♾️AP Calculus AB/BC

Unit 1 Overview: Limits and Continuity

Introducing Calculus: Can Change Occur at An Instant?

Defining Limits and Using Limit Notation

Estimating Limit Values from Graphs

Estimating Limit Values from Tables

Determining Limits Using Algebraic Properties of Limits

Determining Limits Using Algebraic Manipulation

Selecting Procedures for Determining Limits

Determining Limits Using the Squeeze Theorem

Connecting Multiple Representations of Limits

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 (IVT Calc)

Unit 2 Overview: Differentiation

Defining Average and Instantaneous Rates of Change at a Point

Defining the Derivative of a Function and Using Derivative Notation

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

Derivatives of cos x, sinx, e^x, and ln x

The Product Rule

The Quotient Rule

Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Unit 3 Overview: Differentiation: Composite, Implicit, and Inverse Functions

The Chain Rule

Implicit Differentiation

Differentiating Inverse Functions

Differentiating Inverse Trigonometric Functions

Selecting Procedures for Calculating Derivatives

Calculating Higher-Order Derivatives

Unit 4 Overview: Contextual Applications of Differentiation

Interpreting the Meaning of the Derivative in Context

Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Rates of Change in Applied Contexts other than Motion

Intro to Related Rates

Solving Related Rates Problems

Approximating Values of a Function Using Local Linearity and Linearization

Using L'Hopitals Rule for Determining Limits in Indeterminate Forms

Unit 5 Overview: Analytical Applications of Differentiation

Using the Mean Value Theorem

Extreme Value Theorem, Global vs Local Extrema, and Critical Points

Determining Intervals on Which a Function is Increasing or Decreasing

Using the First Derivative Test to Determine Relative (Local) Extrema

Using the Candidates Test to Determine Absolute (Global) Extrema

Determining Concavity

Using the Second Derivative Test to Determine Extrema

Sketching Graphs of Functions and Their Derivatives

Connecting a Function, Its First Derivative, and its Second Derivative

Introduction to Optimization Problems

Solving Optimization Problems

Exploring Behaviors of Implicit Relations

Unit 6 Overview: Integration and Accumulation of Change

Integration and Accumulation 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

Integrating Using Substitution

Integrating Functions Using Long Division and Completing the Square

Integrating Using Integration by Parts

Integrating Using Linear Partial Fractions

Evaluating Improper Integrals

Selecting Techniques for Antidifferentiation (AB)

Unit 7 Overview: Differential Equations

Modeling Situations with Differential Equations

Verifying Solutions for Differential Equations

Sketching Slope Fields

Reasoning Using Slope Fields

Approximating Solutions Using Euler’s Method

Finding General Solutions Using Separation of Variables

Finding Particular Solutions Using Initial Conditions and Separation of Variables

Exponential Models with Differential Equations

Logistic Models with Differential Equations

Unit 8 Overview: Applications of Integration

Finding the Average Value of a Function on an Interval

Connecting Position, Velocity, and Acceleration of 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

Finding the Area Between Curves That Intersect at More Than Two Points

Volumes with Cross Sections: Squares and Rectangles

Volumes with Cross Sections: Triangles and Semicircles

Volume with Disc Method: Revolving Around the x- or y-Axis

Volume with Disc Method: Revolving Around Other Axes

Volume with Washer Method: Revolving Around the x- or y-Axis

Volume with Washer Method: Revolving Around Other Axes

The Arc Length of a Smooth, Planar Curve and Distance Traveled

Unit 9 Overview: Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Defining and Differentiating Parametric Equations

Second Derivatives of Parametric Equations

Finding Arc Lengths of Curves Given by Parametric Equations

Defining and Differentiating Vector-Valued Functions

Integrating Vector-Valued Functions

Solving Motion Problems Using Parametric and Vector-Valued Functions

Defining Polar Coordinates and Differentiating in Polar Form

Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

Finding the Area of the Region Bounded by Two Polar Curves

Unit 10 Overview: Infinite Series and Sequences

Defining Convergent and Divergent Infinite Series

Working with Geometric Series

The nth Term Test for Divergence

Integral Test for Convergence

Harmonic Series and p-Series

Comparison Tests for Convergence

Alternating Series Test for Convergence

Ratio Test for Convergence

Determining Absolute or Conditional Convergence

Alternating Series Error Bound

Finding Taylor Polynomial Approximations of Functions

Lagrange Error Bound

Radius and Interval of Convergence of Power Series

Finding Taylor or Maclaurin Series for a Function

Representing Functions as Power Series

2024 AP Calculus AB Exam Guide

2024 AP Calculus BC Exam Guide

Download AP Calculus Cheat Sheet PDF Cram Chart

What is U-Sub and how do I use it?

What to Know Before Taking AP Calculus AB

What Calculator Functions Will Save Your Life?

Is AP Calculus AB/BC Hard? Is AP Calc Worth Taking?

What are Riemann Sums?

How Can I Get a 5 in AP Calculus AB/BC?

Unit 1 Review - Limits & Continuity

Best AP Calculus AB/BC Quizlet Decks By Unit

What is U-Substitution?

How do I take a derivative?

What Memes Are Perfect for AP Calculus AB/BC?

Unit 2 Review - Differentiation: Definition & Fundamental Properties

How do you defining and taking derivatives?

What is a Limit?

What is implicit differentiation and how do I do it?

