Last Updated: 8/19/17

Page Contents

• Course Information Sheet
• Student Learning Outcomes for Math 90
• Course Textbook
• Homework Assignments
• Links of Interest for Math 90

Course Information Sheet

Here is a link for a PDF of the Course information Sheet given out during the first day of classes. It gives all the important information about how this course works (textbook info, office hours, details of policies regarding exams, quizzes, homework, grading, etc.).

Student Learning Outcomes for Math 90

In order to achieve success in this course, it's helpful for the student to have a clear idea of the concepts and skills they'll need to understand and master upon passing this course. These are referred to as Student Learning Outcomes (or "SLO's") for the course. The CCSF Math Department puts significant effort into formulating SLO's for our courses. An outline of topics and SLO's for Math 90 can be found in the PDF document here.

Course Textbook

Course Text:  College Algebra (6th Edition), by Stewart, Redlin, and Watson.

Note that, in our section of Math 90, you are not required to purchase the "WebAssign" support materials. But if you end up getting the WebAssign package anyway, and you want to access its support materials, see this link.

You can purchase our course textbook at the college bookstore.

If buying textbooks is a significant financial burden, look into the free CCSF Student Bookloan Program.

Students should obtain their textbook and have it available for study starting on the first day of classes. If you don't have a textbook by the first day of class, there are a number of copies of the textbook on 2-hour (or more) reserve in the college library (e.g. so you can access and read the book while waiting for delivery of a text purchased online).

We'll begin the semester by reviewing portions of Chapters 1 and 2 of the text, and then proceed to cover much if not all of Chapters 3-7...and part of Chapter 8 if time permits.

Homework Assignments

Homework assignments will be updated to the list below weekly as the semester proceeds, and the homework assigned during each week will typically be collected on the first day of the following week. We'll begin with a review of three different methods for solving "quadratic equations":

• the method of factoring;
• the method of completing the square; and
• making use of the quadratic formula.

This will be followed by a discussion of complex numbers, which will be useful in many situations throughout the course. The list of HW exercises below will be augmented as we proceed through the semester. Enjoy!

• §1.6: #1-5 all, 7, 9, 11, 17-27 odd, 33, 37, 41, 45, 47, 53, 57, 63, 65, 67, 69, 73, 83, 87, 97, 100.

Additional (non-textbook) Problems : Read the "ac test/method" handout (PDF, 148 KB) and do the exercises at the end of the handout.

For Monday, August 28: Turn in your solutions for exercises assigned from §1.6 above, as well as the exercises at end of the "ac test/method" handout (PDF above). Also, read ahead on complex numbers in §3.5 for Monday. (Note: We won't usually skip around the text, but §3.5 is well-motivated by the Quadratic Formula...and it does not require knowledge of the material from §1.7 to §3.4.)

Motivated by the "negative discriminant case" of the Quadratic Formula, we'll take a brief detour here to study the "complex numbers":

• §3.5: #1-4all, 5-13 odd, 17, 21, 25, 27, 31, 35, 37, 41, 47, 52, 59, 67, 69, 71.

• §1.7: #1-5 all, 13, 21, 25, 29, 41, 49, 55, 57, 63, 71, 88.
Also, as part of our "beginning of the semester review", you should look over our book's "Chapter P" on pages 1-53 ("P" is for Preliminaries). Do you remember:
• The laws of exponents?
• How to work with rational exponents?
• How to simplify expressions involving radicals?
• How to multiply, factor, and simplify polynomial expressions?.
In Math 90 we assume that you have learned (and retained) that material...so review and refresh yourself as needed.

For Monday, September 11: Turn in your solutions for exercises assigned from §1.7 above.

