Welcome to Unit 6 - Area, Volume, & Additional Topics of AP Calculus AB

I will do my best to create a positive learning environment for each of you.
Most weeks we will utilize handfuls of technological tools.

Most Daily/ Weekly assignments will be due the next day.

Wednesday Afternoon Office Time (2:20pm - 3:00pm)

Be Your Best, Do Your Best, & Breathe!

Unit 6A – Quote – “Do your best, give your best and know that in doing
so you'll enhance the quality of your life" - VeryBestQuotes.com

Unit 6B – Quote – “Every Accomplishment Starts with The Decision to Try." - Gail Devers

Unit 6 - AP Calculus National Objectives

Students will be able to use:

The Objectives from Units 5 & 6 in context with analyzing functions defined by an integral.
- Applying definite integrals to problems involving area, volume, and cross-sectional volumes.
Integrating Functions using Long Division and Completing the Square
-Applying Euler’s Method to differential functions.

Jan 2^nd

Jan 3^rd

Jan 4^th

Jan 5^th

Jan 6^th

Unit 6 Packet

PDF Version

AP Calculus AB
Topic/Concept

Holiday

Disk Method

(13 School Days until Exams)

Washer Method

Review

Unit Test 6A

Week 19

2^nd & 3^rdPeriod

1. Watch the following video & take Notes

Disk Method

3. "PSWA" - Picture Set-up Work Answer - Non-calculator for Packet Pages 26 - 27

4. The Answers for Pages 26 - 27 are on the = Disk Method Examples

1. Discuss National Events, Holiday Break Events, HW, Limit results, & Put Journal in the Back Tray

butterfly jounal.png

2. Disk & Washer PPT

3. = Washer Method Examples

2^nd Period

3^rd Period

5. Your Turn!

(Candy = Life Savers)

6. Work on Project

1. Discuss HW & Quiz # 1 results

2. Disk, Washer, & Cross Section PDF, Animations, & Notes

3. The Shell Method

4. Groups = Free Response Practice # 1 & # 2

5.

6.

7. Work on Project

Unit Test 6A

HW 9 due Wednesday = 1 Volunteer per rotational problem & Upload HW

2^nd Period

3^rd Period

Bring a drink for Wednesday's class

"Big Ideas" Weekly Journal Entries due Jan 4^th

Homework Grade = Review Quiz # 1 due on or before Jan 5^th
Classwork Grade = Review Quiz # 2 due on or before Jan 12^th
AP Classroom Problem Set #6 due on or before Jan 10^th by 7 am
Work on Project

HW 10 due Thursday = 1 Volunteer per rotational problem & Upload HW

2^nd Period

3^rd Period
Read Chapters 5 & 6

Read Chapter 7

HW 11 "PSWA" due Monday by 7am
HW 11 Link
Watch AP Central Videos
Work on Project
Do a Good Deed For 2 Different People!

Thurs' HW
AP Classroom Problem Set #6 due Jan 10^th by 7 am

AP Calculus AB Songs

# 49 Dimensions

#89 Volume of Rotations

#31 Natural Logarithms and e^x

National Events

January 2

Science Fiction Day
Buffet Day

Jan 3

International Mind-Body Wellness Day

Jan 4

World Braille Day
Trivia Day
Spaghetti Day

Jan 5

Bird Day
Keto Day

Jan 6

Cuddle Up Day

Jan 8

Bubble Bath Day
World Typing Day

Extra Practice:

Cross Sectional Volume - Video Clip

Final Exam List of Topics

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

Keep up the Good Work for this Semester in All of Your Classes!

Stay Safe, Do Your Best, Give Your Best,

Cut Two 2 x 5 cm rectangles, tape to pencil, rotate, decide the name of the rotated shape, and calculate the volume of each rotated shape

(Candy = correct answers)

3. Doughnut/Bagel Activity = Pages 30 - 31 & Song Time!