Mathematics 110

Mondays and Wednesdays, 1:30-2:50

Hegeman 308: Daniel Newsome Presiding

 

-Office: Learning Commons, Stone Row basement [map]

-Email: dnewsome@bard.edu

-Office Hours:  Mondays and Fridays from 3:00-4:00

                                           ...or by appointment.

-Parent Webpage: http://www.mifami.org

 

 

Updated: 2/24/20 12:06 PM

 

Textbook: Precalculus by Collingwood, Prince, and Conroy. 

Open source text, dated June 19, 2019.

Link to PDF  

 

Due

Date

Assignment

Extras-Options-Addenda

Mon.

1a

1/27

1a: First Class.  Meet and Greet.  Nothing due today for obvious reasons.

 

 

Wed.

 

1b

 

1/29

1b: Have this done for 1/29: 

 

   -Read all of Ch1.

 

   -Do the following exercises on pp. 8-10: 1, 3, 4, 5, 7, 8, 10, 11, 13, 15, and 17.  Come to class ready to do them on the board if necessary.

   

   -Turn in full presentation of 1.4 on p8 and 1.10 on p9.  [See below for expectations on turned-in homework.]

Notes on HW assignment.

For 1.4, notice that the cylinder must circumscribe (not inscribe) the square base described in the problem.  Also note that the numerical answer provided at the end of the book is the mass of the air in the cylinder, not the amount of kilograms that it exceeds the mass of the tower itself.  The wording in the book is a bit unclear.

 

1.13: Solution and written up well

 

Student Examples of HW-1

 

My Example of HW-1

 

General Impressions of 1st HW Assignment:

  - Get a stapler if you don't already have one.

  - Get or make a compass and straight edge.

  - Many of you needed much more prose to explain the math.  Tell the story of the problem. 

  - Some of the drawings were great.  Some were just ok.  Some were pretty bad. 

  - Layout was good on most, but a few were chaos.

 

Mon.

 

2a

 

2/3

2a:  The following is due on Monday, 2/3: 

  

   -Read Ch2.

 

   -Do these problems: pp. 22-24: 1, 2, 5, 7, 9, 11a, 11c, 12, and 13.  Some of these are quite hard.  Don't get discouraged.

 

   -Do the Extra Materials for Ch2 [Hard copy handed out in class.].      

        Conversions, Excel, and Repeating Decimals.

 

   -Turn in the "Extra Materials for Ch2" handout and the following problems from Collingwood, Ch2 (pp. 22-24):  Write up 7 & 9.

 

In class: Issues from Ch2.  Then "Completing the Square" and problem 3.2a, 3.2c.  Example 3.3.1.  Then discuss exercises 3.1a, 3.6a-b, 3.8b if time.

Note for Example 2.3.2:

   Given: Michael has a velocity of 15ft/s to the right, and Aaron is going 8ft/s to the left.

 

Extra Credit: problems 2.3 and 2.4*,

 

*Problem 4: The answers in the back for part b are inverted, columns for rows, and it assumes that you put the origin of your graph 2 miles directly below Erik's boat.

 

HW Ch2 Solutions: These are just the computations.

 

2.7-Full_Solution-byMe

This would earn 10/10.

 

2.9-Full Solution by Anon. Student

This did earn 10/10.

Wed.

 

2b

 

2/5

2b:  Chapter 3: Horizontal & Vertical Lines AND Circles

 

   -Read Ch3.

 

   -Do exercises on pp. 31-32:  3.1, 3.2, 3.4, 3.5, 3.6, and 3.8.  You may need to review how to complete the square for some of these. 

 

   -Turn in exercises 3.2b and 3.4

 

In class: Go over problem similar to 4.3.  Area of triangle, etc.

y = (x, 2) for any x -- horizontal line at y = 2 

x  = (4, y)  for any y  --  vertical line  at x = 4

 

All points that are a fixed distance from a given point is a circle: 

 

Khan-Completing the Square

 

Ch3 Solutions to Assigned Exercises: a bit messy

Ch3-Solutions

 

More detailed look at 3.2a with additional comments on circles.

 

Due

Date

Assignment

Extras-Options-Addenda

Mon.

 

3a

 

2/10

 

-Read Chapter 4 (pp. 33-50).  This is a long one.  We'll spend two classes on Chapter 4.

 

   -Do Exercises: 4.1, 4.2, 4.3, 4.4, 4.5 found on p51. 

 

   -Turn in the following ch4 problems: 4.3 (all parts).  This is an expansive problem.  Accurate and relatively large graphs are very useful.  Graph paper for the graphs is also helpful, but not necessary.

 

   -Turn in: Make a linear model to predict the world's population in the year 2050.  Use population data points from the years 1900 and 1999 only.  Then make another linear model using only the population data from 1999 and 2012 to predict the population for 2050.  Comment on these models.  [Look up necessary data.]

 

Notes:  Choose your perpendicular for problem 4.3a wisely.  There is one easy perpendicular, and there are 2 much harder ones.  Choose the easy one.  The mathematics in this problem is figuring out which is the easy perpendicular, not doing the calculation. 

        Problem 4.3b requires that you find x and y intercepts.  Hint:  What are the coordinates of intercepts in terms of ordered pairs, (x, y)?

 

A few World Population Graphs.

 

Solutions to the exercises assigned for today.

Ch4 Solutions (part 1)

Wed.

 

3b

 

2/12

 

    -Turn in problem 4.6 (all parts)...   from Ch4 exercises.  As always, draw excellent diagrams and use lots of prose to describe what you are doing.

 

 

  -Make an Excel Quadratic Formula Calculator.  Input a, b, and c, and output the two values for x.  Here is a PDF for guidance: QuadCalculator.

 

 

 

Detailed Solution to 4.6 Methods in this problem will be useful for the quiz.

Note: The diagram in this PDF has many of the answers included.  I added them to the diagram as I figured them out.

 

General Notes on HW:

1) GET STAPLERS!  I'll start marking –1 for unstapled HW.  Next week, –2, etc.

2) Identify the HW below your name with the due date.  E.g. "Exercises 2.7 and 2.9 - Due Feb. 3rd.

3) Many of you still need much more prose.  Walk me through your thinking, don't just calculate.  That's not only boring, but it is not really mathematics.  It's computation.  

 

Mon.

 

4a

 

2/17

   Turn in Take-Home Quiz-1: The Circle and the Line.  Due today.  

Problems 1-3 can be answered directly on the quiz itself.  I suggest you do the calculations on another sheet of paper and then transfer your pristine solutions to the quiz sheet.  Unless for some reason you want me to see them, I don't want to see your scribbles.  Problem #4 should be done on your own paper and presented like a homework write-up.  Full commentary, diagrams, pertinent calculations, jokes, etc.

Staplers for Sale!

 

GoogleSheets - almost identical to Excel

Wed.

 

4b

 

2/19

Do these problems from chapter 4:  4.8, 4.9, and 4.16.  [4.8 is quite hard.]

 

Read Ch5 and then do the following problems:  5.1, 5.2, 5.5, 5.6, 5.9, 5.10.

 

Turn in problem 5.6.

Time is running out to turn in back homework for credit.  The older the assignment, the less credit available.  Because the solutions are posted for most of the previous homework, if you want some credit, you need to do it well and with clear diagrams and commentary.  A description of how homework should be done is below. 

 

Here is the solution to 4.8.  Try to do it first, before you look at this.

 

Solution to 5.6 and other problems - These are rather abbreviated.

 

5.6 Student Solutions

 

Mon.

 

5a

 

2/24

Ch6  (We'll be doing an abbreviated version of this chapter)

 

Do 6.5, 6.6, 6.10, and 6.13. 

 

Turn in:  6.10. All the bells and whistles.

Turn in this worksheet: The Square Root of a Square Root

PDF of Ch6 Assigned Exercises

 

Ch6 Solutions -  coming soon...

Due

Date

Assignment

Extras-Options-Addenda

Wed.

 

5b

 

2/26

 Ch7

Read over Ch7.

Do these exercises:  7.1 and 7.2

Turn in: 7.1b and 7.2c.  Remember to walk me through these problems.  Don't just present the calculations.  Your presentation should be understandable to anyone who is familiar with this material.  Your presentation should be a self-contained essay.  Your presentation should be the 2nd, not the first draft and nicely formatted. If possible, your presentation should be entertaining too.  What's on your mind?  Talk to me.

              [Staples required.] 

 

7.1 and 7.2 Exercises-Answers

and Notes for doing 7.2

 

7.1 and 7.2 solutions coming soon...

 

A few of you might benefit from doing your homework in the Math Study Room.  The details of when, where, and who are below.

Mon.

 

6a

 

3/2

Ch7, pt2

 

Wed.

 

6b

 

3/4

Review of chapters 1 – 7.

 

TakeHome Midterm Exam

 

Mon.

 

7a

 

3/9

Ch8

 

Wed.

 

7b

 

3/11

 

Due

Date

Assignment

Extras-Options-Addenda

Mon.

 

8a

 

3/16

8a: 

 

Wed.

 

8b

 

3/18

8b: 

 

3/23

Spring Break

 

3/25

Spring Break 

 

3/30

Cancelled- Rescheduled 5/18

 

4/1

Cancelled- Rescheduled 5/19

 

Mon.

 

9a

 

4/6

9a: 

 

Wed.

 

9b

 

4/8

9b: 

 

Mon.

 

10a

 

4/13

10a: 

 

Wed.

 

10b

 

4/15

10b: 

 

Mon.

 

11a

 

4/20

11a: 

 

Wed.

 

11b

 

4/22

11b: 

 

Mon.

 

12a

 

4/27

12a: 

 

Wed.

 

12b

 

4/29

12b: 

 

Mon.

 

13a

 

5/4

13a: 

 

Wed.

 

13b

 

5/6

13b: 

 

Mon.

 

14a

 

5/11

Monday

14a: 

 

Wed.

 

14b

 

5/13

Wednesday

14b: 

 

Mon.

 

15a

 

5/18

Monday

15a:  Exam

 

15b

 

5/19

Tuesday

15b:  Special Problems

 

 

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 - RKC 101 - Sun–Wed, 7:00–10:00

Sunday

Monday

Tuesday

Wednesday

Julia Sheffler

 

Jiangli Liu

Yuexin Ma, (Echo)

Riti Bahl

Riti Bahl temporarily

 

Felicia Flores

 

Yiyang Zhou

 

t.b.a.

The Math Study Room is a place where you can casually do your homework and have other students with math backgrounds help you when you need it. 

It is a great place to get the help you need without the pressure of a professor.


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

 

Expectations

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 [dnewsome@bard.edu] 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. 

 

 

Grading

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.