
  • Work
  • Other Applications of Definite Integrals