# Calculus (AP Math BC) 2017-2018

Welcome to Calculus!

## Pointer to:

• Kwikis (just below current homework)

## Assignments

### Calculus Homework

Homwork Sources:

https://www.youtube.com/watch?v=lEOjMAmkI-U

Next Test: Wednesday, December 13 (generally every other Wednesday)

Due Date Assignment
Tue 8/22
* Sign Up for WeBWork
* TurnIn: Observations Please
* Though you will need to be have and know how to use a hand held graphing calculator (e.g. TI-84) for the AP exam, you will find the Demos Graphing Calculator which runs on computers, smart phones, and tablets, to be very useful. Start by trying it on a computer. You can save your work if you click sign-in in the upper left hand corner of the window.
* Work through this brief introduction to graphing functions in Desmos.

Wed 8/23
Turn In: Second draft of Headlands Bicycle problem on page 2 of kwiki 20002 Note that you may need to make an assumption about my ride to get a unique solution for flat, uphill, and downhill miles. Be sure to state your assumption.
* Spend 30 minutes working on the questions.
* Then spend 15 minutes writing a second draft of your answers and graphs.
* I do not want to see your initial work. Use new paper for your second draft.

Thu 8/24
* Read Whitman section 1.3 Functions
* Do exercises 13, 14, 15, 16
* Be prepared to talk about kwiki 20003 questions 4, 5, and 6.

Fri 8/25
* WeBWork: “Orientation”
Your login is all lower case lastname_firstname
e.g. newton_isaac using the names you entered. Although the closing time is midnight Sunday, I expect you to spend 45 minutes (or less) to work your way through this orientation tonight.
* Precalc Quiz: 30 minutes, 2 free response questions.

Mon 8/28
* Consider what you learned your first week of your journey through Calculus. You should talk about amount functions, rate functions, locally linear, and our seven easy pieces of “nice” function curves. Your tasks are to create two documents that will help students learn about these concepts.

1. Building Rate Functions: Take a look at this mathlet - Building a Rate Function. The mathlet needs user guide:
— (a) a set of instructions how to use the buttons, boxes, etc.; and
— (b) a paragraph explaining how $$f'(x)$$ is defined and what $$f'(x)$$ means.
Be sure to explain and use the concepts of amount functions, rate functions, and locally linear.

2. Using Rate Functions: Make nice version of the Seven Easy Pieces table (see kwiki 20005 question 1) and write a paragraph describing what the table says.

TurnIn: in typed second drafts of your work for tasks 1 and 2. (You can handwrite parts that might be difficult for you to do with a computer.)

* (For a few of you who haven’t finished WeBWork: “Orientation”, it closes Sunday evening.)

Tue 8/29
* Review HMC Functions and Transformations of Functions
* Start and Finish WeBWork: “New Functions from Old”

* You might take a look at my interactive diagram from today’s slopes question.

Wed 8/30
* TurnIn: Redo questions 1 and 2 of today’s kwiki.
— Briefly explain why each answer is correct.
— Sketch the requested graph of $$f'$$ on the graph of $$f$$.
— Sketch the requested graph of $$g$$ on the graph of $$g'$$.

* Take another careful look at Building a rate function

Thu 8/31
* WeBWork: “Exponential Functions”
* Put the difference quotient equation $f'(a) = \lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$ on a PostIt. Place this PostIt on your bathroom mirror.
* Take a look at Geometry of a Difference Quotient.
* Your notes should include the concepts of stationary and critical points, and our definition of $$e$$.

Fri 9/1
* WeBWork: “Inverse Functions and Logarithms” Pls attempt to finish this WeBWorK assignment tonight (but stop after 45 minutes if you are not done.)
Exponential and Log Functions is a brief review.

* Check your understanding of seven easy pieces with graph match - big derivative puzzle (described at Places to Visit)

* Use Looking at $$b^x$$ at (0,1) to approximate the value of $$b$$ that gives a graph tangent to $$y=x+1$$

Tue 9/5
* WeBWork: “Chapter 1 Review”
* Use Looking at $$b^x$$ at (0,1) to approximate the value of $$b$$ that gives a graph tangent to $$y=x+1$$
* HeadsUp: Test on Wednesday

Wed 9/6
Test (No calculators)

Thu 9/7
* Actively read HWS Intro to Limits.
* WeBWork: “bic Limit of a Function” (one night only)

Fri 9/8
* Review One sided limits and Limit Properties
* WeBWork: “bic Calculating Limits Using the Limit Laws”

Mon 9/11
An Important Trig Limit
* Work on a first draft of your solution to evaluating $\lim_{\theta \rightarrow 0^{+}} \frac{\sin \theta}{\theta}$ See Kwiki 20011 Note: The kwiki question is structured to get you to think about the problem. Your solution need not be organized to mirror my kwiki questions.

* TurnIn: a typed second draft of a complete write-up. Be sure to include at least one diagram.
A complete write-up has a title and four labeled sections:
__ Problem a full statement of problem
__ Game Plan a summary of your approach
__ Solution
__ Final Thoughts comments about the problem and/or your solution

Tue 9/12
* Read at least first page of Continuity Notes
* WeBWork: “bic-Continuity”
* Bring your graphing calculator to class.

Wed 9/13
* WeBWork: “Shrinking Circle Problem”
TurnIn: An organized second draft write-up of your work on this problem. This can be neatly handwritten.
Note: If you do not solve the problem, come up with a question whose answer would help you get to a solution.

Thu 9/14
* Carefully read Adjectives for Functions
* Do exercises 1, 2, 4, 5, 6 (on last page). Be sure to bring your Calculus notebook to class so that I can see your work.
* Be prepared to discuss any of the problems on Kwiki 20014 by writing responses in your notebook.
* Take a careful look at my sample write-up

Fri 9/15
* Be prepared to discuss all problems on the back of Kwiki 20015 by writing responses in your notebook.
* TurnIn: A second draft of complete write-up for question 3:
$$\bullet$$ $$f(x)$$ even and differentiable $$\implies f'(x)$$ odd
Consider why this statement is true by looking at the geometry behind the $$h \rightarrow 0$$ difference quotient. Draw a good diagram labeling the relevant points. [Hint: Start with just two points in the first quadrant.]

(Take a careful look at my sample write-up)

Mon 9/18
TurnIn: a Poster for WeBWork: “bic-alien-headlight”
— Solve the problem. A graphing calculator or Desmos might help, but guess and check is not an acceptable method.
— Plan a poster presentation of your solution using the standard write-up format.
— Use Desmos to make a diagram.
— Use one piece of standard
$$8.5 \times 11$$ paper.

Tue 9/19
* Second Derivative Exercises #1,2,4,6
* ReCheck your understanding of seven easy pieces with graph match - big derivative puzzle (described at Places to Visit)
* Start reviewing for Wednesday’s Test.

Wed 9/20
Test

Fri 9/22
Do Derivative Rules 1 worksheet twice. Use stratch paper (or another copy of this worksheet) for your first drafts. Neatly write your second drafts on the worksheet, and bring it to class.

Mon 9/25
* Read and Do exercises for Derivative Short Cuts - Power Rule
Sec 3.1 #1,3,4,5;
sec 3.2 #1-5(all) 7,9

* Make a Desmos graph of $$f(x)=ax^2+bx+c$$.
___ Use sliders for the parameters ($$a$$, $$b$$, and $$c$$) to explore what each parameter does.
___ Save your file, because you will be doing more with it Monday.

Tue 9/26
* Read and Do exercises for Product Rule Section 3.3 #1,2,5,6

* Make a Desmos graph of $$f(x)=ax^2+bx+c$$.
___ Use sliders for the parameters ($$a$$, $$b$$, and $$c$$) to explore what each parameter does.
___ What is the path of the vertex of the parabola as you change $$b$$?
___ Write an equation for function $$g(x)$$ that uses parameters $$a$$ and $$c$$ and tracks the path of the vertex.

TurnIn: A printout of your Desmos graphs of $$f(x)=ax^2+bx+c$$ and $$g(x)$$. Make $$f(x)$$ a solid curves and $$g(x)$$ a dashed curve. Be sure your printout shows your equations.

* Do question 4 on today’s kwiki

Wed 9/27
* Read and Do exercises for Quotient Rule Sec 3.4 #1,2,5,8,9
* Finish Practice on back of Kwiki 20020

Thu 9/28
* Read and Do exercises for sin $$x$$ derivative Sec 4.4 #4
* Read and Do exercises for Trig Derivatives Sec 4.5 #1, 8, 18
* Be sure you understand all of the derivative questions on kwikis 20019, 20020, and 20021.

Fri 9/29
* WeBWork: “derivatives-practice-01-bic”

Mon 10/2
* Read Introduction to Chain Rule to see examples using Leibniz notation. Recall the chain rule allows us to find derivatives of composite functions. The chain rule says we can treat $$\frac{dy}{dx}$$ as if it were a fraction.
* Carefully watch the first 12 minutes of Derivative formulas through geometry 3B1B Part 3 You may need to stop the video and/or replay sections to understand what is going on.
* Rewatch the Geometry of $$(1/x)'$$ section, and work on the Pause and Ponder Question.
* TurnIn: A complete writeup explaining the geometry of the derivative of $$\displaystyle f(x)=\frac{1}{x}$$. (This should be a second draft)

Tue 10/3
* Work through the Explore notes on An Intuitive Notion of the Chain Rule
* Be prepared to put solutions to Kwiki 20023 on the class boards
* Test on Wednesday.

Wed 10/4
Test

Fri 10/6
Two day assignment:
* WeBWork: “derivatives-practice-02-bic”
* Actively watch Visualizing the chain rule and product rule: 3B1B 4

Tue 10/10
* WeBWork “Parabola-triangle” (only 1 problem)
* TurnIn: a second draft of a “Parabola-triangle” write-up
Use Desmos to make a diagram for your paper. See Sample write-up

* Exponential and Log Derivatives: Exercises (Sec 4.7): #1-5(all), 7, 10, 12

Thu 10/12
* Be prepared to present any question on kwiki 20026. Use Desmos to make graphs for question 2 and a straight edge to approximate slopes for question 3.
* Actively watch Derivatives of exponentials – 3B1B
* Without looking at your notes, take a blank sheet of paper and make a seven easy pieces chart. Add to the chart ideas on how $$f''(x)$$ tells you something about each of the seven easy pieces.

Fri 10/13
* Implicit Differentiation
++ Read section 4.8 and do #1, 2, 3, 4

* Using Derivatives: Curve Sketching 1:
++ Read 5.1 Maxima and Minima
++ Read 5.2 The first derivative test and do #2,4,6
++ Read 5.3 The second derivative test and do #2,4,6 (same problems)

Mon 10/16
* Read and do selected exercises in Inverse Trig Derivatives
Sec 4.9 # 1, 2, 4, 5, 8
* Start WeBWork: “Min-Max-bic” [Note: work on problem 5, but a correct answer might not get the green correct response. There is a bug in the code.]
(One hour rule: Stop after one hour of Calculus.)

Tue 10/17
* WeBWork: “Min-Max-bic” (if you haven’t already finished it)
* Actively rewatch Visualizing the just the chain rule: 3B1B
* You can look at Mapping Diagrams explore parallel number line representations of functions.

* Dessert problem on Kwiki 20029
* Test on Wednesday.

Wed 10/18
Test

Fri 10/20
* Goal: Find the volume of the largest cone that can be inscribed in a sphere of radius $$a$$.
* TurnIn a second draft of a complete write-up.
___ Be sure to include in the Final Thoughts section:
______ Why do you think your answer is reasonable?
______ and any other thoughts

Mon 10/23
* Be sure you can explain each of the properties of integrals listed on Kwiki 20031
* WeBWork “definite-integrals-intro-bic”
* Stop working on Calculus after 45 minutes. I will reopen the WeBWork for anyone who needs one more night to finish (but not to start) the WebWork on Monday if you need it.
* Work on UC apps (if you have time)

Tue 10/24
* TurnIn: a second draft of your solution to this question from kwiki 20032.
Without using a calculator, show that $\frac{\pi}{2} < \int_0^{\pi} \cos(\sin x) \, dx \le \pi$ A neatly handwritten second draft is fine, but be sure to include a title and all four labeled sections.

