AP Calculus BC

Chain rule, implicit differentiation, and related rates

Derivatives of inverse functions, inverse trig derivatives, and logarithmic differentiation

Understanding derivatives through tangent lines and slope

Understanding derivatives through real-world rates of change

The most fundamental differentiation rule for polynomials

Essential rules for differentiating linear combinations of functions

Differentiating the product of two functions

Differentiating fractions and rational functions

Finding derivatives of composite functions

Finding derivatives of sine, cosine, tangent, and other trig functions

Finding derivatives involving e^x and other exponential functions

Finding derivatives involving ln(x) and other logarithmic functions

Finding derivatives when y is not isolated

Finding how rates of change are related to each other

Second derivatives, third derivatives, and beyond

Using logarithms to simplify difficult differentiation problems

Linear approximation, differentials, error estimation, and tangent line approximation

Mean Value Theorem, Rolle's Theorem, Extreme Value Theorem, and IVT applications

Position, velocity, acceleration, speed, displacement, and distance

Using calculus to find maximum and minimum values in real-world situations

Using derivatives to sketch accurate graphs of functions

Understanding the theoretical foundation connecting average and instantaneous rates

Evaluating indeterminate forms using derivatives

Using tangent lines to approximate function values

Using derivatives to find numerical solutions to equations

Finding absolute maximum and minimum values on closed intervals

The product rule in reverse for integrating products of functions

Approximating area under curves using rectangles

The connection between derivatives and integrals

Finding area enclosed by two functions

Finding volumes by rotating regions around an axis

Finding volumes of solids with holes using washers

Finding volumes using cylindrical shells

Basic u-substitution, definite integrals with u-sub, and complex substitutions

Accumulation concept, interpreting integrals, FTC connections, and rate in vs rate out

Average value, MVT for integrals, net change theorem, and real-world applications

Trig substitution, advanced u-sub, integration strategies, and reduction formulas

Arc length in rectangular, parametric, and polar; surface area of revolution

Alternating series test, error bound, conditional vs absolute convergence

Function approximation, solving DEs with series, physics applications, and error analysis

Derivatives, tangents, and area in polar form

Comparing series to determine convergence

Testing convergence of alternating series

Testing convergence with ratios and roots

Key series formulas and how to use them