AP Calculus BC

2.1: Defining the derivative of a function at a point and as a function

2.2: Connecting differentiability and continuity

2.3: Determining derivatives for elementary functions

2.4: Applying differentiation rules

3.1: The chain rule for differentiating composite functions

3.2: Implicit differentiation

3.3: Differentiation of general and particular inverse functions

3.4: Determining higher-order derivatives of functions

4.1: Identifying relevant mathematical information in verbal representations of real-world problems involving rates of change

4.2: Applying understandings of differentiation to problems involving motion

4.3: Generalizing understandings of motion problems to other situations involving rates of change

4.4: Solving related rates problems

4.5: Local linearity and approximation

4.6: L’Hospital’s rule

5.1: Mean Value Theorem and Extreme Value Theorem

5.2: Derivatives and properties of functions

5.3: How to use the first derivative test, second derivative test, and candidates test

5.4: Sketching graphs of functions and their derivatives

5.5: How to solve optimization problems

5.6: Behaviors of implicit relations

6.1: Using definite integrals to determine accumulated change over an interval

6.2: Approximating integrals with Riemann Sums

6.3: Accumulation functions, the Fundamental Theorem of Calculus, and definite integrals

6.4: Antiderivatives and indefinite integrals

6.5: Properties of integrals and integration techniques, extended

6.6: Determining improper integrals

7.1: Interpreting verbal descriptions of change as separable differential equations

7.2: Sketching slope fields and families of solution curves

7.3: Using Euler’s method to approximate values on a particular solution curve

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

7.5: Deriving and applying exponential and logistic models

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

8.6: Determining the length of a planar curve using a definite integral

9.1: Finding derivatives of parametric functions and vector-valued functions

9.2: Calculating the accumulation of change in length over an interval using a definite integral

9.3: Determining the position of a particle moving in a plane

9.4: Calculating velocity, speed, and acceleration of a particle moving along a curve

9.5: Finding derivatives of functions written in polar coordinates

9.6: Finding the area of regions bounded by polar curves

10.1: Applying limits to understand convergence of infinite series

10.2: Types of series: Geometric, harmonic, and p-series

10.3: A test for divergence and several tests for convergence

10.4: Approximating sums of convergent infinite series and associated error bounds

10.5: Determining the radius and interval of convergence for a series

10.6: Representing a function as a Taylor series or a Maclaurin series on an appropriate interval