Calculas 1

AP Calculus BC Semester I : Course Outline

Unit 1: Functions and Graphs

Lesson 1: Functions and Function Notation
Lesson 2: Absolute Value and Piecewise Defined Functions
Lesson 3: Inequalities
Lesson 4: Composition and Combination of Functions
Lesson 5: Exponential and Logarithmic Functions
Lesson 6: Transformation of Functions
Lesson 7: Trigonometric Functions
Lesson 8: Polynomial and Rational Functions

Unit 2: Limits and Continuity

Lesson 9: Vectors and Vector-Valued Functions
Lesson 10: Polar Coordinates and Graphs
Lesson 11: Parametric Equations and Conic Sections
Lesson 12: Intuitive Definition of a Limit
Lesson 13: Algebraic Techniques for Finding Limits
Lesson 14: One-Sided Limits
Lesson 15: Infinite Limits

Unit 3: Derivatives

Lesson 16: Limits at Infinity
Lesson 17: Limits of Special Trigonometric Functions
Lesson 18: Continuity
Lesson 19: Definition of the Derivative
Lesson 20: Differentiation Rules
Lesson 21: The Chain Rule
Lesson 22: Derivatives of Exponential Functions
Lesson 23: Derivative of Logarithmic Functions
Lesson 24: Derivatives of Inverse Functions

Unit 4: Application of the Derivative

Lesson 25: Differentiability and Continuity
Lesson 26: Implicit Differentiation
Lesson 27: Logarithmic Differentiation
Lesson 28: Parametric Derivatives
Lesson 29: Differentiation with Polar Curves
Lesson 30: Differentiation of Vector-Valued Functions
Lesson 31: Tangent and Normal Lines
Lesson 32: Position, Velocity, and Acceleration (PVA)
Lesson 33: Related Rates
Lesson 34: Relative Extrema and the First Derivative Test
Lesson 35: Concavity and the Second Derivative Test
Lesson 36: Absolute Extrema and Optimization
Lesson 37: Rolle's Rule and the Mean Value Theorem
Lesson 38: Differentials
Lesson 39: L'Hospital's Rule