AP Calculus AB & BC: Exam Prep
About the Course
Get an indepth look at continuity, integrals, and limits through this online calculus course. Learn to graph functions, simplify equations, and calculate derivatives as you prepare for the AP Calculus AB and AP Calculus BC exams. Our team of experienced, professional educators designed the videos in this course to be brief yet engaging; they also crafted short, multiplechoice quizzes to help you measure your proficiency in the topics covered in the course.
Course Topics
Chapter  Objectives 

Functions  Define functions and learn how to work with them in complex equations and more. 
Graphing and Functions  Learn how to graph functions on the Cartesian plane and find the slope of a point. 
Limits  Understand how to describe and determine the limits of functions. 
Continuity  Explore continuity in functions and the different types of discontinuity. 
Exponential and Logarithmic Functions  Learn about derivatives for logarithmic and exponential functions. 
Exponentials and Logarithms  Understand the concepts of exponents and logarithms and how to solve equations involving them. 
Exponents and Polynomials  Explore exponent properties, rational exponents, polynomial equations, and simplifying equations. 
Applications of Derivatives  Learn how to use derivatives in math problems and real life through linearization, Newton's method, and optimization. 
Calculating Derivatives and Derivative Rules  Understand how to calculate derivatives with limits, use the chain rule, and graph various derivatives. 
Differential Equations  Explore equations that include derivatives and how to solve ordinary and partial derivative equations. 
Area Under the Curve and Integrals  Learn about Riemann sums and how to calculate the area under a curve with integrals. 
Graphing Derivatives and L'Hopital's Rule  Understand how to graph derivatives using differential calculus and L'Hopital's rule about indeterminate forms. 
Integration and Integration Techniques  Explore the techniques used in integration, like the substitution technique and integration by parts. 
Integration Applications  Learn how to use Newton's method for rootfinding problems, areas between functions, and volumes of revolution. 
Rate of Change  Understand how motion is related to slopes, tangents, and the derivative in calculus. 
Geometry and Trigonometry in Calculus  Explore basic geometry and trigonometry concepts and how they're related to calculus. 
Using Scientific Calculators for Calculus  Learn how to use your scientific calculator for functions, exponentials, graphing, and more. 
Infinite Series  Understand summations of infinite sequences of numbers and the various types of infinite series. 
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77% developed We are actively adding lessons to this course. You can study for exams and supplement your learning right now. For students preparing for an exam, we'll label this course 100% developed when it is ready to prepare you for the exam on its own.
