# Calculus (AP Math BC) 2016-2017

## Pointer to:

• Kwikis (just below current homework)

## BC Exam Preparation

Here are pointers to important information about the BC Exam from the College Board:

You should take the time to read each of them.

## Assignments

### Calculus Homework

Homework Sources:

Next BC Prep Quiz: Mon April 24

Final Exams: Wed 4/26 and Thu 4/27 (Details coming)

Due Date Assignment
Tue 1/3
WeBWork: WinterBreak-2016

Wed 1/4
* Finish ladder problem. Kwiki 19065

* Start your journal. Each day spend a few minutes summarizing the concepts we worked on in class and in the homework. You might use the journal to ask yourself questions on concepts. For example, when finding volumes of revolution when is it better to use shells than to use washers?

* (Optional: You might want to review volume by shells by actively watching MIT Volume of revolution via shells.)

Thu 1/5
* Carefully read HWS Integration by Parts Introduction
* Use Integration by Parts on $\int x e^{-x} \, dx$ Be sure to check your answer.

* TurnIn: A second draft of the appraoch and solution sections of either question 2 (Ladder Problem) or question 4 (Volume of Intersecting Cylinders using rectangular shells) from Kwiki 19066.
(Note: You will be doing more work on this writing assignment for Friday.)

Fri 1/6
* Determining $$u$$ and $$dv$$ takes some practice. Actively watch MIT Integration by parts 1
* Finish Kwiki 19067 — (but don’t look up answers and/or solutions)
* TurnIn: A third draft of the complete write-up (all four sections and a title) you started yesterday.

Mon 1/9
* WeBWorK bic_spring_misc_01
— Note: Only two tries on matching question.
* Finish Napkin Ring Problem from Kwiki 19068
* Remember, your journal should include an entry after each class

Tue 1/10
* Be prepared (as a group) to put any of the volume problems from today’s Kwiki on the board.

* Work on Particle, the dog (question 3 of the Kwiki).
* TurnIn: A brief second draft of a write-up of your approach and solution sections for part (a) of the Particle, the dog question
— Find an equation for a function, $$P(x)$$ that takes the owner’s $$x$$ value and produces the distance Particle has traveled along the sine curve since starting at the origin. Be sure to explain how you developed $$dP$$, a distance element.
Hint: You will ultimately need to use a calulator to get values for $$P(x)$$ other than $$P(0)$$.
Note: If you do not have an equation for $$P(x)$$, write question where the answer to that question would help you get closer to a equation for $$P(x)$$. Explain how the answer would help you.

Wed 1/11
* Test
* Update your journal, print it, and bring it to class.

Thu 1/12
* The distance Particle, the Dog travels along a curve is called arc length.
Compute the length of the curve $y=x^{3/2} \, \, \text{ for } \,\, x \in [0,4]$
* Actively watch MIT arclength
* Put comments on arc length into your journal. (In preparation for the next test, be sure to start a new page in your journal for this entry.)

Fri 1/13
* TurnIn: Demonstrate at least two methods to evaluate $\int \cos^2 x \, dx$

* Update your journal with at least three things you learned from taking Wednesdays’s test, working with your group on the redux, and going over questions on the with the class.

Tue 1/17
* Work on problems 4-7 on the extended kwiki 19071
* Prepare short write-ups of two problems (4 or 7) and (5 or 6).
* TurnIn: Two second draft problem write-ups, each should be on its own page. Each should fit on a single side.

Wed 1/18
* Read about pumping liquids and pulling up a rope using work elements Penn work element
* WeBWorK Work-bic-1

Thu 1/19
* Background on partial fractions can be found in HWS Partial Fractions
* WeBWorK partial-fractions-1
* Be sure you are caught up on previous WeBWorK

Fri 1/20
* Do Revisiting Integrals worksheet

Mon 1/23
* Finish Kwiki 19076-with-Homework. Note that there is a third section that contains some homework questions.

Revisiting Integrals in light of doing the kwiki in class. Explain why $$f(x)$$ needs to be invertible on $$[a,b]$$ both from a geometric and algebraic point of view.
— Question 6 on $\displaystyle \int_0^\infty f(x) \,dx$

Tue 1/24
* Actively watch MIT Improper Integrals video
* WeBWorK Improper-bic

Wed 1/25
* Test
* New (or revisited) topics:
— partial fractions
— Riemann Sums
— probability
— work
— improper integrals

* Journals:
— Make sure you have comments on Revisiting Integrals
TurnIn: Last two weeks of your journal.

Thu 1/26
* WeBWorK Misc_Set_04
* Put in a pagebreak and Update your journal.

Mon 1/30
* WeBWorK Misc_Set_05
* Be sure to finish all open WebWork before it closes Sunday night (01/30/2017 at 12:01am).

Tue 1/31
* Polar Coordinates:
— Do sec 10.1 #1,3,5,9,12,13,21

* Improper Integrals Resources:
HWC Improper Integral notes
MIT Improper Integrals video

Wed 2/1
* Polar derivatives:
— Do 10.2 #1, 2, 3, 7, 8

* Improper Integrals: Be prepared to go work with your group to present solutions and comments on questions 2-5 on yesterday’s kwiki 19079.

Thu 2/2
* Polar area:
— Do 10.3 #12, 21
— Finish #6 on Kwiki 19081

— improper integrals
— polar area

Fri 2/3
Parametric Curves:
* WeBWorK parametric-intro
* Be sure you understand question 2(a) on Kwiki 19082
— See Building a cycloid mathlet
* Explore graphing parametric curves using the Desmos Graphing Calculator.

Mon 2/6
* Finish WeBWorK parametric-intro by midnight Saturday. You can look at solutions starting on Sunday
* WeBWorK parametric-bic-ii
TurnIn Solution to problem 6. Use Desmos Graphing Calculator to create a graph of your solution.

Tue 2/7 * TurnIn: A complete, typed write-up of the Coin Toss Problem.
– Be sure to address the questions in today’s DoNow

* Work on the Nail Drop Problem
– See Nail Drop Demo
– Think about how you would model the sample space.

Wed 2/8
* Test
TurnIn: Last two weeks of your journal.

Fri 2/10
* TurnIn: Second Draft of Clara - Cowculus
Note: You will be turning in at least one more revision next week.

Mon 2/13
* TurnIn: A third draft of Clara - Cowculus
— The key question is the area of the grazing region. You should be able to set-up the area elements (yes, plural) and integrals.
— After doing that, you can focus on evaluating the integrals or focus on making an interesting Desmos Graphing Calculator dynamic diagram.
— My Moving Cycloid is a working example of a dynamic diagram which contains some comments on how I put it together.

Tue 2/14
* Watch Khan– Differential Equation Introduction
* Actively watch Khan– Finding a particular linear solution to a DE
* WeBWorK DiffEQ_01_bic (no reopens)

Wed 2/15
* Review Solutions to WeBWorK DiffEQ_01_bic
* More on slope fields:
Khan– Creating a slope field
Khan– Slope field to visualize solutions
Khan– Matching Differential Equations and slope fileds

* Sequences:
— Read Intro to Sequences 11-1
— Do section 11-1 #1-6

Thu 2/16
* Actively watch Khan– Intro Separable DEs
* WeBWorK DiffEQ_02_bic

* Update your journal with comments on separable DEs, converging geometric series

Fri 2/17
* Sequences:
— Reread Intro to Sequences 11-1
— Be able to explain: “If a sequence is bounded and monotonic then it converges”
— Be able to explain: Example 11.1.15.
* Series:
— Read Intro to Series 11-2
— Do section 11-2 #1-5

Tue 2/21
* Actively watch MIT Integral test
* Reread Integral Test and do:
— section 11-3 #5,6,9

* Update your journal in preparation for Wednesday’s test.

Wed 2/22
* Test
TurnIn: Last two weeks of your journal.

Fri 2/24
Taylor polynomials are polynomials that can approximate functions where the value of function and the values of all of the derivatives are known for some point $$(a, f(a))$$. For now let’s assume $$a$$ is zero. In this case $$p_1(x)=1+f'(0)x$$, our good friend, the tangent in Taylor form. A key idea is that the derivatives of $$f(x)$$ and $$p_n(x)$$ take on the same values at $$x=a$$. The phrase Maclaurin polynomial is used to indicate a Taylor polynomial where $$a = 0$$, (we know “all about” $$(0,f(0)$$)

* Actively watch Khan– Intro Taylor and Maclaurin Polynomials – Part 1
* Do Kwiki 19085 question 3.
* Develop an $$11^{th}$$ degree Taylor polynomial for $$f(x)=\sin(x)$$ at $$a=0$$.

