# Learn College Algebra Fast

# (from someone who can actually explain it)

# Chris is a Stanford-educated tutor with over 10 years experience tutoring College 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 normal people. Through his videos he has helped countless students, and he can do the same for you.

Start My Trial! | Sample College Algebra Videos |
---|

# College Algebra

##### Colleges vary in how they break down Algebra and Math Analysis topics, so I've put everything before Pre-Calc in one place. Whatever your school calls each class, the stuff you learn is pretty much standard, so you can count on the chapters below pretty much having you covered.

# 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.

### The X-Y Plane:

*vocab,*

plotting points,

The Four Quadrants#### 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.

### Basic X-Y Graphs:

*segments, circles*

collinear points,

X- & Y-Intercepts#### 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.

### 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,

Distribution & Multiplication#### 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, 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, Equations of Lines, & Linear Equations

#### 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. Exponents, Factoring & Canceling:

### Exponents, Canceling & Rational Expressions

#### 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 (of all types)

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

### Roots, Radicals, Rationalizing Denominators, & Rational Exponents

#### 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.

### Imaginary & Complex Numbers

#### 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.### Complex Fractions

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

# VI. Solving Equations, Systems & Inequalities:

### 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!

### 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.

### 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 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.### Solving Square Root Equations

#### In this chapter we take a look at how to solve equations where the variable is under a square root. 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.

### Solving Rational Equations

(x in denominator)#### 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.### Rational & Polynomial Inequalities

#### In this chapter we'll return to the Big Three of inequalities -- number lines, test points, and interval notation -- for perhaps the final time (nostalgic yet?).

# VII. Word Problems & Applications:

### 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?

### Rational Equations & "Table" Word Problems

#### 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.# VIII. Functions

### Lines, Equations of Lines, & Linear Equations

#### 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.

### 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.

### Even & Odd 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, Transformations & Piecewise Functions

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

### How To Find X- & Y-Intercepts

#### 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.

### Transformations, Reflections, Isometry & Mapping

#### These videos tell you what translations, rotations, and dilations are, as well as showing you the steps to do reflect a shape or function across a line using graphical techniques.

# IX. Exponentials & Logarithms:

### Exponential Functions & Equations

*graphing exponentials*

solving equations

matching bases

exponential growth

exponential decay

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

### Logarithms (logs):

*graphing logs*

log properties

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.

# X. Polynomials & Rational Functions:

### Graphing Parabolas (a.k.a. Quadratics)

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 (mimima/maxima).

### Synthetic & Long Division of Polynomials

#### 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.

### Polynomials & Rational Zeros

#### In this chapter we'll put our synthetic division skills to the test by using "p/q" to fully factor higher-power polynomials containing x

^{3}, x^{4}and x^{5}. Plus calculator graphing tips!### Graphing Rational Functions

#### Rational functions bring with them a crazy list of math terms: asymptotes (horizontal, vertical, oblique & slant), domain, range, and intercepts. You're welcome.

### Rational & Polynomial Inequalities

#### In this chapter we'll return to the Big Three of inequalities -- number lines, test points, and interval notation -- for perhaps the final time (nostalgic yet?).

### Partial Fraction Decomposition

#### In this chapter we'll learn a somewhat tedious process of splitting up a perfectly good rational expression into a couple fractions with A's and B's in the numerator.

# XI. Conic Sections

### Circles, Ellipses, Hyperbolas & Parabolas: The "Conics"

#### 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.

# XII. Probability, Sequences & Permutations:

### Sequences, Series & Sigma Notation

#### 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)

#### 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.### Probability

#### 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.

# XIII. Matrices:

### Matrices & Cramer's Rule

#### 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.