# Algebra

##### Topics sometimes go by lots of different names, but we've tried to put almost all of them somewhere on the page below. To scan the page quickly, use the green search bar above, which will highlight a word or phrase on the page.

# I. Numbers & Calculations:

### Prime Numbers, Factoring, Factorization & Divisibility

#### In this chapter we'll get into the basics of prime numbers and "prime factoroization", which we'll use in fractions and roots throughout Algebra and Algebra 2. I also get into divisibility rules, which show up -- among other places -- on the SAT.

### Fractions & Mixed Numbers

#### Everything you need to know about fractions: reducing, least common denominators, addition, subtraction, multiplication, division, converting improper fractions to mixed numbers, converting to decimals. Also the tricky problem of converting repeating decimals to fractions.

### Exponents & Exponent Rules

#### In this chapter we'll introduce the concept of exponents, as well as rules for combining and canceling exponents. Also, we'll talk about the special cases of exponents of 0 and 1, and what happens with negative exponents.

### Percents & Interest

#### We'll start by comping percentages using basic ratios, then we'll move on to using a decimal-based approach since that's what you'll need for more advanced problems. I also point out the most common types of trick questions about percents, including common types of SAT questions, and computing interest.

### Roots & Radicals

#### In this chapter we'll learn how to reduce radicals using a couple different methods. If you have a tough teacher and you have to know how to rationalize denominators and deal with variables under the root, then you'll need our Algebra 2 Roots & Radicals page.

### Order of Operations (PEMDAS)

#### In this chapter we'll introduce Order of Operations, often referred to simply by its ultra-useful acronym PEMDAS. We'll also get into how to do PEMDAS on your calculator, and a few common calculator mistakes to avoid.

# II. Geometry:

### Pythagorean Theorem

#### This chapter covers the basic formula and how to use it on right triangles, as well as the most common mistake students make with it. Also included is a video about simplifying radicals, since that comes up a lot with Pythagorean.

### Distance & Midpoint Formulas

#### This chapter teaches you the formulas for finding the distance and midpoint between two points on the X-Y plane, as well as word problems using these formulas.

# III. Variables & Equations:

### Variables & Expressions, and Translating Words Into Equations

#### In this chapter I explain what "x" is, what expressions are, how to plug in values to "evaluate" expressions, and how to turn word problems into equations so you can solve them. We'll also go over how to check whether a number is a solution of an equation or not.

### Solving Basic Equations

#### Solving basic equations by addition/subtraction, multiplication/division, combining like terms, and any combination of the three. Finally, we can figure out the value for x that would make 3x-4=6 a true statement. What a relief!

### Polynomials & Combining Like Terms

#### Combining "like terms", adding and subtracting polynomials and monomials.

### Distribution & Multiplication

#### Distribution (a.k.a. "multiplying stuff out") is when you have a number or variable in front of a set of parentheses that has to get multiplied by each term, such as 2(x-5).

### Cross Multiplication, Cross Canceling

#### Cross "multiplication" refers to what you do when you have two fractions across an equal sign from each other. You cross "cancel" when you are multiplying fractions. Confused yet? This chapter will sort you out.

### Ratios & Proportions

#### Ratios are mostly word problems that lead to cross multiplication equations, and most students find them pretty basic. In this chapter we'll work some typical problems about marbles and pizzas, and I'll emphasize the one trick they always pull on the SAT.

### Complex Fractions

#### Problems where you have to simplify a giant fraction which has more fractions inside the numerator and denominator.

# IV. "Linear" Equations, Inequalities & Variation:

### Rate-Time Word Problems

#### Rate, time and distance show up in these word problems (Rate x Time = Distance). Example problems include: How far did someone drive in 3 hours? If two trains leave stations and different times, how long until they pass each other? What units should my answer be, and how do I convert?

### Lines

#### Slope-Intercept Form, Point-Slope Form, Standard Form, Vertical Lines, Horizontal Lines, Perpendicular Lines: in this chapter, we experience the splendor of all the different types of linear functions, and master the equations and graphing of each.

### Variation - Direct, Inverse & Joint

#### Ratios are mostly word problems that lead to cross multiplication equations, and most students find them pretty basic. In this chapter we'll work some typical problems about marbles and pizzas, and I'll emphasize the one trick they always pull on the SAT.

### Solving Linear Inequalities & Interval Notation

#### Inequalities are just equations with an "<" or ">" instead of "=". In this chapter, we'll look at how to solve a few different types of "linear" inequalities: ones with just X, where you present the answer in Interval Notation, and ones with X & Y, where you shade one side of the line or another. We'll also cover systems of inequalities, "and" vs "or", etc. For other types of inequalities, try this page.

### Solving Absolute Value Equations & Inequalities

#### Absolute value signs (i.e. |x+3|) wreak havoc on equations and inequalities, often resulting in multiple answers and interval notation, but I'll give you simple steps to memorize for dealing with them. If you need to graph absolute value functions, check out thelibrary functions page.

### Solving Systems of Equations (2 or 3 equations at once)

#### Whenever you're given two or three equations at the same time, they're "simultaneous equations. This chapter covers "elimination" and "substitution" techniques to solve for X & Y, and explains finding the intersection of lines (or not as in the case of parallel & coincident lines). I also demonstrate solving three equations, three unknowns.

# V. Quadratic Stuff (i.e. stuff with x

^{2}):### FOIL (a.k.a. "Multiplying Out Parentheses")

#### FOIL is an acronym that helps you multiply out parentheses in problems like (x-5)(x+2), and you've got to be able to do this before you can factor. This chapter covers the easier 2-by-2 FOIL problems, as well as 2-by-3 and beyond.

### Factoring Quadratics (and other stuff too)

#### In this chapter we'll learn factoring, which is basically "reverse FOIL," including special cases like difference of squares and lead coefficients. If you have a super-hard teacher and this chapter doesn't cover you, check out the Algebra 2 Factoring Chapter for more advanced problem types.

### Solving Quadratic Equations

*Factoring*

Completing the Square

Quadratic Formula

Quadratic Inequalities

Word Problems#### "Quadratic" means "squared", for some reason, so this chapter is about solving equations with x

^{2}'s in them. You'll have to learn several tricky techniques -- square rooting, factoring, completing the square, and/or the Quadratic Formula -- but I give you tips to make them easier, and to decide which to use in different situations.# VI. Advanced topics:

### Intro to Functions

*Domain & Range*

Inverse Functions

Composite Functions#### In this chapter we'll introduce functions, the vertical line test, function notation (i.e. plugging numbers into functions), graphing functions the easy way (by plugging in). Also introduced are domain, range, finding inverse functions, x-intercepts, y-intercepts, and graphing functions.

### ALGEBRA 2 TOPICS

#### Some Algebra 1 teachers are crazy, putting all kinds of advanced Algebra 2 topics in Algebra 1. If what you're covering isn't listed above, click here for the Algebra 2 class page.