In order to review the topics that were on Exam #2, and to give you a chance to improve your exam score, I will give a series of make-up exam exercises that you can use to replace some of your Exam #2 scores. The first one will be Monday at the end of class, and will cover the quadratic formula and complex numbers (similar to #3 and #5 on Exam #2). I have reopened those WebWork sets so that you can complete those exercises if you didn’t previously.


  • Quadratic Equations-Quadratic Formula – due Mon May 6
  • ComplexNumbers – due Mon May 6
  • Graphs-Graphs of Quadratic Equations – due Tues May 7
  • Trigonometry-Right Triangles Trigonometric Ratios – due Wed May 8

Schedule for the remainder of the semester:


We introduced equations of circles, and did some examples from the “Graphs of Quadratic Equations” WebWork.

First we looked at circles centered at (0,0), which have equations of the form

x^2 + y^2 = r^2

where r is the radius of the circle (note that the equation comes from the Pythagorean Theorem–it is satisfied by points (x,y) that are distance r from the (0,0)!)

Next we looked at how the center can be “shifted” to a different point:

Two examples from the WebWork; in the second example we have to “complete the squares” on the x-terms and y-terms in order to put it in “standard form” so that we can find the center and radius:

We then started trigonometry. We reviewed the definitions of the trig ratios (sine, cosine, tangent) and their reciproicals (cosecant, secant, cotangent):

We did some examples from the “Trigonometry-Right Triangles Trigonometric Ratios” WebWork: