The Fundamental Theorem Of Calculus Homework Video

AB Calculus Homework

We will have our 5.5, 5.6, and Motion Exam on Thursday, March 15th.

A wide variety of resources for all tests and retests can be found on the AB Practice Tests Tab.

This will be our first Calculator Allowed test of the year.

5.5, 5.6, and Motion Exam Tests & Study MaterialsStudy Guide / 5.5, 5.6, & Motion Practice Test / Practice Test Solutions

More Motion FRQ Practice: FRQ Topic: Motion Problems

Professor Leonard PlaylistsCalculus 1 (Covers almost all of AP Calculus AB) / Calculus 2 (Covers the rest of AP Calculus AB & most of AP Calculus BC)

Khan Academy: Calculus Part 1 /All of AP Calculus AB

AP Prep. Quartet: AB Practice Test Depot / AB FRQ Index Tab / AB FRQ WebsiteCracking the AP Calculus AB Exam

Wednesday 3/7/2018 – Thursday 3/8/2018 (Two Day Assignment)

AP Practice - Motion Packet #1 (distributed in class and in documents)

Performdetailed test correctionsusing: AP Practice - Motion Packet #1 - Complete Solutions (in documents; video solutions for some problems are hyperlinked)

Why detailed corrections?  Most of the packet contains actual AP FRQ's and it is time to begin the real preparation for the AP exam.  You should always perform detailed corrections for FRQ's to get ready for the real deal on May 15th.

This walks you through the first problem with the proper keystrokes for your calculator:

AP Practice – Motion Packet #1 – Calculator Tutorial for Problem #1 (in documents)

Want to see what the actual FRQs on this topic will look like?  Explore: FRQ Topic: Motion Problems at your leisure.

Tutorial Videos:

2011 AB FRQ #1 / 2012 AB FRQ #6 / 2011 AB Form B FRQ #5 / 2013 AB FRQ #2

Motion - Distance Traveled Integrals vs. Displacement Integrals (Net Change in Position Integrals)

Motion - Speeding Up vs. Slowing Down / Motion Problems - Particle Motion

Motion - AP Particle Motion Problems, especially Free Response Questions

Monday 3/5/2018 – Tuesday 3/6/2018 (Two Day Assignment

AP Curriculum Model - Calculus - Motion - Bellwork (in documents; slides 5-7 are just meant to give you an idea of what Motion FRQs have looked like on recent AP exams)

AP Curriculum Model - Calculus - Motion (distributed in class and in documents; must be 100% complete for credit)

Correct with: AP Curriculum Model - Calculus - Motion - SOLUTIONS (in documents)

Optional Exploration: FRQ Topic: Motion Problems

Tutorial Videos:

Motion - Distance Traveled Integrals vs. Displacement Integrals (Net Change in Position Integrals)

Motion - Speeding Up vs. Slowing Down

Motion Problems - Particle Motion

Motion - AP Particle Motion Problems, especially Free Response Questions

Thursday 3/1/2018 - Friday 3/2/2018 (Two Day Assignment

You will have the opportunity for in class retests on Friday 3/2/2018.

Homework:

Chapter 5 Review Project #1 (distributed in class and in documents)

Perform detailed corrections with: Chapter 5 Review Project #1 - Complete Solutions (distributed in class and in documents)

AB FRQ Website(Get used to using this website as a resource!)

Tutorial Videos: 2011 Form B FRQ 2 (You can easily find youtube video solutions for almost any FRQ on theAB FRQ Website!)

Tuesday 2/27/2018 - Wednesday 2/28/2018 (Two Day Assignment)

5.6 Full Lecture with Professor Leonard

5.6 Bellwork (in documents and distributed in class)

5.6 Notes - Derivatives of Inverse Trig Functions (in documents; Wednesday we will start on slide #27)

Read 5.6; all of the main derivative rules for the ENTIRE AP Test are on pg. 378 (Rules 1-10 and 12-21).  That's it!  Get them memorized before May 15th!

5.6 Day 1 (5-11 odd, 17-19 odd, 27-33 odd) - Had enough Professor Leonard?  Try some Patrick JMT instead! - Inverse Trig. Pre-Calc.

5.6 Day 2 (43-51(odd), 73-77(odd), 81, 91-94, 97) - Had enough Professor Leonard?  Try some Patrick JMT instead! - Inverse Trig. Calc.

Correct with: 5.6 MORE Complete Solutions (in Calculus Book Solutions)

There are always typed solutions available on the Calculus Book Solutions tab (on the left sidebar of the class website).  There are always typed solutions available for the odd problems at: calcchat.com.

Tutorial Videos:

5.6 Pre - Inverse Trigonometric Functions

5.6 Pre - Evaluating Inverse Trig. Functions Using a Right Triangle Approach

5.6 Pre - Evaluating Inverse Trig. Functions Using a Right Triangle Approach - Specifically with a Composite Expression

5.6 Pre - Solving Trigonometric Equations

5.6 - Derivatives of Inverse Trig. Functions

Monday 2/26/2018

In class test review for the Mid-Winter Break Practice Test / Detailed Solutions.

No additional homework.  Prepare for retests or go on to the next assignmentFriday is an in class retest day.

2012 AB MCQ Tutorial Videos:

1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / 25 / 26 / 27 / 28

76 / 77 / 78 / 79 / 80 / 81 / 82 / 83 / 84 / 85 / 86 / 87 / 88 / 89 / 90 / 91 / 92

Saturday 2/17/2018 - Sunday 2/25/2018 - Mid-Winter Break Calculus Extravaganza

AB Mid-Winter Break Practice Exam - INSTRUCTIONS (distributed in class and hyperlinked here)

AB Mid-Winter Break Bellwork – Calculator Examples (distributed in class and in documents)

I would advise students to take advantage of the free printing at the Covington Library.  You only need to print out the pages with MCQs.  Getting used to the feel and format of the actual test prior to AP Exam Day really helps.

Be prepared to AB share your detailed test correctionson 2/26/2018 (first day after break).

D's and F's on the last three exams and not sure what to do before your next test/retest?

1) Actively quiz yourself using:AB Practice Tests Tab / AB Practice Test Depot.  Predict what sort of problems will be on the exam (I try to help you with that by posting many practice exams.).  Solve those predicted problems prior to each exam; that would be active quizzing!  Create your own examples.  Skimming notes is crap as a college math study habit.  Re-writing or annotating notes while reworking examples out of your notes is active studying.  When in doubt, work through one of those blank tests from the AB Practice Tests Tab, score yourself, perform detailed test corrections, and use the problems you got incorrect to guide your further study.

2) Aim to complete and understand 100% of the homework (including MCQs/FRQs):  

  a) Come in to the Q&A sessions, before school, or after school and get every question you have on every problem answered.  And/or form study groups for the same purpose.  If you get stumped by a problem over break, write down your question, snap a picture with your phone, and email me the question.  I will generally respond within 48 hours.

  b) If you have to use the solutions or get help on a problem, find a similar problem to attempt on your own after you understand the first problem.  Stop being obsessed with doing the minimum.

  c) If you have to look up a formula to start a problem, copy that formula down in pen in the margin of your work, say the formula out loud, make a flash card for that formula, etc.  Use every possible trick to commit as many of these formulas to memory as possible.  Looking above at the previous problem for a formula does VERY LITTLE for long term memory building for many students.  Looking isn't good enough for AP Exams.

3) Re-evaluate your study habits:  Experiment with new study habits prior to college to find what works best for you.  

Study Habits for Math in College / Study Habits for Calculus / Study Habits for AP Calculus

4) Order a Princeton Review AP Prep. Book for Calc. or check one out from the school library.  Force yourself to schedule 1-2 hour blocks where you just start at the beginning of that book and move forward (all the way back to limits).

5) Schedule a retest for 4.1-5.4 Test - Part 1 - Blue Partand/or 4.1-5.4 Test - Part 1 - Purple Partas soon as you PROVE you are ready to yourself using your improved study habits!

Friday 2/16/2018 - Part 2 Test Review Day!

Read pages 365-367. A new integration rule is introduced there.
5.5 Part 2 (67-85(odd), 107).

5.5 Notes - Bases Other than e and Applications (in documents)
Correct using the answers in the back of the book, 5.5 Complete Solutions (in Calculus Book Solutions), and/or calcchat.com.

Tutorial Videos:

5.5 - Integration of Exponential Functions with Bases Other than e

Thursday 2/15/2018

Performdetailed test correctionsfor your 4.1-5.4 Test Form D - Part 2 (exams will be returned in class) using:

4.1-5.4 Test Form D - Part 2 -  Solutions and Rubric (in documents)

Be prepared to AB share your detailed test corrections at the start of class Friday!

Then move onto: 4.1-5.4 Test Form D – Part 2 – Targeted Review (in documents).

Want a rematch?  4.1-5.4 Test Form D - Part 2 - Blank Copy (in documents)

Wednesday 2/14/2018 - Part 1 Test Review Day!

4.1-5.4 Test Form Z - Part 1 - Test Correction and Targeted Review Assignment (in documents)

4.1-5.4 Test Form Z - Part 1 - Extended Solutions and Scoring Rubric (in documents)

Want a rematch? 4.1-5.4 Test Form Z - Part 1 - Blank Copy (in documents)

Alternative Option - Complete 2-3 appropriate FRQs as your targeted review:

Table Problems / Graph of f, f’, or f’’ / Rate In/Rate Out Application Problems.

Tuesday 2/13/2018

5.5 Full Lecture with Professor Leonard

5.5 Bellwork - Day 1 (in documents and distributed in class)

Correct with: 5.5 Bellwork - Day 1 - Detailed Solutions (in documents)

Read 5.5.

5.5 Day 1 (1-38 as needed for review, 42, 43, 45, 49, 51, 55, 59, 63, 65)

5.5 Notes - Bases Other than e and Applications (in documents)

Tutorial Videos:

5.5 - Derivatives of Log Functions with Bases Other than e

5.5 - Derivatives of Exponential Functions with Bases Other than e

5.5 - Integration of Exponential Functions with Bases Other than e

Monday 2/12/2018 

4.1-5.4 Test - Part 2 (administered during class; focuses on 5.1-5.4

See the AB Practice Tests Tab for a study guide and preparation materials.

Your homework will be 4.1-5.4 Test - Part 1Detailed Corrections(tests returned in class; solutions emailed to you and posted in your Skyward Family/Student Access)

Friday 2/9/2018

4.1-5.4 Test - Part 1 (will also serve as your in class Ch.4 Retest; administered during class or untimed before/after school on Friday) 

See the AB Practice Tests Tab for a study guide and preparation materials.

