# Algebra II—Semester A (2014-2015)

Nothing complex here...except complex numbers.

*Shmoop's Algebra II course has been granted a-g certification, which means it has met the rigorous iNACOL Standards for Quality Online Courses and will now be honored as part of the requirements for admission into the University of California system.*

You had so much fun in Algebra that you had to come back for more? Yeah, we don't blame you.

Algebra II has all the expressions and equations you've seen before…and then some. You're sure to see some old familiar friends along the way (we're looking at you, polynomials), along with a few unfamiliar faces (we're looking—or at least *trying* to look at you, imaginary numbers).

Semester A starts off with expressions, polynomials, and a beautiful thing we've all seen before: factoring. After being able to rearrange polynomials in more ways than a contortionist, we'll venture into the land of the imaginary. (Feel free to extend an invite to your imaginary childhood friend, Maurice.) We'll finish up the semester by working with more equations and inequalities than you can shake a dotted line at.

With loads of readings, problem sets, and activities, we'll cover:

- interpreting, factoring, and manipulating expressions;
- multiplying and dividing polynomials and rational expressions;
- working with imaginary and complex numbers;
- creating linear, quadratic, exponential, and absolute value equations;
- graphing and solving nonlinear equations and inequalities.

P.S. Algebra II is a two-semester course. You're looking at Semester A, but you can check out Semester B here.

## Course Breakdown

### Unit 1. Seeing Structure in Expressions

We'll start the course off by diving headfirst into expressions! With the help of factoring, radicals, and even sequences and series, we'll be able to pluck out different parts of an expression and figure out if two expressions are two peas in a pod or two peas in…separate pods. Because sometimes, one pod is just too cramped.

### Unit 2. Arithmetic with Polynomials and Rational Expressions

You may have dealt with polynomials and rational expressions in the past, but you ain't never seen 'em like this before. Not only will we gain some new tips and tricks to help us deal with these pesky expressions, we'll learn and even *prove* a few theorems along the way. Yeah, we mean business.

### Unit 3. The Complex Number System

You might think imaginary numbers are about as helpful as Maurice, your imaginary friend from kindergarten. We'll fill you in on a little secret: while Maurice can't deal with negatives under the radical or tell you about the Fundamental Theorem of Algebra, imaginary numbers can—and *will*. Then again, Maurice can make a mean imaginary apple cobbler. We all have our strengths.

### Unit 4. Creating Equations

This unit is all about using the magic of the equal sign to create and solve problems. (We'd use the magic of Houdini, but we're still working on that rope escape trick.) By creating and graphing every type of equation you can possibly think of, we'll learn how to tell them apart and understand which type of equation is applicable to which situation.

### Unit 5. Reasoning with Equations and Inequalities

For this unit, we're going how to put all the equations we created to use. We're going to graph our creations—both separately and together—and see how to use them to solve problems. More often than not, they can do a significant portion of the work for us, and who doesn't love outsourcing their work? So put your feet up, grab a piña colada, and let equations and inequalities do the work for you. (Not really.)

## Sample Lesson - Introduction

#### Lesson 5: Plotting Complex Numbers on the Coordinate Plane

Optical illusions can break our brains. At first, you think you see one thing, but then you realize (or are told) that things are not what they appear to be.

Our mind is about to shift again. The optical illusion: an ol' fashioned coordinate plane.

We might have always looked at an axis one way, thinking they are all the same. The *x*-axis represents the *x-*values and the *y*-axis represents the *y-*values, right? When it comes to complex numbers, it isn't that simple.

The usual Cartesian plane is only useful when we're working with real numbers. We're upgrading our numbers, though, going from real to complex, so we'll have to upgrade our plane, too.

When we throw complex numbers into the mix, we need to find a place to plot the *i*'s. Imaginary numbers prefer hiding in dark places like under the bed or in the attic. Silly imaginary numbers.

We're going to let the imaginary numbers hang out along the *imaginary*-axis. That means that the real numbers will be along the *x*-axis. When real numbers and imaginary numbers mix it up, we'll be ready to plot them on the complex plane.

- Credit Recovery Enabled
- Course Length: 18 weeks
- Grade Levels: 10, 11, 12
- Course Type: Basic
- Category:
- Math

- Prerequisites:

Algebra I—Semester A

Algebra I—Semester B

Geometry—Semester A

Geometry—Semester B

Just what the heck is a Shmoop Online Course?

Courses Tutorial

### Common Core Standards

The following standards are covered in this course:

A-REI.4bA-SSE.1b

A-SSE.1a

A-SSE.3c

CCSS.Mat.Content.HSA-REI.B.3.1

CCSS.Math.Content.HSA-APR.A.1

CCSS.Math.Content.HSA-APR.B.2

CCSS.Math.Content.HSA-APR.B.3

CCSS.Math.Content.HSA-APR.C.4

CCSS.Math.Content.HSA-APR.C.5

CCSS.Math.Content.HSA-APR.D.6

CCSS.Math.Content.HSA-APR.D.7

CCSS.Math.Content.HSA-CED.A.1

CCSS.Math.Content.HSA-CED.A.2

CCSS.Math.Content.HSA-CED.A.3

CCSS.Math.Content.HSA-CED.A.4

CCSS.Math.Content.HSA-REI.A.2

CCSS.Math.Content.HSA-REI.B.3

CCSS.Math.Content.HSA-REI.D.11

CCSS.Math.Content.HSA-SSE.A.1

CCSS.Math.Content.HSA-SSE.A.2

CCSS.Math.Content.HSA-SSE.B.3

CCSS.Math.Content.HSA-SSE.B.4

CCSS.Math.Content.HSN-CN.A.1

CCSS.Math.Content.HSN-CN.A.2

CCSS.Math.Content.HSN-CN.A.3

CCSS.Math.Content.HSN-CN.B.4

CCSS.Math.Content.HSN-CN.C.7

CCSS.Math.Content.HSN-CN.C.8

CCSS.Math.Content.HSN-CN.C.9

CCSS.Math.Content.HSN-RN.B.3