From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.

Pre-Algebra II—Semester A

We've got the powers.

If math just sat still, like a bump on a log, it wouldn't be of much use to anyone. Not even mathematicians would get excited about it—and you should see some of the things they get worked up over. Lucky for everyone, then, that math is full of sound and fury, signifying something awesome.

(Levels of awesome may vary.)

In this Common Core-aligned course, we'll peel back the veil and uncover the mysteries of all the algebra that comes before Algebra. With boatloads of problem sets, readings, and quizzes, we'll cover

  • rational and irrational numbers
  • radicals, exponents, and number theory
  • linear equations and inequalities with one and two variables
  • transformations of geometric figures
  • linear functions

P.S. Pre-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. Rational and Irrational Numbers

Get ready for the next level of numbers: rational and irrational numbers. Sure, they might be as different as apples and orangutans, but it's good to have some variety. We'll learn how to convert rational numbers into fractions, how to identify those pesky irrationals, and even how to approximate irrational numbers using rationals. We wouldn't suggest approximating apples with orangutans, though; that might get messy.

Unit 2. Radicals, Exponents, and Number Theory

If anything proves that good things come in small packages, it's exponents. Well, maybe not always good, but certainly powerful. These tiny little numbers can really pack a punch, so we suggest putting on some headgear. In this unit, we'll learn about the complicated relationship between exponents and radicals, and how one operation always undoes the other. Oh, maybe it isn't that complicated.

Unit 3. Equations and Inequalities in One Variable

Equations are the ultimate balancing act. If the two sides don't match up exactly, everything will topple over. With only a little bit of practice, though, we'll be able to juggle, shuffle, and slide numbers around an equation without the slightest wobble. After that, we'll use those same skills to tackle inequalities, the hippie-like cousins to equations. They don't care much about any single value;  as long as the answers fall within a certain range, they go with the flow. Pretty groovy, right?

Unit 4. Equations and Inequalities in Two Variables

We'll cover how two-variable equations can describe all kinds of relationships—the good, the bad, the ugly, and the math-y. Mostly that last one, if we're being honest.

Unit 5. Geometric Transformations

Sorry, numbers and letters, but we need a break from you. Instead, we'll be movin' and groovin' with figures this unit, except for a few tricky definitions and a quick tango with the coordinate plane. Just be careful; some of these shapes have sharp edges. The last thing we want is for you to get a nasty cut mid-disco.

Unit 6. Linear Functions

We're going introduce you to functions nice and slow as we go over the basics: learning the definition of a function, seeing how to identify them by sight in tables and graphs, and visualizing them on the coordinate plane. Then we'll zoom in on linear function and all of their different parts and pieces—no dissection necessary (or wanted). Leave that for your science class.

Unit 7. Graphing Linear Equations and Inequalities

Just knowing linear equations inside and out isn't enough: we also have to know how to graph them. Lucky for us, then, that their graphs have a purpose other than looking cool. They can make problems easier to understand and solve—especially when there are real-world applications lurking in the wings. Obviously, looking cool doesn't hurt, either.

Sample Lesson - Introduction

Lesson 6: Solving Inequalities Using Multiplication and Division

Addition and subtraction are great, but sometimes we need another level of solving power. It's just like when you exchange your handsaw for a chainsaw, or add extra thrusters to your rocket ship. Your tool has to be up to the challenge of your problem. For us, the extra boosters are multiplication and division.

With these added boosters, there's no way the atmosphere is keeping us in this time.


Thankfully, utilizing this new, heavier-duty solving mechanism doesn't actually make our solution more complex. In fact, multiplication and division in inequalities follow the same rules that addition and subtraction do, which is to say that they follow the same rules regular equations do. It all boils down to our Golden Rule of algebra: Everything you do to one side you have to do to both.

There is one very important thing to not overlook. The information in this lesson only applies when we are talking about multiplying or dividing by a positive factor. If our factor is negative, the rules are slightly different, and all those rules are covered in the next lesson. Just remember to keep on the positive side of things for now and you'll be just fine.

  • Credit Recovery Enabled
  • Course Length: 18 weeks
  • Grade Levels: 7, 8
  • Course Type: Basic
  • Category:
    • Math
    • Middle School
  • Prerequisites:
    Pre-Algebra I—Semester A
    Pre-Algebra I—Semester B

Just what the heck is a Shmoop Online Course?

Courses Tutorial