# Making Algebra 2 fun *tolerable*

# Chris is a Stanford-educated tutor with over 10 years experience tutoring Algebra 2 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 2

##### Algebra 2 classes can cover lots of crazy stuff. If you don't see what you need below, it's probably on our Precalc page.

# I. Exponents, Factoring & Canceling:

#### Combining exponents, canceling terms, multiplying rational expressions and equations, multiplying and dividing variables with various exponents, negative exponents: if it's got an exponent, this chapter covers it.

#### In these videos we'll cover all forms of factoring polynomials, from "factoring stuff out" to quadratics to sum and difference of cubes. We'll also learn factoring by u-substitution & grouping.

#### This chapter covers everything you'll ever be asked to do to or with a root or a "rational" (fraction) exponent. Topics covered: simplifying roots & radicals, reducing roots, dividing roots, adding-subtracting-multiplying-and-dividing radicals, and rationalizing denominators.

#### This video covers a quick topic that usually first comes up when you're learning factoring or the quadratic formula, but will keep popping up as you learn rational exponents and any other situation where roots and radicals are involved.

#### All is not as it seems in this exciting and short chapter. We're talking square roots of negative numbers, finding high exponents of "i" like i

^{27}, and rationalizing imaginary and complex denominators.#### Problems where you have to simplify a giant fraction which has more fractions inside the numerator and denominator.

# II. Solving Equations, Systems & Inequalities:

#### 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.

#### 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.

#### "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.#### In this chapter we take a look at how to solve equations where the variable is under a square root or a radical. Often we'll be able to simply square both sides of the equation, but we'll always have to be careful to check for extraneous solutions.

# III. Word Problems & Applications:

#### Rational Equations are the problems where you have a bunch of x's and x

^{2}'s in the denominator of a giant fraction, and you have to find the least common denominator and simplify in order to solve for X. And I teach a great method using tables to solve nasty word problems involving stuff like boats rowing upriver and faucets filling tubs.#### 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?

# IV. Functions

#### 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.

#### 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.

#### Usually in math, the names don't make any sense. But this is an exception: "even" and "odd" refer to whether the exponents on the x's are even or odd!

#### Time to master graphing all kinds of standard functions (a.k.a. library functions or parent functions) using transformations. Vertical stretch, horizontal stretch, translating/moving graphs up down left right. We'll also cover those Frankenstein-esque combo functions: piecewise functions.

#### 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.

#### As soon as the variable in an equations moves up to the exponent, you've got yourself an exponential and you may need logs (logarithms or logarithmic equations). In chapter we'll analyze and graph them, and look at some common types of problems such as compound interest.

#### In this chapter you'll get all the basics on logarithms (logs) and log equations, as well as how to graph them and use them to solve tough exponential equations. I also devote a video to the difference between graphing logs vs graphing exponentials.

# V. Graphing Polynomials & Conics

#### In this chapter we'll focus on the anatomy of parabolas: vertex, axis of symmetry, vertex form, x-intercepts, roots, and the discriminant. We'll also cover word problems where you are asked to maximize/minimize the area or volume of a shape (minima/maxima).

#### In this chapter we'll learn a somewhat tedious process of dividing polynomials by each other, a skill that's kind of fun once you get the hang of it and which will serve you well in Pre-Calc & Analysis.

#### In this chapter we'll emphasize the similarities and differences between the equations of these four shapes, and we'll discuss why conic sections are called that.

# VI. Probability, Sequences & Permutations:

#### Common confusion: a "series" is just a sequence with plus signs between the terms instead of commas. All other questions, check out the chapter page, which includes a free printable pdf of all the formulas for arithmetic and geometric sequences.

#### Make

_{n}C_{r}and_{n}P_{r}pay for what they've done by mastering them and using them to execute on your upcoming test. Also in this chapter: brush up for this common SAT question.#### This chapter "probably" (lol) covers mutually exclusive events, dependent probability, and, or, colored rocks, coin flips, regular dice, weighted dice, and even the Binomial probability formula.

# VII. Matrices:

#### This chapter covers the basics - matrix addition, subtraction, multiplication, and determinants - along with advanced moves like solving systems with row operations and Cramer's Rule.