Welcome to Unit 1 - Integral & Limit Techniques of AP Calculus BC

Unit 1 Quote: “I Will Achieve Great Things Through Small Steps."

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

Tuesday Afternoon Office Time (2:30 pm - 3:30 pm)

Be Your Best, Do Your Best, & Breathe!

Unit 1 - Integral Technique Objectives

Students will be able to:

1.1 The concept of a limit can be used to understand the behavior of functions.
1.2 Continuity is a key property of functions that is defined using limits.
2.2 A function’s derivative, which is itself a function, can be used to understand the behavior of the function.
(Higher – order Derivatives & 2nd Derivative Applications)
2.3 The derivative has multiple interpretations and applications including those that involve instantaneous rates of change. (Particle Motion, Slope Fields, & Euler's Method)
3.2 The definite integral of a function over an interval is the limit of a Riemann sum over the interval and can be calculated using a variety of strategies.
3.3 The Fundamental Theorem of Calculus, which has two distinct formulations, connects differentiation and integration. (Integration By Parts & Partial Fractions)
3.4 The definite integral of a function over an interval is a mathematical tool with many interpretations and applications involving accumulation.
3.5 Anti-differentiation is an underlying concept involved in solving separable differential equations. Solving separable differential equations involves determining a function or relation given the rate of change.
(Logistic Growth and Growth Rates)

	Jan 20th	Jan 21st	Jan 22nd	Jan 23^rd	Jan 24th

AP Calculus BC Topic/Concept	Holiday	Workday	Separating the Variables, Euler's Method, & Slope FIelds *Friday*	*Integration By Parts* *Monday*	*Trigonometric Powers - Part 1* *Tuesday*
Week 1
3^rdPeriod			1. Welcome, "Olympic Theme Song", Role Call, National Events, Worksheet Packet, & National Events 2. Euler's Method PPT 3. - Review 4. AP Central Login Code: = AW2L46 Problem Set due Feb 11^th by 7 am 5. Song Time!!!	1. Discuss HW results, Warm-up = Bowling Quiz # 1, & - Is it Still True?" 2. Integration by Parts -PPT 3. - Euler's Method 4. Song Time!!! KA)	1. Discuss Trig Identity Foldable - Markers & Scissors, HW, & Warm - up Problems 2. Song “Integral of sin²x and cos²x” - # 37 3. Trig Integral PPT & Problems 4. Trig Identity Review
			HW 1 - Euler upload & HW Volunteer Problems for Mon's Class by 7:00 am - Watch & Listen to the Video = Euler's Method Song, Example, Real - Life Application, & Slope Field Example (Ignore the pronunciation of "Euler" in the video.)	Watch AP Central Videos Integration by Parts - Class Link due Tues by 7am Class Link 2 Assignments due Tuesday by 7am - Integration By Parts # 1 - Integration By Parts # 2	HW 3 - = Homework Problems & upload for Thursday by 7 am Say Something Nice To Three People!!!
AP Calculus BC Songs			"Olympic Theme Song" Calculus Parody Review VIdeo - "Euler's Method"	Integration By Parts Songs: Song # 1 Song # 2 AP Calculus Theme Song # 21 - Tune (Down By The Riverside tune - 45 sec only)	Integral of sin²x and cos²x - Song # 37 - "Jingle Bells"
National Events	Cheese Lovers Disk Jockey MLK Holiday Buttercrunch	Granola Bar Squirrel Appreciation Hugging	Polka Do Blonde Brownie	Handwriting Pie Day	Peanut Butter Compliment Saturday Opposite Day Seed Swap Day Sunday Green Juice Day Peanut Brittle Day

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Week 2

	Jan 27^th	Jan 28^th	Jan 29^th	Jan 30^th	Jan 31^st

AP Calculus BC Topic/Concept	Quiz # 1 *Wednesday*	Functional Growth Rates & Trigonometric Powers - Part 2 *Thursday*	Exponential Growth/ Decay & Logistic Growth - Part 1 Friday
Week 2
3^rdPeriod	Quiz # 1 "G R A N D" G - Graphical R - Real World A - Algebraic N - Numerical D - Descriptive Cell Phones & Smart Watches = Back Table	1. Discuss Functional Growth Rate PPT, Grow "Functional Pets", Warm - up Problems, & Discuss HW 2. Relay Game - "1 line at a time" Problems 3. = Trig Review 4. Discuss Quiz results?	1. Discuss HW 5 2. Tootsie Roll Activity = "Beep" Activity - Each student is numbered for "Effect". 3. Warm - up = Pre-Calculus Logistic Growth Review 4. Guided Notes & Video Clip # 1 5. Your Turn! 6. Guided Notes & Video Clip # 2 - Part 1
	HW 3 - = Homework Problems & upload for Thursday by 7 am "Big Ideas" Weekly Journal Entries Due Feb 20^th & Apr 24^th	Read 6.1 - 6.3 HW 5 due Friday by 7am & = HW Volunteers Read & Take Notes on the University of Notre Dame's Exponential Growth Review	HW 6 & HW Volunteers for Mon's Class by 7:00 am Enjoy the two L'Hopital Review Songs below!! Read the Calculus Review Concepts	Something Nice For Your Grandparents or a Senior Citizen!!!
AP Calculus BC Songs		Oh Calculus # 53 - Tune Oh Christmas Tree	L'Hopital Song # 1 L'Hopital L'Hopital Song # 2 L'Hopital
National Events	Chocolate Cake Day Bubble Wrap	Plan For Vacation Blueberry Pancake Kazoo Day	Corn Chip Puzzle	Croissant Day	Hot Chocolate Backward Fun At Work Big Wig Inspire Your Heart with Art Saturday Dark Chocolate Get Up Day Baked Alaska Ice Cream for Breakfast Sunday TATER TOT DAY BUBBLE GUM DAY HEAVENLY HASH DAY GROUNDHOG DAY

Week 3

	Feb 3rd	Feb 4th	Feb 5th	Feb 6th	Feb 7th

AP Calculus BC Topic/Concept	Logistic Growth - Part 2	Quiz # 2	*Logistic Growth - Part 3*	*Partial Fractions - Part 1* Curriculum Expo	*Partial Fractions* *- Part 2* *AP Exam Meeting*
Week 3
3^rdPeriod	1. Discuss National Events, HW 6, Warm - up Problems - Part 1 & Part 2. & Bowling Quiz # 2 2. Guided Notes & Video Clip # 2 - Part 2 3. Your Turn! = Groups of 3 = "Light" Activity 4. Groups = Page 26	Quiz # 2 "G R A N D" G - Graphical R - Real World A - Algebraic N - Numerical D - Descriptive Cell Phones & Smart Watches = Back Table	Logistic HW 7, & Video Link Groups = Pages 25 - 26 = 20 min 3. "Free Style" Bingo Rules 4. Play "Free Style" Bingo	1. Partial Fraction PPT - Part 1 = 2 Types 2. Take Notes on the Logistic Growth/Partial Fraction Connection - Video Clip 3. Song TIme! 4. Discuss Quiz results	1. Discuss HW 9 & HW 10 2. = Worksheet Page 20 # 2 =Seatmate Partners 3. - Partial Fractions 4. - Integration by Parts 5. AP Exam Meeting
	HW 7 Upload due Wed by 7 am = Classwork Grade Read the Long Division Examples Problem Set # 1 due Feb 13th by 7 am	Mon's HW	Watch & Practice the Graphing Calculator Instructions on Solving Systems of Linear Equations HW 9 & HW 10 due Friday by 7 am = Classwork Grade & = HW Volunteers Watch AP Central Videos	Wed's HW Watch & Take Notes on the Video Clip Extra Video on Logistic Formulas Give A Small Gift To A Friend!!! (❁´◡`❁) "Big Ideas" Weekly Journal Entries Due Feb 20^th & Apr 24^th	Bring some fruit for Monday's class - Grapes still attached, Apples, Bananas, Strawberries, etc. Extra Practice Problem - ppt of Logistic Growth Formulas Problem Set due Feb 13^th by 7 am Watch AP Central Videos
AP Calculus BC Songs	Parts and Partial Fractions # 83 - Tune Three Blind Mice Euler's Method # 82 - Tune Twinkle Twinkle Little Star		#2 - What a Wonderful World Limits # 74 - Tune The Rubber Tree Plant L'Hopital # 77 - Tune Total Eclipse of the Heart L'Hopital # 81 - Tune If You're Happy and You Know It	Partial Fraction # 54 Don't Cry for me Argentina tune from Evita	Derivatives - Long Division & Product Rule Implicit Differentiation # 79 RESPECT Tune Separating the Variable # 23 Itsy Bitsy Spider Tune
National Events	CARROT CAKE Women Physicians	HOMEMADE SOUP THANK A MAIL CARRIER	WEATHERPERSON	CHOPSTICKS FROZEN YOGURT Optimist	BUBBLE GUM Wear Red PERIODIC TABLE FETTUCCINE ALFREDO SEND A CARD TO A FRIEND Saturday KITE FLYING Sunday PIZZA BAGEL AND LOX TOOTHACHE PORK RIND

Week 4

	Feb 10th	Feb 11th	Feb 12th	Feb 13th	Feb 14^th
	Monday	Tuesday	Wednesday	Thursday	Friday
AP Calculus BC Topic/Concept	*Unit 2 Begins - Improper Integrals - Part 1 & 2 and Direct Comparison Tests*	Integral & p - series Tests	*Review*	Unit Test 1	*Limit Comparison, Telescoping, & Geometric Tests*
Week 4				*Open House*
3^rdPeriod	1. Discuss National Events & HW Volunteers 2. Improper Integrals - Classwork Examples = Worksheet Packet # 1, 2, 5, 4 3. Direct Comparison Test - # 1 & 2 and 5 & 7 4. Discuss Harmonic, Fibonacci Patterns Powerpoint Link, & Video Link 5. Grapes, Apples, Bananas, Strawberries, etc.	1. Integral Series Test = Take Notes on the following videos & fill-in the chart on Worksheet Page 7,: - Video # 1 - Video # 2 - Video # 3 2. Read p-series notes = Worksheet Packet Page 8 3. Take Notes on the Video for the p-series Test 4. Pre-Calculus Review Video = Partial Sums 5. Worksheet Packet Pages 10 -11 = p-Series Investigation Activity 6. Take Notes on the Integral Test examples = Worksheet Page 12 - Video Link	1. Discuss Bowling Quiz # 3 2. Butterfly Suitcase Review Game	Unit Test 1 "G R A N D" G - Graphical R - Real World A - Algebraic N - Numerical D - Descriptive Cell Phones & Smart Watches = Back Table = Unit Test Points	1. Discuss HW 1, HW 2, & Classwork Grade results 2. Warm - up Problems = 3. Limit Comparison Test = Classwork Examples # 1 & 2 (Learn the "Limit Lingo") 4. Watch the Limit Comparison Video Clip & Take Notes 5. Telescoping Demo & Classwork Examples = # 1 -5 6. Discuss Geometric Series Test Example Problems = Pre - Calculus Review pdf version 7. Telescoping Series, Geometric Series, & Alternating Series are the only 3 of the 10 Tests that have a "Sum". 8. Discuss Unit Test results???
	Problem Set # 1 due Feb 13th by 7 am HW 1 due Fri by 7am Classwork Grade # 1 due Fri by 7 am HW 2 = HW Volunteers for Fri by 7am "Big Ideas" Weekly Journal Entries Due Feb 20th	Mon's HW	Mon's HW Watch AP Central Videos well &	Mon's HW due Friday by 7 am	Read Chapter 8 & 9 HW 4 = *Classwork Grade # 2* = Worksheet Pages 18 - 20 & 25 - 27 (Page 27 = Volunteers) due Tues by 7 am Give a Small Gift to Yourself! (❁´◡`❁) Belated Valentine's Day Activity Exchange = ???
AP Calculus BC Songs	Discontinuities # 4 - Tune Three Blind Mice Follow Me # 59 - Tune Follow Me	Twinkle Writing # 38 - Tune Twinkle Twinkle Little Star	Oh Calculus # 53 - Tune Oh Christmas Tree		#1 - Take It To The Limit
National Events	Cream Cheese Brownie Umbrella	Inventor's Peppermint Patty White Shirt/T-Shirt Don't Cry Over Spilled Milk Make a Friend	Plum Pudding	Giving Hearts CHEDDAR DAY TORTELLINI DAY Pancake - Ihop	CREAM-FILLED CHOCOLATES DAY FERRIS WHEEL ORGAN DONOR Valentine's Saturday Red Sock Gumdrop Sunday No One Eats Alone Do A Grouch A Favor Almond