AP Calculus AB study guides
Unit overviews and topic breakdowns with timelines, key figures, and vocabulary.
Unit 1: Limits and Continuity
Read unit overview →11.1 Introducing Calculus: Can Change Occur at an Instant?21.2 Defining Limits and Using Limit Notation31.3 Estimating Limit Values from Graphs41.4 Estimating Limit Values from Tables51.5 Determining Limits Using Algebraic Properties61.6 Determining Limits Using Algebraic Manipulation71.7 Selecting Procedures for Determining Limits81.8 Determining Limits Using the Squeeze Theorem91.9 Connecting Multiple Representations of Limits and Continuity101.10 Types of Discontinuities, Infinite Limits, and the IVT
Unit 2: Differentiation — Definition and Fundamental Properties
Read unit overview →12.1 Defining Average and Instantaneous Rates of Change22.2 Defining the Derivative of a Function32.3 Using Derivative Notation42.4 Estimating Derivatives at a Point52.5 Connecting Differentiability and Continuity62.6 Applying the Power Rule72.7 Derivative Rules: Constant, Sum, Difference, and Constant Multiple82.8 Connecting Derivative Rules with the Power Rule92.9 Derivatives of sin(x), cos(x), eˣ, and ln(x)102.10 The Product Rule112.11 The Quotient Rule122.12 Derivatives of tan(x), cot(x), sec(x), and csc(x)
Unit 3: Differentiation — Composite, Implicit, and Inverse Functions
Read unit overview →13.1 The Chain Rule23.2 Applying the Chain Rule33.3 Implicit Differentiation43.4 Differentiating Inverse Functions53.5 Differentiating Inverse Trigonometric Functions63.6 Selecting Procedures for Calculating Derivatives73.7 Applying Multiple Differentiation Rules83.8 Calculating Higher-Order Derivatives93.9 Second Derivatives of Implicit Equations103.10 Connecting Derivatives and Limits
Unit 4: Contextual Applications of Differentiation
Read unit overview →14.1 Interpreting the Meaning of the Derivative in Context24.2 Straight-Line Motion: Position and Velocity34.3 Straight-Line Motion: Acceleration and Speed44.4 Rates of Change in Applied Contexts54.5 Introduction to Related Rates64.6 Setting Up and Solving Related Rates Problems74.7 Advanced Related Rates Problems84.8 Approximating Values Using Local Linearity94.9 Linearization and Differentials104.10 Using L'Hôpital's Rule for Indeterminate Forms
Unit 5: Analytical Applications of Differentiation
Read unit overview →15.1 Using the Mean Value Theorem25.2 Extreme Value Theorem and Critical Points35.3 Determining Intervals of Increasing and Decreasing45.4 Using the First Derivative Test55.5 Using the Candidates Test for Absolute Extrema65.6 Determining Concavity and Points of Inflection75.7 Using the Second Derivative Test85.8 Sketching Curves of Functions and Their Derivatives95.9 Connecting f, f', and f''105.10 Solving Optimization Problems
Unit 6: Integration and Accumulation of Change
Read unit overview →16.1 Exploring Accumulations of Change26.2 Approximating Areas with Riemann Sums36.3 Riemann Sums, Summation Notation, and Definite Integral Notation46.4 The Fundamental Theorem of Calculus and Accumulation Functions56.5 Interpreting the Behavior of Accumulation Functions66.6 Applying Properties of Definite Integrals76.7 The Fundamental Theorem of Calculus and Definite Integrals86.8 Finding Antiderivatives and Indefinite Integrals96.9 Common Indefinite Integrals and Basic Rules106.10 Integrating Using Substitution116.11 Integrating Using Long Division and Completing the Square
Unit 7: Differential Equations
Read unit overview →17.1 Modeling Situations with Differential Equations27.2 Verifying Solutions for Differential Equations37.3 Sketching Slope Fields47.4 Reasoning Using Slope Fields57.5 Introduction to Separation of Variables67.6 Finding General Solutions Using Separation of Variables77.7 Finding Particular Solutions Using Initial Conditions87.8 Exponential Models with Differential Equations97.9 Applications of Differential Equations
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