Become a Master of Pre Calculus & Trigonometry and Ace your next Exam! In this course, you will master the concepts of PreCalculus from beginner to advanced, with our stepbystep video tutorials and test your knowledge with over 1100 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. The topics of the course include:

Functions and Their Graphs

The Rectangular Coordinate Plane

Midpoint of a Line Segment

The Pythagorean Formula

Complex Plane – Distance and Midpoint Formulas

Absolute Value of a Complex Number

Vertices of a Right Triangle Formula

Collinear Points Formula

Equations of Circles

Function Definition

Domain and Range of Relations and Functions

Vertical Line Test

Function Notation

Graphing Linear Functions

Finding the Slope of a Line

Finding the Equation of a Line

Parallel and Perpendicular Lines

Graphs of Basic Functions

PiecewiseDefined Functions

Increasing, Decreasing, and Constant Intervals

Graphing Transformations – stretching, shrinking, reflecting

Graphing Transformations – horizontal and vertical shifts

Even and Odd Functions

Finding the Difference Quotient

Function Composition

Polynomial and Rational Functions

Finding the Vertex Form of a Parabola

Graphing Parabolas

The Remainder Theorem

The Factor Theorem

The Rational Zeros Theorem

The Fundamental Theorem of Algebra

Conjugate Zeros Theorem

Descartes’ Rule of Signs

Intermediate Value and Boundedness Theorems

Finding the Zeros of a Polynomial Function

Exponential and Logarithmic Functions

The Horizontal Line Test

Finding OnetoOne Functions Algebraically

Finding the Inverse of a Function

Proving that two functions are inverses

Domain Restrictions, Finding the Inverse

Exponential Functions and Their Graphs

Solving Exponential Equations without Logs

Solving Compound Interest Formula Word Problems

Solving Continuous Compound Interest Formula Word Problems

Logarithmic Functions

Properties of Logarithms

Inverse of an Exponential / Logarithmic Function

Evaluating Logarithms Using the Change of Base Formula

Solving Exponential Equations with Logarithms

Solving Logarithmic Equations

Systems of Equations and Inequalities

Solving Linear Systems in Two Variables

Solving Linear Systems in Three Variables

FInding the Equation of a Parabola Given Three Points

Linear Systems Word Problems

Partial Fraction Decomposition

Solving Nonlinear Systems of Equations

Solving Nonlinear Systems of Inequalities

Matrices and Determinants

GaussJordan Elimination

Matrix Addition and Subtraction

Scalar Multiplication

Matrix Multiplication

Inverse of a Matrix

Matrix Equations

Determinants Using Laplace Expansion

Determinants Using Triangular Form

Transpose of a Matrix

Adjugate of a Matrix

Inverse Using the Adjugate and Determinant

Cramer’s Rule

Area of a Triangle – Determinants

Collinear Points – Determinants

Writing the Equation of a Line – Determinants

Analytic Geometry

Conic Sections

The Parabola

The Ellipse

The Hyperbola

Sequences

Series and Summation Notation

Finding the nth term for an arithmetic sequence

Finding the nth term for a geometric sequence

Evaluating arithmetic series

Evaluating infinite and finite geometric series

Counting Theory

Combinations

Permutations

Angles in Trigonometry

Measuring angles using degrees

Complementary angles

Supplementary angles

Degrees, Minutes, and Seconds

Converting Between Decimal Degrees and Degrees, Minutes, and Seconds

Determine if two Angles are Coterminal Angles

Relationships between Angles: Vertical Angles, Angles formed by a Transversal and Parallel Lines

Solving for the Missing Angle Measurements with Similar Triangles

Solving for the Missing Lengths with Similar Triangles

Finding the Trigonometric Function Values of an Angle

Finding Trigonometric Function Values Given One Value and the Quadrant

Finding Trigonometric Function Values Based on Reciprocal Identities

Finding Trigonometric Function Values Based on Pythagorean Identities

Finding Trigonometric Function Values Based on Quotient Identities

Finding Trigonometric Function Values of an Acute Angle

Writing a Function in Terms of its Cofunction

Solving Equations Using Cofunction Identities

Finding Reference Angles

Special Angles as Reference Angles

Finding Angle Measures with Special Angles

Finding Trigonometric Function Values of NonAcute Angles
Functions and Their Graphs
In this lesson, we will cover the basics of the coordinate plane.
In this lesson, we review the complex plane and how to plot complex numbers.
In this lesson, we learn how to find the midpoint of a line segment.
In this lesson, we will learn how to use the distance formula, to find the distance between two points on the coordinate plane.
In this lesson, we learn how to find the distance between two points in the complex plane. Additionally, we learn how to find the midpoint of a line segment in the complex plane.
In this lesson, we learn how to find the absolute value of a complex number.
In this lesson, we will learn how to use the distance formula to determine if three points are the vertices of a right triangle.
In this lesson, we will learn how to use the distance formula to determine if three points are collinear.
In this lesson, we will learn how to find the equation of a circle, as well as learn about the equation of a circle in general and standard form.
In this lesson, we learn about the definition of a relation and the definition of a function.
In this lesson, we learn about the domain or the set of allowable xvalues and the range or the set of allowable yvalues.
In this lesson, we learn about the vertical line test. This test allows us to determine if a relation is a function.
In this lesson, we learn how to use function notation.
In this lesson, we learn how to graph linear functions.
In this lesson, we learn how to find the slope of a line.
In this lesson, we learn how to write the equation of a line in slopeintercept form, pointslope form, and standard form.
In this lesson, we will learn how to sketch the graphs of basic functions.
In this lesson, we will learn about piecewisedefined functions, or functions that have different definitions across the domain.
In this lesson, we will learn about increasing, decreasing, and constant intervals.
In this lesson, we will learn about stretching or shrinking a graph.
In this lesson, we will learn about horizontal and vertical shifts.
In this lesson, we will learn about even and odd functions.
In this lesson, we will learn about performing operations with functions.
In this lesson, we will learn how to find the difference quotient.
In this lesson, we will learn about function composition.
Polynomial Functions
In this lesson, we will learn how to find the vertex form of a parabola.
In this lesson, we will learn the various techniques available for sketching the graph of a parabola.
In this lesson, we will learn about the remainder theorem.
In this lesson, we will learn about the factor theorem.
In this lesson, we will learn about the rational zeros theorem.
In this lesson, we will learn about the fundamental theorem of algebra.
In this lesson, we will learn about the conjugate zeros theorem.
In this lesson, we will learn about Descartes' Rule of Signs.
In this lesson, we will learn about the intermediate value and boundedness theorems.
In this lesson, we will learn how to find the zeros of polynomial functions.
Exponential / Logarithmic Functions and Their Graphs
In this lesson, we will learn how to use the horizontal line test to determine if a function is onetoone.
In this lesson, we will learn how to determine if a function is onetoone using an algebraic method.
In this lesson, we will learn how to determine if two functions are inverses using function composition.
In this lesson, we will learn how to find the inverse of a domain restricted function.
In this lesson, we will learn about exponential functions.
In this lesson, we will learn how to solve exponential equations when logarithms are not required.
In this lesson, we will learn how to solve word problems that involve the compound interest formula.
In this lesson, we learn how to solve word problems that involve the continuous compound interest formula.
In this lesson, we will learn how to work with logarithmic functions.
In this lesson, we will learn about the properties of logarithms, the product property, quotient property, and power property.
In this lesson, we will learn how to find the inverse of an exponential / logarithmic function.