Algebra II (College)

Algebra II: The Search for Shmoop Gold.

This course has been recommended for ACE CREDIT®, which means it is considered for credit at thousands of colleges and universities across the country. For more information, click here.


Up until now, the math courses you've taken have probably been a stroll down Easy Street. Algebra I was an invariable breeze. Geometry was a yearlong game of Pictionary. You're bopping along, thinking, "Algebra II can't be that much harder, right?"

Uh. Well. This is awkward.

We don't mean to alarm you, but Algebra II is a mountain compared to the molehill that was Algebra I. And we're going to need a bit more than a pair of worn-out Nikes to make our way over it in one piece. (Shopping trip to REI, anyone?)

Our trek up Mount Algebra II will be a tough one. Although you need to hang on to all of the basics you learned in your previous courses, you'll be doing a lot more than solving linear equations. Sure, we'll see a few of our old friends again, like polynomials and systems of equations, but we'll also meet a few strangers like logarithms, trig functions, and statistics. They might be a bit rough around the edges, but we'll use our irresistible charms to befriend them in no time.

Ultimately, these topics serve to prepare us for courses like Statistics, Precalculus, and Calculus. And, you know, real life.

You've already learned the basics of equations, functions, expressions, graphs, and number systems. Once you've got all those packed away in your thermal-resistant backpack, here's a roadmap of what's up ahead.

  • We'll start at base camp, talking about numbers. We've got rational and irrational numbers, and our new best friends, the complex numbers. Don't let the name freak you out; they're not that complicated.
  • We'll start this climb off easy by staying on the well-worn trails of polynomials. After some factoring review, we'll shake things up by bringing in complex solutions to quadratic equations and take a moment to admire the Fundamental Theorem of Algebra.
  • Adding, subtracting, and multiplying polynomials is old hat to us, but dividing them is a whole new ball of wax. Well, we've got a box of specially made gloves—long division, synthetic division, and the Remainder Theorem—to make handling that wax easy peasy. We'll even roll that ball into a brand-new form: rational expressions.
  • Then, we'll enter Equation Valley, where radical and rational equations bloom year-round. Take a whiff of those solutions; that's the good stuff right there.
  • If a picture is worth a thousand words, then we're about to be heirs to a veritable word dynasty. That's 'cause now's the time when we'll graph all kinds of polynomial, rational, and root functions. And just so we don't get too bored, we'll solve systems of equations with them as well. After all, one equation can get pretty lonely all by itself on a graph—and if there's one thing misery loves, it's company. Or possibly cake.
  • Speaking of not getting bored, don't you hate it when you have to add or multiply the same thing over and over and over and...we'll stop. Anyway, sequences and series are two special types of functions that are ideal for tossing tedium to the curb.
  • Logarithms and exponential functions go together like peas in a pod, or orcas in a pod, or people in a pod. They're super tight is what we're saying, and we can't learn about one without the other.
  • Then comes one of the most harrowing part of our journey: trig functions. As long as we remember our trig ratios from geometry, and keep an emergency unit circle in our back pocket, we should scale the final heights and draw ever closer to the summit.
  • Then comes a rest stop at Fort Function, where we'll revisit all our old friends and get to know them a little better. We'll even get to meet some exotic functions like piecewise and absolute value functions.
  • The odds are that one 1 of every 2 students loves statistics. We're so glad that one is you. Statistically speaking, you'll consume more information about this topic than you bargained for.
  • We'll reach the top of the mountain when we learn about probability and how it affects real-world decisions. For instance, in the future we'll know that if we're planning on climbing to the top of a giant mountain, we should probably bring a coat or something.

So strap on those weatherproof boots, tighten that bandana (if you're into the Kid Rock look, anyway), and finish carving that hiking stick. We're about to reach new heights with our algebra skills. And if we're going to be on this journey together, the least you could do is share some of that trail mix. Sheesh.


Unit Breakdown


  1. Algebra II (College) - Number Systems

    We'll start the course off by diving headfirst into some numbers. Sure, you've been dealing with numbers for your whole mathematical career, but here we'll delve into the structure of integers, rational numbers, and real numbers. A tour of the complex number plane may even be in order.

  2. Algebra II (College) - Introduction to Polynomials

    You may have dealt with polynomials 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.

  3. Algebra II (College) - Polynomial Division and Rational Expressions

    Had enough of long division? We sure hope not. We'll show you how to do it with polynomials and then move on to doing arithmetic with rational expressions. There'll be some throwbacks to factoring throughout, so make sure those skills are still sharper than a fine cheddar.

  4. Algebra II (College) - Radical and Rational Equations

    This is where we'll get you acquainted with radical and rational equations. All the algebra you'll need to solve equations with these guys will be covered in gory detail. We'll even take a moment to use our newfound knowledge to model some situations. What would a unit be without some applications?

  5. Algebra II (College) - Polynomial, Rational, and Root Functions

    You'll find a smorgasbord of functions in this unit. We'll take everything we've learned about polynomial, rational, and root functions and use it to create some pretty accurate graphs of these guys. As always, we've saved plenty of room for some tasty real-world apps.

  6. Algebra II (College) - Sequences and Series

    We'll cap the semester off with a tour of sequences and series. We'll introduce you to some nifty formulas to work with them, and give you a brand-spanking new tool for your mathematical toolbox to help you prove statements—proof by induction. Try to contain your excitement.

  7. Algebra II (College) - Exponential and Logarithmic Functions

    We won't lie to you: we've packed a lot into this unit. We'll start off with logarithms and exponents and their rules. Soon after, we'll throw these bad boys into equations and solve them in every way under the sun: algebraically, graphically, and with technology.

  8. Algebra II (College) - Trigonometric Functions

    Here we'll give you the keys to the trig kingdom. After introducing the unit circle and a brief review of the basic trig ratios, we'll take things to the next level. We're talkin' graphing trig functions and showing you how to shift and flip them all over the coordinate plane. And how could we forget about applications? We'll wrap things up with some activities on what you can actually do with your new found trig knowledge.

  9. Algebra II (College) - Building Functions

    This unit is for the practically minded everyman in all of us. We're actually going to get our hands dirty (well...not literally) by building functions. Taking all the functions we've learned about so far, we'll throw 'em together in every which way we can think of to make new ones.

  10. Algebra II (College) - Statistics

    In this unit, we'll run the statistical gamut—from summary stats and the normal distribution to populations, samples, and simulations. We'll lay down the foundation for properly collecting real-world data and even get our hands dirty summarizing it. By the end of it all, your head will be fit to burst with all kinds of statistical knowledge.

  11. Algebra II (College) - Probability

    This unit is all about taking what we know about a situation and making the best possible guesses and extrapolations about it that we can. Some will be wrong, but we're also betting that a good number of them will be right. And given that our universe is a giant floating bubble of randomness and chaos, we think being able to predict events through math is pretty neat.

Please Wait...