Unit 1 - Limits & Continuity

Intro to Limits

Real World Continuity Examples

Intro to Limits

Intro to Limits Website

Khan Academy - Limits of Composition Video Clip

Definition of Derivatives

Formal Definition

Squeeze Theorem Proof Examples -Video Clip

AP Calculus AB - "Paul's Notes" - Website Link

Unit 1 Review

Zweigmedia Applied Calculus Tutorials

Principles of Calculus Modeling.- From Dartmouth

AP Central Video Resources & Problem Set Problems AP Central Login Code: 36V9AE To enroll in the section online, sign into https://myap.collegeboard.org and enter the section join code	Stay Safe, Do Your Best, & Give Your Best
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Introducing Calculus Defining Limits and Using Limit Notation Estimating Limit Values from Graphs Estimating Limit Values from Graphs Determining Limits Using Algebraic Properties of Limits Determining Limits Using Algebraic Manipulations Selecting Procedures for Determining Limits Determining Limits Using the Squeeze Theorem	9. Connecting Multiple Representations of Limits 10. Exploring Types of Discontinuities 11. Defining Continuity at a Point 12. Confirming Continuity over an Interval 13. Removing Discontinuities 14. Connecting Infinite Limits and Vertical Asymptotes 15. Connecting Limits as Infinity and Horizontal Asymptotes 16. Working with the Intermediate Value Theorem 2.1 Defining Average and Instantaneous Rates of Change at a Point

Unit 2 - Derivatives

	Calculus Derivative Practice Problems - Website Link	AP Calculus AB - "Paul's Notes" - Website Link	Flash Card Review of Derivatives - Website Link
	Higher Order - Video Clip	Implicit Derivative - Video	Online Derivative Practice - Transum Link

AP Central Video Resources & Problem Set Problems
AP Central Login Code: 36V9AE

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2.1 Defining Average and Instantaneous Rates of Change at a Point

2.2 Defining the Derivative of a Function and Using Derivative Notation

2.3 Estimating Derivatives of a Function at a Point

2.4 Connecting Differentiability and Continuity

2.5 Power Rule

2.6 Derivative Rules – Constant, Sum, Difference, and etc.

2.7 Derivatives of cos x, sin x, ex, and ln x

2.8 The Product Rule

2.9 The Quotient Rule

2.10 Finding the Derivatives of Tangent, Cotangent, Secant, and Cosecant Functions

3.1 The Chain Rule

3.2 Implicit Differentiation

3.3 Differentiating Inverse Functions

3.5 Selecting Procedures for Calculating Derivatives

3.6 Calculating Higher - Order Derivatives

Unit 3 - Applications of Derivatives

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MVT Formula

Rolle's Theorem - VIdeo Clip

Paul's Notes - AP Calculus AB - Website Link

Related Rates Problems, if needed
Theorem Review Worksheet - Do the Problems and then check your answers, if needed

Related Rates -Shadow Example

Optimization - Examples

Intermediate Value Theorem - Video Clip

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Mean Value Theorem #1 - Video Clip

Mean Value Theorem #2 - MVT

Extreme Value Theorem- Video Clip

L'Hopital's Rule Free Response Examples - Video Clip

1st & 2nd Derivative Test - Video Clip

Flash Card Review of Derivatives - Website Link

AP Central Video Resources & Problem Set Problems
AP Central Login Code: 36V9AE

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3.1 The Chain Rule
3.2 Implicit Differentiation
3.3 Differentiating Inverse Functions
3.4 Differentiating Trig Functions
3.5 Selecting Procedures for Calculating Derivatives
3.6 Calculating Higher - Order Derivatives
4.1 Interpreting the Meaning of the Derivative in Context
4.2 Straight – Line Motion – Connecting Position, Velocity, & Acceleration
4.3 Rates of Change in Other Applied Contexts
4.4 Introduction to Related Rates
4.5 Solving Related Rates Problems
4.6 Approximating Values of a Function Using Local Linearity & Linearization
4.7 Using L’Hopital’s Rule for Finding Limits of Indeterminate Forms

5.5 Using the Candidates Tests to Determine Absolute Extrema

5.6 Determining Concavity of Functions over Their Domain

5.7 Using the 2^nd Derivative Test to Determine Extrema

5.8 Sketching Graphs of Functions and Their Derivatives

5.9 Connecting a Function, Its 1^st Derivative, and its 2^nd Derivative

5.10 Introduction to Optimization Problems

5.11 Solving Optimization Problems

5.12 Exploring Behaviors of Implicit Relations

Unit 4 - Introduction to Integrals

Calculus Derivative Practice Problems - Website Link

Intro to Integrals - Link

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Paul's Notes - AP Calculus AB - Website Link

Summation Notation -Video Clip

Online Integral Practice - Transum Link

AP Central Video Resources

6.1 Exploring Accumulations of Change

6.2 Approximating Areas with Riemann Sums

6.3 Riemann Sums, Summation Notation, and Definite Integral Notation

6.4 The Fundamental Theorem of Calculus and Accumulation Functions

6.5 Interpreting the Behavior of Accumulation Functions Involving Area

6.6 Applying Properties of Definite Integrals

6.7 The Fundamental Theorem of Calculus and Definite Integrals

6.8 Finding Antiderivatives and Indefinite Integrals – Basic Rules & Notation

Unit 5 - Applications of Integrals

Calculus Derivative Practice Problems - Website Link

AP Calculus AB - "Paul's Notes" - Website Link

Average Value & Mean Value Theorem for Integral - Video Clip

Online Integral Practice - Transum Link

Online Trig Quiz Link

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AP Central Video Resources AP Central Login Code:
6.1 Exploring Accumulations of Change 6.9 Integrating Using Substitution 6.14 Selecting Techniques for Antidifferentiation 7.1 Modeling Situations with Differential Equations 7.2 Verifying Solutions for Differential Equations 7.3 Sketching Slope Fields	7.4 Reasoning Using Slope Fields 7.6 Finding General Solutions Using Separation of Variables 7.7 Finding Particular Solutions Using Initial Conditions and Separation of Variables 8.1 Finding the Average Value of a Function on an Interval 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts

Unit 6 & Unit 7 - Area, Volume, & Additional Topics

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Cross Sectional Volume - Video Clip

Final Exam Topic List

Limits

Properties of Limits

Algebraic Limits

Graphical Limits

Sandwich/Squeeze Theorem

Continuity

Discontinuity

Limits w/Infinity

Difference Quotient

AROC – Average Rate of Change

IROC – Instantaneous Rate of Change

Tangent & Normal Lines
Volume

Disk Method

Washer Method

Applications of Curve Sketching

Trig Derivatives

Basic Derivatives

Reversed Difference Quotient

Higher Order Derivatives

The Chain Rule

Transcendental Derivatives

Implicit Differentiation

Inverse Function Derivatives

Derivatives of Trig Inverses

Rolle’s Theorem

Mean Value Theorem

Extreme Value Theorem

L’Hopital’s Rule

Linearization

Particle Motion

Differentials
Slope Fields
Position

Velocity

Acceleration
Volume

Area

Cross Sectional

FTC-Part 2

Integrals as Net Change

U – Substitution

Separating the Variables

Area Between Curves

Long Division with Integrals

Completing the Square with Integrals
Derivatives – Power, Product,
Quotient, Ln, Log, Trig, e, a^x, Inverse Functions, Trig Inverse
Integrals – U-sub
Mean Value Theorem with Integrals
Average Value
Maximum
Minimum
Concavity
Point of Inflection
FTC-Part 1

LRAM

RRAM

MRAM

Trapezoid Method

Summation Notation

Integrals

Anti-derivatives

1^st & 2^nd Parametric Derivatives

Related Rates

1^st & 2^nd Derivative Vocabulary

1^st & 2^nd Derivative Tests

Particle Motion

Rectilinear Motion

Optimization

IVT – Intermediate Value Theorem

Derivative Curve Sketching

Exponential Differentials

Derivative Graphs f, f’, f”

Extra Math Help

*AP Central Video Resources*
6.10 Integrating Functions using Long Division and Completing the Square 7.8 Exponential Models with Differential Equations 8.4 Finding the Area Between Curves Expressed as Functions of x 8.5 Finding the Area Between Curves Expressed as Functions of y 8.6 Finding the Area Between Curves That Intersect at More Than Two Points 8.7 Volumes with Cross Sections - Squares and Rectangles	8.8 Volumes with Cross Sections - Triangles and Semicircles 8.9 Volume with Disk Method - Revolving Around x - or y - axis 8.10 Volume with Disk Method - Revolving Around other Axes 8.11 Volume with Washer Method - Revolving Around x - or y - axis 8.12 Volume with Washer Method - Revolving Around other Axes

Unit 8 - Final Exam

Resources for Unit 8:
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