• §1.8: #1-5all, 11, 13, 23, 29, 41, 43, 57, 61, 67, 73, 87, 89.
• §2.1: #1-5 all, 8, 9, 13, 15, 17, 23, 27, 29, 32, 35, 45, 49, 51, 55, 57, 59, 81, 85.
  • If you'd like a short tutorial on "set-builder notation" see this link.
• §2.2: #1, 3, 4, 5, 9, 10, 13, 21, 26, 27, 31, 35, 37, 47, 51, 53, 55-59 all, 61, 63, 71, 72.
• Here's a link to the piecewise-curve discussed in class. And here's a link to graphs of basic functions (i.e. powers functions, reciprocal power functions, root functions, etc.).

For Monday, September 18: Turn in your solutions for exercises assigned from §1.8, 2.1-2.2 above.

• §2.3: #1, 3, 4, 5, 7, 19, 23-26 all, 37, 47, 49, 51.

Note: We will skip §2.4 (you can read it if you wish...but it's actually a preliminary Calculus topic). If you'd like to prepare for next week's topics, you can begin reading §2.5 (on basic "geometric transformations" of the coordinate plane, and their relationship to the graphs of functions).

For Monday, September 25: Turn in your solutions for exercises assigned from §2.3 above. While you should not turn in §2.5...nevertheless, try to do as much as you can of the homework for that section (see below), in preparation for our conclusion of that topic (i.e. "geometric transformations of graphs") next week.

Note: Our exam will be on Thursday, Sept. 28...see the class handout (from Tuesday, 9/19) for a summary of topics and practice problems for the exam.

• §2.5: #1-5 all, 7, 9, 11, 17, 19, 21, 23, 31, 33, 39, 41, 49, 51, 53, 55, 61, 63, 65, 67, 78, 91.
• Here are some interactive Desmos modules I constructed where you can experiment with concepts related to "shifts & scalings" of graphs in §2.5:
  • Heuristic mapping diagrams for Horizontal Scaling on a number line and Vertical Scaling on a number line.
  • You can experiment "shifting & scaling" with the piecewise-linear function discussed in class here.
  • Here's the "bump function" example from the end of class on Tuesday, 9/26.
  • Here's a more complicated piece-wise defined function with which you can experiment "shifting & scaling" the graph.

For Monday, October 2: Turn in your solutions for exercises assigned from §2.5.

• §2.6: #1-4 all, 11, 15, 21, 25-37 odd, 41, 47, 53, 55, 60, 61, 65.
• §2.7: #1-7 all, 9, 10, 11, 13, 17, 21, 23, 24, 25, 27, 31, 33, 35, 37, 38, 39, 41, 47, 51, 55, 67, 81, 86.

For Tuesday, October 10: Turn in your solutions for exercises assigned from §2.6-2.7.

• §3.1: #1-5 all, 7, 9, 15, 23, 25, 31, 55, 61, 68.
• Note: A nice summary of the process of "expressing a quadratic function in standard (geometric) form" appears here...with a number of nicely worked out examples. It's a good idea to see if you can read through and understand the summary of the process, and follow the steps illustrated in the examples there.

For Monday, October 16: Turn in your solutions for exercises assigned from §3.1

• §3.2: #1-4 all, 7, 9-14 all, 15-35 odd, 41, 43, 45, 51, 78, 79, 85.
If an nth degree polynomial function P(x) "factors completely" with all roots real numbers, then we can write: P(x) = a_n(x-r₁)(x-r₁)…(x-r_n-1)(x-r_n). The graph can then be understood as a curve having x-intercepts r₁, r₂… r_n, and vertical scaling factor a_n. Here is a Desmos module illustrating the concept, with slider values for r₁ through r_n.

Due Monday, October 23: Exercises assigned from §3.2 and exercises from classroom handout on "Graphing Polynomial Functions".

• §3.3: #1, 2, 3-9 odd, 13, 19, 25, 29, 33, 35, 43, 45, 55, 57, 59, 61, 68.
• §3.4: #1, 3, 7-19 odd, 33, 51, 59, 63-71 odd, 91.

Recall...we already covered §3.5 near the beginning of the semester...so we'll proceed to §3.6

Due Monday, October 30: Exercises assigned from §3.3-3.4...also read section §3.6 and begin working on the exercises.

