The Official SAT Question of the Day

Friday, April 29, 2011

Week 34

Precalculus will be exploring the law of sines and cosines and working through the ever challenging "ambiguous case" for law of sines. To review trigonometry for the upcoming exam try this online set of tutorials and practice or this set of videos. Let me know if it helps!
Homework with odd answers:*

Khan Academy

Algebra II is moving from operations with rational expressions to solving rational equations. We will again apply all modalities to solve these equations: numeric, graphic, and algebraic. It is important to be able move between these modalities and use each to help you solve the more difficult problems.

Examples for Simplifying Complex Rational Expressions:

Videos of the Week:
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3
Solving Rational Equations 1
Solving Rational Equations 2
Solving Rational Equations 3

Reference Sheets:

Homework* with odd answers:

*Modified from University of Houston

Friday, April 15, 2011

Week 33

First and foremost, have a great Spring Break. I know I will.

Secondly, take this extended time to do some work on Khan Academy. It is an excellent tool for you to practice and prepare for finals. In addition, you can take your math skills to new heights and new topics. Enjoy.

Algebra II is moving into basic operations with rational functions. As always, the basics of multiplication, division, addition, and subtraction of fractions comes back to haunt us all. I think the reference sheet for this one could be of real help to keep you organized, focused, and always pointed in the right direction.

Reference Sheet:

Completed Notes on Adding and Subtracting Rational Expressions:

Operations with Rational Expressions Videos:
Multiplying and Dividing Rational Expressions 1
Multiplying and Dividing Rational Expressions 2
Multiplying and Dividing Rational Expressions 3
Adding and Subtracting Rational Expressions 1
Adding and Subtracting Rational Expressions 2
Adding and Subtracting Rational Expressions 3

Homework (with odd solutions):

Final Review Packets:

Precalculus will graph the other 4 trigonometric functions with all their pecularities and nuances. I highly recommend watching some of the videos I have posted below. Remember to pause and rewatch them to get a true idea of how these functions behave.

Cosecant Secant Cotangent

Graphing Trigonometric Functions Videos:
Graphs of Trig Functions
Graphing Trig Functions
More Trig Graphs
Determining an equation of a trig graph


Final Review Packets:

Friday, April 8, 2011

Week 32

Algebra 2 finalizes their investigation and construction of the graphs of rational functions. It is absolutely essential to make the connection between the algebraic manipulations and understandings of these functions and their graphs. I will be away from school both Thursday and Friday of next week trying to learn how to better use the SmartBoard (you know I need that). Remember to take advantage of the exercise practice at Please find a rather complicated rational function below. The steps to graphing it can be found here.

Graphing Rational Functions Powerpoint:

Operations with Rational Expressions Guided Notes:

Reference Sheets:

Rational Function Videos:
Asymptotes of Rational Functions
Rational Function Example
Another Rational Function Example!

Homework with odd solutions:

Final Review Packets:

Precalculus is going to continue with sine and cosine functions in the attempt at mastering all the different transformations that result in changes in amplitude, vertical shift, phase shift and period. The change in one parameter, amplitude, is captured in the image below:

Transformations of sine functions

Plotting a Sine or Cosine Wave

Khan Academy videos:
Graphs of trigonometric functions
More graphs of trig functions!

Precalculus Homework:

Final Review Packets:

Friday, April 1, 2011

Week 31

Fourth Quarter is now here. Your grade from the first three quarters cannot be changed--the only thing you can control, as a student, is your grade fourth quarter. Please, scholars, do thy best to finish strong. A great way to keep your basic skills up as we move through fourth quarter and prepare thyself for finals is to login at and keep marching through the exercises.

*For Parents: I added an e-mail subscription to the sidebar so that you can receive an e-mail everytime the blog is updated. Just type your e-mail in and follow the steps that follow. It should take about 20 seconds.

Algebra II begins rational functions, which are graphically somewhat different than previous functions, but they nevertheless require a great deal of the skills we have been building all year. Factoring fun will remain a large part of our life. Here are two graphical examples of rational functions:

To explore the graphs of rational functions try this applet.

Rational Expressions and Functions, part I
Rational Expressions and Functions, part II

Rational Functions Blank Note Guide and Graphing Powerpoint:

Reference Sheet:


Saturday School:

Precalculus is ending the year with a bang. We are investigating the graphs of the six trigonometric functions and the unique types of behavior they can model. The coming week we will start with graphing sin(x), cos(x), and possibly tan(x). We will be relying on a curriculum that can be found online here. Here is a graph of sin(x):

File:Tan drawing process.gif

To explore transformations of sine functions try this applet.

Trigonometry Videos


Saturday School: