# Algebra 2 Worksheets

## About our Algebra 2 Worksheets

Our Algebra 2 worksheets are designed to show you how math works. Visually. We focus on plotting, visualizing, and graphing algebraic functions. So you can literally see the results.

Interestingly, a small set of algebraic functions can be used to describe the shapes of a surprisingly large number of real-world objects and happenings. This key idea allows us ultimately to program a computer with algebra to create models of the real world. The creation of mathematical models, commonly known as modeling, is perhaps the single most important of the algebra 2 topics

So, relax. Our Algebra 2 worksheets aren’t going to delve into the annoying, nitty-gritty details of doing complicated, multi-page calculations the old school way using paper and pencil. These days, if you can understand conceptually the fundamentals of algebra, it’s pretty easy to use a simple web app to do all the calculations and heavy lifting.

### What the Worksheets Cover

At a very high level, Algebra 2 can be described as the math used with two unknown variables, x and y. This corresponds to 2-dimensional problems that can be drawn out as a graph or plot on a piece of paper. Drawing out real world problems mathematically is known as modeling. Graphs are frequently used in science also, especially for analyzing experimental results.

It will be easier if you’ve mastered the algebra 1 worksheets before moving on to algebra 2.

Download the printer-friendly worksheets below, and also find the complete video solutions and lessons here.

###### Problem Set 1: Plotting Lines by Hand
PS1 is about lines. Simple, straight lines. There is an equation for a line, and you will learn how to plot them graphically.

A line maybe doesn’t sound that exciting, yet note that the goal of almost all scientific experiments is to manipulate a bunch of collected data such that the points fall on a line. Almost all of the math in engineering and businessis usually, ultimately ends up as making a simple line.
###### Problem Set 2: Plotting Lines and Simple Parabolas with a Computer
PS2 teaches you how plot shapes on a computer using a free, simple web app (https://www.desmos.com/calculator). We will focus on plotting lines and parabolas.

###### Problem Set 3: Plotting Polynomial Functions
PS3 formally introduces the concept of algebraic functions, and we cover the topics such as range, domain, limiting behavior, roots, and multiplicity (repeated roots), all in Plain English. We’ll learn how to plot polynomial functions, specifically quadratic functions and cubic functions.

Don’t worry, this is going to be easy, because the computer is going to do all the hard work of plotting the algebraic functions.
###### Problem Set 4: Plotting Parabolas by Hand Using the Vertex

PS4 changes the focus away from using the computer. Will go back to paper and pencil, now that we better understand our friend the parabola. You’ll learn how to just “see” what a function looks like in your mind and draw it out on paper. You might actually find that you can do algebra faster and better than the computer anyhow, now that you have a few basic skills down.

###### Problem Set 5: Modeling with the Parabola

PS5 focuses on computer modeling. We will look at some real world problems such as flight paths (of jumping fish!) and satellite dishes. Will focus on the parabola again. A new topic will be understanding the standard form of an equation, so that we can make simple adjustments to represent arbitrary shapes. And we make cool computer graphics too.

###### Problem Set 6: Plotting Conic Sections

PS6 focuses on plotting conic sections, which include our friend the parabola that has been studied extensively by this point. Other conic sections include circles, ellipses, and hyperbolas. We will also introduce the concept of asymptotes, which is related to limiting behavior.

###### Problem Set 7: Logs and Exponential Functions

PS7 is about logarithms, commonly called logs. We will emphasize base 10 logarithms and also the natural logarithm. Logs are very closely related to exponents, which are covered in the algebra 1 topics.

###### Problem Set 8: Vectors and Complex Numbers
PS8 covers vectors and complex numbers. Whereas algebraic functions represent shapes, vectors represent motion. These concepts can be combined to model how objects move about around in the real world.

Complex numbers are a seeming workaround to the impossible case of taking the square root of a negative number. We introduce a mathematical trick known as an imaginary number, which turns out to be an extremely useful thing. Engineering analysis of anything that vibrates or oscillates requires imaginary numbers. And in the real world, it is usually the case that things vibrate or oscillate.
###### Problem Set 9: Matrices and Systems of Equations
PS9 focuses on matrices. Matrices are necessary to analyze problems with more than two dimensions. This is of course useful for modeling our three-dimensional (3D) world. In fact, computers don’t really do algebra, they do matrix math.

Perhaps the most powerful computer program in existence for doing math is called MatLab (https://www.mathworks.com/). It’s an abbreviation for Matrix Laboratory.