# 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 Materials**: **Study Guide** / **5.5, 5.6, & Motion Practice Test** / **Practice Test Solutions**

More Motion FRQ Practice: **FRQ Topic: Motion Problems**

**Professor Leonard Playlists**: **Calculus 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 Website** / **Cracking 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)

Perform**detailed test corrections**using:** 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 assignment**. **Friday** 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 corrections**on 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 Part**and/or **4.1-5.4 Test - Part 1 - Purple Part**as 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**

Perform**detailed test corrections**for 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 1****Detailed 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 corrections**using: **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**** Resources**: ** 4.1-5.4 Test Topics** (in documents) /

**/**

**Table Problems****/**

**Graph of f, f’, or f’’**

**Rate In/Rate Out Application Problems****Optional**** Resources**: **4.1-5.4 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 corrections**as 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**** Resources**: **Table Problems**** &****Graph of f, f’, or f’**** FRQs**

**Optional**** Resources:****AP Exam Review - The Big Theorems**; **AP Exam Review - The Big Theorems - Expanded Multiple Choice Solutions**, **AP 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 the**CHAIN 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 curious**: **Proof 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 little**or **as much**additional **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 #1****Video 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?** Read**:

**(in documents or click the**

**FRQ Instructions and Scoring Commentary****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**

**Read**: **FRQ 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 Problems**, **Graph 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 Problems**, **Graph 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 Problems**, **Graph 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 **optional**practice 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 **

**4.5****Part 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 Assignment**: **AB 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 Assignment** / **Solutions**

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 1**: **Chapter 3 Test** & **3.7 Mini-Test****Detailed Corrections**

Perform **detailed test corrections**using: **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 2**: **Ch.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).

**NEW**: **Ch.3 Test - Optimization Problems Revisited - Solutions** (in documents)

**Homework Part 3**: **Tuesday Homework**

**Option 1**: **Chapter 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 2**: **Create 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**

**Read**: **Math 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 idea****; **if 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 or**just 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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