* Try out your polynomials on Desmos:
— [Desmos — first three Taylor polynomials of f(x)=e^x]
— [Desmos — Starting Taylor polynomials of f(x)=sin(x)]

TurnIn: The journal entry you make on this homework assignment summarizing what your understanding of Taylor polynomials.

Mon 2/27
* WeBWorK seq_series_03-bic
* Whitman 11-3 11-4 read and do:
— section 11-3 #5,6,9
— section 11-4 #1-5 (all)

* Explore An Alternating Series:
— You can build up points using Demos Start Alternating Series v1
— The first 100 points are plotted at Demos Alternating Harmonic Demo

Tue 2/28
Whitman 11-5 Comparison Tests #1-4 (all)
Whitman 11-7 Ratio Test #1-3 (all)
* Actively watch MIT Intro Ratio Test
* Finish Kwiki 19093

Wed 3/1
Whitman 11-6 Absolute Convergence #1-7 (odd)
Whitman 11-8 Power Series #1,2,3
* Actively Watch: MIT Radius of Convergence

Thu 3/2
Whitman 11-9 Calculus with Power Series #1-5 (all)
* Actively Watch: MIT Taylor Series of a polynomial

Fri 3/3
* Actively Watch: MIT Comparison Tests
* WeBWorK Power-Series-bic

Mon 3/6
* Do questions 6, 7, 8 on the back of today’s kwiki (19097).
* I’ve reopened WeBWorK Power-Series-bic
* Read Tips on Using Tests of Convergence
* TurnIn convergence-tests-worksheet

Tue 3/7
TurnIn: A unit circle ($$C_1$$) fits snuggly into a 2 by 2 square. Find the radius of the largest circle ($$C_2$$) that fits snuggly in the region of the lower left hand corner of the square outside the unit circle.
* Spend 30 minutes on this problem. (Start by sketching a good diagram.)
* Spend 5 minutes planning an organized write-up. You might not have a complete solution, but you should have things to say about the problem.
* Spend 15 minutes writing (it need not be typed, but you will be turning in a revision on Thursday) an organized Four Sections write-up.

Wed 3/8
* Test
TurnIn: Last two weeks of your journal.

Thu 3/9
TurnIn: a full write-up to the Snuggly Circle problem.

Fri 3/10
* Actively Watch MIT Graphing DE with IVC
* Assume the power series $p(x)=x-4 x^3+16 x^5-64 x^7+256x^9+...$ is a Maclaurin series for some function $$f(x)$$. Write an equation for $$f(x)$$.

Mon 3/13
* Turn-in: Bacteria Growth Problem

Tue 3/14
* The MAA Mean Policeman is a fun introduction to the Mean Value Theorem from the 1960’s.
* Watch Khan– Mean Value Theorem

* Update your journal on MVT

Wed 3/15
* WeBWorK MVT-intro (Just one problem)
* Watch Five Unusual Proofs. Put comments on the video in your journal

Thu 3/16
* Finish both sides of Kwiki 19103
* WeBWorK DiffEQ_06_bic

Fri 3/17
* Actively watch Khan– Intro Eulers Method
* (Today’s Slides on Eulers Method can be reviewed.)
* Finish WeBWorK DiffEQ_06_bic

* Update your journal on Euler’s Method and our discussion of the symmetric difference quotient from today’s class.

Mon 3/20
* WeBWorK DiffEQ_05a_bic
* Finish question 1 on Kwiki 19104. (You might find this Video on Using a Google Spreadsheet for Euler’s Method to be of value. Let me know.)
* (WeBWorK DiffEQ_06_bic is still open)

* Update your journal. Wednesday’s test is coming.

Tue 3/21
* TurnIn Questions 8 and 9 on the back of today’s Kwiki 19105. A Handwritten second draft of responses is fine.