• §3.6: #1-5 all, 7-11 odd, 25, 31, 33, 35, 41, 43, 45, 46, 49, 53, 55, 58, 71.

Due Monday, November 6: Exercises assigned from §3.6...also continue reading section §3.7 and begin working on the exercises.

• §3.7: #1-7 all, 9, 13, 15, 25, 27, 31, 33, 47, 49, 53, 55, 59.
• §4.1: #1-5 all, 11, 15, 18, 19-27 odd, 33, 48.
• §4.2: #1-3 all, 5, 7, 11, 13, 15, 21, 23, 33.

Due Monday, November 20: Exercises assigned from §3.7 - §4.2.

• §4.3: #1-5 all, 7, 9, 15, 18, 27, 31, 33, 35, 37, 39, 51, 53, 57, 59, 61, 71, 73, 75, 83, 85, 95.
• §4.4: #1-7 all, 13, 15, 19, 23, 29, 37, 45, 47, 51, 57, 59.

Due Monday, November 27: Exercises assigned from §4.3 - §4.4.

• §4.5: #1-3 all, 5, 11, 13, 29, 33, 37, 39, 45, 63, 81, 85, 91, 93.
• §4.6: #1, 13, 15, 23, 27, 29, 35, 36.
• §7.1: #1-5 all, 7, 15, 31, 33, 47, 49, 59, 62.
• §7.2: #1-5 all, 7, 9, 11, 15, 29, 31, 64, 67. 64, 67.
• §7.3: #1-6 all, 9, 11, 21, 27, 29, 37, 41.
• §7.4: #1-4 all, 5, 11, 21, 32, 33.
• Note: An interesting (optional) discussion of the gemoetry relating conic sections (parabolas, ellipses, and hyperbolas) to plane sections of a (double) cone can be found on this web page.

Links of Interest for Math 90 Students

• Desmos is a very "dynamic" web-broswer based graphing utility. It provides lots of opportunity to explore various graphical and computational aspects of functions. I've used it in class to illustrate various concepts, and I encourage you to experiment with it on your own as well. It may help you develop and expand your understanding...and have some fun playing with ideas.
• People have discovered many proofs of the Pythagorean Theorem. How many? This question was posed to "Dr. Math" at the Math Forum website. Dr. Math refers to the Pythagorean Theorem webpage on Alex Bogomolny's "Cut-the-Knot" math website, which gives details for many proofs of the Pythagorean Theorem. Some of the proofs on that webpage are illustrated with fun interactive Java applets...where you can click and drag various points of a diagram and modify its configuration...bringing the ideas behind the constructions to life. You'll have to scroll down the page past Alex's preliminary remarks to get to the proofs.
• In general, it's difficult to visualize what the graph of an arbitrary equation in x and y will look like in the xy-plane. Here is a link to the Implicit Function Graphing Tool, which you can use to view the graphs of equations in x and y. This is a a Java applet which you can access using any (relatively recent) web browser. It's easy to use and is based on a simple to understand algorithm (see the "How it works..." link on the webpage). If the applet doesn't seem to work, make sure you are entering your equations in the required format (see the "Entering Functions" link). SUGGESTION: Try viewing the graph of x^2 + |y| = 4, or x^4 y^3 +5 x^2 y^2 - x^2 +2 y^2 - y/3 = 6, or similar equations. Experiment!

  Note: If the java applet above isn't working (it can be buggy sometimes), you can try this alternate option.

• If you have an older computer that doesn't support Desmos, but does support Java, you can try xFunctions which is a Java applet that runs in Java capable browsers. (Be patient, it may take a minute to load the Java code into your browser.) XFunctions has eight different "utility screens" that allow you to:
  • View the graphs of many interesting function, and use the mouse to trace over the curve while reading off x and f(x) values.
  • Graph up to eight function on the same screen (in different colors) to compare behaviors.
  • Animate families of functions.
  • ...and many other capabilities.