# Stonebraker's Algebra 2

Below is a selection of materials from my Algebra 2 course. The study guides are highly-condensed summaries of various topics, good for cramming and just for having around while solving problems. Below, the worksheets and practice tests provide a look at what sorts of questions I ask my students.

### Study guides / summaries.

• Lines. (PDF)
Different forms for line equations, tips for graphing, slopes... just the basics.
• Function transformations (PDF)
A quick reference sheet about the different sorts of function transformations, and how to tell what will happen to a graph based on the expression. Examples of finding the transformed rule.
Tips and methods for factoring quadratic expressions, mainly the "hard" ones where the first coefficient is not 1. Also how to recognize a perfect square and not get fooled by imposters!
• Square roots and complex numbers (PDF)
Definitions and properties for working with square roots, including how to simplify them. Imaginary and complex numbers, performing operations on them and simplifying them.
Lays out the different methods for solving a quadratic equation, including how to recognize when a certain method will work. Rules for the discriminant. Example of a solution using the complete-the-square method.
• Polynomial basics (PDF)
Vocabulary for describing polynomial expressions and their graphs. How to figure out end behavior. This sheet was especially popular with my classes!
• Polynomial expressions (PDF)
Roots (or zeros) of polynomials, and how to find them. Factoring tricks, "possible" rational roots, and long division.
• Algebra of functions (PDF)
Recognizing a function's domain from its formula. Performing operations on functions. Composition of functions. Finding the inverse of a function.
Rational exponents and properties involving exponents. Methods for solving equations with radicals and powers in them.

### Selected worksheets and problems.

• Drawing lines in Desmos (PDF) (ODT)
An introduction to using Desmos and a "tactile" way of getting a feel for what "y=mx+b" means. Students use sliders to draw specific lines, then move on to drawing specific shapes by putting together multiple lines.
• The Function Game (PDF) (ODT)
This is my implementation of Kenny Felder's "Function Game" from his Advanced Algebra II course, generously available in its entirety online. Students give each other numbers, perform secret calculations on them, and try to guess what the rules for the functions are.
• Function transformation practice test (PDF) (ODT)
A practice test for my "function transformations" unit. I put a great emphasis on understanding how functions transform early in my course, giving the topic nearly two weeks and testing on it separately.
• Parabola game with Desmos (PDF) (ODT)
Another Desmos activity. This time students adjust sliders for a, h, and k to get a parabola which passes through three "target" zones. This is intended to give them some familiarity with the meaning of these parameters in a vertex-form quadratic. Redoing this activity with standard form (a, b, c) is much more challenging!
• Parabolas practice test (PDF) (ODT)
The practice test for my parabolas unit. The questions where I show a graph and the students have to state an expression for it cause a lot of headaches.
• Finding polynomial turning points with Calculus honors assignment (PDF) (ODT)
Because taking derivatives of polynomails is easy and fun, I teach my honors students how to do it so they can find the turning points (extrema) of polynomials instead of only finding the zeros. This is the assignment I give them.
• Polynomial properties review (PDF) (ODT)
A first review packet leading up to the polynomials test. These questions cover terminology, recognizing the features of a graph from the formula, and sketching polynomials when given a function in factored form.

### Notes on file formats:

• I create nearly all my materials in the OpenOffice suite, which is free and open source, so they are saved in version 1.2 of the OpenDocument format. If you want to edit them I strongly recommend using OpenOffice to do it. Microsoft Word can open the files, but depending on your version of Word they may be essentially useless. For example, when I try it in Word 2010, it says my ODTs are "corrupt" and then offers to "recover" some of the data. It gets the text mostly right, but the drawings are completely wrecked, and they're the most time-consuming part to make!
• My text documents are mostly written using a font called "Korinna BT". It seems to be pretty widely available if you search for it. If you don't have/want it, you may need to massage the formatting and spacing to make things look right.

## LICENSING  This page hand-coded by Steve Stonebraker (sstoneb@gmail.com) in HTML and PHP.