Wednesday 2/7/2018 - Thursday 2/8/2018

In class, we will have our AB share and Q&A for the Semester Final Exam.

4.1-5.4 Material on the 2008 AP Exam (in documents)

Perform detailed test correctionsusing: 4.1-5.4 Material on the 2008 AP Exam – Complete Solutions (in documents) / Alternate 2008 Multiple Choice Solutions Link

Tutorial Videos: 2008AB FRQ #2  2008AB FRQ #3 / 2008AB FRQ #6

Optional Resources4.1-5.4 Test Topics (in documents) / Table Problems /Graph of f, f’, or f’’ / Rate In/Rate Out Application Problems

Optional Resources4.1-5.4 Quiz #1 / 4.1-5.4 Quiz #1 Detailed Solutions (in documents; counts in place of any missing assignment) 

Tuesday 2/6/2018

5.3 Full Lecture with Professor Leonard

5.3 Notes - Derivatives of Inverses (in documents; make sure you understand the algebraic definition of an inverse AND memorize the derivative rule for an inverse; you are nearly guaranteed exactly 1 question involving inverses on the AP Exam in May)

Read 5.3.
5.3 (1, 3, 29, 31, 71, 73, 75, 81, 83)

5.3 MORE Complete Solutions (in Calculus Book Solutions)

Tutorial Videos:

5.3 - Derivatives of Inverses

5.3 Pre - Inverse Functions

Monday 2/5/2018

5.4 Notes - Exponential Functions Differentiation and Integration (in documents)

Start on slide 20 and go through the rest of the slides (USE SLIDESHOW!).  Work through the bellwork and examples with those around you.

5.4 Part 2 (99, 103, 107, 111, 115, 117, 119, 121, 127, 129, 135, 140)

5.4 Part 2 - MORE Complete Solutions (in Calculus Book Solutions)

Tutorial Videos:

5.4 Full Lecture with Professor Leonard

5.4 - Integration of Exponential Functions with Base e

Friday 2/2/2018

Check to see if your final was Form C or Form D.

Open the appropriate version of the solutions:

AB 1st Semester Final – Form C – Solutions and Scoring Rubric (in documents)

or

AB 1st Semester Final – Form D – Solutions and Scoring Rubric (in documents)

Perform detailed test correctionsas normal.

Even though you wouldn’t have to on an actual AP test, when doing test corrections force yourself to use accurate notation and calculus terminology at all times as you rework any problem you missed from scratch.

Also work through any problem you guessed on!  Aim to understand every problem inside and out.

Not satisfied with your score on the final?  Please consider utilizing the resources at the top of the page ("The AP Prep Quartet") extensively between now and May 15th.  May 15th is a long way away, but you can guarantee yourself a 3+ by putting enough time in mastering the relevant content AND test format.  On another note, I tend to grade harder than the actual College Board FRQ scorers, because I want your notation to ultimately meet a college standard AND an AP Exam standard.

Optional ResourcesTable Problems &Graph of f, f’, or f’ FRQs

Optional Resources:AP Exam Review - The Big TheoremsAP Exam Review - The Big Theorems - Expanded Multiple Choice SolutionsAP Exam Review - Just Mean Value Theorem / Big Theorem Tutorial Video Links: Intermediate Value Theorem / Mean Value Theorem / Rolle's Theorem / Extreme Value Theorem

Thursday 2/1/2018

5.4 Full Lecture with Professor Leonard

5.4 Notes - Exponential Functions Differentiation and Integration (in documents; today we won't go past slide 19)

Read 5.4.
5.4 Part 1 (1, 3, 13, 15, 17, 21, 25, 29, 31, 39-59(odd), 60, 63, 65, 69, 73)

5.4 Part 1 - MORE Complete Solutions (in Calculus Book Solutions)

Desmos Graphing Calculator Link

Tutorial Videos:

5.4 - Derivatives of Exponential Functions with Base e

5.4 Pre - Solving Exponential Equation

Wednesday 1/31/2018

5.1-5.2 Bellwork AND Solutions (in documents; two versions of solutions on last two pages)

5.1 and 5.2 Combined Assignment:
5.1 (47, 50, 53, 56, 60, 70, 76, 78, 81, 85, 102)
5.2 (5, 9, 12, 16, 23, 33, 39, 44, 53, 57)

5.1 and 5.2 Combined Assignment - MORE Complete Solutions (in Calculus Book Solutions)

Friday 1/26/2018 - Monday 1/29/2018

Semester Final Exam (administered during class)

Thursday 1/25/2018

5.1-5.2 Full Lecture with Professor Leonard

Read 5.2.

5.2 Notes - Integration Involving Natural Logarithmic Functions (in documents)

5.2 Part 1 (7, 15, 21, 23, 31, 36, 37, 43, 55)

5.2 MORE Complete Solutions - Part 1 (in Calculus Book Solutions)

Tutorial Videos:

5.2 - Integration Involving Natural Logarithmic Functions

5.2 Pre - Long Division of Polynomials

5.2 - Long Division Before Integration

4.2 Pre - Summation Notation

4.2-4.3 - Definite Integral Using Summation Notation

Wednesday 1/24/2018

2007AB FRQ #3 (just parts a-c) (in documents and will be distributed in class; scoring rubric and solutions on 2nd page; for more "Big Theorem" resources, access: AB Semester 1 Final - Study Guide / AB Practice Tests Tab)

Tutorial Videos:2007 AB FRQ #3 Video Solutions

5.1-5.2 Full Lecture with Professor Leonard

Read pg. 329, Example 6.  Seriously, read it!

5.1 Notes Part 2 - Logarithmic Differentiation (in documents)

5.1 Part 2 (65, 69, 71, 75, 77, 80, 83, 88, 89, 93, 101, 103)

5.1 MORE Complete Solutions – Part 2 (in Calculus Book Solutions)

Tutorial Videos:

Intermediate Value Theorem / Mean Value Theorem / Rolle's Theorem / Extreme Value Theorem

Second Fundamental Theorem of Calculus(Don't forget theCHAIN RULE VERSION!)

Fundamental Theorem of Calculus

5.1 - Logarithmic Differentiation - An Application of Implicit Differentiation

5.1 - Differentiation of Natural Logarithmic Functions

Tuesday 1/23/2018

5.1-5.2 Full Lecture with Professor Leonard

Read 5.1 and watch 5.1 review videos on logarithm properties as necessary!

5.1 Notes Part 1 - The Natural Logarithmic Function - Differentiation (in documents)

For the intensely curiousProof of Derivative of ln(x) Rule Video / Alternate Videos

5.1 Part 1 (7-10, 19-35 odd, 47, 49-52, 57, 59) - This is the first book assignment of 2nd semester (fresh start!), so aim to understand every step of every problem.  Come in before school, after school, or during in class Q&A sessions to get every question you have answered.

5.1 MORE Complete Solutions - Part 1 (in Calculus Book Solutions)

Tutorial Videos:

5.1 - Differentiation of Natural Logarithmic Functions

5.1 - Logarithmic Differentiation - An Application of Implicit Differentiation

5.1 Pre - Logarithm Properties

5.1 Pre - Solving Logarithmic Equations by Exponentiation

5.1 Pre - Solving Natural Logarithmic Equations by Exponentiation

Monday 1/22/2018

MCQ Practice for Semester Final (distributed in class and in documents)

I expect every student to try (and correct) at least 15 MCQs of their choice.

After that, do as littleor as muchadditional MCQ practice as you find appropriate to get ready for your final!

I will be available for MCQ Q&A before and after school all week.

Friday 1/19/2018

No official assignment for Friday, so that you can have more flexibility in choosing how to prepare for your Semester Final Exam.  

Finish missing work (accepted up to Thursday, January 25th).  Study for finals.

Optional:AB Semester 1 Final - Study Guide / MCQ Practice for Semester Final(in documents and linked here)

Optional:AP Exam Review - The Big Theorems (in documents; we haven't covered the material for MCQs 7 & 11 yet); AP Exam Review - The Big Theorems - Expanded Multiple Choice Solutions (in documents)

Optional:AP Exam Review - Just Mean Value Theorem (in documents)

Sources for MCQ & FRQ Practice: AB Practice Test Depot / AB FRQ Website / Youtube for FRQ Solutions / AB FRQ Problem Index / Table Problems / Graph of f, f’, or f'’

Thursday 1/18/2018

AP Calculus AB First Semester Review Notes PART 3 (distributed in class earlier and in documents) 

Correct with: AP Calculus AB First Semester Review Notes PART 3 - Detailed Solutions (in documents; 2012 AB FRQ #1Video Solution)

Your semester final is guaranteed to have a Table Problems FRQ (if you click the link, you will find FRQs, scoring rubrics, sample responses, and video solutions covering this topic).

Tutorial Videos included: Table Problems FRQs

Wednesday 1/17/2018 

Did you remember to do last night's reading assignment?ReadFRQ Instructions and Scoring Commentary(in documents or click the link)

Apply what you read last night while performing detailed test corrections and error analysis for your Chapter 4 Test (tests returned during class) using

Chapter 4 Test Form C - Solutions and Rubric(in documents).

After you finish your corrections, read through Chapter 4 Test Form C - Minimum Work Kid (MWK) Solution (in documents).

If you prefer a blank copy of the test to perform corrections or practice with: Chapter 4 Test Form C - Blank Copy (in documents)

Tuesday 1/16/2018

ReadFRQ Instructions and Scoring Commentary(in documents or click the link)

Semester Final Review Bellwork – Day 2 – FRQ Graph Problem (distributed in class and in documents, solutions begin on page 3)

AP Calculus First Semester Review Notes PART 2 – Graphical Analysis (distributed in class and in documents; solutions begin on page 2; 2012 AB FRQ #3 Video Solution

Your semester final is guaranteed to have a Graph of f, f’, or f’’ FRQ (if you click the link, you will find FRQs, scoring rubrics, sample responses, and video solutions covering this topic).

Tutorial Videos Included: Graph of f, f’, or f’’ FRQs

Friday 1/12/2018 - Monday 1/15/2018

AP Calculus AB First Semester Review Notes PART 1 (distributed in class and in documents)

Correct with: AP Calculus AB First Semester Review Notes PART 1 - Detailed Solutions (in documents)

Sources for MC & FRQ Practice: Semester Final Study Guide /AB Practice Test Depot / AB FRQ Website / Youtube for FRQ Solutions / AB FRQ Problem Index

Thursday 1/11/2018

Chapter 4 Test (administered during class; FRQ Topics: Table ProblemsGraph of f, f’, or f’’, and Applications).