* (WeBWork “definite-integrals-intro-bic” is still open for people who did not finish it over the weekend.)

Wed 10/25
Cube rooting with Oyler
Oyler, the calculator-less mathematician, needs a good approximation of the cube root of 65. Help Oyler get a value without using a calculator (even for arithmetic - mixed numbers are fine). You can return to this decade in order to check that your value is within 2 ten-thousandths of a calculator’s result.

TurnIn On Wednesday: Status Report
Your status report should be just one page.
* If you have a solution, great! Turn in a clean summary of your solution.
* If not, no worries. What question would you like to ask so that an answer would help you get closer to a solution. Write up you your ideas, your question, and explain how your question will help you.

A full typed write-up will be due on Friday.

Thu 10/26
* Finish question 8 on the back of Kwiki 20034
* Cube rooting with Oyler due Friday.

Fri 10/27
TurnIn complete (title and four labeled sections), typed with formatted equations Cube rooting with Oyler

Mon 10/30
Work at least one hour on your UC (or other college) applications.

(If you are not applying to college this Fall, TurnIn a status report on the Fuel Consumption Problem No 9 on Kwiki 20034)

Tue 10/31
* WeBWork: “antiderivatives-1-bic”

Wed 11/1
* Test (Up to area functions, but nothing on derivatives of area functions)

* Note: Integration Intro - Gaining Geometric Intuition is a nice applet which may help you get a better sense of our geometric interpretation of integrals

Fri 11/3
* Actively watch MIT Related rates 1
* Related Rates problems #1-6 (all)

Mon 11/6
* The Fundamental Theorem of Calculus (FTC) says: $F(x) = \int_a^x f(t) \,dt \implies F'(x) = f(x)$ * WeBWork “FTC-1-bic”
* Here are solutions to the related rates problems.

Tue 11/7
* Actively MIT Using FTC to find derivative functions (Note: They refer to this part of the FTC as part 2 rather than part 1.)
* Finish today’s Kwiki 20040

* TurnIn: Neatly write-up (handwritten is ok) a second draft of your solution to either question 5 or 6.

Wed 11/8
* Read Using FTC-2 and do sec 7.2 #1-5 (all), 11-15 (all), 18

Thu 11/9
Spend 45 minutes on volume worksheet 1. For each question, you need to:
* Determine the dimensions of the geometric object we are given.
* Use those dimensions and some geometry to compute the volume.
* Set up a volume element
* Set up an integral
* Evaluate your integral
* Check your work

Be sure to develop $$dV$$, the volume element, before setting up your integral.

Notes:
* I’m working on an applet for the pyramid problem. Comments are welcome
* The cylindar and sphere volume demos are in Places to Visit.

Mon 11/13
* WeBWork “Misc_Set_01”

* Bring a graphing calculator to class on Monday

Tue 11/14
* Read and do selected exercises in Limits Revisited – L’Hôpital’s Rule
Sec 4.10 #1-7 (all)

Wed 11/15
* Test (Anything except L’Hôpital’s Rule)

Fri 11/17
* TurnIn: A complete typed write-up of your solution to the Intersecting Cylinders Problem.
(See Sample write-up).

* Note: There will be an assignment over Thanksgiving Break

Mon 11/27
* WeBWork “Thanksgiving-2017”

* Enjoy the break

Tue 11/28
* Actively watch Newton’s Method Intro - Khan Talent Search

* Actively watch MIT Volume of paraboloid – disks
Note: Develop $$dV$$, the volume element, before setting up your integral.

