Algebra II—Semester A

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.

This course has also been certified by Quality Matters, a trusted quality assurance organization that provides course review services to certify the quality of online and blended courses.


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 us venturing into the land of the imaginary. (Feel free to extend an invite to your imaginary childhood friend, Maurice.) After getting our bearings, we'll check out a familiar landmark, our old friends the polynomials. They've learned some tricks, though, including shoving themselves under radicals and stacking each other into rational expressions and equations. We'll finish up the semester by working with more sequences and series than you can shake a finite stick at.

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

  • working with imaginary and complex numbers;
  • multiplying and dividing polynomials and rational expressions;
  • creating linear, quadratic, exponential, radical, and absolute value equations;
  • graphing and solving nonlinear equations and inequalities;
  • using formulas for arithmetic and geometric sequences and series.

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


Here's a sneak peek at a video from the course. BYOP (bring your own popcorn).


Unit Breakdown


  1. Algebra II—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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—Semester A - 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.

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