AP Calculus Multiple Choice Questions

AP Calculus AB/BC Multiple Choice Help (MCQ)

AP Calculus Free Response Question (FRQ) Overview

Score Higher on AP Calculus 2024: MCQ Tips from Students

Score Higher on AP Calculus 2024: FRQ Tips from Students

2015 FRQ Review

2016 FRQ Review

2017 FRQ Review

Justifying and Explaining Your Answers

2018 FRQ Review

Review: Using the Graph of a Derivative FRQ

2019 FRQ Review

Review: Table/Data Questions

🎉NMSI AP Reader Chat: Calculus (AB and BC)

🌶️ AP Calc Cram Review: Unit 1: Limits and Continuity

AP Calc AB Cram Unit 1: Limits and Continuity

AP Calc AB Cram Unit 2: Differentiation: Definition and Fundamental Properties

🌶️ AP Calc Cram Review: Unit 2: Differentiation: Definition and Fundamental Properties

🌶️ AP Calc Cram Review: Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

AP Calc AB Cram Unit 3: Differentiation: Composite, Implicit, and Inverse Functions

AP Calc AB Cram Unit 4: Contextual Applications of Differentiation

🌶️ AP Calc Cram Review: Unit 4: Contextual Applications of Differentiation

AP Calc AB Cram Unit 5: Analytical Applications of Differentiation

🌶️ AP Calc Cram Review: Unit 5: Analytical Applications of Differentiation

AP Calc AB Cram Unit 6: Integration and Accumulation of Change

🌶️ AP Calc Cram Review: Unit 6: Integration and Accumulation of Change

🌶️ AP Calc Cram Review: Unit 7: Differential Equations

AP Calc AB Cram Unit 7: Differential Equations

AP Calc BC Cram Unit 6: BC Concepts (Integration by parts, Using Linear Partial Fractions, and Improper Integrals)

🌶️ AP Calc Cram Review: Unit 6 BC Concepts (Integration by parts, Using Linear Partial Fractions, and Improper Integrals)

AP Calc BC Cram Unit 7 and 8 BC Concepts (Euler's Method, Logistics Models, and Arc Length)

🌶️ AP Calc Cram Review: Unit 7 and 8 BC Concepts (Euler's Method, Logistics Models, and Arc Length)

AP Calc AB Cram Unit 8: Applications of Integration

🌶️ AP Calc Cram Review: Unit 8: Applications of Integration

AP Calc BC Cram Unit 9: Parametric Equations, Polar Coordinates

🌶️ AP Calc Cram Review: Unit 9: Parametric Equations, Polar Coordinates

AP Calc AB Cram Free Response Practice

🌶️ AP Calc Cram Review: Free Response Practice

🌶️ AP Calc Cram Review: Free Response Practice

AP Calc AB Cram Free Response Practice

🌶️ AP Calc Cram Review: Unit 10: Infinite Sequence and Series Part 1

AP Calc BC Cram Unit 10: Infinite Sequence and Series Part 1

🌶️ AP Calc Cram Review Free Response Practice

AP Calc AB Cram Free Response Practice

🌶️ AP Calc Cram Review: Unit 10: Infinite Sequence and Series Part 2

AP Calc BC Cram Unit 10: Infinite Sequence and Series Part 2

AP Calc AB Cram Free Response Practice

🌶️ AP Calc Cram Review Free Response Practice

AP Calc BC Cram Free Response Tips and Tricks

🌶️ AP Calc Cram Review Free Response Tips and Tricks

AP Calc AB Finale

🌶️ AP Calc AB Finale May 3, 2021

🌶️ AP Calc BC Finale May 3, 2021

AP Calc BC Finale

AP Calc AB Finale Slides

AP Calc BC Finale Slides

🌶️ AP Calculus AB + BC Finale Watch Party Admin 2

🌶️ AP Calculus AB Finale Watch Party Admin 3

🌶️ AP Calculus BC Finale Watch Party Admin 3

Limits, Continuity & Differentiability

Finding Derivatives

Related Rates

Curve Sketching

Calc BC Tests for Series Convergence

The Fundamental Theorem of Calculus

Tabular Calculus FRQs

Taylor Series (BC)

Separable Differential Equations

Sample FRQ and Strategies

Sample FRQs (BC)

Multi-Topic Questions for 2020

Graphical Limits

Algebraic Limits

Helping Students Master Taking Derivatives Part I (for Teachers)

Limits @ Infinity and Horizontal Asymptotes

Continuity Part I

Polar Coordinates and Calculus (for BC teachers)

Continuity Part II

The Limit Definition of the Derivative

Introduction to Finding Derivatives

Helping Students Master Taking Derivatives Part II (for Teachers)

Practicing Derivative Rules

The Product and Quotient Rules

The Chain Rule

Interpreting Derivatives through Tables and in context

Interpreting Derivatives through Graphs and in context

Practicing Derivative Rules II

Implicit Derivatives

Related Rates

f, f', f''

Increasing and Decreasing Functions

Optimization Problems

Concavity

Fall Semester Review (2019)

Integration Techniques Part II

Position, Velocity & Acceleration

Using FTC and Integral Defined Functions

Presentation Slides, FTC and Integral Defined Functions

Q and A

Interpreting the Meaning of a Derivative/Integral

Q and A

Separable Differential Equations

Existence Theorems

L'Hospital's rule

Q&A Student Study Session