Announcements

In order to review the topics that were on Exam #2, and to give you a chance to improve your exam score, I am giving a series of make-up exam exercises that you can use to replace some of your Exam #2 scores. The first two last week were on the quadratic formula and then multiplication/division of complex numbers (similar to #5 on Exam #2); the next one on Monday (May 8) will be on complex fractions (#4 on Exam #2). The Exam #2 solutions are available on OpenLab Files.

I have reopened the relevant WebWork sets so that you can complete those exercises if you didn’t previously. I have also extended some other open sets until Wed May 15:

WebWork:

• Quadratic Equations-Quadratic Formula – due Wed May 15
• ComplexNumbers – due Wed May 15
• Rational Expressions-Complex Fractions 1 – due Wed May 15
• Rational Expressions-Complex Fractions 2 – due Wed May 15
• Graphs-Graphs of Quadratic Equations – due Wed May 15
• Trigonometry-Right Triangles Trigonometric Ratios – due Mon May 20
• Trigonometry-Coordinate Plane Unit Circle – due Mon May 20

Exam #3 will be consists of (a) a set of take-home exercises, to be handed out Wed May 15, and (b) a set of in-class exercises on Mon May 20, when the take-home exercises will also be collected. The final exam is on Wed May 22.

Topics

We did additional exercises from the Final Exam Review on: (1) an equation of a circle and (2) a system of nonlinear equations. Both of these topics will be on Exam #3:

We then covered the two “special right triangles” (“30-60-90” and “45-45-90”) and did some of the WebWork exercises that use these:

#11 from “Right Triangles Trigonometric Ratios”:

We then introduced “trig in the coordinate plane” and did a WebWork exercise from “Trigonometry-Coordinate Plane Unit Circle”:

Announcements

In order to review the topics that were on Exam #2, and to give you a chance to improve your exam score, I am giving a series of make-up exam exercises that you can use to replace some of your Exam #2 scores. The first one was at the end of this class on Monday, on the quadratic formula. The exercises on Wed May 4 will cover multiplication and division of complex numbers (similar to #5 on Exam #2); next Monday (May 8) will be complex fractions (#4 on Exam #2).

I have reopened the relevant WebWork sets so that you can complete those exercises if you didn’t previously. I have also extended some other open sets until Wed May 15:

WebWork:

• Quadratic Equations-Quadratic Formula – due Wed May 15
• ComplexNumbers – due Wed May 15
• Rational Expressions-Complex Fractions 1 – due Wed May 15
• Rational Expressions-Complex Fractions 2 – due Wed May 15
• Graphs-Graphs of Quadratic Equations – due Wed May 15
• Trigonometry-Right Triangles Trigonometric Ratios – due Mon May 13

Also, Exam #3 will be consists of (a) a set of take-home exercises, to be handed out Wed May 15, and (b) a set of in-class exercises on Mon May 20, when the take-home exercises will also be collected.

The final exam is on Wed May 22.

Topics

We first covered a remaining topic from algebra: systems of equations. First we started with a system of 2 linear equations, which we solved by the substitution method:

Then we looked at a system of equations where at least one equation is “nonlinear” (in the examples we look at, quadratic), taken from the Final Exam Review exercises:

We again used the substitution method–in this case that resulted in a single quadratic equation, which we solved by factoring. That gave the 2 x-values; we also needed to find the corresponding y-values:

We then reviewed the trig ratios, and did some additional exercises from the WebWork:

In this exercise, we needed to use the Pythagorean Theorem:

In this exercise we used the fact that the sum of all angles in any triangle is 180 degrees. We then used the trig ratios to solve for the lengths of the unknown sides:

Announcements

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.

WebWork:

• 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:

Topics

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: