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- Real Numbers
- Algebraic Properties of Real Numbers (Reflexive, Symmetric, Transitive, and Substitution)
- Algebraic Properties of Addition and Multiplication
- Overview of Exponents
- Square Roots and Estimating Square Roots
- Simplifying Square Roots
- Solving Equations with One Variable (Properites of Equality)
- Solving Common Formulas for One Variable
- Solving Inequalities and Graphing Inequality Solutions
- Solving Compound Inequalities Involving And
- Solving Compound Inequalities Involving Or
- Solving Absolute Value Equations
- Graphing Absolute Value Equations
- Solving Absolute Value Inequalities

- Coordinate Plane Overview
- Introduction to Relations
- Relations as Functions (Introduction to Functions)
- Evaluating Functions and Function Notation
- Operations with Functions
- Composition of Functions
- Inverse Relations and Inverse Functions
- Graphs of Common Parent Functions
- Horizontal and Veritcal Translations of Functions
- Stretching and Compressing Functions (Horizontally and Vertically)
- Reflections of Functions (Horizontal and Vertical)

- Slope of a Line
- Graphing Linear Functions Given a Point and a Slope
- Writing and Graphing Linear Equations in Slope-Intercept Form
- Writing and Graphing Linear Equations in Point-Slope Form
- Writing and Graphing Linear Equations in Standard Form
- Writing and Graphing Horizontal and Vertical Lines
- Finding x-Intercepts and y-Interecepts of Linear Functions
- Slopes of Parallel and Perpendicular Lines
- Graphing Linear Inequalities in Two Variables
- Evaluating and Graphing Piecewise Functions

- Solving a System of Linear Equations by Graphing
- Solving a System of Linear Equations by Substitution
- Solving a System of Linear Equations by Elimination (Linear Combination)
- Solving a System of Linear Equations by Elimination by Multiplying First
- Solving a System of Linear Inequalities by Graphing
- Solving a System of Three of More Linear Inequalities
- Linear Programming
- Applications of Linear Programming
- Plotting Points and Graphing Equations in Three Dimensions
- Evaluating Functions of Two Variables
- Solving a System of Linear Equations with Three Variables

- Introduction to Matrices
- Scalar Multiplication with Matrices
- Adding and Subtracting Matrices
- Multiplying Matrices
- The Identity Matrix
- Determinants of 2×2 Matrices
- Determinants of 3×3 Matrices
- Cramer's Rule for Two Equations
- Cramer's Rule for Three Equations
- Finding the Inverse of a 2×2 Matrix
- Using Inverse Matrices to Solve a System of Two Equations
- Using Row Operations and Augmented Matrices to Solve a System of Two Equations

- Graphing Quadratic Functions in Vertex Form
- Graphing Quadratic Functions in Standard Form
- Graphing Quadratic Functions in Intercept Form
- Factoring Out the Greatest Common Factor
- Factoring Expressions by Grouping
- Factoring Quadratic Expressions (c > 0)
- Factoring Quadratic Expressions (c < 0)
- Factoring the Difference of Two Perfect Squares
- Factoring Perfect Square Trinomials
- Completing the Square (a = 1)
- Completing the Square (a ? 1)
- Changing Quadratic Forms (Standard, Vertex, Intercept)
- Graphing Quadratic Inequalities
- Solving a System of Quadratic Inequalities by Graphing
- Writing Quadratic Equations Given Three Points on a Parabola
- Writing Quadratic Equations Given the x-Intercepts and a Point on the Parabola
- Writing Quadratic Equations Given the Vertex and a Point on the Parabola

- Solving Quadratic Equations by Factoring
- Complex and Imaginary Numbers and Conjugate Pairs
- Evaluating Powers of i
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Graphing Complex Numbers and Absolute Value of Complex Numbers
- Solving Quadratic Equations by Taking Square Roots
- Solving Quadratic Equations by Completing the Square
- Solving Quadratic Equations by Quadratic Formula
- Analyzing the Discriminant
- Solving Quadratic Inequalities Algebraically

- Introduction to Polynomials
- Classifying Polynomials by Degree and Number of Terms
- Evaluating Polynomial Functions
- Adding and Subtracting Polynomials
- Multiplying Polynomials
- FOILing Binomials
- Binomial Expansion with Pascal's Triangle
- Dividing Polynomials Using Long Division
- Dividing Polynomials Using Synthetic Division
- The Remainder Theorem and Synthetic Substitution
- The Factor Theorem
- Factoring Polynomials (Grouping and Difference of Two Squares)
- Factoring Sum and Difference of Two Cubes
- Factoring Polynomials in Quadratic Form
- Solvling Polynomials by Factoring
- Synthetic Division with Imaginary Numbers
- Fundamental Theorem of Algebra and Rational Root Theorem
- Writing Polynomials of Least Degree Given Roots/Zeros
- Writing Polynomials of Least Degree Given Irrational/Complex Roots/Zeros
- Sketching the Graph of a Polynomial Given Its Roots (Multiplicity of Roots)
- End Behavior of Polynomials

- Introduction to nth Roots
- Radical Form vs. Rational Exponent Form
- Simplifying nth Roots (Product Property)
- Simplifying nth Roots by Rationalizing the Denominator (Quotient Property)
- Solving Equations Using nth Roots
- Properties of Rational Exponents
- Adding and Subtracting with nth Roots
- Graphing Radical/Square Root Functions
- Graphing Radical/Square Root Inequalities
- Solving Equations with One Radical
- Solving Equations with Two Radicals
- Solving Equations with Rational Exponents
- Solving Equations with Extraneous Solutions
- Solving Radical Inequalities

- Simplifying Rational Expressions
- Multiplying Rational Expressions
- Dividing Rational Expressions
- Adding and Subtracting Rational Expressions with Like Denominators
- Finding the Least Common Multiple of Polynomials
- Adding and Subtracting Rational Expressions without Like Denominators
- Simplifying Complex Fractions
- Graphing Rational Functions Using Transformations
- Graphing Rational Functions by Finding Asymptotes
- Graphing Rational Functions with Two Vertical Asymptotes
- Graphing Rational Functions with Holes
- Solving Rational Equations
- Direct Variation and Inverse Variation
- Joint Variation and Combined Variation

- Exponential Growth and Compound Interest Equations
- Exponential Decay Equation
- Graphing Exponential Equations for b > 1 (Growth)
- Graphing Exponential Equations for 0 < b < 1 (Decay)
- Introduction to Logarithms
- Logarithmic Form vs. Exponential Form
- Evaluating Logarithmic Expressions
- Evaluating Logarithmic Expressions Using the Change of Base Formula
- Properties of Logarithms
- Expanding and Condensing Logarithmic Expressions
- Approximating Logarithmic Expressions
- Graphing Logarithmic Functions for b > 1
- Solving Exponential Equations
- Solving Logarithmic Equations
- Inverse Functions (Exponential and Logarithmic Functions)
- The Natural Base, e

- Introduction to Conic Sections
- Introduction to Parabolas
- Graphing Parabolas with Vertex at (0,0)
- Graphing Parabolas with Vertex at (h,k)
- Introduction to Circles
- Graphing Circles with Center at (0,0)
- Graphing Circles with Center at (h,k)
- Introduction to Ellipses
- Graphing Ellipses with Center at (0,0)
- Graphing Ellipses with Center at (h,k)
- Introduction to Hyperbolas
- Graphing Hyperbolas with Center at (0,0)
- Graphing Hyperbolas with Center at (h,k)
- Graphing Advanced Conics (Adding/Subtracting Radicals from (x,y) Coordinates)
- Graphing Circles Advanced
- Graphing Ellipses Advanced
- Graphing Hyperbolas Advanced
- Tips for Classifying Conic Sections
- Putting Conic Equations in Standard Form