The 3 Forms of the Pythagorean Theorem: youtu.be/u5dqIuw525M?t=29s and youtu.be/ewgTe9QGEAY

Principles of logarithms: youtu.be/Gn8wjz4Ci4k ,

The Volume Formulas: youtu.be/KbSBv4qyzV4

Principles of logarithms: youtu.be/Gn8wjz4Ci4k ,

The Volume Formulas: youtu.be/KbSBv4qyzV4

**EXTRA! EXTRA!**

As we move into final exam time, there are some topics you might want to review from pre-calculus or even geometry. We have discussed these in class. They can help you here and now and in the future in other math classes.

Here are some videos on a few of these topics:

The 3 Forms of the Pythagorean Theorem: youtu.be/u5dqIuw525M?t=29s and youtu.be/ewgTe9QGEAY

Principles of logarithms: youtu.be/Gn8wjz4Ci4k ,

The Volume Formulas: youtu.be/KbSBv4qyzV4

**Weeks 17, 18 (Expect a quiz at any time - Always have all required materials.)**

Apr 30 (Monday)

Apr 30 (Monday)

- Review General Integration and Integration by Mental Substitution
- Vote on day to take Integration Test (Wednesday or Thursday)

**May 1 (Tuesday)**

- Review Integration by Substitution

**May 2 (Wednesday)**

- Review Integration by Parts. Note the following: general_integral_forms.pdf and integration_practice_problems.pdf

**May 4, 2018 (Friday)**

- Integration Test: Standard Integration, Integration by substitution, Integration by parts, possibly some extra-credit.

**Following Days**: Continue review for final examHomework (dates shown are due dates, at the start of the period):

**Notes: Answers to Test on Setting-up Area Integrals: calculus_test_q3-2__wo_.pdf**

**Required Class Materials for the Spring Semester:**

- Spiral-bound full-size notebook dedicated to Calculus (homework, class notes are to entered in here in order, with dates, page numbers and problem numbers clearly indicated - dates at the top of each page, page numbers in the margin column on the left, problem numbers next to the problem, all key-steps shown as taught in class).
- 3-ring binder (at least 1/2"). Containing: Abundant supply of loose-leaf paper (preferably college-ruled); all handouts to-date; graphpaper
- 2 or more pencils, #2 lead, full-size OR mechanical pencil with #9 (preferable) or #7 lead
- good quality erasers
- ruler (inches and mm) at least 6 inches long
- graphing calculator acceptable for AP exams. [note: I will only give class demos for the TI84. If you have a different calculator, you will be responsible for mastering its usage yourself.]
- These supplies must be available every math class of the semester.

**you will receive an F for every time that we check and you do not have these supplies with you**.

**IMPORTANT!!**

Expect a

__timed__quiz

*on your ability to differentiate*

**at any time**__all__important functions and function forms. In other words (using differentials):

Click for a list of the differential rules you will need to know:

This will be a regular occurence.

**The latest score will negate all previous scores -- for better or worse**.

**Weeks 15, 16 (Expect a quiz at any time - Always have all required materials.)**

Apr 16 & 18 (Monday & Wednesday)

Apr 16 & 18 (Monday & Wednesday)

- Short classes. We will work around fieldtrips, absences, etc. The goal is a test on Thursday covering Summation and Taylor Series

**Apr 19, 20, 2018 (Thursday, Friday)**

- [Make-up test for those absent last week was
*moved to Thursday April 26*]. Integration by parts, summation expansions. p. 354: 1 - 14

**Apr 23 & 25, 2018 (Monday & Wednesday)**

- Integration by parts discussed and practiced,

**Apr 26, 2018 (Thursday)**

- Make-up last exam during class
- Other students will work on Reading Mathematical Instructions (Tabular Integration & Inverse Trig & Log Functions, p. 353) : practice problems p. 354: 11-14; p. 355: 17-24

**Apr 27, 2018 (Friday)**

- Apr 27, 2018 (Friday)
- Make up exam for students still needing to take it.
- Other students will continue Tabular Integration & Inverse Trig & Log Functions

**Week 14 (Expect a quiz at any time - Always have all required materials.)**

Apr 9, 2018 (Monday)

Apr 9, 2018 (Monday)

- In-class/homework: Summation Notation & Binomial Expansion (Read and Study the problems Classwork & Homework for_calculus in groups of 1 or 2 tables apiece), then try the problems in-class and at home.

**Apr 10 - 12, 2018 (Tuesday - Thursday)**

- Practice as necessary for Friday's exam - expect quizzes.

**Apr 13, 2018 (Friday)**

*Tests (AB & BC)*: Shared topics/different emphasis. AB will be tested primarily on comprehension of summation notation; BC on Taylor and Maclaurin Series.

**Week 13 (Expect a quiz at any time - Always have all required materials.)**

Apr 2, 2018 (Monday)

Apr 2, 2018 (Monday)

- In-class/homework: Summation Notation -- Review and quiz on expansion by terms

**Apr 3, 2018 (Tuesday)**

- Return and discuss quizzes.
- First official Taylor Series Expansion.
- Homework for Thursday and class study: p. 500: Section 10.2 Exercises: 1 - 20.

**Apr 4 & 5, 2018 (Wednesday & Thursday)**

- Class discussion of study problems (student initiated)
- Discussion of summation processes

**Apr 6, 2018 (Friday)**

- Summation techniques
- Parsing the Taylor Series. "When is x not x"?

**Week 12 (Expect a quiz at any time - Always have all required materials.)**

Mar 26, 2018 (Monday)

Mar 26, 2018 (Monday)

- In-class/homework: Integration by Substitution -- p. 346: 1 - 23 (odd). Mental "Integration by Substitution"
- Initial Quiz on basics

**Mar 27 & 28, 2018 (Tuesday & Wednesday)**

- Class discussion - questions answered - students present solutions: basic integration - one step substitution.
- Introduction to Summation Notation, Arithmetic and Geometric Series

**Mar 29, 2018 (Thursday)**

- General Review
- Development of Taylor Series and Maclaurin Series

**Mar 30, 2018 (Friday)**

- Comparison of circumstances warranting "Mental Integration by Substitution" - continue examining problems on pp. 346,7
- More on Taylor Series and Maclaurin Series

**Week 11 (Expect a quiz at any time - Always have all required materials.)**

Mar 12, 2018 (Monday)

Mar 12, 2018 (Monday)

- Review past weeks Unit Test

**Mar 13, 2018 (Tuesday)**

- Study Multiple Choice questions from last year's AB AP Exam. Work on vocabulary and understanding of arithmetic and geometric series (Section 10.1 from the text.)

**Mar 14, 2018 (Wednesday)**

- In-class: Read and discuss beginning of section 10.1 for "applied vocabulary" development. Homework: Continue reading section 10.1

**Mar 15, 2018 (Thursday)**

- Read pp. 480-487. Try p. 489: 1 - 10

**Mar 16, 2018 (Friday)**

- Discuss homework
- Quiz?

**Week 10 (Expect a quiz at any time - Always have all required materials.)**

Mar 5, 2018 (Monday)

Mar 5, 2018 (Monday)

- General summary of Unit 3 Topics

**Mar 6, 2018 (Tuesday) - Election Day - No School**

Mar 7, 2018 (Wednesday)

Mar 7, 2018 (Wednesday)

- Review for Unit 3 Test (Volume & Integration and other topics)

**Mar 8, 2018 (Thursday)**

- Continue reading 10.1 Classwork/Homework: Do p. 489: 1 - 10.

**Mar 9, 2018 (Friday)**

- Unit 3 Test

**You should be studying the following rules for differentiation -- print out and bring to class (click on file):**Differential Rules.pdf

Week 9 (Expect a quiz at any time.)

**Feb 26, 2018 (Monday)**

- Basic Forms of Integration (discussion of which forms should be memorized)
- Visual u-substitution strategy

**Feb 27, 2018 (Tuesday)**

- Practice using visual u-substitution. The following problems will provide good practice: Basic forms for indefinite integration.pdf
- Discussion of the test (slight)

**Feb 28, 2018 (Wednesday)**

- Classwork/homework: problems from worksheet above
- Classwork/homework: We will also cover these problems tomorrow and Friday: volumes_of_rotation.pdf

**Mar 1, 2018 (Thursday)**

- Homework Discussion
- More on Volumes: Set up integrals to find volumes using "cross-sections": p. 414: Section 8.3: 1, 2

**Mar 2, 2018 (Friday)**

- You will need 2 differently colored pencils (red, orange, blue, green -- colors that contrast well and will stand out on graph paper), calculator you plan to use on AP exam [Note: this will continue for now into the indefinite future.]

**You should be studying the following rules for differentiation -- print out and bring to class (click on file):**Differential Rules.pdf

**Week 8 (Expect a quiz at any time.)**

Feb 20, 2018 (Tuesday)

Feb 20, 2018 (Tuesday)

- Discussion of the re-test (worked out version of the re-test)

**Feb 21, 2018 (Wednesday)**

- Finding and evaluating integrals practice
- Set up integrals to find the areas (but do not integrate): pp. 402, 3: 1 - 6, 9 - 14, 15 - 27, 35, 37, 38

**Feb 22, 2018 (Thursday)**

- Homework Problem Discussion

**Feb 23, 2018 (Friday)**

- Test based on this week's homework

**You should be studying the following rules for differentiation -- print out and bring to class (click on file):**Differential Rules.pdf

**Week 7 (Expect a quiz at any time.)**

Feb 12, 2018 (Monday)

Feb 12, 2018 (Monday)

- Discussion of the
**Towing Project** - Intuition understanding of velocity equation basic on examination of the equation.

**Feb 13, 2018 (Tuesday)**

- Review of Differentiation: ln u, e^u, product review, quotient rule (intuitive development)
- Discussion of Problem 3 on Volumes of Rotation homework

**Feb 14, 2018 (Wednesday)**

- Review of Integration
- Questions from homework
- Homework: Study calculus test (differentials and related rates).pdf for tomorrow's retake.

**Feb 15, 2018 (Thursday)**

- Open discussion
- Remember!

- Re-take of Test (Differentials, Related Rates)
**in class**. __Bring your math journal____Have your old test with you__

**Feb 16, 2018 (Friday)**

- Integration by substitution

**Week 6 (Expect a quiz at any time.)**

**Feb 5, 2018 (Monday)**

- Differentiation review: Constant, Coefficient, Power of a Variable, Sum/Difference
- Setting up Area Integrals

**Feb 6, 2018 (Tuesday)**

- Differentiation review: Trig Functions, Chain Rule
- Setting up Area Integrals
- Work the problems: areas_homework_2.pdf
- Print out and bring to class on Wednesday: rotated_areas.pdf

**Feb 7, 2018 (Wednesday)**

- Differentiation review: Product Rule, Chain Rule
- Setting up Area and Volume-of-Rotation Integrals

**Feb 8, 2018 (Thursday)**

- Differentiation review: Quotient Rule, Chain Rule
- Setting up Area and Volume-of-Rotation Integrals

**Feb 9, 2018 (Friday)**

- Differentiation review: Exponential Rules, Chain Rule
- Setting up Area and Volume-of-Rotation Integrals

**--- ALWAYS EXPECT A QUIZ ---**

Week 3

Jan 22, 2018 (Monday)

Week 3

Jan 22, 2018 (Monday)

- Materials Check!
- Read and study:
*Section 6.1*"Estimating with Finite Sums" - pp. 277, 8: 1 - 17
- Review: Graphs of parabolas

**Jan. 23, 2018 (Tuesday)**

- Review: "Completing the Square", Graphs of circles, ellipses, hyperbolas
- Discuss
*Section 6.1*

**Jan. 24, 2018 (Wednesday)**

- Discuss problem set from
*Section 6.1*

**Jan. 25, 2018 (Thursday)**

- Questions from class
- Read and discuss in class: Section 6.2. Definite Integrals
- pp.291, 2: 1 - 6; 7 - 35 (odd) [due Tuesday]

**Jan. 26, 2018 (Friday)**

- Questions from class

**Jan 4, 2018 (Thursday)**

- p. 231: 11, 13, 15, 16, 32

**Jan 9, 2018 (**

**Tuesday)**

- p. 247: 2 - 8 (in-class, as much as possible)

**Jan 10, 2018 (Wednesday)**

- Discussion of problems from class
- pp. 257 - 261: 5, 7, 9, 11, 13, 16, 18, 19, 22, 25

**Jan 11, 2018 (Thursday)**

Expect a

__timed__quiz

*on your ability to differentiate*

**at any time**__all__important functions and function forms. In other words:

- constant rule (cf)' = cf'
- variable-to-a-constant-power rule: d(x^n)/dx = nx^(n-1)
- sum/difference rule: (f + g)' = f'' + g'
- product rule: (uv)' = u'v + uv'
- quotient rule: (u/v)' = (vu' - v'u) / v^2;
- (sin u)' = (cos u) u'
- (cos u)' = -(sin u) u'
- (tan u)' = (sec^2 u) u'
- (sec u)' = (sec u)(tan u) u'
- e-to-a-power rule: (e^u)' = u'(e^u)
- natural-log rule: (ln u)' = (1/u) u'

**The latest score will negate all previous scores -- for better or worse**.

**Project:**

p. 258: 21 (Work both a and b, then revisit the problem as follows.)

It is winter and the pond has frozen into an almost frictionless sheet of ice.

