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#### Conic Sections

FREEConic 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:

#### Equations of Lines, Parabolas and Circles

Equations of lines and circles covers the algebraic representation of parallel lines, perpendicular bisectors, circles, and introduces the theory and problems for parabolas Topics include:

- Parallel and Skew Lines
- Parallel Planes and Lines
- Converse of Parallel Lines Theorem
- Constructing the Perpendicular Bisector
- Introduction to Parabolas
- Finding the Vertex of a Parabola by Completing the Square
- Finding Intercepts, Domain, Range and Vertex of a Parabola
- The Circle
- Computing Difference Quotients

#### Polynomial and Rational Functions

Polynomial and rational functions covers the algebraic theory to find the solutions, or zeros, of such functions, goes over some graphs, and introduces the limits. Topics include:

- Power Functions
- Integer Power Functions
- Polynomial Functions
- Graphing Polynomial Functions
- Graphing Polynomial Functions with Repeated Factors
- Find an Equation of the Polynomial Function
- Finding Maximum and Minimum Values
- Finding Zeros of a Polynomial Function
- Using the Conjugate Zeros Theorem
- The Reciprocal Transformation
- Introduction to Rational Functions
- Limits of Rational Functions
- Limits at a Glance
- Graphing Rational Functions, n less than m
- Graphing Rational Functions, n=m
- Graphing Rational Functions, n>m
- Graphs with Holes

#### Exponential and Logarithmic Functions

Exponential and logarithmic functions covers concepts from powers and logarithms, including some emphasis on the natural logarithm and applications to problems of growth and decay Topics include:

- 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)
- Evaluating a Logarithmic Expression in terms of Known Quantities
- Exponential Functions
- Logarithmic Functions
- Properties of Logarithms
- The Number e and the Natural Logarithm
- Exponential Growth and Decay

#### Basic Trigonometry

Basic trigonometry covers the definitions and formulas for the basic trigonometric ratios, as well as the fundamental theorems and some applications Topics include:

#### Trigonometric Functions

Trigonometric functions covers the concepts, formulas, and graphs used in trigonometry, and introduces some of the basic identities Topics include:

- Radian Measure of Angles
- The Definitions of Sine and Cosine
- Evaluating Sine and Cosine at Special Acute Angles
- Evaluating Sine and Cosine at Other Special Angles
- Graphs of the Sine and Cosine Functions
- Transforming the Graphs of Sine and Cosine
- More Transformations of Sine and Cosine
- Find an Equation for the Sine or Cosine Wave
- The Tangent Function
- Evaluating the Tangent Function
- Graph of the Tangent Function
- Transforming the Tangent Graph
- Intercepts and Asymptotes of Tangent Functions
- Trigonometric Identities
- The Reciprocal Trigonometric Functions
- Graphing the Reciprocal Trigonometric Functions
- Using Trigonometric Identities
- Transforming the Cotangent Graph
- Transforming Secant and Cosecant
- Asymptotes of Secant, Cosecant, and Cotangent

#### Advanced Trigonometry

Advance trigonometry covers the inverse trigonometric functions, solving equations involving trig concepts, and additional identities, including those of double and half angles Topics include:

- The Inverse Sine Function
- The Inverse Cosine Function
- The Inverse Tangent Function
- Using the Inverse Trigonometric Functions
- Solving Trigonometric Equations
- Trigonometric Equations that Require Factoring
- The Cosine Addition Formulas
- The Sine Addition Formulas
- Using the Sine and Cosine Addition Formulas to Prove Identities
- The Double-Angle Formulas
- Other Forms of the Cosine Double-Angle Formula
- The Half-Angle Identities
- Angle Inclination of a Line

#### Vectors and Parametric Equations

Vectors and parametric equations covers the geometric and algebraic representations of vectors, operations, and applications to parametric equations and 3D coordinate systems Topics include:

- The Geometric Representation of Vectors
- Adding Vectors
- The Resultant of Two Forces
- Components of a Force
- Navigation Problems
- Algebraic Representation of Vectors
- Addition and Scalar Multiplication of Vectors
- Unit Vectors
- The Vector Equation of a Line
- Motion Along a Line
- Parametric Equations and Motion
- Parametrizing a Line Segment
- Parametrizing a Circle
- The Dot Product of Vectors
- The Angle Between Vectors
- Introduction to the 3D Coordinate System
- Vector Operations in 3D
- The Midpoint and Distance Formulas in 3D
- Lines in 3D
- Perpendicular, Parallel and Skew Lines in Space
- Introduction to Planes
- Vectors and Planes
- The Angle Between Planes

#### Polar Coordinates and Complex Numbers

Polar coordinates and complex numbers covers the polar/rectangular relationship and the representation of basic graphs. Also introduces the complex plane and applications. Topics include:

- Introduction to Polar Coordinates
- Converting from Rectangular Coordinates to Polar
- Converting from Polar Coordinates to Rectangular
- The Distance Formula in Polar Coordinates
- Lines in Polar Coordinates
- Symmetry of Polar Graphs
- Graphing Polar Equations
- Families of Polar Curves: Circles, Cardiods, and Limacon
- Families of Polar Curves: Roses
- Families of Polar Curves: Conic Sections
- The Complex Plane
- Trigonometric Form of Complex Numbers
- Converting Complex Numbers From Rectangular Form to Trigonometric
- Multiplying Complex Numbers
- Dividing Complex Numbers
- DeMoivre's Theorem
- The Euler Formula
- Finding the Roots of a Complex Number
- More Roots of Complex Numbers

#### Systems of Linear Equations and Matrices

Systems of linear equations and matrices covers methods to find the solutions to a system, including methods using matrices, supported by the main concepts from matrix algebra Topics include:

- Square Matrices
- The Identity Matrix
- The Inverse of a Square Matrix
- Solving Linear Systems Using Matrix Algebra
- 2x2 Determinants
- 3x3 Determinants
- Simplifying Determinants
- Cramer's Rule
- Area With Determinants
- The Cross Product of Vectors
- Area With the Cross Product
- Invertible Square Matrices and Determinants

#### Topics in Discrete Math

Topics in discrete math covers concepts, formulas, notation and problems related to combinatorics, with applications to probability and binomials Topics include:

- Pascal's Triangle
- Binomial Theorem
- Introduction to Probability
- Fundamental Counting Principal
- Permutations
- Combinations
- Combinations vs. Permutations
- Probability of Multiple Events
- Probability of Independent Events
- Using the Complement to Calculate Probability
- Probability of Dependent Events
- Conditional Probability

#### Linear Equations and Inequalities

Linear equations and inequalities covers their applications to problem solving, including absolute values, graphing and inequalities with 2 variables Topics include:

- Solving and Graphing Compound Inequalities
- Graphing 2 Variable Inequalities
- 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
- Solving Linear Inequalities
- Solving a Three-part Linear Inequality
- Applied Linear Inequalities
- Set Operation: Union
- Set Operation: Intersection
- Solving "Greater Than" Absolute Value Inequalities
- Solving "Less Than" Absolute Value Inequalities

#### Introduction to Functions

Functions teaches students how to properly use function notation, how to find domain and range, and how to graph different function transformations. Topics include:

- Computing Difference Quotients
- Seven Elementary Functions and Their Graphs
- Finding the Domain of a Function
- Graphing the Transformation y = a f(x) + k
- Graphing the Transformation y = f(x - h)
- Domain Restrictions and Functions Defined Piecewise
- The Reflection y = f(-x)
- Symmetry of Graphs: Odd and Even Functions
- The Greatest Integer Function
- The Transformation y = f(bx)