Basic | Intermediate | Advanced

**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:

- Counting units on a given graph
- Using the slope formula
- Given an equation
- Using Slope Intercept form to find Linear Equations

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

**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

**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