Bring your graphing calculator to class

Wed 11/29
Newton’s Method:
* Read about Newton’s Method which includes a nice interactive graph.
* Use Newton’s Method to approximate a solution to $$2\cos x = 3x$$ using a seed $$x_0 = \pi/6$$. Find $$x_2$$
* Actively watch MIT Newton’s method

Thu 11/30
* Read Integration Techniques – Substitution
* Evaluate: $\int_{-2}^{2} x^2 \cos \big(\frac{x^3}{8} \big) \, dx$
* Actively watch MIT u substitution video
* Do Integration Techniques – Substitution sec 8.1 #1-11 (odd), 12

* You should be able to read and write sums using sigma notation.
___ Take a quick look at Intro to Sigma Notation – Notes to be sure you are comfortable.
___ This Intro to Sigma Notation – Coursera Video might be useful to students who need more tutoring on $$\sum$$ notation.

Fri 12/1
* WeBWorK: integral_techniques_1a. This set closes at 7am on Friday.
* Finish questions 3 and 4 on kwiki 20048.

Mon 12/4
* Do All problems on side 1 of Volume Problems
Be sure to start by developing a complete volume element $$dV$$ before setting up an integral. (e.g. $$dV=xydx$$ would need more development)

* TurnIn Select any four (other than question 1) of your solutions to rewrite as neatly written, organized second drafts. Neatly handwritten is fine. Be sure to identify each question with the question number and title, but there is no need to copy the question statement.

* Finish question 1 on today’s kwiki — the consistency of the two antiderivatives.

Tue 12/5
* Find the volume of the solid generated by rotating the region bounded by $$y=0$$, $$x=4$$, and $$y=\sqrt{x}$$ around the line $$x=6$$. Using washers and then shells.
* You can find my two volume mathlets up at Places to Visit)
* Actively watch MIT Volume of revolution via shells

* Our next test is on Wednesday, Dec 13 (note this change).

Wed 12/6
* Revisit today’s kwiki 20050.
___ Start with scratch paper and redo each of the five questions without looking at your notes. This may require you to consult your notes, but you need to get to a place where you can write a complete solution without notes.
___ Edit each solution, and then enter your neatly written solutions into your notebook.
___ Bring your notebook to class.

* Start working on the problems (shell method) on side 2 of Volume Problems (For now, ignore “numerical integration.”)
Note: Volume Problems – Solutions will be available on Friday.

Thu 12/7
* Actively Watch Khan – Intro to Riemann Sums: Left Boxes
* Actively Watch Khan – Generalizing a Riemann Sum: $$n$$ equally spaced $$\Delta x$$s

* Without looking at your notes, try to redo the questions on today’s Torus kwiki. (If need be look at your notes.)

Fri 12/8
* Play with Riemann Sum Mathlet
* Use four subintervals and left endpoints to approximate the value of $\int_{-1}^{3} x^3 \, dx$ (No electronic help. Do this with just paper and pencil.)
* Actively watch MIT Intro Riemann Sum

* The security certificate for our WeBWork server expired in early December. You can get around the error message by using the a Firefox brower on your computer or phone. Experiment tonight, so that you will be ready to use WeBWork this weekend.

Fri 12/8
* Play with Riemann Sum Mathlet
* Use four subintervals and left endpoints to approximate the value of $\int_{-1}^{3} x^3 \, dx$ (No electronic help. Do this with just paper and pencil.)
* Actively watch MIT Intro Riemann Sum

* The security certificate for our WeBWork server expired in early December. You can get around the error message by using the a Firefox brower on your computer or phone. Experiment tonight, so that you will be ready to use WeBWork this weekend.

Be aware of the homework for Wed 12/13

Mon 12/11
* WeBWorK: Revisiting_Definite_Integral_1
Be sure you can use WeBWork (you will have to tell your browser to proceed to this “unsafe site”. An advanced button is used on some browers. Email me by 9am Saturday if you cannot get to WeBWork. I will send you a PDF of the questions. You will then need to turn in your answers and work supporting your answers.

* Keep working on Wednesday’s assignment.
* Bring you graphing calculator to class each day

Tue 12/12
* Work on Wednesday’s TurnIn
* Be prepared to put up question 1 from Kwiki 20053
* Note: Thank you Josh, for pointing me to MIT Series Calculation Using a Riemann Sum, a video that can help you understand questions 3 and 4 on Kwiki 20053.

