# Making Algebra fun *tolerable*

# Chris is a Stanford-educated tutor with over 10 years experience tutoring Algebra to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to non-math people. Through his videos he has helped countless students, and he can do the same for you.

# 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:

#### By request, this chapter video covers the most important skill you'll need for Algebra and beyond: addition and subtraction of negative numbers using the number line. You can add and subtract any number with the number line, but negatives are where it's really great.

#### 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.

#### 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.

#### 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.

#### 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. And if you're super-advanced, "compound interest", where you have to calculate how interest builds over n weeks, months, years, etc.

#### 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.

#### 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:

#### 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.

#### The videos in this topic introduce you to the X-Y plane (aka "rectangular coordinate system"), explain what the "origin" is, explain how to graph points, explain "the four quadrants", and tell you how to plot points.

#### If you're new to X-Y graphs, this is the place for you. We'll start with segments and lines without equations (for equations of lines from algebra, click here). Then we'll look at graphs of circles and rectangles, and x- and y-intercepts.

#### 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:

#### 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.

#### These videos explain the process of solving algebraic equations by addition/subtraction, multiplication/division, combining like terms, and any combination of the three (multi-step problems like 3x-5=7).

#### Combining "like terms", adding and subtracting polynomials and monomials. Also covered: distribution (a.k.a. "multiplying stuff out"), where 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" 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 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.

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

#### 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.

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

#### 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?

#### 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.

#### When a word problem talks about two things being "proportional", this is what they're talking about. Or maybe they're "inversely proportional". "Joint" variation just refers to when you have three things that are proportional or inversely proportional instead of just the two, which is basically just ratios in disguise.

#### 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 Equations*

Absolute Value 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 the library functions page.

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

^{2}):#### 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.

#### In this chapter we'll learn factoring, which is basically "reverse FOIL," including special cases like difference of squares and lead coefficients.

#### "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:

#### 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.

#### 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.

#### By popular demand, this short video explains the process of finding x-intercepts and y-intercepts for any function. These are also known as "zeroes" of a function, and you'll see why by the end of this.

##### (There's lots more geometry on the Geometry page.)