Do not discuss the Chapter 4 Test until next Wednesday (when you will get your exams back).

Preparation materials: Ch.4 Quiz / Solutions.  Additional Ch.4 Practice Test / Solutions.

Wednesday 1/10/2018

4.6 Bellwork – Definite Integral Approximations When Given a Table of Values (distributed in class and in documents; solutions begin on the 2nd page) - I want your score: +__/7.

Self select 5+ from: Chapter 4 AB-BC Test Prep Questions 1-10 (in your textbook, pg. after 322 or click the link).

Correct with: Chapter 4 AB/BC Test Prep Questions - Complete Solutions (in Calculus Book Solutions)

Select problems you feel will be help you solidify your conceptual and procedural understanding of integration and integration applications.

Alternative Assignment:work through, score, and perform detailed corrections for 2+ FRQs: Table ProblemsGraph of f, f’, or f’’, and Applications.

Tuesday 1/9/2018

Chapter 4 Review – Part 2 -Self select 10+ problems from the Chapter 4 Review on pages 318-320 based on what you had difficulty with on the quiz, what you feel you need more practice with, or what you find interesting conceptually.

Problems from 55-84, 87-90, 61 and 63 would be good choices for many students.

Chapter 4 Review Complete Solutions (in Calculus Book Solutions)

Alternative Assignment:work through, score, and perform detailed corrections for 2+ FRQs: Table ProblemsGraph of f, f’, or f’’, and Applications.

Monday 1/8/2018

Chapter 4 Quiz #1 (distributed in class and in documents)

Score yourself (+___/28) and perform detailed quiz corrections (complete sentence(s) describing errors/stuck points required as always!) using: Chapter 4 Quiz #1 - Detailed Solutions and Scoring Rubric (in documents)

Additional optionalpractice test (you can work through this additional practice test and detailed corrections in place of 10 points of missing homework; just write the assignment names at the top of your test):

Chapter 4 Test Form AB (distributed in class and in documents; entirely optional; I will do a full Q&A Wednesday after school for this version of the exam.)

Chapter 4 Test Form AB - SOLUTIONS AND RUBRIC (in documents)

Friday 1/5/2018

4.6 Bellwork – Definite Integral Approximations (distributed in class and in documents)

Correct with: 4.6 Bellwork Solutions (distributed in class and in documents)

4.6 Classwork – Integral Approximations from a Table of Values (distributed in class and in documents; I want your score: +__/8)

Read 4.6.  IGNORE ALL REFERENCES TO SIMPSON'S RULE.

4.6 (5, 9, 13, 20, 40, 49a, 53) (Trapezoidal Rule Only, IGNORE ALL REFERENCES TO SIMPSON'S RULE!)

4.6 MORE Complete Solutions (in Calculus Book Solutions)

4.6 Notes - Trapezoidal Sum for Approximation of Definite Integrals (in documents)

Tutorial Videos (and other resources):

4.6 - Trapezoidal Sum

Table Problems FRQs / Graph of f, f’, or f’’ FRQs / Applications FRQs

Thursday 1/4/2018 

4.5Part 3 (81, 83, 85, 93, 95, 103, 104, 107, 117, 119)

Please change the limits of integration on 81, 83, and 85!

If you feel your learning targets are already met &/or are looking for more challenging problems, consider choosing problems from 4.5 (67-74).

Correct using: 4.5 MORE Complete Solutions - Part 3 (in Calculus Book Solutions) & 4.5 Complete Solutions (in Calculus Book Solutions)

4.5 AB Notes Day 4 - Integration of Even and Odd Functions (in documents)

Tutorial Videos: 

4.5 - Definite Integration using u-substitution

4.5 Pre (4.4) - Evaluating Simple Definite Integrals

4.5 - Definite Integrals of Even and Odd Functions

Khan Academy Adaptive Learning for 4.5

Wednesday 1/3/2018 

Reminder: if you turn in all of your homework for the semester (even late), I will raise your grade by one category.  For example, this would raise a B+ to an A-.  The last day to turn in late work is January 25th.  To be eligible for the curve on the Semester Final Exam, you must have all homework completed for the semester.

4.5 Bellwork - Day 3 (distributed in class and in documents; solutions in today's notes)

4.5 Classwork (distributed in class and in documents; answers on last two pages)

Correct using: 4.5 Classwork - Detailed Solutions (in documents)

4.5 AB Notes Day 3 - Integration of Even and Odd Functions (in documents)

Tutorial Videos:

4.5 - Definite Integrals of Even and Odd Functions

4.5 - Definite Integration using u substitution

Tuesday 1/2/2018

In class, we will review the Winter Break Practice Exam / Solutions.

Self select 10+ problems from the Chapter 4 Review (1-10, 13-16, 33-84, 87-90, Trapezoidal Sum Only: 91-94) on pages 318-320.

