AP Calculus BC Semester I: Course Outline

Unit 1: Functions and Graphs
1. Lesson 1: Functions and Function Notation
  1. Topic 1: Definition of a function
  2. Topic 2: Vertical line test
  3. Topic 3: Function notation
  4. Topic 4: Finding input & output values
  5. Topic 5: Domain & range
2. Lesson 2: Absolute Value and Piecewise Defined Functions
  1. Topic 1: Piecewise defined functions
  2. Topic 2: The absolute value function
  3. Topic 3: Solving equations involving absolute values
3. Lesson 3: Inequalities
  1. Topic 1: Solving inequalities
  2. Topic 2: Solving inequalities involving absolute values
4. Lesson 4: Composition and Combination of Functions
  1. Topic 1: Composition of functions
  2. Topic 2: Inverse functions
  3. Topic 3: Non-invertible functions
5. Lesson 5: Exponential and Logarithmic Functions
  1. Topic 1: The family of exponential functions
  2. Topic 2: The number e
  3. Topic 3: Logarithmic functions
  4. Topic 4: Solving exponential and logarithmic functions
  5. Topic 5: Changing the base of logarithmic functions
6. Lesson 6: Transformation of Functions
  1. Topic 1: Horizontal & vertical shifts
  2. Topic 2: Reflections & symmetry
  3. Topic 3: Vertical stretches & compressions
  4. Topic 4: Horizontal stretches & compressions
7. Lesson 7: Trigonometric Functions
  1. Topic 1: Radians and arc length
  2. Topic 2: The sin and cosine functions
  3. Topic 3: Other trigonometric functions
  4. Topic 4: Inverse trigonometric functions
  5. Topic 5: Trigonometric identities
8. Lesson 8: Polynomial and Rational Functions
  1. Topic 1: Variations
  2. Topic 2: Power functions
  3. Topic 3: Polynomial functions
  4. Topic 4: Rational functions
9. Lesson 9: Vectors and Vector-Valued Functions
  1. Topic 1: Vectors
  2. Topic 2: Components of a vector
  3. Topic 3: Addition, subtraction, & scalar multiplication
  4. Topic 4: The zero and unit vectors
10. Lesson 10: Polar Coordinates and Graphs
  1. Topic 1: Polar coordinates
  2. Topic 2: Coordinate conversion
  3. Topic 3: Polar graphs
  4. Topic 4: Special polar graphs
11. Lesson 11: Parametric Equations and Conic Sections
  1. Topic 1: Parametric equations
  2. Topic 2: Eliminating the parameter
  3. Topic 3: Finding parametric equations
Unit 2: Limits and Continuity
1. Lesson 12: Intuitive Definition of a Limit
  1. Topic 1: Definition
  2. Topic 2: Using tables & graphs to find limits
  3. Topic 3: Application: Using limits to find velocity
2. Lesson 13: Algebraic Techniques for Finding Limits
  1. Topic 1: Calculating limits using limit laws
  2. Topic 2: Direct substitution property
  3. Topic 3: Indeterminate forms
3. Lesson 14: One-Sided Limits
  1. Topic 1: Definition of one-sided limits
  2. Topic 2: Finding one-sided limits
  3. Topic 3: Existence of limits
4. Lesson 15: Infinite Limits
  1. Topic 1: Definition of infinite limits
  2. Topic 2: Vertical asymptotes
5. Lesson 16: Limits at Infinity
  1. Topic 1: End-behavior of functions & horizontal asymptotes
  2. Topic 2: Limit laws for infinite limits
  3. Topic 3: Oblique asymptotes
6. Lesson 17: Limits of Special Trigonometric Functions
  1. Topic 1: Special limits involving the sine function
  2. Topic 2: Special limits involving the cosine function
  3. Topic 3: Special limits involving the tangent function
7. Lesson 18: Continuity
  1. Topic 1: Continuity at a point
  2. Topic 2: Continuity on a closed interval
  3. Topic 3: Continuity on an open interval
  4. Topic 4: Intermediate Value Theorem
Unit 3: Derivatives
1. Lesson 19: Definition of the Derivative
  1. Topic 1: The derivative as the slope of a tangent
  2. Topic 2: The derivative as the rate of change
  3. Topic 3: The derivative as a function
2. Lesson 20: Differentiation Rules
  1. Topic 1: Constant rule, constant multiple rule
  2. Topic 2: Power rule
  3. Topic 3: Sum rule, difference rule
  4. Topic 4: Product rule
  5. Topic 5: Quotient rule
  6. Topic 6: Trigonometric rules
3. Lesson 21: The Chain Rule
  1. Topic 1: Chain rule definition
  2. Topic 2: The chain rule with other rules
  3. Topic 3: Higher-order derivatives
4. Lesson 22: Derivatives of Exponential Functions
  1. Topic 1: Exponential rule
  2. Topic 2: Base-a exponentials rule
5. Lesson 23: Derivative of Logarithmic Functions
  1. Topic 1: Natural logarithmic rule
  2. Topic 2: General logarithmic rule
6. Lesson 24: Derivatives of Inverse Functions
  1. Topic 1: Inverse trig rule
  2. Topic 2: Derivatives of Inverses
7. Lesson 25: Differentiability and Continuity
  1. Topic 1: Differentiability implies continuity
  2. Topic 2: Non-differentiable functions
8. Lesson 26: Implicit Differentiation
  1. Topic 1: Derivatives of implicitly defined functions
9. Lesson 27: Logarithmic Differentiation
  1. Topic 1: derivatives of complicated expressions
10. Lesson 28: Parametric Derivatives
  1. Topic 1: Parametric form of the derivative
  2. Topic 2: Parametric form of the second derivative
11. Lesson 29: Differentiation with Polar Curves
  1. Topic 1: Tangents to polar slopes
12. Lesson 30: Differentiation of Vector-Valued Functions
  1. Topic 1: Limits & continuity
  2. Topic 2: Derivatives of vector-valued functions
  3. Topic 3: Differentiation rules & examples
Unit 4: Application of the Derivative
1. Lesson 31: Tangent and Normal Lines
  1. Topic 1: Tangent lines
  2. Topic 2: Normal lines
2. Lesson 32: Position, Velocity, and Acceleration (PVA)
  1. Topic 1: Position & velocity
  2. Topic 2: Acceleration
3. Lesson 33: Related Rates
  1. Topic 1: Defining the problem
  2. Topic 2: Example problems
4. Lesson 34: Relative Extrema and the First Derivative Test
  1. Topic 1: Relative extrema & critical numbers
  2. Topic 2: Increasing, decreasing functions & the first derivative
5. Lesson 35: Concavity and the Second Derivative Test
  1. Topic 1: Concavity
  2. Topic 2: The second derivative test
6. Lesson 36: Absolute Extrema and Optimization
  1. Topic 1: Extreme value theorem
  2. Topic 2: Sample problem
7. Lesson 37: Rolle's Rule and the Mean Value Theorem
  1. Topic 1: Rolle’s rule
  2. Topic 2: Mean value theorem
8. Lesson 38: Differentials
  1. Topic 1: Linear approximation
  2. Topic 2: Differentials
9. Lesson 39: L'Hospital's Rule
  1. Topic 1: Indeterminate forms & L’Hospital’s rule
  2. Topic 2: Proof of L’Hospital’s rule
  3. Topic 3: Other indeterminate forms