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Basic Algebra Topics:

Adding and Subtracting Fractions:

Multiplying and Dividing Fractions
Understanding Exponents

Classification of Real Numbers (Rational, Irrational…..):

Order of Operations
Adding Integers
Subtracting Integers
Multiplying and Dividing Integers
Properties of Real Numbers

Evaluating Expressions:

Simplifying Expressions
Solving Basic Linear Equations

Solving Multi-Step Linear Equations:

Ratios and Proportions
Solving Linear Inequalities
Introduction to Interval Notation
The Coordinate System

Graphing a Line:

Finding the x and y intercepts  
Graphing Horizontal and Vertical Lines

Finding the Slope of a Line:

Using Point-Slope Form to find Linear Equations:

Graphing Linear Inequalities
Solving Systems of Linear Equations (in 2 variables) Using Graphing
Solving Systems of Linear Equations (in 2 variables) Using Elimination
Solving Systems of Linear Equations (in 2 Variables) Using Substitution

Solving Systems of Inequalities:

The Product Rule for Exponents

The Power Rule for Exponents:

The Quotient Rule for Exponents
Exponents of Zero
Simplifying with Negative Exponents
Using Combinations of the Exponent Rules
Adding and Subtracting Polynomials

Multiplying Polynomials:

Special Products in Binomials
Dividing a Polynomial by a Monomial
Dividing a Polynomial by a Binomial, using Long Division
Factoring out the Greatest Common Factor
Factoring Polynomials with 4 terms, using Grouping
Factoring Trinomials, using the AC method
Factoring Trinomials, using the X method
Factoring Trinomials, using the box method
Factoring Binomials, using Special Factoring Techniques
Solving Quadratic Equations by Factoring
Finding the domain of Rational Expressions
Simplifying Rational Expressions

Multiplying and Dividing Rational Expression:

Simplifying Complex Fractions
Adding and Subtracting Rational Expressions (with the same denominators)

Adding and Subtracting Rational Expressions (with different denominators):

Solving Equations with Rational Expressions

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Intermediate Algebra Topics:

Compound Inequalities
Absolute Value Equations
Absolute Value Inequalities
Introduction to Functions
Graphing Piecewise Functions

Transformations on Functions:

Solving Systems of Linear Equations in Three Variables Using Elimination
Solving Systems of Linear Equations using Matrices
Finding the Degree of a Polynomial
Dividing a Polynomial by a Binomial, using Synthetic Division
Direct and Inverse Variation
Simplifying Radicals
Approximating Square Roots
Rational Exponents
Product Rule for Radicals
Product and Quotient Rule for Radicals
Calculating the distance between 2 points
Using the distance formula
Using the midpoint formula
Adding and Subtracting Radical Expressions
Multiplying Radical Expressions
Rationalizing Denominators containing Monomial Radicals
Rationalizing Denominators containing Binomial Radicals

Solving Radical Equations:

Complex Numbers
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers

Dividing Complex Numbers:

Solving Quadratic Equations by Completing the Square
Solving Quadratic Equations using the Quadratic Formula
Solving Quadratic Equations Using the Square Root Property
Solving Quadratic Inequalities
Solving Rational Inequalities
The Algebra of Functions
Composite Functions
Finding the Inverse of a Function
Introduction to Exponential Functions
Graphing Exponential Functions
Using the Compound Interest Formula
Introduction to Logarithms
Finding the Domain of a Logarithmic Function 
Graphing Logarithmic Functions
Properties of Logarithms
Change of Base Formula for Logarithms

Solving Exponential Equations

Solving Logarithmic Equations
Introduction to Conic Sections
Graphing a Parabola in Vertex Form
Graphing Circles
Writing the Equation of Circles
Graphing Hyperbolas
Writing the Equation of a Hyperbola
Graphing Ellipses
Writing the Equation of an Ellipse

Solving Nonlinear Systems of Equations

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Advanced Algebra Topics:

Solving equations with Rational Exponents
Solving equations that are Quadratic in Form
Increasing and Decreasing Functions
Obtaining information from a Graph
Relative (Local) Maxima and Relative (Local) Minima
Even and Odd functions

The difference quotient:

Finding the average rate of change of a function
Stretching and shrinking the graph of a function
End behavior of Polynomial Functions
Finding the Zeroes of Polynomial Functions by Factoring
Multiplicities of Zeroes
The Intermediate Value Theorem
Turning Points on a Polynomial Function

Graphing a Polynomial Function (degree >2)

The Remainder Theorem
The Rational Zeroes Theorem
Descartes Rule of Signs
Finding Zeroes of a Polynomial Function
Finding a Polynomial Function with Given Zeros
Finding Vertical Asymptotes of Rational Functions
Finding Horizontal Asymptotes of Rational Functions

Graphing a Rational Function:

Solving Polynomial Inequalities
Exponential Growth and Decay
Finding the Determinant of a 2x2
Finding the Determinant of a 3x3
Cramer’s Rule
Locating Foci in an Ellipse

Locating Foci and Asymptotes in a Hyperbola:

Graphing a Parabola using Latus Rectum
Introduction to a Sequence
Recursive Formulas
Fibonacci Sequence
Factorial Notation
Summation Notation
Arithmetic Sequences
Finding the Sum of the first n Terms in an Arithmetic Sequence
Geometric Sequences
Finding the Sum of the first n Terms in a Geometric Sequence
Finding the Sum of an infinite Geometric Series
Writing a Repeating Decimal as a Fraction
The Binomial Theorem
Evaluating a Binomial Coefficient
Finding a Particular Term in a Binomial Expansion

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