High School AP Calculus BC

Module One: Limits and Continuity

-Using limits to analyze instantaneous change

-Estimating limit values using graphs and tables

-Determining limits using algebraic properties and manipulation

-Evaluating limits of indeterminant form

-Evaluating limits using substitution

-Squeeze Theorem

-Intermediate Value Theorem

-Determining continuity and exploring discontinuity

-Connecting limits, infinity and asymptotes

Module Two: Differentiation: Definition and Fundamental Properties

-Definition of a derivative

-Average and instantaneous rates of change

-Determining differentiability

-Estimating derivatives

-Rules of differentiation

-Product rule

-Quotient rule

-Derivatives of trigonometric, exponential, and logarithmic functions

Module Three: Differentiation: Composite, Implicit, and Inverse Functions

-Chain rule

-Implicit differentiation

-Differentiating inverse functions

-Differentiating composite functions

-Differentiating inverse trigonometric functions

-Selecting procedures for calculating derivatives

-Calculating higher-order derivatives

Module Four: Contextual Applications of Differentiation

-Interpreting and applying the derivative in motion

-Rates of change in other applied contexts

-Related rates

-Approximating values using local linearity and linearization

-L'Hospital's Rule

Module Five: Contextual Applications of Differentiation

-Mean value and extreme value theorem

-Determining function behavior

-First derivative test

-Determining absolute extrema using the candidates test

-Determining concavity of functions

-Second derivative test

-Connecting graphs of functions and their derivatives

-Optimization problems

-Exploring behaviors of implicit relations

Module Six: Integration and Accumulation of Change

-Riemann Sums and the definite integral

-Accumulation functions involving area

-The Fundamental Theorem of Calculus

-Applying properties of the definite integrals

-Finding indefinite integrals and antiderivatives

-Integrating using substitution and integration by parts

-Integrating using linear partial fractions

-Evaluating improper integrals

-Integrating functions using various methods

-Selecting techniques for antidifferentiation

Module Seven: Differential Equations

-Solutions of differential equations

-Sketching and reasoning using slope fields

-Approximating solutions using Euler's Method

-Finding solutions using separation of variables

-Exponential models with differential equations

-Logistic models with differential equations

Module Eight: Applications of Integration

-Average value and connecting position using integrals

-Velocity and acceleration using integrals

-Using accumulation functions and definite integrals contextually

-Finding the area between curves

-Area between curves with multiple intersections

-Volumes with discs

-Volumes with washers

-Volumes with cross sections

-Arc length of a smooth planar curve

-Arc length and distance traveled

Module Nine: Parametric, Polar and Vector-Valued Equations

-Differentiating parametric equations and finding arc length

-Differentiating and integrating vector-valued functions

-Solving motion problems using parametric functions

-Solving motion problems using vector-valued functions

-Defining polar coordinates

-Differentiating in polar form to

find area bounded by polar curves

Module Ten: Infinite Sequences and Series

- Convergent and divergent infinite series 

-Convergent and divergent geometric series

-Integral test for convergence, harmonic and p-series

-Comparison test for convergence

-Additional tests to determine convergence

-Alternating series and their error bound

-Taylor polynomial approximations and evaluating error

-Radius and convergence interval of power series

-Taylor or Maclaurin series for a function

-Representing functions as power series