The visual guide to
AP® Calculus BC
10 units, 131 topics. Each topic is explained in writing, drawn as a lesson you can watch, and checked with practice questions.
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Each unit is as wide as its share of the exam's multiple-choice section.Filled: topics you've opened.
Unit 1Limits and Continuity
- Introducing Calculus: Change at an Instant
- Defining Limits and Using Limit Notation
- Estimating Limit Values from Graphs
- Estimating Limit Values from Tables
- Determining Limits Using Algebraic Properties
- Determining Limits Using Algebraic Manipulation
- Selecting Procedures for Determining Limits
- Determining Limits Using the Squeeze Theorem
- Connecting Multiple Representations of Limits
- Exploring Types of Discontinuities
- Defining Continuity at a Point
- Confirming Continuity Over an Interval
- Removing Discontinuities
- Connecting Infinite Limits and Vertical Asymptotes
- Connecting Limits at Infinity and Horizontal Asymptotes
- Working with the Intermediate Value Theorem
Unit 2Differentiation: Definition and Fundamental Properties
- Defining Average and Instantaneous Rate of Change at a Point
- Defining the Derivative of a Function and Using Derivative Notation
- Estimating Derivatives of a Function at a Point
- Connecting Differentiability and Continuity
- Applying the Power Rule
- Derivative Rules: Constant, Sum, Difference, and Constant Multiple
- Derivatives of cos x, sin x, e^x, and ln x
- The Product Rule
- The Quotient Rule
- Finding the Derivatives of tan x, cot x, sec x, and csc x
Unit 3Differentiation: Composite, Implicit, and Inverse Functions
Unit 4Contextual Applications of Differentiation
- Interpreting the Meaning of the Derivative in Context
- Straight-Line Motion: Connecting Position, Velocity, and Acceleration
- Rates of Change in Applied Contexts Other Than Motion
- Introduction to Related Rates
- Solving Related Rates Problems
- Approximating Values of a Function Using Local Linearity and Linearization
- Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Unit 5Analytical Applications of Differentiation
- Using the Mean Value Theorem
- Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
- Determining Intervals on Which a Function Is Increasing or Decreasing
- Using the First Derivative Test to Determine Relative Local Extrema
- Using the Candidates Test to Determine Absolute Global Extrema
- Determining Concavity of Functions Over Their Domains
- Using the Second Derivative Test to Determine Extrema
- Sketching Graphs of Functions and Their Derivatives
- Connecting a Function, Its First Derivative, and Its Second Derivative
- Introduction to Optimization Problems
- Solving Optimization Problems
- Exploring Behaviors of Implicit Relations
Unit 6Integration and Accumulation of Change
- Exploring Accumulation of Change
- Approximating Areas with Riemann Sums
- Riemann Sums, Summation Notation, and Definite Integral Notation
- The Fundamental Theorem of Calculus and Accumulation Functions
- Interpreting the Behavior of Accumulation Functions Involving Area
- Applying Properties of Definite Integrals
- The Fundamental Theorem of Calculus and Definite Integrals
- Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
- Integrating Using Substitution
- Substitution in Definite Integrals
- Integrating Functions Using Long Division and Completing the Square
- Integrating Using Integration by Parts
- Repeated Integration by Parts and the Tabular Method
- Integrating Using Linear Partial Fractions
- Evaluating Improper Integrals with Infinite Limits
- Improper Integrals with an Infinite Discontinuity
- Selecting Techniques for Antidifferentiation
Unit 7Differential Equations
- Modeling Situations with Differential Equations
- Verifying Solutions for Differential Equations
- Sketching Slope Fields
- Reasoning Using Slope Fields
- Approximating Solutions Using Euler's Method
- Euler's Method: Step Size and Error
- Finding General Solutions Using Separation of Variables
- Finding Particular Solutions Using Initial Conditions and Separation of Variables
- Exponential Models with Differential Equations
- Logistic Models with Differential Equations
- Logistic Growth: Fastest Growth and the Inflection Point
Unit 8Applications of Integration
- Finding the Average Value of a Function on an Interval
- Connecting Position, Velocity, and Acceleration Using Integrals
- Using Accumulation Functions and Definite Integrals in Applied Contexts
- Finding the Area Between Curves Expressed as Functions of x
- Finding the Area Between Curves Expressed as Functions of y
- Area Between Curves With More Than Two Intersections
- Volumes with Cross Sections: Squares and Rectangles
- Volumes with Cross Sections: Triangles and Semicircles
- Volume with Disc Method: Revolving Around the x- or y-Axis
- Volume with Disc Method: Revolving Around Other Axes
- Volume with Washer Method: Revolving Around the x- or y-Axis
- Volume with Washer Method: Revolving Around Other Axes
- The Arc Length of a Smooth, Planar Curve
- Distance Traveled Along a Curve
Unit 9Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- Defining and Differentiating Parametric Equations
- Eliminating the Parameter and Converting to Rectangular Form
- Second Derivatives of Parametric Equations
- Horizontal and Vertical Tangents on Parametric Curves
- Finding Arc Lengths of Curves Given by Parametric Equations
- Defining and Differentiating Vector-Valued Functions
- Integrating Vector-Valued Functions
- Solving Motion Problems Using Parametric and Vector-Valued Functions
- Defining Polar Coordinates and Differentiating in Polar Form
- Graphing Polar Curves: Circles, Cardioids, Roses, and Limacons
- Finding the Area of a Region Bounded by a Single Polar Curve
- Finding the Area of the Region Bounded by Two Polar Curves
Unit 10Infinite Sequences and Series
- Defining Convergent and Divergent Infinite Series
- Sequences Versus Series
- Partial Sums and Telescoping Series
- Working with Geometric Series
- Geometric Series in Context
- The nth Term Test for Divergence
- Integral Test for Convergence
- The Harmonic Series
- p-Series
- The Direct Comparison Test
- The Limit Comparison Test
- Alternating Series Test for Convergence
- Ratio Test for Convergence
- Choosing a Convergence Test
- Determining Absolute or Conditional Convergence
- Alternating Series Error Bound
- Finding Taylor Polynomial Approximations of Functions
- Maclaurin Polynomials and How Degree Improves the Fit
- Lagrange Error Bound
- Radius of Convergence of a Power Series
- Interval of Convergence and Testing the Endpoints
- Finding Taylor or Maclaurin Series for a Function
- The Series Worth Memorizing
- Representing Functions as a Power Series
- Differentiating and Integrating Power Series Term by Term
- Using Series to Evaluate Limits and Integrals