# Math Analysis

##### Math Analysis is basically pre-calc with no trigonometry. The schools that have a class called Math Analysis usually put trig in the Algebra 2 year (often calling that class Trig/Algebra 2), and move some of the tougher Algebra 2 concepts to this class. Either way, the one thing you can count on about Math Analysis is that there's nothing you can count on. In this class I've included all the topics that I've seen in the Math Analysis classes in West L.A., but this class seems to vary quite a bit, so your class might have slightly different topics. Most should be here, but if one is missing, check the Algebra 2 or pre-calculus class pages.

# I. Exponents, Radicals & Factoring

### 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.### 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.# II. Functions

### 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.

### 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.

# III. Polynomials & Rational Functions

### 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.

# VIII. 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.

### 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.