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 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:
Exponents, Canceling & Rational Expressions
Exponent Rules & Rational Expressions: Multiplying/Dividing
Exponent Rules & Rational Expressions: Multiple exponents
Exponent Rules & Rational Expressions: Combining Rules
Common Algebraic Canceling Mistakes
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.
Factoring Polynomials (of all types):
Difference of squares
Sum and Difference of Cubes
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.
Roots, Radicals, Rationalizing Denominators, & Rational Exponents
Simplifying Roots & Radicals
Variables Under Radicals
Adding & Multiplying Roots
Dividing Roots & Rationalizing Denominators
Rational Exponents (a.k.a. fractions upstairs)
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 i27, and rationalizing imaginary and complex denominators.
Fractions within Fractions: Using the LCD
Simplifying Complex Fractions: Multiple Variables
Simplifying Complex Fractions: Multiple Variables with Coefficients
Problems where you have to simplify a giant fraction which has more fractions inside the numerator and denominator.
II. Solving Equations, Systems & Inequalities:
Solving Systems of Equations (2 or 3 equations at once)
Solving Systems of Equations with Substitution
Solving Systems w/ Elimination (addition, subtraction)
Solving 3 Simultaneous Equations with 3 Unknowns
Finding the Intersection of Lines (the graphing method)
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.
Solving Linear Inequalities & Interval Notation
Solving Inequalities with just x
Systems of Inequalities (with just x)
Linear Inequalities with both x & y
Systems of Inequalities with both x & y
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.
Solving Quadratic Equations
Completing the Square
"Quadratic" means "squared", for some reason, so this chapter is about solving equations with x2'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.
Solving Square Root Equations (Radical Equations)
Solving equations with only one square root
Solving equations with two square roots
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 & "Table" Word Problems
Solving Rational Equations (x's in denominators)
Rate/Time Word Problems Using Tables
"Working Together" Rate/Time Word Problems (free)
Rational Equations are the problems where you have a bunch of x's and x2'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 Word Problems
Basic Rate-Time-Distance Word Problems
Tough Rate-Time-Distance 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, Equations of Lines, & Linear Equations
How To Graph Lines (a.k.a. Linear Functions)
How to Find the Slope of a Line
Horizontal & Vertical Lines
Slope-Intercept Form of a Line: y=mx+b
Standard Form of a Line: Ax+By=C
Point-Slope Form: y-y1=m(x-x1)
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!
Graphing Library Functions (a.k.a. Parent Functions), Transformations & Piecewise Functions:
Intro to Graphing Transformations
Intro to "Library Function" Graphs (a.k.a. "Parent Functions"): square roots, parabolas, cubics, etc
Medium-Difficult Parent Function Transformation Examples
Crazy Transformation Examples
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.
Exponential Functions & Equations
solving exponential equations
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.
solving log equations
change of base formula
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
Graphing Parabolas (a.k.a. Quadratics)
Parabolas -- Vertex Form Graphing & Vocab
How to put quadratics in "vertex form"
The Discriminant of a Parabola
Maximum & Minimum Word Problems
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.
Circles, Ellipses, Hyperbolas & Parabolas: The "Conics"
Intro to Conics
Parabolas: Directrix & Focus
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:
Sequences, Series & Sigma Notation
Intro to Sequences and Series
Arithmetic Sequences & Series
Geometric Sequences & Series
SAT-type Sequence Questions (Word Problems)
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.
Permutations & Combinations (a.k.a. Combinatorics)
Intro to Permutations & Combinations
Permutations: a closer look
Combinations: a closer look
Tricky Permutation and Combination Problems for SAT
Binomial Expansions & Pascal's Triangle
Make nCr and nPr 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.
Matrices & Cramer's Rule
Basic Matrix Operations
Inverse & Identity Matrices
Solving Systems: Matrix Row Operations (Gauss Jordan or Gaussian Elimination)
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.