Handouts

• AP Calculus AB & BC Course Description

These worksheets are mostly from the 2006–2007 school year. Some changes may have been made since.

• Assignment Sheets
• Review Packets
• Chapter 1: Functions and Models
• Chapter 2: Limits and Rates of Change
• Chapter 3: Derivatives
• Chapter 4: Applications of Differentiation
• Chapter 5: Integrals
• Chapter 6: Applications of Integration
• Chapter 7: Inverse Functions
• Chapter 8: Techniques of Integration
• Chapter 9: Further Applications of Integration
• Chapter 10: Differential Equations
• Chapter 11: Parametric Equations and Polar Coordinates
• Chapter 12: Infinite Sequences and Series

Assignment Sheets

The dates on these assignment sheets are from the 2006–2007 school year. I therefore recommend referring to them only for assignment number and problems.

• Chapters 1–2
• Chapter 3
• Chapter 4
• Chapter 7
• Chapter 5
• Chapter 6
• Chapters 8–9
• Chapter 10
• Chapter 11
• Chapter 12
• AP Review (assignment sheet not available)

Review Packets

• Chapter 2
• Chapter 3, test 1
• Chapter 3, test 2
• Chapter 4
• Chapter 7
• Chapter 5
• Chapter 6
• Chapter 8, test 1
• Chapter 8, test 2, and Chapter 9
• Chapter 10
• Chapter 11
• Chapter 12, test 1
• Chapter 12, test 2

MV review packets

• Review Material
• Chapter 13
• Chapter 14
• Chapter 15, part 1
• Chapter 15, part 2
• Chapter 16
• Chapter 17, part 1
• Chapter 17, part 2

Chapter 1: Functions and Models

• Review

Chapter 2: Limits and Rates of Change

• 2.1: The Tangent and Velocity Problems
• 2.2: The Limit
• 2.3: Limit Laws
• 2.4: Linear Limits with δ-ε
• 2.4: Quadratic Limits with δ-ε
• 2.4: Infinite Limits with δ-ε
• 2.4: Homework Worksheets #1 and #2 for δ-ε
• 2.4: Further Practice with δ-ε Proofs
• 2.4: Summary of δ-ε Limit Definitions
• 2.5: Continuity
• 2.6: The Tangent and Velocity Problems Revisited

Chapter 3: Derivatives

• 3.1: The Derivative
• 3.2: Derivatives as Functions
• 3.3: Derivative Formulas (part 1 of 2) and Notation
• 3.3: Derivative Formulas (part 2 of 2) and the Product and Quotient Rules
• 3.5: Derivatives of Trigonometric Functions (part 1 of 2)
• 3.5: Derivatives of Trigonometric Functions (part 2 of 2)
• 3.6: The Chain Rule
• 3.7: Implicit Differentiation
• 3.8: Higher-Order Derivatives
• 3.9: Related Rates
• 3.10: Linearization and Differentials

Chapter 4: Applications of Differentiation

• 4.1: Critical Points and Extreme Values
• 4.2: The Mean Value Theorem
• 4.3: 4.Derivatives and the Shape of a Graph
• 4.4: Infinite Limits
• 4.5: Curve Sketching
• 4.7: Optimization
• 4.9: Newton’s Method
• 4.10: Antiderivatives
• Related Rates — Practice Problems for Homework
• Optimization — Practice Problems for Homework
• Particle Motion — Practice Problems for Homework

Chapter 5: Integrals

• 5.1: Sums and the Area Problem
• 5.2: Signed Areas and the Definite Integral
• 5.3: The Fundamental Theorem of Calculus, part 1 of 2
• 5.3: The Fundamental Theorem of Calculus, part 2 of 2
• 5.4: Integral Practice and Indefinite Integrals
• 5.5: Evaluating Integrals Using u-Substitution
• Integration Practice

Chapter 6: Applications of Integration

• 6.1: The Area Between Curves
• 6.2: Volume with Slices, Disks, and Washers
• 6.3: Volume with Cylindrical Shells
• 6.4: Work
• 6.5: Average Value
• Summary of Calculating Volume of Solids of Revolution
• Homework Assignment #61

Chapter 7: Inverse Functions

• 7.1: Inverse Functions
• 7.2: Exponential Functions and Derivatives
• 7.3: Logarithmic Functions
• 7.4: Derivatives of Logarithmic Functions
• 7.5: Inverse Trigonometric Functions and Derivatives
• 7.7: Indeterminate Forms and L’Hôpital’s Rule
• Graphs of Inverse Trigonometric Functions
• Logarithmic and Exponential Function Practice Problems

Chapter 8: Techniques of Integration

• 8.1: Integration by Parts
• 8.2: Trigonometric Antiderivatives
• 8.3: Trigonometric Substitution
• 8.4: Partial Fractions
• 8.5: Strategies for Antidifferentiation
• 8.7: Approximate Integration with the Left, Right, Midpoint, and Trapezoidal Sums
• 8.7: Approximate Integration with Simpson’s Rule
• 8.8: Improper Integrals
• Summary of Riemann Sums

Chapter 9: Further Applications of Integration

• 9.1: Arc Length
• 9.2: Surface Area

Chapter 10: Differential Equations

• 10.1: Differential Equations
• 10.2: Slope Fields and Euler’s Method (part 1 of 2)
• 10.2: Slope Fields and Euler’s Method (part 2 of 2)
• 10.3: Separable Differential Equations
• 10.4: Exponential Growth and Decay
• 10.5: Logistic Equations
• The Generalized Logistic Curve
• Summary of Major Differential Equations

Chapter 11: Parametric Equations and Polar Coordinates

• 11.1: Parametric Equations and Vector Functions
• 11.2: Calculus with Parametric Equations and Vector Functions
• 11.3: Polar Coordinates and Equations
• 11.4: Calculus with Polar Equations
• Additional Vector Function Problems (Homework Assignments #90–93)
• Additional Parametric Equation Problems (Homework Assignments #99–100)
• Review Problems

Chapter 12: Infinite Sequences and Series

• 12.1: Sequences (part 1 of 2)
• 12.1: Sequences (part 2 of 2)
• 12.2: Series
• 12.3: The Integral Test
• 12.4: The Comparison Test
• 12.5: Alternating Series
• 12.6: Absolute and Conditional Convergence and the Ratio and Root Tests
• 12.8: Power Series
• 12.9: Representing Functions as Power Series
• 12.10: Taylor and Maclaurin Series and the Lagrange Error Bound
• Strategies for Sequences and Series