AP Calculus AB/BC
Comprehensive coverage of AP Calculus AB and BC topics including limits, derivatives, integrals, series, and more.
Limits and Continuity
Understanding limits, continuity, and the foundations of calculus
What is a Limit?
An intuitive introduction to the concept of limits in calculus
Limit Notation and Terminology
Master the formal notation and vocabulary used when working with limits
Estimating Limits from Tables
Learn to estimate limit values by examining tables of function values
Estimating Limits from Graphs
Visualize limit behavior by reading and interpreting function graphs
One-Sided Limits in Detail
Understanding left-hand and right-hand limits and when they matter
Direct Substitution Method
The simplest limit technique: when you can just plug in the value
Factoring Method for Limits
Use factoring to simplify and evaluate limits with indeterminate forms
Rationalizing to Evaluate Limits
Use conjugate multiplication to handle limits with radicals
Limits at Infinity
Understanding what happens as x grows without bound
Infinite Limits and Vertical Asymptotes
When functions shoot off to infinity at a specific point
What is Continuity?
Understanding when a function is continuous at a point
Types of Discontinuity
Classifying the different ways a function can be discontinuous
Derivatives
Differentiation rules, techniques, and applications
What is a Derivative?
Understanding the fundamental concept of derivatives
Derivative Notation
Understanding the different ways to write derivatives
Derivative as Slope
Understanding derivatives through tangent lines and slope
Derivative as Rate of Change
Understanding derivatives through real-world rates of change
The Power Rule
The most fundamental differentiation rule for polynomials
Constant Multiple and Sum Rules
Essential rules for differentiating linear combinations of functions
The Product Rule
Differentiating the product of two functions
The Quotient Rule
Differentiating fractions and rational functions
The Chain Rule
Finding derivatives of composite functions
Derivatives of Trigonometric Functions
Finding derivatives of sine, cosine, tangent, and other trig functions
Derivatives of Exponential Functions
Finding derivatives involving e^x and other exponential functions
Derivatives of Logarithmic Functions
Finding derivatives involving ln(x) and other logarithmic functions
Implicit Differentiation
Finding derivatives when y is not isolated
Related Rates
Finding how rates of change are related to each other
Higher-Order Derivatives
Second derivatives, third derivatives, and beyond
Logarithmic Differentiation (Technique)
Using logarithms to simplify difficult differentiation problems
Applications of Derivatives
Using derivatives to solve real-world problems
Critical Points and Extrema
Finding maximum and minimum values of functions
The First Derivative Test
Using the derivative to classify critical points as maxima, minima, or neither
The Second Derivative Test
Using the second derivative to classify critical points
Optimization Problems
Using calculus to find maximum and minimum values in real-world situations
Curve Sketching
Using derivatives to sketch accurate graphs of functions
Mean Value Theorem
Understanding the theoretical foundation connecting average and instantaneous rates
L'Hôpital's Rule
Evaluating indeterminate forms using derivatives
Linear Approximation
Using tangent lines to approximate function values
Newton's Method
Using derivatives to find numerical solutions to equations
Absolute Extrema on Closed Intervals
Finding absolute maximum and minimum values on closed intervals
Integration
Antiderivatives and the reverse process of differentiation
Introduction to Antiderivatives
Understanding the reverse process of differentiation
Indefinite Integrals and Notation
Understanding integral notation and basic integration rules
U-Substitution Method
The chain rule in reverse - substitution technique for integration
Integration by Parts
The product rule in reverse for integrating products of functions
Riemann Sums and Area Approximation
Approximating area under curves using rectangles
Definite Integrals and the Fundamental Theorem
The connection between derivatives and integrals
Area Between Curves
Finding area enclosed by two functions
Volumes of Revolution: Disk Method
Finding volumes by rotating regions around an axis
Volumes of Revolution: Washer Method
Finding volumes of solids with holes using washers
Volumes of Revolution: Shell Method
Finding volumes using cylindrical shells
Advanced Integration (BC)
Advanced integration techniques for Calculus BC
Parametric & Polar (BC)
Parametric equations and polar coordinates for Calculus BC
Introduction to Parametric Equations
Understanding curves defined parametrically
Calculus with Parametric Equations
Derivatives, tangent lines, and arc length for parametric curves
Introduction to Polar Coordinates
Understanding curves in polar form
Calculus with Polar Coordinates
Derivatives, tangents, and area in polar form
Sequences & Series (BC)
Sequences, infinite series, and convergence tests for Calculus BC
Introduction to Sequences
Understanding sequences and their behavior
Introduction to Infinite Series
Understanding infinite series and partial sums
The Integral Test
Using integrals to test series convergence
Direct and Limit Comparison Tests
Comparing series to determine convergence
Alternating Series Test
Testing convergence of alternating series
Ratio and Root Tests
Testing convergence with ratios and roots
Power & Taylor Series (BC)
Power series, Taylor series, and Maclaurin series for Calculus BC