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Fun Stuff

Calculus

Overview

Overview

Applying derivatives to analyze functions

Using the mean value theorem

Extreme value theorem, global versus local extrema, and critical points

Determining intervals on which a function is increasing or decreasing

Using the first derivative test to find relative (local) extrema

Using the candidates test to find absolute (global) extrema

Determining concavity of intervals and finding points of inflection: graphical

Determining concavity of intervals and finding points of inflection: algebraic

Using the second derivative test to find extrema

Sketching curves of functions and their derivatives

Connecting a function, its first derivative, and its second derivative

Solving optimization problems

Exploring behaviors of implicit relations

Limits and continuity

Defining limits and using limit notation

Estimating limit values from graphs

Estimating limit values from tables

Determining limits using algebraic properties of limits: limit properties

Determining limits using algebraic properties of limits: direct substitution

Determining limits using algebraic manipulation

Selecting procedures for determining limits

Determining limits using the squeeze theorem

Exploring types of discontinuities

Defining continuity at a point

Confirming continuity over an interval

Removing discontinuities

Connecting infinite limits and vertical asymptotes

Connecting limits at infinity and horizontal asymptotes

Working with the intermediate value theorem

Optional videos

Differential equations

Modeling situations with differential equations

Verifying solutions for differential equations

Sketching slope fields

Reasoning using slope fields

Finding general solutions using separation of variables

Finding particular solutions using initial conditions and separation of variables

Exponential models with differential equations

Differentiation: composite, implicit, and inverse functions

The chain rule: introduction

The chain rule: further practice

Implicit differentiation

Differentiating inverse functions

Differentiating inverse trigonometric functions

Selecting procedures for calculating derivatives: strategy

Selecting procedures for calculating derivatives: multiple rules

Calculating higher-order derivatives

Further practice connecting derivatives and limits

Optional videos

Interpreting the meaning of the derivative in context

Straight-line motion: connecting position, velocity, and acceleration

Rates of change in other applied contexts (non-motion problems)

Introduction to related rates

Solving related rates problems

Approximating values of a function using local linearity and linearization

Using L’Hôpital’s rule for finding limits of indeterminate forms

Applications of integration

Finding the average value of a function on an interval

Connecting position, velocity, and acceleration functions using integrals

Using accumulation functions and definite integrals in applied contexts

Finding the area between curves expressed as functions of x

Finding the area between curves expressed as functions of y

Volumes with cross sections: squares and rectangles

Volumes with cross sections: triangles and semicircles

Volume with disc method: revolving around x- or y-axis

Volume with disc method: revolving around other axes

Volume with washer method: revolving around x- or y-axis

Volume with washer method: revolving around other axes

Integration and accumulation of change

Exploring accumulations of change

Approximating areas with Riemann sums

Riemann sums, summation notation, and definite integral notation

The fundamental theorem of calculus and accumulation functions

Interpreting the behavior of accumulation functions involving area

Applying properties of definite integrals

The fundamental theorem of calculus and definite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule

Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals

Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals

Integrating using substitution

Integrating functions using long division and completing the square

Optional videos

Differentiation: definition and basic derivative rules

Defining average and instantaneous rates of change at a point

Defining the derivative of a function and using derivative notation

Worked example: Derivative from limit expression

Estimating derivatives of a function at a point

Connecting differentiability and continuity: determining when derivatives do and do not exist

Applying the power rule

Derivative rules: constant, sum, difference, and constant multiple: introduction

Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule

Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x)

The product rule

The quotient rule

Finding the derivatives of tangent, cotangent, secant, and/or cosecant functions

Optional videos

AP Calculus AB solved free response questions from past exams

AP Calculus AB 2017 free response

AP Calculus AB 2015 free response

AP Calculus AB 2011 free response