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AP Calculus AB study notes
Short notes for every topic in AP Calculus AB, unit by unit, each with key terms and a sample AP-style question.
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Study AP Calculus AB free in APrepUnit 1: Limits & Continuity
- 1.1Can Change Occur at an Instant?
- 1.2Defining Limits & Limit Notation
- 1.3Estimating Limits from Graphs
- 1.4Estimating Limits from Tables
- 1.5Limits Using Algebraic Properties
- 1.6Limits Using Algebraic Manipulation
- 1.7Selecting Procedures for Limits
- 1.8The Squeeze Theorem
- 1.9Connecting Representations of Limits
- 1.10Types of Discontinuities
- 1.11Defining Continuity at a Point
- 1.12Continuity over an Interval
- 1.13Removing Discontinuities
- 1.14Infinite Limits & Vertical Asymptotes
- 1.15Limits at Infinity & Horizontal Asymptotes
- 1.16The Intermediate Value Theorem (IVT)
Unit 2: Differentiation: Definition & Rules
Unit 3: Composite, Implicit & Inverse Derivatives
Unit 4: Contextual Applications of Differentiation
Unit 5: Analytical Applications of Differentiation
- 5.1The Mean Value Theorem
- 5.2Extreme Value Theorem & Critical Points
- 5.3Increasing & Decreasing Intervals
- 5.4The First Derivative Test
- 5.5The Candidates Test
- 5.6Concavity
- 5.7The Second Derivative Test
- 5.8Sketching Functions & Derivatives
- 5.9Connecting f, f', and f''
- 5.10Introduction to Optimization
- 5.11Solving Optimization Problems
- 5.12Behaviors of Implicit Relations
Unit 6: Integration & Accumulation of Change
- 6.1Exploring Accumulations of Change
- 6.2Approximating Areas with Riemann Sums
- 6.3Riemann Sums & Integral Notation
- 6.4FTC & Accumulation Functions
- 6.5Interpreting Accumulation Functions
- 6.6Properties of Definite Integrals
- 6.7FTC & Evaluating Definite Integrals
- 6.8Antiderivatives & Indefinite Integrals
- 6.9Integration Using Substitution
- 6.10Long Division & Completing the Square
- 6.14Selecting Antidifferentiation Techniques
Unit 7: Differential Equations
Unit 8: Applications of Integration
- 8.1Average Value of a Function
- 8.2Motion with Integrals
- 8.3Accumulation in Applied Contexts
- 8.4Area Between Curves (in x)
- 8.5Area Between Curves (in y)
- 8.6Area with Multiple Intersections
- 8.7Volumes: Square & Rectangle Cross Sections
- 8.8Volumes: Triangle & Semicircle Cross Sections
- 8.9Disc Method (around an axis)
- 8.10Disc Method (around other axes)
- 8.11Washer Method (around an axis)
- 8.12Washer Method (around other axes)