Overview
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

Finding Trigonometric Function Values Using a Calculator

Finding Unknown Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan

Solving Right Triangles

Solving Word Problems that involve angles of elevation

Solving Word Problems that involve angles of depression

Radian Measure

Converting between Radians and Degrees

Finding the Arc Length on a Circle

Finding the Area of a Sector of a Circle

The Unit Circle and Circular Functions

Solving Word Problems with Linear & Angular Speed
Expected Outcomes
 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
 Summation Notation
 Arithmetic Sequence
 Arithmetic Series
 Geometric Sequence
 Geometric Series
 Combinations
 Permutations
 Counting Theory
 Angles
 Acute Angles, Obtuse Angles, Right Angles, Straight Angles
 Finding the Complement of an angle
 Finding the Supplement of an angle
 Degrees, Minutes, and Seconds
 Converting Between Decimal Degrees and Degrees, Minutes, and Seconds
 Determine if two Angles are Coterminal Angles
 Solving for Missing Angles in Similar Triangles
 Solving for Missing Sides in Similar Triangles
 Solving for Missing Angles with a Transversal Crossing Two Parallel Lines
 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 the Six Trigonometric Function Values of an Acute Angle
 Writing a Trigonometric Function in Terms of its Cofunction
 Solving Trigonometric 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
 Finding Trigonometric Function Values Using a Calculator
 Finding Unknown Angle Measures Using Inverse Trigonometric Functions
 arcsin, arccos, arctan, arcsec, arccsc, arccot
 How to Solve Right Triangles When Two Sides are Known
 How to Solve Right Triangles Given an Angle and a Side
 How to Solve Word Problems that Involve Angles of Elevation
 How to Solve Word Problems that Involve Angles of Depression
 Radians
 Converting Between Radians and Degrees
 Finding Arc Length on a Circle
 Finding the Area of a Sector of a Circle
 Understanding Trigonometry Using the Unit Circle
 Circular Functions
 Solving Trigonometry word problems with Linear and Angular Speed