(c) How fast will the boat be approaching the dock when 8 feet of rope is out (from boat to ring)? Justify your answer. Draw your idea of the shape of the rope from the boat to the ring on the dock.

(d) According to calculus, how fast will the boat be moving when the angle shown equals 0 degrees? How fast, according to reality?

(e) At home, try a similar experiment as follows:

You need:

- a heavy skillet
- a towel
- a strong thick piece of twine (or thin piece of rope) about 12 feet (4 meters) long
- a chair or stool you can stand on.
- two observers (or a video camera).

- Place the skillet on a towel on the floor about 6 feet (2 meters) away from the chair so that the pan's handle is pointing at the chair.
- Tie a string to the handle (it should have a convenient hole through which you can do this).
- Position one observer on the right of the chair and one on the left.
- You assignment is to put the string at a constant pace toward you. You need to do this fast enough that you feel the resistance of the pan, but not too fast. Make sure your pulling hand(s) extend beyond the edge of the chair. Be careful about maintaining your balance throughout. If it appears unsafe, try doing the same thing either standing on a low step-stool or just standing with your feet making a bridge to the left and right. BE SAFE!
- One observer will be given the assignment of announcing the precise moment the string is vertical. The other observer has the assignment of observing anything unusual about the pan. [One video will accomplish the same task if it is focused on the point directly below your hands.

Consider trying the same experiment with a lightweight toy car being dragged toward you in a similar way, except without the towel.

MID-TERM EXAM:

Because calculus is a building topic, Chapter 5 mastery will represent about 80% of first semester mastery.

Additional Topics: (Almost 20%)

Problems testing higher order thinking:

Because calculus is a building topic, Chapter 5 mastery will represent about 80% of first semester mastery.

- For that reason,
. [We will finish the chapter at the start of the next semester.]**about 80% of the mid-term exam will be derived from sections 5.1 through 5.4** - In other words,
.*our current homework and practice problems will constitute an almost full review for the mid-term exam*

Additional Topics: (Almost 20%)

- Limits: practice p. 97: 1-20 (any problem with a gray background).
- Derivatives:
- Be able to find the derivative of a function using the definitions on page 101 and 102. Good practice: p. 107: 1-12
**Know**the differentiation rules 1 - 7: p. 118 - 124;**Know**the differentiation rules for sin, cos, tan, sec, csc, cot. These are on p. 144 and 146.**Know**the chain rule and how to apply it (Rule 8 on page 156).**Know**the differentiation rules for e^u and ln(u). Shown on p. 180 and p. 182.

- Be able to find the equation of a line using the point-slope equation of page 5.

Problems testing higher order thinking:

- There will be at least one or two problems within the exam that tests higher order thinking. Such a problem requires you to solve an unfamiliar problem using a combination of any of the topics reviewed above or covered as part of our current chapter.

CALCULUS AB (BC review the following and be responsible for understanding):

Monday (Nov 27) to Friday (Dec 1): Continuing Chapter 5:

By Thursday, you should have accomplished the following:

On p. 214, read and learn the "Concavity Test" and the Definition of "Point of Inflection". These topics and their applications will be discussed in class based on student interest and queries.

Your goal is to be able to master the following

On Friday, we will consolidate and discuss the above.

EXPECT 2-3 QUIZZES. These will be both review quizzes on any topic from the first quarter and quizzes on current topics.

CALCULUS BC:

Monday (Nov 27) to Friday (Dec 1): Continuing Chapter 5:

By Thursday, you should have accomplished the following:

On p. 214, read and learn the "Concavity Test" and the Definition of "Point of Inflection". These topics and their applications will be discussed in class based on student interest and queries.

Your goal is to be able to master the following

__assigned problems__:- p. 220: 3, 5, 7, 9, 13, 15, 17, 21 - 29 (odd), 30, 31, 33, 35, 39, 41, 45, 47.
- p. 231: 1a, 1b, 2, 3, 5, 6, 7, 9, 12

On Friday, we will consolidate and discuss the above.

EXPECT 2-3 QUIZZES. These will be both review quizzes on any topic from the first quarter and quizzes on current topics.

CALCULUS BC:

- Be able to do above AB work, for which you will share mastery responsibility with AB students.
- Self-study: Section 5.5: Read and practice for understanding. We will discuss as time allows.
- Self-test with following problems: pp. 246, 7: 1 - 19 (odd), 23 - 26, 31

calculus_test_q2-2_wo.pdf | |

File Size: | 221 kb |

File Type: |

**This week we will focus on maxima, minima, inflection points**

Thursday or Friday, Nov 16 or17: Test on one of these two days

- Above is the test worked out.

- Do Now
- Questions from class about 5.2 Exercises

- See worked-out quiz using the link above.
- Decision on test day
- Questions from class on problem set from §5.2 (Monday)
- Classwork/Homework: Continue working on Monday's assignment

quiz_2_worked_out.pdf | |

File Size: | 130 kb |

File Type: |

Monday, Nov 13: §5.2 cont'd

- Do Now
- Questions from class about §5.1 problems
- Expect a 1-problem quiz on §5.1 [Worked out above]
- Classwork/Homework: pp. 208, 9: *1, 3, 5, 7, *9, 10, *11,12, *15, 17, 19, 21 [Starred problems will be worked in class, if there is sufficient time.]

Thursday, Friday, Nov 9,10: §5.3

Tuesday, Wednesday, Nov 7, 8: §5.2 cont'd

Monday, Nov 6:

- Q&A
- pp. 220,221: 1-19 (odd); 21, 25, 29, 31, 32, 33, 35, 37, 39, 41, 46-48

Tuesday, Wednesday, Nov 7, 8: §5.2 cont'd

- Q&A on §5.1 and §5.2
- pp. 200,201: 5-10, 11, 13, 14, 15, 31, 41
- pp. 208,9: 3, 4, 7, 9, 11, 12, 15, 17, 19, 21, 23, 25

Monday, Nov 6:

- Mean Value Theorem for Derivatives
- Definitions: Increasing, Decreasing Functions

Friday, Nov 3: §5.2

- Do Now
- Discussion regarding test

Thursday, Nov 2: §5.1

- Review of Differentiation (work in groups): pp. 189, 190: 5, 9, 13, 21, 29, 31-34, 35, 37, 39, 41, 43 (Find the pattern!), 53, 54, 57, 59 - 65
- Homework (due Friday): Finish problems left from previous night

Wednesday, Nov 1: §5.1

- In-class: Discussion of problems on pp. 200, 201
- Read/discuss selected problems, examples
- Homework (due Friday): pp. 200, 201: Exercises 4.4: 5, 7, 9, 11, 12, 15, 27, 29, 31, 35, 37, 41, 43, 44

Tuesday, Oct 31: §5.1

In-class: Introduction to Extreme Values of Functions

Read/discuss examples in §4.3.

Homework: none

In-class: Introduction to Extreme Values of Functions

Read/discuss examples in §4.3.

Homework: none

Monday, Oct 30: Small Test

You will need:

You will need:

- pencils (mechanical pencils are highly recommended).
**(No work in pen!)** - eraser(s)
- loose-leaf paper
**(I will not accept raggedy-edge paper)**.

Below is a copy of this test that has been worked out for you to look at.

calculus_test_q2-1_worked_out.docx | |

File Size: | 98 kb |

File Type: | docx |

Friday, Oct 27:

- Open discussion of §4.4
- Review of all topics: p. 189: Review Exercises

Thursday, Oct 26: More on §4.3

- Open discussion on differentiation of (and understanding of) inverse trigonometric functions
- Review of key trigonometry identities
- Graph techniques for translating and understanding trigonometric relationships using a non-unit circle (to avoid fractions)
- Homework: Read §4.4 and bring your questions with you to class

Wednesday, Oct 25: §4.3, §4.4

- In-class: Limited open discussion on Monday's and/or Tuesday's assignments.

- Read/discuss examples in §4.4.

- Homework (due Friday): pp. 186,7: Exercises 4.4: Choose 1 from #29-32; 1 from #33-36; 1 from #37-42, 43-48

Tuesday, Oct 24: §4.3

In-class: Limited open discussion on Monday's assignment.

Read/discuss examples in §4.3.

Homework (cont'd for Wednesday): p. 178. §4.3 Exercises: select from 1-26; select from 27-29

In-class: Limited open discussion on Monday's assignment.

Read/discuss examples in §4.3.

Homework (cont'd for Wednesday): p. 178. §4.3 Exercises: select from 1-26; select from 27-29

Monday, Oct 23: §4.2

In-class: Read/discuss examples in §4.2.

Homework (due Wednesday): p. 170, §4.2: Choose from 1-42

In-class: Read/discuss examples in §4.2.

Homework (due Wednesday): p. 170, §4.2: Choose from 1-42

**Quarter 2,**

Oct 16 - 20, 2017

We covered strategies using the

**chain rule**to solve problems from pp. 160, 161: §4.1: 3, 5, 13, 16, 23, 38, 46, 50