Chapter 4 Review Complete Solutions (in Calculus Book Solutions)

A bit lost?  Alternative assignment: Self select 10+ Video Problems with Chapter 4 Topics

Chapter 3 Retest Corrections & 3.7 Retest Corrections (retests returned in class; solutions emailed to you)

Tutorial Videos:

4.6 - Trapezoidal Rule

Saturday 12/16/2017 - Monday 1/1/2018

Winter Break AssignmentAB Winter Break Practice Exam - Instructions (linked here and distributed in class Thursday) /Solutions

I always suggest printing out all AP Practice Exam materials.  Covington Library gives each person 75 FREE pages of printing every week!

Friday 12/15/2017

4.5 AB Notes Day 2 - Integration by Substitution - Part 2 (in documents)

4.5 Part 2 (41, 51, 55, 60, 63-79(odd)) & Winter Break AssignmentSolutions

For 4.5 Part 2, you can either use formal u-substitution or informal u-substitution (see part of the notes posted in documents).

Correct using: 4.5 MORE Complete Solutions - Part 2 (in Calculus Book Solutions)

Tutorial Videos:

4.1 - Initial Value Problems - Solving Basic Differential Equations with an Initial Condition

4.5 - Definite Integration using u substitution

4.5 - Integration using u substitution

4.5 - Many u-substitution videos (scroll down for additional videos!)

4.5 - Integration by u-substitution - longer videos

4.5 Professor Leonard Lecture / Khan Academy / Patrick JMT / Krista King

Thursday 12/14/2017

Please see announcement at the top of the page about your Winter Break Assignment and my absence tomorrow.

Read using slideshow: 4.5 AB Notes Day 1 - Integration by Substitution (in documents)

Read 4.5.  Make sure every single example makes sense to you. 

If necessary, provide annotated examples from the homework problems in your notes for every property and situation you uncover in the reading, including reading the examples.

4.5 Part 1 (1-6, 13-37 every other odd (e.o.o), 48, 53)

Correct with: 4.5 MORE Complete Solutions - Part 1 (in Calculus Book Solutions)

If your work looks different than mine, critically examine every bit of your notation for errors.

NO SHORTCUTS! Go through the full u-substitution procedure for 13-37 e.o.o and 48/53.

1) Examine the integral and choose an appropriate u.

2) Find du.

2a) (Only for Definite Integrals) Find the limits of integration in the u-universe.  Find u(a) and u(b).

3) Substitute.  Now your integral should be in terms of u.

4) Evaluate the integral in the u-universe.

5) Don't forget to substitute back into the x-universe!

6) At step 4) OR step 5), you should check your result by differentiation.  If you are comfortable taking chain rule derivatives in your head, you could even perform this check mentally.

Tutorial videos:

4.5 - Integration using u substitution

4.5 - Definite Integration using u substitution

4.5 - Many u-substitution videos (scroll down for additional videos!) / 4.5 - Integration by u-substitution - longer videos

4.5 - Integration by u-substitution

4.5 Professor Leonard Lecture / Khan Academy / Patrick JMT / Krista King

Tuesday 12/12/2017 - Wednesday 12/13/2017 (Two Day Assignment)

Chapter 3 Retest & 3.7 Retest (administered during class; you could also take an un-timed retest before or after school at a later date).  All Chapter 3 homework must be complete to take a retest, as usual.

4.4 Day 3 Notes and Day 4 Notes - Fundamental Theorem of Calculus (in documents; you are responsible for all material up through slide 34)

This is part of your homework: Calculator Skills Required for the AP Calculus Exams (distributed in class and in documents; I want your score: +__/4).

4.4 Part 3 (107-110, 113-117)

4.4 MORE Complete Solutions - Part 3 (in Calculus Book Solutions)

Tutorial Videos:

4.4 - Evaluating a Definite Integral on a TI83/84

Solving an Equation on a TI83/84 - Intersect Method

Solving an Equation on a TI83/84 - Finding the Zeroes Method

2.1 - Evaluating a Derivative at a Point Using the nderiv Function on a TI-83/84

More exhaustive lecture on finding the average value of a function and the mean value theorem for integrals.

4.4 - Accumulation Functions

4.4 - Net Change Theorem

4.4 - AP Motion Problems - Particle Motion

4.4 – Net Change Theorem Application Problems

4.2-4.3 - Sigma (Summation) Notation - Basic

4.3 - Riemann Sum Connection to Definite Integrals

If you read 4.2, read 4.3, and watch some of those 4.2-4.3 videos linked above, you can get a basic idea of the connection between definite integrals and infinite sums.  All definite integrals can be re-written as sums...but Liebniz saved you from writing definite integrals in summation notation.

Monday 12/11/2017

1) Click the Link and follow the instructions in the document: Link

2) Follow the instructions.  Lots of clicking and saving.  If a link is broken, move on.

3) Read AB Winter Break Practice Exam - Instructions (in documents and will be distributed in class later this week).  That document outlines your assignment for Winter Break which includes multiple choice practice, FRQ practice, and serves as a practice version of your semester final (upcoming on Jan.26th/Jan.29th).

4) Did you read 4.4 yet?  Read 4.4!

5) 4.4 Part 2 (39, 45,47, 51, 56, 63, 66, 69, 77, 85, 87, 89, 99) - This is Monday's actual homework assignment!
To complete problems 77, 85, 87, 89, read pages 289-90 carefully.