Wed 12/13
* Test 7 A scientific calculator will be useful (and allowed) on problem 1. Mr, Tran has calculators you can borrow if you do not bring one.

* A 10 question “Final Exam”
Each question includes:
— the question
— correct answer
— complete solution
— the concept(s) behind the solution
See BC Topic List

* TurnIn: Two documents – stapled together.
1— The Questions (typed)
2— The Answers, Solutions, and concepts behind each question. This can be neatly handwritten on a printed version of your questions.

* Note: Here are Solutions to washer and shell volume problems.

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## Kwikis

### Set 5

• Kwiki 20031 Introducing Definite Integrals
• Kwiki 20032 cone in sphere, Working with the idea of a Definite Integral
• Kwiki 20033 Working with the idea of a Definite Integral, $$f''(x)$$ and inflection points (Note: I’ve revised question 6)
• Kwiki 20034 More working with the idea of a Definite Integral, antiderivatives
• Kwiki 20035 Average value of a function
• Kwiki 20036 Area functions
• Kwiki 20037 Area functions, walking out on a tangent

### Set 4

• Kwiki 20024 chain rule, exponents and logs
• Kwiki 20025 derivatives of $$y=b^x$$ and $$y=\ln(x)$$
• Kwiki 20026 follow that particle, derivatives of $$y=b^x$$ and $$y=\ln(x)$$, limits with graphs, chain rule with graphs,
• Kwiki 20027 Introducing implicit differentiation, velocity vs speed, seven easy pieces and $$f''(x)$$, revisiting Kwiki 20026
• Kwiki 20028 implicit differentiation, derivatives of inverse trig functions
• Kwiki 20029 optimization problem, $$(x^x)'$$
• Kwiki 20030 $$(x^x)'$$, deriving (part of) the cheer,

### Set 3

• Kwiki 20017 $$\displaystyle \frac{\sin 0}{0}$$ redux, IVT, hiker problem
• Kwiki 20019 Product Rule, Calculus on a parabola, more on power rule
• Kwiki 20020 More on power rule, Quotient Rule
• Kwiki 20021 slope of a line and trig, derivatives of trig functions
• Kwiki 20022 composite functions and Leibnitz notation, rope around the Earth
• Kwiki 20023 Building on geometry of derivative formulas, chain rule practice

### Set 2

• Kwiki 20011 An important trig limit
• Kwiki 20012 defining continuous with limits, using the cheer, difference quotients, exponential functions,
• Kwiki 20013 graphing calculator and a discontinuity, from yesterday
• Kwiki 20014
• Kwiki 20015 introduced Taylor Form of a line, logs
• Kwiki 20016 from yesterday, $$\displaystyle \frac{\sin 0}{0}$$ redux

### Set 1

• Kwiki 20001 slope, attributes of graphs
• Kwiki 20002 dividing by zero, attributes of graphs
• Kwiki 20003 functions, amount functions and rate functions, tangents, seven easy pieces (part I), composite functions, rational numbers
• Kwiki 20004 functions, amount functions and rate functions, composite functions, rational numbers, seven easy pieces (part II),
• Kwiki 20005 seven easy pieces (part II)
• Kwiki 20006 using seven easy pieces
• Kwiki 20007 $$f$$ $$f'$$ match
• Kwiki 20008 Odd and Even functions, Using a difference quotient on $$f(x)=b^x$$.
• Kwiki 20009 Odd and Even functions, logs and exponents
• Kwiki 20010 Review questions, limits using graphs of functions

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## Getting Started

Please read this entire page. Be sure to Sign Up for WeBWork before 7am Tuesday, August 22.

### Text

We are using:

• Whitman Calculus, an open source text book. You can read it on-line Whitman online, download to any device that can show PDFs, or print selected pages.

• 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.

#### Sign Up for WeBWork

You need to fill out this form To get a set up an WeBWorK account. Be prepared to give a (and remember) a password for your account. (Yes, the submit button says “Never submit passwords through Google Forms.” Your WeBWorK password is not a high level security item.) Details about using WeBWorK will be available soon. If you can't wait, you can sign-in as a guest.

### Calculators

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