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AII.1 (Random) Field Properties

a. Identifying Field properties (distributive, associative, etc) (Integers)
b. Identifying Field properties (Polynomials)
c. Identifying Field properties (Complex Numbers)
d. Classifying Numbers into Fields (Natural, Whole, Real, etc.)

AII.2 (Random) Rational Expressions

a. Classifying Polynomials by Degree
b. Classifying Polynomials by Number of Terms
c. Adding Polynomials
d. Subtracting Polynomials
e. Multiplying Monomials (includes negative exponents)
f. Dividing Monomials (includes negative exponents)
g. Multiplying and Dividing Monomials (includes negative exponents)
h. Multiplying Polynomials
i. Dividing Polynomials (Requires Factoring!)
j. Mixed Polynomial Expressions (Multiple Operations) (Requires Factoring!)
k. Multiplying Rational Expressions (Easier) (Requires Factoring!)
l. Multiplying Rational Expressions (Harder) (Requires Factoring!)
m. Dividing Rational Expressions (Easier) (Requires Factoring!)
n. Dividing Rational Expressions (Harder) (Requires Factoring!)
o. Adding Rational Expressions(Easier) (Requires Factoring!)
p. Adding Rational Expressions (Harder) (Requires Factoring!)
q. Subtracting Rational Expressions(Easier) (Requires Factoring!)
r. Subtracting Rational Expressions (Harder) (Requires Factoring!)
s. Mixed Rational Expressions (Multiple Operations with simplify)(Easier) (Requires Factoring!)
t. Mixed Rational Expressions (Multiple Operations with simplify) (Harder) (Requires Factoring!)
u. Finding Equations of Vertical Asymptotes of Rational Functions
v. Finding Equations of Horizontal Asymptotes of Rational Functions

AII.3 (Random) Radical Expressions

a. Simplifying Radical Expressions (Numbers Only)
b. Adding Radical Expressions (Numbers Only)
c. Subtracting Radical Expressions (Numbers Only)
d. Multiplying Radical Expressions (Numbers Only)
e. Dividing Radical Expressions (Numbers Only)
f. Simplifying Combinations of Radical Expressions (Multiple Operations -- Numbers Only)
g. Simplifying Radical Expressions (Includes Variables) (Requires some factoring)
h. Adding Radical Expressions (Includes Variables) (Requires some factoring)
i. Subtracting Radical Expressions (Includes Variables) (Requires some factoring)
j. Multiplying Radical Expressions (Includes Variables)
k. Dividing Radical Expressions (Includes Variables & Requires Rationalizing Denominators)
l. Converting Radicals to Exponents (Rationals)
m. Converting Exponents (Rationals) to Radicals

AII.4 (Random) Absolute Value

a. Solving Absolute Value Equations (1 variable)
b. Reading Absolute Value Graphs (1 variable)
c. Solving Absolute Value Inequalities (1 variable)
d. Reading Absolute Value Inequality Graphs (1 variable)
e. Verifying Solutions of Absolute Value Inequality (1 variable)
f. Graphing an Absolute Value Equation (2 variables)
g. Reading Absolute Value Graph (2 variables)
h. Verifying Solutions of Absolute Value Inequality (2 variables)

AII.5 (Random) Factoring

a. Factoring: Pulling out the GCF
b. Factoring Trinomials (a=1) (Grid Factoring Video)
c. Factoring Trinomials (a>1) (Grid Factoring Video)
d. Factoring: Difference of Squares
e. Factoring: Perfect Square Trinomials
f. Factoring: Sum and Difference of Cubes
g. Factoring: Group Factorable
h. Factoring: Combination -- Hard Factorable

AII.6 (Random) Solving Quadratics

a. Identifying the Number of Solutions of a Quadratic Using the Discriminant
b. Solving Quadratics By The Square-Root Method
c. Solving Quadratics by Graphing
d. Solving Quadratics by Factoring
e. Solving Quadratics by Completing the Square
f. Solving Quadratics with the Quadratic Formula (Real Solutions)
g. Solving Quadratics that have Imaginary Solutions
h. Solving Quadratics (both imaginary and real solutions)
i. Finding Fixed Points for Quadratic Functions

AII.7 (Random) Radical / Rational Equations

a. Solving Equations with Rational Expressions
b. Solving Equations with Radical Expressions
c. Word Problems of Radical Expressions

AII.8 (Random) Transformations of Functions

a. Writing the Equation of a Basic Function from a Graph (Parabola, Line, Absolute Value, etc)
b. Writing the Equation of a Basic Function from a Table (Parabola, Line, Absolute Value, etc)
c. Describing the Transformation of a Basic Function
d. Writing the Equation of a Transformed Function

AII.9 (Random) Functions, Domain, Range, etc.

a. Finding Domains of Functions
b. Finding Ranges of Functions
c. Finding Zeros of Functions
d. Finding Inverses of Functions
e. Finding Composition of Functions
f. Using Composition of Functions to Identify Inverse Functions
g. Finding Values of Functions
h. Finding areas of Increasing or Decreasing for Functions
i. Describing End Behavior of Polynomials
j. Finding X and Y-Intercepts of Functions

AII.10 (Random) Roots of Polynomials

a. Finding Zeros of a Polynomial
b. Graphing a Polynomial
c. Finding zeros of a Polynomial from a Graph
d. Finding the X-Intercepts of a Polynomial
e. Finding a Polynomial equation from Zeros

AII.11 (Random) Basics of Matrices

a. Adding/Subtracting Matrices
b. Adding/Subtracting Matrices with Variables
c. Multiplying Matrices
d. Multiplying Matrices with Variables
e. Matrix Word Problems
f. Finding Determinants of Matrices
g. Using Determinants of Matrices to find the area of a triangle
h. Using Cramer's Rule
i. Solving a System with Augmented Matrix
j. Finding Inverse with Augmented Matrix

AII.12 (Random) Solving Systems with Matrices

a. Solving Linear Equations in Two or Three Variables with Linear Combination
b. Solving Two Linear Equations in Two or Three Variables with Substitution
c. Finding Matrix Inverses
d. Solving a System of Equations with Matrices
e. Setting up a System of Equations with Matrices

AII.13 (Random) Linear Programming

a. Graphing Linear Inequalities
b. Linear Programming Problems (Graph Supplied)
c. Linear Programming Problems

AII.14 (Random) Nonlinear Systems of Equations

a. Solving Nonlinear Systems of Equations using Linear Combination
b. Solving Nonlinear Systems of Equations using Substitution
c. Solving Nonlinear Systems of Equations using Graphing

AII.15 (Random) Identifying Graphs And Piecewise Functions

a. Identifying the degree of the polynomial
b. Identifying the function graph (exponential / logarithmic / polynomial / absolute value / etc)
c. Identifying the function table (exponential / logarithmic / polynomial / absolute value / etc)
d. Finding Domain of Piecewise Functions
e. Finding Range of Piecewise Functions
f. Evaluating Piecewise Functions
g. Graphing Linear Piecewise Functions
h. Graphing Piecewise Functions

AII.16 (Random) Sequences and Series

a. Identifying Arithmetic/Geometry Sequences
b. Writing the first n terms of an Arithmetic Sequence
c. Defining an Arithmetic Sequence with Recursion
d. Finding the n^th term formula for an Arithmetic Sequence
e. Finding Arithmetic Means
f. Evaluating Summations of Arithmetic Series (Number Arches Video)
g. Writing the first n terms of a Geometric Sequence
h. Defining a Geometric Sequence with Recursion
i. Finding the n^th term formula for a Geometric Sequence
j. Finding Geometric Means
k. Evaluating Finite Summations of Geometric Series
l. Evaluating Infinite Summations of Geometric Series

AII.17 (Random) Complex Numbers

a. Fixing Radicals into Imaginary Numbers
b. Adding Complex Numbers
c. Subtracting Complex Numbers
d. Multiplying Complex Numbers
e. Dividing Complex Numbers
f. Simplifying iⁿ

AII.18 (Random) Graphing Conic Sections

a. Graphing a Circle
b. Graphing an Ellipse
c. Graphing a Parabola
d. Graphing a Hyperbola
e. Identifying the Type of Conic from an Equation or a Picture
f. Identifying the Type of Conic using the Discriminant
g. Changing Equations to Standard Form (Completing the Square)
h. Changing Equations to Standard Form (Another Method)

AII.19 (Random) Scatterplots and Line of Best Fit

a. Finding the Best Fit Line from a Data Set or a Scatterplot
b. Identifying the Best Fit Equation type from a Data Set or a Scatterplot
c. Finding the Best Fit Curve from a Data Set
d. Identifying the Slope from a Data Set or Scatterplot
e. Identifying the Correlation
f. Predicting a Value according to a Data Set or Scatterplot

AII.20 (Random) Direct and Inverse Variation

a. Identifying Direct Variation
b. Identifying Inverse Variation
c. Identifying Variation of a Graph
d. Setting up and Solving Inverse Variation Problems
e. Setting up and Solving Direct Variation Problems
f. Setting up and Solving Joint Variation Problems
g. Direct Variation and Inverse Variation Word Problems

(Random) Logs

a. Identifying the Base
b. Logarithmic to Exponential
c. Exponential to Logarithmic
d. Evaluating Logs (by hand)
e. Expanding Expressions (easier)
f. Expanding Expressions (harder)
g. Contracting Expressions (easier)
h. Contracting Expressions (harder)
i. Solving Equations with Logs
j. Evaluating Logs using the Change of Base Formula
k. Finding Inverses

(Random) Division of Polynomials

a. Using the Rational Root Theorem
b. Using Synthetic Division
c. Using Long Division
d. Using Box Division
e. Using Descartes's Rule of Signs
f. Using Synthetic Division to Find Roots
g. Finding Roots of Polynomials with Rational Roots
h. Finding Roots of Polynomials with at most 2 Irrational or Imaginary Roots

(Random) Normal Distributions

a. Properties of Normal and Standard Normal Distributions and the Empirical Rule 68-95-99.7
b. Finding the Z-Score
c. Using Tables of the Normal Distribution (given z-score)
d. Using Tables of the Normal Distribution (given a sample piece of data)
e. Using Tables of the Normal Distribution (given probability)
f. Comparing Two Normal Curves (with Z-Scores)

(Random) Combinations And Permutations

a. Identifying Permutations and Combinations
b. Calculating Permutations (And other cases where order matters)
c. Calculating Combinations
d. Calculating Rearrangements of Words

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