4.4 MORE Complete Solutions - Part 2 (in Calculus Book Solutions)

4.4 Day 2 Notes - Fundamental Theorem of Calculus (in documents)

You may find the following videos helpful (each of which was found with a 5 second google/youtube search):

Simple example of finding the average value of a function.

Second fundamental theorem of calculus. Examples are towards the end.

Tutorial Videos:

4.4 - The SECOND Fundamental Theorem of Calculus / 4.4 - Average Value of a Function

4.4 - Accumulation Functions / 4.4 - Net Change Theorem

4.4 - AP Motion Problems - Particle Motion / 4.4 – Net Change Theorem Application Problems

Friday 12/8/2017

4.4 Day 1 Notes - Fundamental Theorem of Calculus (in documents)

4.4 Examples using PROPER FORMAT (distributed in class and in documents; use as templates to follow for the homework!)

Read 4.4.

4.4 Part 1 (1-23, 27-38)

4.4 MORE Complete Solutions - Part 1 (in Calculus Book Solutions)

Optional Notes: 4.4 - A Deeper Look Including Historical Background (in documents)

Tutorial Videos:

4.4 - Basic Definite Integrals

4.4 - Fundamental Theorem of Calculus

4.4 - Evaluating a Definite Integral on a TI83/84

4.4 - PROOF for the Fundamental Theorem of Calculus (for the curious student!)

4.4 Professor Leonard Lecture / Khan Academy / Patrick JMT / Krista King

Thursday 12/7/2017

4.2 Bellwork - Area Approximations (distributed in class and in documents; solutions on the 2nd page)

Then read: 4.3 Notes - Definite Integrals and Their Properties (in documents)

4.3 Bellwork - Part 2 - Graphical Aid(distributed in class and in documents)

Go back and read 4.2.  Seriously, read it! 

If you are reading a college level math textbook without taking notes (with annotations!), highlighting, and/or outlining, you are probably wasting time.

Then read 4.3. 

4.3 (19, 21, 27, 31, 33-34, 39, 43-44, 48-49, 52)

Tutorial Videos:

4.3 - Basic Integral Properties / 4.3 - Introduction to Definite Integrals

4.2-4.3 - Sigma (Summation) Notation - Basic / 4.3 - Riemann Sum Connection to Definite Integrals

4.2-4.3 Professor Leonard Lecture / 4.2-4.3 Khan Academy / 4.2-4.3 Patrick JMT /  4.2-4.3 Krista King

Supplemental - Annotating Math Lecture Notes

Wednesday 12/6/2017

Read: How Schools (K-12) Fail the Smartest Students

Consider Exploring BEFORE College: Why Do Students Switch Out of STEM Majors in College? / Link 2 / Link 3

4.2 Bellwork - Day 1 (in documents)

DO NOT USE calcchat or the answers in the back of your book today, because I modified the problems!
Use: 4.2 MORE Complete Solutions (in Calculus Book Solutions)

4.2 (33-36 LRAM & RRAM), (41-42 MRAM), (43-44 RRAM), (57 & 59 MRAM with 4 rectangles of equal width)

BEST DONE ON GRAPH PAPER!

LRAM = Left Riemann Sum, RRAM = Right Riemann Sum, MRAM = Midpoint Sum

4.2 Notes - Riemann Sums (in documents) 

Optional: Read 4.2.

Tutorial Videos:

4.2 - LRAM - Left Riemann Sum / 4.2 - RRAM - Right Riemann Sum

4.2 - MRAM - Midpoint Riemann Sum / 4.2 - Trapezoidal Sum

4.2-4.3 Professor Leonard Lecture / 4.2-4.3 Khan Academy / 4.2-4.3 Patrick JMT / 4.2-4.3 Krista King

Monday 12/4/2017 – Tuesday 12/5/2017 (Two Day Assignment)

Optional Reading/Exploration: How to Study for a College Math Test

Optional Reading/Exploration: How to Study Actively / How to Test & Quiz Yourself While Studying

Optional Reading/Exploration: How to Take Notes in a Math Class

Homework Part 1Chapter 3 Test & 3.7 Mini-TestDetailed Corrections

Perform detailed test correctionsusing: Chapter 3 Test Solutions and Scoring Rubrics(in documents; tutorial videos are linked for each problem)

&

3.7 Mini-Test - Form A - Solutions & Scoring Rubric (in documents)

Be prepared to AB share your detailed test corrections at the start of class Tuesday.

Homework Part 2Ch.3 Test - Optimization Problems Revisited (distributed in class and in documents)

Correct your initial work finding the primary equation using the solutions in Chapter 3 Test Solutions and Scoring Rubrics.  Confirm your final answers using DESMOS (graph your primary equation on DESMOS using an appropriate domain and look for that absolute extrema action).

NEWCh.3 Test - Optimization Problems Revisited - Solutions (in documents)

Homework Part 3Tuesday Homework

Option 1Chapter 3 Targeted Review - Find 1-2 problems from 3.1-3.9 and the chapter 3 review in the book like each problem you missed on the test OR covering the same topics as each problem you missed on the test, complete them, and score them. Calcchat, the complete solutions, and the MORE complete solutions for each section are excellent resources for review.

Option 2Create Your Own - Write a similar problem of your own for each one you missed.  Solve the problem.  Verify your solution.  Feel free to use DESMOS or other resources to verify your solutions!

Friday 12/1/2017

ReadMath Study Skills for College – BASIC (Just read it as an exploration of possible study strategies!)

4.1 Classwork - Rewrite and Integrate! (distributed in class and in documents)

4.1 Bellwork – Differentiation and Integration Warmup (distributed in class and in documents; get to memorizing!)

4.1 Part 2 (57-65 odd, 70, 71, 73, 76, 77)

Correct with: 4.1 MORE Complete Solutions - Part 2 (in Calculus Book Solutions) mmm...notation.

4.1 Notes - Part 2 - Basic Gravitational Motion (in documents)

Tutorial Videos:

4.1- Vertical Gravitational Motion Problems

4.1 - Basic Indefinite Integration

4.1 - An Introduction to Indefinite Integration

4.1 - Initial Value Problems - Solving Basic Differential Equations with an Initial Condition

4.1 Full Lectures / Professor Leonard Full Lecture

Thursday 11/30/2017

1) Please use SLIDESHOW!: Read 4.1 Notes - Antidifferentiation (in documents)

2) That wasn't so bad.  When starting out in Chapter 4, always take a derivative to check your anti-differentiation!  (Very enthusiastic video covering that ideaif you start that video, go ahead and finish it!  8 minutes of his sassiness won't kill you.  Some would call that a horrible math video, but if you went through the notes first, all of his sass should make sense.  I bet you can find way better math videos for 4.1 using appropriate search terms of your own!).

3) Next: Read 4.1. (seriously, read it!).

4) Now, explore some of these videos until you have your head wrapped around all of this new information: Introduction to the Antiderivative / Introduction to Indefinite Integration / Full Lectures / Professor Leonard Full Lecture

5) Whenever you are ready, start on: 4.1 Part 1 (17, 21, 27, 29, 35, 38, 41, 42, 45-47, 49) - Be brutal about correcting your notation errors!

Correct with: 4.1 MORE Complete Solutions - Part 1 (in Calculus Book Solutions) mmm...notation.

Tutorial Videos:

4.1 - Basic Indefinite Integration / Professor Leonard Full Lecture

4.1 - An Introduction to Indefinite Integration

4.1 - Initial Value Problems - Solving Basic Differential Equations with an Initial Condition

Tuesday 11/28/2017 - Wednesday 11/29/2017 (Two Day Assignment)

Chapter 3 Test (administered during class on Tuesday)

3.7 Test (administered during class on Wednesday)

2.6 & 3.7 - University Related Rates & Optimization Problems (distributed in class and in documents)

Correct with: 2.6 & 3.7 - University Problems - Solutions (in documents)

Optional - Explore the Source Links Below:

Stanford Math 41 Materials Link / UW Math 124 Final Exams Link / UW Math 124 Materials Link

Tutorial Videos:

3.7 - Cylinder Optimization

2.6 - Trig. Related Rates

2.6 - Cone Draining into Cylinder Video 1 / Video 2

3.7 - Sphere in a Cone

Monday 11/27/2017

Self select 5+ problems from Chapter 3 AB-BC Test Prep Questions (which start on the page after 246 in the physical textbook orjust click the hyperlink)

Correct with: Chapter 3 AB-BC Test Prep Questions - Complete Solutions (in Calculus Book Solutions)

Self select problems you feel will best help you meet the learning targets for Chapter 3 (which will of course be assessed on your Chapter 3 Test on Tuesday, 11/28/2017):

Chapter 3 Learning Targets (a.k.a. Study Guide)

Tuesday 11/21/2017 - Wednesday 11/22/2017

#11-#13 from Ch.3 Practice Test Walk-through (in documents; USE SLIDESHOW!)

#16 Tutorial Videos

Chapter 3 PRACTICE Test #2 - 2015 (distributed in class and in documents; this practice test is longer than the typical test for this chapter)

Perform detailed test corrections using: Chapter 3 PRACTICE Test #2 - Complete Solutions (in documents)

I also want your score: +___/34.

Read 3.9.

3.9 (1-6, 21-26, 43-48) - Use tangent line approximations if the differentials approach doesn't make sense to you!

3.9 Notes - Differentials and Tangent Line Approximation (in documents)

3.9 Supplemental Notes - Tangent Line Approximations (in documents)

Tutorial Videos:

3.9 - Tangent Line Approximation (don't forget your squiggle!)

3.9 Supplemental - Tangent Line Approximations on the AP Exam - Video 1 / Part 2

3.9 Supplemental - Tangent Line Approximations on the AP Exam - Video 2

Presentation on theme: "4.4 The Fundamental Theorem of Calculus"— Presentation transcript:

1 4.4 The Fundamental Theorem of Calculus

2

3

4

5 Evaluating a Definite Integral
Evaluate each definite integral.

6 A definite integral involving absolute value

7 Using the fundamental theorem to find area
Find the area of the region bounded by the graph , the x-axis, and the vertical lines x=0 and x=2.

8

9 Using Mean Value Theorem
Find the values of c guaranteed by the mean value theorem for integrals over the given interval.

10

11 Finding the Average Value of a Function
Find the average value of on the interval [1,4].

12 The Definite Integral as a Function
Evaluate the functionat

13

14 Using the Second Fundamental Theorem of Calculus

15 Using the Second Fundamental Theorem of Calculus
Find the derivative of


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