AP Calculus AB

2.1: Defining Average and Instantaneous Rate of Change at a Point

2.2: Defining the Derivative of a Function and Using Derivative Notation (includes equation of the tangent line)

2.3: Estimating Derivatives of a Function at a Point

2.4: Connecting Differentiability and Continuity

2.5: Applying the Power Rule

2.6: Derivative Rules: Constant, Sum, Difference, and Constant Multiple (includes horizontal tangent lines, equation of the normal line, and differentiability of piecewise)

2.7: Derivatives of cos(x), sin(x), e^x, and ln(x)

2.8: The Product Rule

2.9: The Quotient Rule

2.10: Derivatives of tan(x), cot(x), sec(x), and csc(x)

3.1: The Chain Rule

3.2: Implicit Differentiation

3.3: Differentiating Inverse Functions

3.4: Differentiating Inverse Trigonometric Functions

3.5: Selecting Procedures for Calculating Derivatives

3.6: Calculating Higher-Order Derivatives

4.1: Interpreting the Meaning of the Derivative in Context

4.2: Straight-Line Motion: Connecting Position, Velocity, and Acceleration

4.3: Rates of Change in Applied Contexts Other Than Motion

4.4: Introduction to Related Rates

4.5: Solving Related Rates Problems

4.6: Approximating Values of a Function Using Local Linearity and Linearization

4.7: Using L'Hopital's Rule for Determining Limits of Indeterminate Forms

5.1: Using the Mean Value Theorem

5.2: Extreme Value Theorem, Global Versus Local Extrema, and Critical Points

5.3: Determining Intervals on Which a Function is Increasing or Decreasing

5.4: Using the First Derivative Test to Determine Relative Local Extrema

5.5: Using the Candidates Test to Determine Absolute (Global) Extrema

5.6: Determining Concavity of Functions over Their Domains

5.7: Using the Second Derivative Test to Determine Extrema

5.8: Sketching Graphs of Functions and Their Derivatives

5.9: Connecting a Function, Its First Derivative, and Its Second Derivative (includes a revisit of particle motion and determining if a particle is speeding up/down)
5.10: Introduction to Optimization Problems
5.11: Solving Optimization Problems
5.12: Exploring Behaviors of Implicit Relations

6.1: Exploring Accumulation of Change

6.2: Approximating Areas with Riemann Sums

6.3: Riemann Sums, Summation Notation, and Definite Integral Notation

6.4: The Fundamental Theorem of Calculus and Accumulation Functions

6.5: Interpreting the Behavior of Accumulation Functions Involving Area

6.6: Applying Properties of Definite Integrals

6.7: The Fundamental Theorem of Calculus and Definite Integrals

6.8: Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

6.9: Integrating Using Substitution

6.10: Integrating Functions Using Long Division and Completing the Square

6.11: Selecting Techniques for Antidifferentiation

7.1: Interpreting verbal descriptions of change as separable differential equations

7.2: Sketching slope fields and families of solution curves

7.3: Solving separable differential equations to find general and particular solutions

7.4: Deriving and applying a model for exponential growth and decay
Unit 8: Applications of Integration

8.1: Determining the average value of a function using definite integrals

8.2: Modeling particle motion

8.3: Solving accumulation problems

8.4: Finding the area between curves

8.5: Determining volume with cross-sections, the disc method, and the washer method