PreCalculus: The First Half (approximately)


Here are the assignments from the first day to 3/11/20, the start of The New Normal (the virus).

I moved here them because the original site was getting cluttered.





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








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.







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.



This would earn 10/10.


2.9-Full Solution by Anon. Student

This did earn 10/10.






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



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












-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)







    -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. 


Several of you did excellent jobs on 4.6.  I didn't have the time to scan the best ones, so I'm not posting any of them.


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.  







   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






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 by Julia and Fiona







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


6.10 solution


6.10 by Ian and Zuka











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


Emma A's and Monroe B's Solutions to 7.1 and 7.2.


Math Study Room.  The details of when, where, and who are below.






Ch7, pt2


Do these problems: 7.4, 7.5, 7.11, 7.18 (clever trick), 7.19 (very hard), and 7.20 (pretty hard).  PDF of assigned exercises.


Turn in 7.11.  Tell the story of 7.11.


Get extra credit for exact answers to any of these:  7.19a ,  7.19b,  7.19c.


Feel free to take advantage of the Math Study Room.  The details of when, where, and who are below.




In Class: 

Show perpendicular rotations

Sum of Consecutive Numbers


7.4: Rewrite in vertex form and determine the conditions whereby the parabola sits on the x-axis.

Here is an animation of 7.4a.


7.5:  It's just a 3-point problem with limits on the domain and range (no negative days and no negative prices).  In other words, where the time and price make sense in the real world.

        Part b is just finding the maximum using the vertex form of the quadratic and then not forgetting that you have 1000 shares (not 1) and that you bought the stock on day 30 (not day 0) and then figuring out the profit, not the overall worth of 1000 shares.


7.11:  Set up perimeter equation.  Solve for the vertical side dimension of the rectangular part.

Then set up the Area equation and substitute in the vertical side dimension in terms of the horizontal side. 

Then complete the square, but all you really need is the b/2 thing.  That will be your horizontal length.  The book gives the radius of the circle for its answer.






Review of chapters 1 – 7.


Turn in problem 7.14.  I'd like good diagrams or illustrations along with an organized presentation with useful prose and a joke or two.


Turn in Calculations Exercises Worksheet: PDF.  I forgot to hand these out  in class (some of you got one)... the rest are in the box outside my office... or you can print it up yourself and do it.


TakeHome Midterm Exam handed out.  Due Monday, 3/9/20.


Homework is looking great in general.

Love those staples too!


Here are 2 short videos of similar triangles formed by perpendicular lines:




MidTerm Take-Home

Midterm PDF



Take a Break with:

-Distorted Reality

-Hippy Flam.










TakeHome Midterm Due.



I've received a couple of questions about 5d and 5e from the midterm.  Here are illustrations to help you understand my meaning: 5d&5e.


Hint for problem 5 set-up.


Hint #2: Use with similar triangles

Series of Videos with Hints for #5 of MidTerm:

I put these videos into a GooglePhoto Album.

The link is here:  GoogleAlbum- MidTerm Hints


FinalBlackboard Picture from these video-hints



Look over this website.  It begins to give you an idea of the scale of our local astronomical neighborhood.

Scale Solar System







Ch8: Composition:  Read the chapter.  This chapter does a relatively good job explaining how compositions of functions are useful. 


Do these problems: 8.1a, 8.2, 8.3, 8.5, 8.7, and 8.9.  (Do all parts unless otherwise indicated.)  Chapter 8 Exercises and Answers and a few solutions.


Turn in 8.7.  You'll need to use the quadratic formula and I'd like you to draw up a pretty good graph.  Remember to comment and explain and walk me through your thought process.  Calculations by themselves  (without comment and organization) will be summarily dismissed.   I simply don't have time to figure out confusing homework.  If you are confused by the assignment, that's fine, write about it.  Explain your confusion. Try graphing  it and approximate an answer from the graph.   If done well, that's an excellent start and will be rewarded.