Course Chapters
Functions
All Videos in Functions
 1. Functions: Identification, Notation & Practice Problems
 2. Transformations: How to Shift Graphs on a Plane
 3. What Is Domain and Range in a Function?
 4. How to Add, Subtract, Multiply and Divide Functions
 5. How to Compose Functions
 6. Inverse Functions
 7. Applying Function Operations Practice Problems
Graphing and Functions
All Videos in Graphing and Functions
 1. What is a Function: Basics and Key Terms
 2. Graphing Basic Functions
 3. Compounding Functions and Graphing Functions of Functions
 4. Understanding and Graphing the Inverse Function
 5. Polynomials Functions: Properties and Factoring
 6. Polynomials Functions: Exponentials and Simplifying
 7. Exponentials, Logarithms & the Natural Log
 8. Slopes and Tangents on a Graph
 9. Equation of a Line Using PointSlope Formula
 10. Horizontal and Vertical Asymptotes
 11. Implicit Functions
Sequences and Series
All Videos in Sequences and Series
 1. What is a Mathematical Sequence?
 2. How to Find and Classify an Arithmetic Sequence
 3. Finding and Classifying Geometric Sequences
 4. Summation Notation and Mathematical Series
 5. How to Calculate an Arithmetic Series
 6. How to Calculate a Geometric Series
 7. Arithmetic and Geometric Series: Practice Problems
Limits
All Videos in Limits
Exponentials and Logarithms
All Videos in Exponentials and Logarithms
Exponents and Polynomials
All Videos in Exponents and Polynomials
 1. What Are the Five Main Exponent Properties?
 2. How to Define a Zero and Negative Exponent
 3. How to Simplify Expressions with Exponents
 4. Rational Exponents
 5. Simplifying Expressions with Rational Exponents
 6. How to Graph Cubics, Quartics, Quintics and Beyond
 7. How to Add, Subtract and Multiply Polynomials
 8. How to Divide Polynomials with Long Division
 9. How to Use Synthetic Division to Divide Polynomials
 10. Dividing Polynomials with Long and Synthetic Division: Practice Problems
Applications of Derivatives
All Videos in Applications of Derivatives
Calculating Derivatives and Derivative Rules
All Videos in Calculating Derivatives and Derivative Rules
 1. Using Limits to Calculate the Derivative
 2. The Linear Properties of a Derivative
 3. Calculating Derivatives of Trigonometric Functions
 4. Calculating Derivatives of Polynomial Equations
 5. Calculating Derivatives of Exponential Equations
 6. Using the Chain Rule to Differentiate Complex Functions
 7. Differentiating Factored Polynomials: Product Rule and Expansion
 8. When to Use the Quotient Rule for Differentiation
 9. Understanding Higher Order Derivatives Using Graphs
 10. Calculating Higher Order Derivatives
 11. How to Find Derivatives of Implicit Functions
 12. How to Calculate Derivatives of Inverse Trigonometric Functions
 13. Applying the Rules of Differentiation to Calculate Derivatives
Differential Equations
All Videos in Differential Equations
Area Under the Curve and Integrals
All Videos in Area Under the Curve and Integrals
 1. Summation Notation and Mathematical Series
 2. How to Use Riemann Sums for Functions and Graphs
 3. How to Identify and Draw Left, Right and Middle Riemann Sums
 4. What is the Trapezoid Rule?
 5. How to Find the Limits of Riemann Sums
 6. Definite Integrals: Definition
 7. How to Use Riemann Sums to Calculate Integrals
 8. Linear Properties of Definite Integrals
 9. Average Value Theorem
 10. The Fundamental Theorem of Calculus
 11. Indefinite Integrals as Anti Derivatives
 12. How to Find the Arc Length of a Function
Graphing Derivatives and L'Hopital's Rule
All Videos in Graphing Derivatives and L'Hopital's Rule
 1. Graphing the Derivative from Any Function
 2. Non Differentiable Graphs of Derivatives
 3. How to Determine Maximum and Minimum Values of a Graph
 4. Using Differentiation to Find Maximum and Minimum Values
 5. Concavity and Inflection Points on Graphs
 6. Understanding Concavity and Inflection Points with Differentiation
 7. Data Mining: Function Properties From Derivatives
 8. Data Mining: Identifying Functions From Derivative Graphs
 9. What is L'Hopital's Rule?
 10. Applying L'Hopital's Rule in Simple Cases
 11. Applying L'Hopital's Rule in Complex Cases
Integration and Integration Techniques
All Videos in Integration and Integration Techniques
 1. Calculating Integrals of Simple Shapes
 2. AntiDerivatives: Calculating Indefinite Integrals of Polynomials
 3. How to Calculate Integrals of Trigonometric Functions
 4. How to Calculate Integrals of Exponential Functions
 5. How to Solve Integrals Using Substitution
 6. Substitution Techniques for Difficult Integrals
 7. Using Integration By Parts
 8. Partial Fractions: How to Factorize Fractions with Quadratic Denominators
 9. How to Integrate Functions With Partial Fractions
 10. Understanding Trigonometric Substitution
 11. How to Use Trigonometric Substitution to Solve Integrals
 12. How to Solve Improper Integrals
Rate of Change
All Videos in Rate of Change

Education Portal Instructors
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