* Update your journal. e.g. Average Value, Logistic Growth, Euler’s Method

Wed 3/22
* Test (possible recent items)
–+ Separable Differential Equations
–+ Modeling Logistic Growth
–+ Euler’s Method
–+ Average Value of a function
–+ Working with data, e.g. approximating derivatives and Riemann sums
* You may use a non-graphing calculator. I will have a few to lend.

* TurnIn: Last two weeks of your journal.

Fri 3/24
* Look at Numerical Integration demo
* TurnIn: WeBWorK find_parabola
When you are done with this problem, write a brief write-up including:
–* Problem
–* Solution
–* Graph
–* Final Thoughts
(e.g. See an example Desmos ) to show the parabola and your three points.

Mon 4/3
* Prep Set 1 Set aside 90 minutes to do the six questions. You can use your TI on the first three questions. Write out your solutions as if you were really taking the test. After that you can use resources (e.g. books, the internet, friends) to get a better understanding of any questions that you did not immediately ace. Feel free to email me with any questions over the break.
* Prep Set 1 Quiz Monday

* (Optional) Send me email if you have made any progress on the infinite product from today’s kwiki 19107

Have a good break.

Tue 4/4
* Watch Khan– Trapezoid Approximations
* Do Khan– Trapezoid Rule Quiz
* Get started on Calculus on a Parabola. (A full write-up on this is coming.)

* Start bringing your graphing calculator to class. * Update your journal.

Wed 4/5
TurnIn: Your second draft of Calculus on a Parabola. Use the standard Problem, Approach, Solution, Final Thoughts, organization.

Thu 4/6
* You will be making an annotated version of the BC Topics Outline provided by the college board. You should start by copying this GoogleDoc – BC Topics List. Note that you will need to use your SFUSD google account to get access to this file.
Do some work on the annotations, e.g. definitions and examples.

* Start tonight. The complete annotated outline will be collected on Friday, April 14.

Mon 4/10
* Test
TurnIn: most recent two weeks of your journal

Tue 4/11
or
Wed 4/12

* BC Prep Quiz 2
(If you do not have a paper copy of prep-set-2-2017.pdf check my schoolloop locker. Send me email if you can’t find it.)

Fri 4/14
* TurnIn: Complete annotated outline

Mon 4/17
* Prep Set 3: Paper copies handed out in class. A PDF is in the School Loop class locker.
* Prep Set 3 Quiz Monday

Tue 4/18
or
Wed 4/19

Nothing assigned.
(Prep Set 4 will be handed out in class.)

Fri 4/21
Read New York Times article on beauty of math

Mon 4/24
* Prep Set 4: Paper copies handed out in class. A PDF is in the School Loop class locker.
* Prep Set 4 Quiz Monday

* Fill out this AP Exams Survey to let me know which classes you will miss for AP exams.
* Multiple Choice Final Exam on both Wednesday and Thursday of this week.

Tue 4/25
* Actively (Re)watch Khan– Taylor Polynomial Remainders Part 1
* (If you didn’t already,) fill out this AP Exams Survey to let me know which classes you will miss for AP exams.
* Study for (Wednesday and Thursday)’s Final
* Follow pointers to College Board’s BC Exam Preparation at the top of this webpage.
* Put fresh batteries into your TI.

Wed 4/26
* Final Part I (no TI Multiple Choice)

Thu 4/27
* Final Part II (TI allowed Multiple Choice)
* TurnIn: Bring last two weeks of journal to class

Mon 5/1
* Prep Set 5: Paper copies handed out in class. A PDF is in the School Loop class locker.
* Prep Set 5 Quiz Monday

Go back to the top

## Kwikis

### Set 1S

• Kwiki 19065 Ladder problem, sphere volume by shells
• Kwiki 19066 DoNow: $$u$$-substitution and chain rule, ladder problem, intersecting cylinders revisited
• Kwiki 19067 Integration by parts
• Kwiki 19068 Napkin rings problem
• Kwiki 19069 Setup up volume elements – washers and shells; begin Particle, the Dog.

Go back to the top

• Copies of Stewart Calculus are available if you want to read a Calculus text with worked examples.

### WeBWorK

As in previous math clases some homework assignments will come from the [Whitman Calculus] text, but other assignments will be done on-line using WeBWorK , an on-line math homework system.