AP Calculus BC

Limit definition, evaluation, one-sided limits, squeeze theorem, and IVT

An intuitive introduction to the concept of limits in calculus

Learn to estimate limit values by examining tables of function values

Visualize limit behavior by reading and interpreting function graphs

Understand left-hand and right-hand limits and when to use them

The simplest limit technique: when you can just plug in the value

Use factoring to simplify and evaluate limits with indeterminate forms

Use conjugate multiplication to handle limits with radicals

Understanding what happens as x grows without bound

When functions shoot off to infinity at a specific point

Understanding when a function is continuous at a point

Classifying the different ways a function can be discontinuous

Derivative as a limit, differentiability, graphical interpretation, and tangent lines

Power rule, product rule, quotient rule, trig derivatives, and higher-order derivatives

Chain rule, implicit differentiation, and related rates

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

Understanding the fundamental concept of derivatives

Master the fundamental rule for differentiating polynomial functions

Understanding the different ways to write derivatives

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

Critical points, first/second derivative tests, concavity, and curve sketching

Setting up and solving optimization problems in business and geometry

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

Finding maximum and minimum values of functions

Using the derivative to classify critical points as maxima, minima, or neither

Using the second derivative to classify critical points

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

Understanding the reverse process of differentiation

Understanding integral notation and basic integration rules

The chain rule in reverse - substitution technique for integration

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

Riemann sums, definite integral definition, properties, and the Fundamental Theorem of Calculus

Antiderivative basics, power rule for integration, trig antiderivatives, and initial value problems

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

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

Area under curves, between curves, horizontal slicing, and multiple regions

Disk method, washer method, shell method, and cross-section volumes

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

Using trig identities to simplify difficult integrals

Decomposing rational functions for integration

Intro to DEs, slope fields, separation of variables, and exponential growth/decay

Exponential growth/decay, Newton cooling, population models, and continuous compounding

Reading tables, approximating derivatives, trapezoidal rule, and Riemann sums from data

FRQ format, calculator tips, justification techniques, and common mistakes

Comprehensive review of all units and full practice exam tips