Material Covered
AP Calculus BC Chapter 1: Functions and Models
1.1 Four Ways to Represent a Function
1.2 Mathematical Models: A Catalog of Essential Functions
1.3 New Functions from Old Functions
1.4 Graphing Calculators and Computers
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
Chapter 2: Limits and Derivatives
2.1 The Tangent Line and Velocity Problems
2.2 The Limit of a Function
2.3 Calculating Limits Using the Limit Laws
2.4 The Precise Definition of a Limit
2.5 Continuity
2.6 Limits at Infinity; Horizontal Asymptotes
2.7 Tangents, Velocities, and Other Rates of Change
2.8 Derivatives
2.9 The Derivative as a Function
Chapter 3: Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions
3.2 The Product and Quotient Rules
3.3 Rates of Change in the Natural and Social Sciences
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Higher Derivatives
3.8 Derivatives of Higher Functions
3.9 Hyperbolic Functions
3.10 Related Rates
3.11 Linear Approximations and Differentials
Chapter 4: Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Indeterminate Forms and L’Hospital’s Rule
4.5 Summary of Curve Sketching
4.6 Graphing with Calculus and Calculators
4.7 Optimization Problems
4.8 Applications to Business and Economics
4.9
4.10 Antiderivatives
Chapter 5: Integrals
5.1 Areas and Distances
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals and the Net Change Theorem
5.5 The Substitution Rule
5.6 The Logarithm Defined as an Integral
Chapter 6: Applications of Integration
6.1 Areas Between Curves
6.2 Volumes
6.3 Volumes by Cylidrical Shells
6.4 Work
6.5 Average Value of a Function
Chapter 7: Techniques of Integration (3 weeks)
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
7.5 Strategy for Integration
7.7 Approximate Integration
7.8 Improper Integrals
Chapter 8: Further Applications of Integration (1 week)
8.1 Arc Length
8.2 Area of a Surface of Revolution
8.3 Applications to Physics and Engineering
8.4 Applications to Economics and Biology
8.5 Probability
Chapter 9: Differential Equations
9.1 Modeling with Differential Equations
9.2 Direction Fields and Euler’s Method
9.3 Separable Equations
9.4 Exponential Growth and Decay
9.5 The Logistic Equation
Chapter 10: Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations
10.2 Calculus with Parametric Curves
