Mathematics 110

Mondays and Wednesdays, 1:30-2:50

Hegeman 308: Daniel Newsome Presiding


 -Office: In the Aether.   Email me for appointment.


-Office Hours:  By appointment.  Please feel free to email me for an appointment.  Seriously.

-Parent Webpage:


Textbook: Precalculus by Collingwood, Prince, and Conroy. 

Open source text, dated June 19, 2019.

Link to PDF .


Updated: 5/20/20 2:10 PM




Zoom Classes-Extras-Options-Addenda

Last Class



Class 16b

Last Class

PreCalculus to Calculus

Our final class attempts to connect the dots between precalc and calc.


Final Class Video: PreCalc-to-Calc [ca. 45']

It ran a bit longer than I anticipated, so let's meet up on Zoom at 2:30.

That's Zoom at 2:30.


Again, no new homework.  Just make that last assignment as good as you can. 

Here's that link... again:  Ch18-HW-PDF


All back-homework that you want me to see should be submitted to me by Monday, May, 25th.


Final Tunes:


BJ-BWS 1.mp3






Class 16a


Today's class looks at the tangent.  What it tells us.  How to interpret its numerical value.  How it fits into the unit circle.  How to graph it.


Class Video: Tangenti.mp4 [ca. 30']

Watch the video and join the Zoom class at 2:15. 

That's 2:15.


No new homework.  Just work on the stuff due next Monday.

Here's the link... again:  Ch18-HW-PDF


Sine to Cosine Shift.jpg

This may assist you with the final homework assignment.


Nice little interactive diagram for tangent here: link


One more class on Wednesday.

Hang in there.



Class 15b

Addendum: The Travelling Sine Wave

Today we look at the travelling sine wave.

This class refers to some ideas from Chapter 19 of our text.  It mostly focuses on the "phase shift" and how that can be utilized to move a wave.

I recommend reading over Chapter 19 (expecially the summary on p262).  This will help you with the homework assigned on Monday.


Class Video: The Travelling Sine Wave [video- ca. 47']

Watch this video and join the Zoom class at 2:45.  That's 2:45.


There is no new homework, just the homework assigned on Monday.

Here's the link... again:  Ch18-HW-PDF

The second part of this homework assignment is sort of the final project for this class.  We are not having a final exam, just this final homework project.  Do your best to make this both mathematically substantial and a beautiful, creative presentation.  Go nuts.  Use your special talents, be they drawing, music, video production, speaking, writing, dance... whatever.  Have fun with it. 


All back-homework that you want me to see should be submitted to me by Monday, May, 25th.


Next week:  We will have a Zoom class like normal on Monday and our final class on Wednesday will be sort of an overview class.




Please email me with the lowest letter grade you would like before I give you a pass or fail. 

E.g. Let's say your GPA is 3.0.  You would not want anything lower than a B, because this would lower you GPA.


Relaxation Blues:




Bit Louder:







Class 15a

Chapter 18: Trigonometric Functions

Watch these 2 videos and join the Zoom class at 2:30.  That's 2:30.

Class Videos for Monday, 5/11/2020:

Pt1: ch18.pt1-Whiteboard-SawSine- video

Pt2: ch18.pt2-Blackboard-sinewave-video


The Pythagorean Theorem in Trig. Notation

cos2(q) + sin2(q) = 12.  

Remember, 1 is the radius of the unit circle.


Homework: Ch18-HW-PDF

The first part of this assignment is due next Monday.  The second part is due the next Monday after class is over. 



Please email me with the lowest letter grade you would like before I give you a pass or fail. 

E.g. Let's say your GPA is 3.0.  You would not want anything lower than a B, because this would lower you GPA.


Zoom Class 5/11/2020-

Nothing of importance in this Zoom Class so I'm not posting it.



Class 14b


Chapter 17b: Addendum- Geometry and Trig.


Watch this video and join the Zoom class at 2:10.

Class Video for 5/6/2020: PolyPerimeter.mp4


Homework PDF: Polygon and Perimeters:

 Due next Wednesday.


Posted 5/20/20: Solution to Polygon to Perimeters Assignment: PolyPerimeters-video


Zoom Class 5/6/2020

Not much content in this one.


Homework tutoring session this Sunday at 4:00 on Zoom.

I'll send a Zoom invitation on Saturday.



Class 14a

Read Chapter 17: The Circular Functions.

This is where we finally get sine, cosine, and tangent. 


Sine is Opposite over Hypotenuse.

Cosine is Adjacent over Hypotenuse.

Tangent is Opposite over Adjacent.


Class Video: Ch17-video

Watch it

and join Zoom at 2:20 or so...



The Homework assignment is described here: HW-Ch17.pdf




Full Solution to 17.5a.jpg.


The Example 17.1.1 on p221 is a bit unclear.  [I was bothered because there was no mention of the cue ball.]  The example is simply describing the trajectory of a ball bouncing off the rail/cushion of a pool table.  Here's a 5 second animation showing the situation:  BilliardBall.mp4


Latitude from GoogleMaps-video


Sad Tune from Keats

[The] spirit is too weak; mortality

Weighs heavily on me like unwilling sleep,

And each imagined pinnacle and steep

Of godlike hardship tells me I must die,

Like a sick eagle looking towards the sky.



Rockin' Andalucia





Class 13a

Chapter 16: Measuring Circular Motion


Watch these video and join the Zoom meeting at 2:00.

Class Video 1: Ch16-BicycleGearing [17:30]

Class Video 2: Ch16-Conversions.mp4 [10:13]


Due for Monday, April 4th.

Assignment: Read over Ch.16.

Do the following: 16.1, 16.2, 16.3a, 16.3c, 16.6.


Turn in complete write-up for 16.6 (all parts)

[include useful drawings, prose, and explanation of method.  Please circle or highlight all results.]

Also Turn in: Figure out the centripital acceleration and g-forces acting on Michael in problem 16.6, using these equations: [link to image]

How long will Michael survive on this ride?

Should it really be called a "merry"-go-round?

Come up with a new name for this ride.


Terrible Quality


Full Solution to 16.6-PDF

Wikipedia on "g-force"


5280ft = 1 mile

12 inches = 1 foot

1 inch = 2.54 cm

[link to image]

I will have a homework tutoring session on Sunday at 6:00 pm. 

I'll send out a Zoom invitation for this later this week.


New Old Tunes








Advising Day.

No Class.








Class 12b

Chapter 15: Measuring an Angle

Class Video 1: Circumference to Radian [ca. 14']

Class Video 2: Degree-Min-Sec-Radian-Conversions [ca. 16']


Homework: Read Ch15 and do the following problems at the end of the chapter: 1, 2, 5, 7, 8


-Turn in: Problem 15.5. Add to this problem a nice diagram and a short discussion of the various ways this calculation is not completely accurate, but close enough.

-Turn in: Problem 15.7f

-Turn in: Problem 15.8.  Just show the calculations with enough prose to make it readable.  Nothing fancy.

Here's a video with the set-up for 15.8: 15.8-Set-up-video

The full solution - 15.8-full solution video


2020.4.22-ZoomClass [ca. 14']


Giovanni’s Solutions








Class 12a

MesoCh14&15: Base Systems plus


Here are the premade video presenations for Class.

-Video Class Part 1 [ca. 12']- Paper Folding to Proxima Centauri- This assignment will count as a quiz and is due next Monday.


Here is the quiz.  Due next Monday (4/27).

Folding to Proxima Centauri-PDF-form

See Video Class Part 1 for context.


-Video Class Part 2-: "Base Systems Vid" [ca. 19']- The first section is poorly made.  Sorry about that.  The PDF will better explain some of this stuff.


-Additional Video to help with making the Spreadsheet:  Excel-BaseConverterTutorial


Assignment on Bases due Wednesday: 


The actual turn-in assignment is described on p7.

Here's how you get the answer: Base13to10-video


-2020.4.20-ZoomClass [37']


Bluesy Tunes


riffin' on


Here's the talk I gave last Friday to the Physics Pholks:

Physics Phriday Colloquium 

"As Above. So Below"



Yesterday's Solutions

Today's Problems



Class 11b

Ch14: Rational Functions

Chapter 14: Class Video [39:08]



Look over Ch14.


Ch14 Homework Assignment: some solutions provided.


Added 4.26.2020

Helpful Hints:

14.1a solution



14.5 calculation details: There are many ways to do these calculations.  Here is one way.


Ian's 14.1c - Nice and tidy and to the point, with good commentary.


2020.4.15-Ch14-ZoomPart(edited) [6:25]


Psychedelic Rap

DG-Beware.mp3-with Manson and Jane's











Ch13: 3 Construction Tools


Look over Chapter 13.


