#### Graphs of Linear Equations

Graphs of Linear Equations reviews the rectangular (Cartesian) coordinate system, and contains lessons on different methods of interpreting the lines and their applications, and has examples of solving different practice problems related to finding the slope and using different forms of writing the equation for a line. Topics include:

#### Functions

Functions teaches students how to properly use function notation and how to answer questions related to them, such as how to find domain and range, how to define a function, and how to interpret word problems with direct and indirect variation. Topics include:

#### Systems of Linear Equations

Systems of Linear Equations teaches students different ways of dealing with problems relating to systems of equations in two or more variables and how to recognize systems with no or infinite solutions both algebraically and with graphs. Students can practice with word problems that apply systems of equations and learn different methods for solving systems including elimination and substitution. Topics include:

#### Matrices

Matrices helps students learn how to properly use matrix operations such as switching and adding scalar multiples of rows , and gives practice with the applications of an augmented matrix. Topics include:

#### Polynomials

Polynomials teaches students how to define a polynomial function and provides practice on how to interpret the graphs of basic polynomials and their transformations, and how to multiply and divide them both with long and synthetic division. Topics include:

- Introduction to Polynomials
- Polynomial Function
- Basic Polynomial Graphs
- Basic Transformations
- Multiplying Polynomials
- Multiplying Complicated Polynomials
- Pascal's Triangle
- Binomial Theorem
- Dividing Polynomials using Long Division
- Dividing Polynomials using Synthetic Division
- Using Synthetic Division to Evaluate Polynomials

#### Factoring

Factoring reviews methods to factor real and imaginary terms out of polynomials, including quadratics, cubics and those of higher degree. Students can learn how to use the rational roots theorem and synthetic division through lectures and practice problems similar to those that would appear on their homework. Topics include:

#### Rational Expressions and Functions

Rational Expressions and Functions defines rational expressions and discusses their domains and asymptotic behavior as functions. Students can learn and practice methods of simplifying, solving and graphing rational functions through various exercises they would find in their homework, including word problems dealing with distance, rate and time and those dealing with work. Topics include:

#### Roots and Radicals

Roots and Radicals introduces students to rational exponents and helps with studying how to simplify and otherwise manipulate expressions with radicals and roots using their properties and rules. Students will learn through practice problems like those found in their homework how to rationalize, combine, expand radicals. Topics include:

- Introduction to Radicals
- Radicals and Absolute Values
- Rational Exponents
- Evaluating Rational Exponents
- Rational Exponents with Negative Coefficients
- Rules for Rational Exponents
- Simplifying Radicals using Rational Exponents
- Multiplying Radicals of the Same Root
- Multiplying Radicals of Different Roots
- Rationalizing the Denominator with Higher Roots
- Rationalizing a Denominator with a Binomial
- Solving an Equation with Radicals
- Introduction to Imaginary Numbers
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Powers of i

#### Quadratic Equations and Inequalities

Quadratic Equations and Inequalities introduces students to the graphs of quadratics, teaches them to find the vertex, intercepts, discriminant, domain and range and interpret the graph in relation to these qualities. It also introduces students to the focus and directrix of parabolas, how to use a sign number line to find the shape of a graph, and other topics that might be found as exercises in homework. Topics include:

- Dilations of Quadratic Graphs
- Vocabulary of Quadratic Polynomials
- Solving Quadratic Equations by Factoring
- Solving Quadratic Equations Using Square Roots
- Solving a Quadratic by Completing the Square
- Deriving the Quadratic Formula
- Overview of the Different Methods of Solving a Quadratic Equation
- The Discriminant of a Quadratic Equation
- Solving Quadratic Equations in Disguise
- Introduction to Parabolas
- Finding the Vertex of a Parabola by Completing the Square
- Finding Intercepts, Domain, Range and Vertex of a Parabola
- Finding the Maximum or Minimum of a Quadratic
- Graphing a Horizontal Parabola
- Graphing a Quadratic Inequality
- Solving a Quadratic Inequality using a Sign Chart
- Focus and Directrix of a Parabola

#### Inverse, Exponential and Logarithmic Functions

Inverse, Exponential and Logarithmic Functions teaches students about three of the more commonly used functions, and uses problems to help students practice how to interpret and use them algebraically and graphically. Students can learn the properties and rules of these functions and how to use them in real world applications through word problems such as those involving compound interest and exponential growth and decay that they will find on their homework. Topics include:

- Definition of One-to-One Functions
- Definition of Inverse
- Finding an Inverse Algebraically
- Proving Two Functions are Inverses
- Finding an Inverse Graphically
- Exponential Functions and their Graphs
- Solving Exponential Equations with the 'Same' Base
- Introduction to Logarithms
- Solving Simple Logarithmic Equations
- Function Notation with Logs and Exponentials
- Graph of Logarithmic Functions
- Product Rule of Logarithms
- Quotient Rule of Logarithms
- Power Rule of Logarithms
- Expanding Logarithms
- Condensing Logarithms
- Common and Natural Logarithms
- Change of Base Formula
- Solving Exponential Equations with the Different Bases
- Solving a Logarithmic Equation
- Solving a Logarithmic Equation with Multiple Logs
- Compound Interest (Finite Number of Calculations)
- Compound Interest (Continuously)
- Exponential Growth and Decay
- Evaluating a Logarithmic Expression in terms of Known Quantities

#### Conic Sections

Conic sections covers the definitions, formulas or algebraic representations, and graphs of circles, ellipses and hyperbolas, as well as applications to nonlinear equations Topics include:

#### Sequences and Series

Sequences and Series teaches students how to define, notate and interpret different types of series and sequences, such as arithmetic and geometric, and how to use mathematical induction in proofs and on their homework. Topics include:

#### Combinatorics

Combinatorics teaches an introduction to probability, and helps students to learn how to do problems that involve permutations, combinations and counting taking into account independent and dependent events, and uses exercises that students might find on their homework, including word problems that involve choosing cards or rolling dice. Topics include:

#### Additional Topics

Additional Topics covers material that many students need help with but that are not usually covered as their own topic in a textbook. It teaches students about step functions, calculators, covers some of the common mistakes made by students in an Algebra 2 class and how to notate and interpret piecewise functions. Topics include:

#### Real Numbers

Real Numbers teaches the definition and properties of real numbers and how to analyze data using problems that apply to every day life, such as those involving mean, median, mode and percentiles. Topics include:

#### Linear Equations

Linear Equations reviews concepts related to the topic and provides a student with help solving practice problems, including how to solve for a parameter and how to solve various word problems found in many Algebra 2 textbooks and homework. Topics include:

- Solving Linear Equations
- Solving for a Parameter in a Linear Equation
- Applied Linear Equations: Geometry Problem
- Applied Linear Equations: Mixture Problem
- Applied Linear Equations: Investment Problem
- Applied Linear Equations: Tax Problem
- Applied Linear Equations: Distance Problem
- Applied Linear Equations: Collection Problem
- Applied Linear Equations: Consecutive Numbers

#### Linear Inequalities

Linear Inequalities reviews the concepts related to the topic and uses lectures and practice problems to teach students methods of solving inequalities and their applications, notating the solutions with unions and intersections, and how to deal with absolute values within the inequality. Topics include:

#### Exponents

Exponents will help students learn how to work with exponential expressions and equations and use the rules and properties of exponents relating multiplication, division, zeros and negatives. It also teaches students how to use scientific and standard notation. Topics include: