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
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.
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.
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.
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.
III. Polynomials & Rational Functions
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
Polynomial Graphs: Zeros, Multiplicity, End Behavior, Fundamental Theorem of Algebra
Complex & Imaginary Roots of Polynomials
Getting Equation From Roots
Finding Rational Roots of Polynomials
Calculator Tricks For Polynomials
In this chapter we'll put our synthetic division skills to the test by using "p/q" to fully factor higher-power polynomials containing x3, x4 and x5. Plus calculator graphing tips!
Graphing Rational Functions
Vertical Asymptotes & Holes
Slant Asymptotes (a.k.a. Oblique Asymptotes)
Rational Function Graphing Examples
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
Partial Fractions with "Non-Repeated Linear Factors"
Partial Fractions: Repeat & Non-Linear Factors
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
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.