Do this: Chapter 13 Assignment

Ch13-Translations Video



Lipsitch-4.13.20-Who Is Immune to the Coronavirus%3FNYT.pdf


Wheat and Chessboard: Rice Volume video and write-up.


Nick's Excellent Transforms- Super presentation of various transformations. 


Take a Break with:

-Distorted Reality-CI-1/4Tone

-Hippy Flam.  L&M-ND

-Dance RT: Tekit...






Ch12: Log Functions


-Read over Chapter 12.

-Do all of 12.1 and 12.8 in the exercises.

-Then read and do all the exercises on this PDF: Newton's Cooling and Radio Carbon Dating

-Turn in: Send me a screen shot of #10, the spreadsheet you make ...

     ...and write up 14b (the papyrus scroll).  Write it up completely, with a little research on Egyptian texts thrown in to give it context.  Fictional set-ups, illustrations, and graphs encouraged.


Zoom Class for 4.13.20


Watching Water... Cool: Video 1

Watching Water Cool: Video 2

Use either one for assignment.


Making the Cooling Spreadsheet: video


Update: Solution: Here is a GoogleSheet with a working spreadsheet: link

Here is an Excel version of the same: link


Nuclear Bombs and Dating Carbon- NYTimes


Wheat and Chessboard: Rice Volume video and write-up.


Break Time:



Buddy H on H: LR-OJ-B.mp3


Harrison Clock and Longitude






-Read Chapter 11: Exponential Modeling


-Then read this: Compount Interest HomeWork, and do the exercises in it.  No need to turn in.  Answers included.


-Do this and turn in: Wheat and Chessboard Problem- Write up a nice explanation and send it along to

Zoom Class: 4.8.2020

Finally, this one is watchable.


The New Remote Math Study Room is now One-on-One tutoring.  Contact Olive at: for an appointment.


A very nice write-up of the Wheat and Chessboard Problem by BeiTong.



-Not Winwood


Maple Syrup




Chapter 10


Read Ch10: Exponential Functions


Read this: Ch10-restrictions on exp-function.pdf


Watch this: -Tuning with Daniel: Video


Do the following problems:  10.2, 10.3, and 10.4.


Turn in:  10.2e and 10.4b.  [Turn in here:]  Please title your files properly.


Zoom Class 4.6.20




4' Video on Problem 10.2


Optional Digressions:

-The Jazz Kittens on Instagram

-Cool Jazz on Ice


The Visage of a Virus: Visualizing CoVid19

For you visual artists out there

A good article on R0 and Rt.  




Finish up all the SIR assignments and turn them in here:

Alert: All homework must be labled as seen here:


E.g. Newsome-Ch10.pdf



Zoom Class: 4.1.2020

I screwed up a video setting in Zoom and the video quality is terrible in parts.

(Experimenting with Sound Tracks)

Now, for something completely different...Black Holes

Overbye-Infinite Visions (PDF)

Black Holes: current overview

Video from Smithsonian




SIR Modeling- Materials and Assignment

This is the full assignment covering 3/18 to and 4/1.

[Same link as above in 3/18]

Zoom Class Video-3.30.20

Additional Materials:

RadioLab-Patient Zero- Excellent episode. Interesting use of sound and music.

Quammen-Malaria-Modeling- Describes the history of mathematical modeling (SIR model)


NYTimes-Interesting Graphics- Virus on the Move- This is another approach to modeling the infection.

Flattening the Curve- NYT

Mandavilli-NYT-Can You Become Immune to the Coronavirus? - Finally, some news on immunity for the Recovered population.


Spring Break - wash your hands


Spring Break- take a breath. 

The New Normal page has been updated with new information:

The New Normal Page




Update 3/21/2020:

I've moved this entire assignment to its own page for organizational reasons.  Here it is:

SIR Modeling- Materials and Assignment

This is the full assignment for 3/30 and 4/1.

Intro Video on Modeling an Epidemic:



I made a short video doing 9.7a.

It's here: 110-PreCalc

Use your Bard Google account for access.



Over Break Additional Materials:

RadioLab-Patient Zero- Excellent episode. Interesting use of sound and music.

Quammen-Malaria-Modeling- Describes the history of mathematical modeling (SIR model)






This class is moving online.  Everything will be orchestrated from this website.

See: The New Normal Page.

Ch9: Inverse Functions.  Read over this chapter.  It's actually pretty good.

Do these problems: 9.1a, 9.1b, 9.2a, 9.2b, 9.3, 9.5, 9.7a, and 9.9.

