AP Calculus

Module 0

Real Numbers

• Real Numbers

Cartesian Plane

• Cartesian Plane

Solving Trig Equations

• Solving Trig Equations Part 2
• Solving Trig Equations Part 3

Graphs/Models

• Graphs/Models

Linear Equations

• Linear Equations

Functions

• Functions

Module 1

Limits

• Limits Algebraic Review
• Limits Graphical Review
• Limits and Continuity
• Limits and Continuity

Visual Calculus

• University of Kansas Visual Calculus
• The Calculus Tutor AB Material

Module 2

Differentiation and Differentiability

• Definition of Derivative
• Differentiation
• Derivatives and Differentiability

Finding F

• Using Your Calculator to Find F

Derivative Rules

• Derivative Rules
• Examples of Derivative Rules

Product/Quotient

• Product/Quotient

Chain Rule

• Chain Rule
• The Chain Rule

Implicit Differentiation

• Implicit Differentation
• Implicit Differentiation
• Implicit Differentiation YouTube

Related Rates

• Related Rates I
• Related Rates II
• Related Rates Part 1
• Related Rates Part 2
• Related Rates - Beginning
• Related Rates - Advanced

Using Tangent Lines

• Using Tangent Lines

Module 3

Extrema on an Interval

• Extrema on an Interval

Theorems

• Rolles Theorem
• Mean Value Theorem
• Module 3 Theorems
• Mean Value Theorem YouTube

Inc/Dec Functions

• Inc/Dec Functions
• Graphing AP Style
• Concavity and SDT Help With Additional Problem
• Concavity and 2nd Derivative
• Limits at Infinity
• Analysis of Functions

Optimization

• Optimization
• Optimization

Differentials

• Differentials
• Differential Approximation
• Redo of MVT Application

Module 4

Area Under the Curve

• Area Under the Curve
• Area Under The Curve Help with #48
• Area Under The Curve Help With #53
• Understand The Relationships For Motion Problems
• Area of Rectangles
• Area - Limit Definition

Riemann Sums and Definite Integrals

• Riemann Sums and Definite Integrals
• Riemann Sums and Definite Integrals Extra Help with Additional Problem Part C

Fundamental Theorem of Calculus

• Fundamental Theorem of Calculus Part I
• Fundamental Theorem of Calculus Part II
• More Help with Fundamental Theorem of Calculus Part II

Integration

• Integration

Integration by Substitution

• Integration by Substitution
• Integration by Substitution - More Help

Module Review

• Module 4 Chapter Review Q&A Session
• Module 4 Free Response Questions
• Module 4 Review

Module 5

Inverse Trigonometric Functions

• Inverse Functions- Finding the Derivative of
• Differentiation of Inverse Trigonometric Functions

Module 6

• Slope Fields
• Differential Equations

Module 7

Area of a Region Between Two Curves

• Area of a Region Between Two Curves
• Area of a Region Between Two Curves - More Help

Volume by Disk Method

• Volume by Disk Method
• Volume by Disk Method

Volume by Cross Section

• Volume by Cross Section
• Volume by Cross Section - March '08

Solids of Revolutions

• Solids of Revolution - YouTube Video
• MORE - Solids of Revolutions - YouTube Video

Volume by Shell and Arc Length

• Volume by Shell and Arc Length

Work Examples

• Work and Other Applications - Examples for Homework
• Work Example Problem
• Work and Other Applications - More HELP

Module 8

• Integration by Parts
• Partial Fractions and L'Hopital's Rule

Improper Integrals

• Improper Integrals and Module 8 Review
• Improper Integrals More HELP

Module 9

Sequences, Series, and Convergences

• Sequences, Series and Convergence
• Integral & P-Series, and Comparison of Series
• Alternating Series Test, Absolute and Conditional Convergence, and Ratio & Root Tests

Module Review

• Module 9A Review

Taylor Polynomials and LaGrange Remainder

• Taylor Polynomials and LaGrange Remainder
• Taylor and Maclaurin Series

Power Series

• Power Series - Interval of Convergence, Differentiation and Integration
• Representing Functions with Power Series - from Geometric Series
• Taylor Series and Polynomial Approximation- Great Applet - Click "Launch Button" Near the Bottom
• Polynomial Aproximation - Power Series - YouTube Video

Module 10

• 10.02-10.03 Parametric Equations and Vectors
• 10.04-10.05 Polar Coordinates, Graphs, and Area in Polar Coordinates
• Calculus of the Polar Rose

Extra Practice

• Extra Practice - 9.07 - Taylor Polynomials Worksheet
• Extra Practice - 9.07 - Taylor Polynomials Answers
• Extra Practice - 9.08 - Radius of Convergence Worksheet
• Extra Practice - 9.08 - Radius of Convergence Answers
• Extra Practice - 9.10 - Taylor/Maclaurin/Power Series Worksheet
• Extra Practice - 9.10 - Taylor/Maclaurin/Power Series Answers
• Extra Practice - Series and LaGrange Remainder Worksheet
• Extra Practice - Series and LaGrange Remainder Answers
• Extra Practice - 9B: AP FRQ 7B Question
• Extra Practice - 9B: AP FRQ 7B Solution
• Extra Practice - 9B: AP FRQ 8B Question
• Extra Practice - 9B: AP FRQ 8B Solution
• Extra Practice - 9B: AP FRQ 9B Question
• Extra Practice - 9B AP FRQ 9B Solution

Extra Resources

Exam Information

• AP Calculus Practice Exams - Do Practice Test Here and Link to Answers
• AP Exam Review Week 1
• Stuff You Must Know COLD

Practice Problems

• Review and Practice - Select "Calculus" from Left Column
• Practice Worksheets with Worked Out Answers for Topics in AB and BC Calculus
• Textbook Website - Do Practice Problems Here
• Solutions to ODD Numbered Problems 8th Edition
• Enlarged Graphs for Homework

Videos

• Calculus - Go to "Free Calculus Videos" in Left Column
• BEST Videos on all Topics in AB and BC
• Videos on all Topics in AB and BC Calculus
• Great Formula Cheat Sheets
• The Calculus Tutor AB Material
• The Calculus Tutor BC Material
• University of Kansas Visual Calculus