Turn in this problem: 9.7a:  Put both lines on the same graph and then draw in y = x.  Notice the symmetry across y = x. 

Turn this in electronically to:

Inverse Functions:

Essentially you are doing this:

(x, y) to (y, x)

Solve for x instead of y.

The range of one is the domain of the other, and vice versa.

Graphically inverting y = x2



[not by best work]


Homework Email:

Must Read: The New Normal Page


Relevant Materials



Problem 7.14 video solution


I've moved the first half of the assignments (the ones we have done already)

to a new page in order to clean up this page, which was getting cluttered.

The older (pre-virus) assignments are now here:

First Half Assignments.


Textbook: Precalculus by Collingwood, Prince, and Conroy. 

Open source text, dated June 19, 2019.

Link to PDF  

Useful Graphing Calculator:  GeoGebra. 

[Geogebra Classic 5 can be downloaded and used offline.  Scroll down to download to a computer.]

You can also use Geogebra 6 online or as an app on a phone.

Another popular one is desmos.  There is no offline version that I am aware of.



Math Study Room - Now One-on-One tutoring.

Contact Olive:





Julia Sheffler

Jiangli Liu

Yuexin Ma, (Echo)

Riti Bahl

Riti Bahl temporarily

Felicia Flores

Yiyang Zhou


Please use this online resource.  Our tutors need the work and would be happy to help out.



Description of Class

"A course for students who intend to take calculus and need to acquire the necessary skills in algebra and trigonometry. The concept of function is stressed, with particular attention given to linear, quadratic,  general polynomial, trigonometric, exponential, and logarithmic functions.  Graphing in the Cartesian plane and developing the trigonometric  functions as circular functions are included."  -Course Catelogue


Treat this class like a job.  Show up on time, do the expected work on time, don't ask for extensions, and don't make excuses.

If you cannot make it to class, email me [] and let me know in advance.  I don't need to know why.

Obviously, emergencies and special situations may occur and these will be accomidated when appropriate. 


This class is mostly about participating and taking the homework seriously. 

The quizzes and exams are just coersive ways to make you take the homework seriously.

Grade breakdown: 

Homework: 50%

Participation: 25%

Quizzes and Exams:  25%

The homework is the most important part of this class.  There will be homework assigned for each class.  Only certain problems from the assigned homework will be turned in, so these problems need to be done like a short essay.  The problem needs to be restated or clearly paraphrased.  Diagrams (if useful) need to be drawn and drawn well.  Prose commentary needs to be written to guide the reader (me) through your thought process.  Interesting mathematical work needs to be shown.  If there is an equal sign, it had better be equal.  Answers need to be highlighted or circled or somehow made obvious.  Also, useful additional sources should be cited.  [If you use a Khan Academy video, provide a link.  If you use another textbook, cite it.  If you use the Math Study Room, say so.]  If you cannot solve the problem, you should figure out an estimate... an approximation... an educated guess... draw some diagrams and write that up as your homework.  Simply stating, "I couldn't figure it out," is not good enough.  Provide a range within which you expect to find the answer, even if you can't figure out how to set up the mathematics.  Most homework that you turn in will require multiple drafts.  I want to see the second (or third) draft, not the first.  Messy first drafts with only the calculations will not be given much credit.

And remember, in most of the homework problems most of the numbers will have units: 5 inches, 24 mph, 8C, -33%, etc.

Don't forget to identify the units and put them in there with the equations.  Units often cancel out, leaving you with a unit for the answer. If the units don't cancel out correctly, that's an excellent indication that something is wrong in your set-up. 

Participation includes attendance and promptness as well as traditional participatory activities like asking questions, volunteering to put something on the board, and laughing at my jokes. 

From my point of view Quizzes and Exams are the least important part of the course.  For whatever reason, students seem to place a great deal of importance on quizes and exams.  Perhaps it is a high school thing.  Perhaps students think that doing well on a test measures something above and beyond doing well on a test.  In any event, I give exams and quizes from time to time. It seems to be what everybody expects from a mathematics course.   The more you do the homework well, the fewer quizzes.








Ch16: Circular Motion






Ch17a: Circular Functions and Deriving basic Trig. Functions

π from polygons exercise.






Ch17b: Angle Addition, Double, and Half Angle Derivations






Ch18: Trig

Ch19: Sinusoidal







Ch20: Inverse Circular







Last Class.







15a:  Last Last day.

Notes on 7.2