Master College Level Algebra with our Step by Step Video Tutorials. Over 4500 Practice Questions! Ace your Algebra Exam!
Description
Become a Master of College Algebra, Pre-Calculus, & Trigonometry and Ace your next Algebra/Pre-Calculus/Trigonometry Exam! In this course, you will master all concepts of College-Level Algebra, Pre-Calculus, and Trigonometry, from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 4500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. Note: the Algebra topics covered from Pre-Calculus are also covered in a College Algebra course. Please read the topics below for further details.
The topics of the course include:
Review of Real Numbers
Operations with Polynomials
Factoring Polynomials
Rational Expressions
Rational Exponents
Radical Expressions
Solving Linear Equations/Inequalities
Solving Word Problems with Linear Equations
Complex Numbers
Solving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)
Solving Word Problems with Quadratic Equations
Solving Quadratic/Rational Inequalities
Solving Radical Equations/Inequalities
Solving Advanced Absolute Value Equations/Inequalities
The Coordinate Plane
Graphing Circles
Distance and Midpoint Formulas
Relations and Functions
Domain and Range
Vertical Line Test
Increasing, Decreasing, Constant Intervals
Graphing Linear Functions
Slope
Forms of a Line
Graphs of Basic Equations (Parent Functions)
Graphing Transformations
Function Operations
The Difference Quotient
Composition of Functions
Solving Linear Systems in Two/Three Variables
Solving Systems of Linear Inequalities in Two Variables
Solving Word Problems with Linear Systems
Curve Fitting, Finding the Equation of a Parabola Given Three Points
Partial Fraction Decomposition
Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination
Matrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)
Finding the Inverse of a Matrix
Solving Linear Systems using the Inverse of a Matrix
Finding the Determinant of a Matrix
Finding the Inverse of a Matrix Using Cofactors
Solving Linear Systems using Cramer's Rule
Applications of determinants: Area of a Triangle, test for collinearity, equation of a line
Determine if functions are one-to-one using the Horizontal line test/algebraic methods
Finding the Inverse of a One-to-One Function
Finding the Inverse of a Domain Restricted Function
Graphing the Inverse of a Function
Graphing Exponential Functions
Solving Exponential Equations with Like Bases
Solving Compound Interest Word Problems
Solving Continuous Compound Interest Word Problems
Graphing Logarithmic Functions
Properties of Logarithms
Expanding Logarithms
Condensing Logarithms
Change of Base Rule for Logarithms
Solving Exponential and Logarithmic Equations
Solving Exponential and Logarithmic Inequalities
Applications of Exponential and Logarithmic Functions
Finding the Vertex Form of a Parabola
How to Graph a Parabola
The Remainder Theorem
Using the Remainder Theorem to test for Zeros of a Polynomial Function
The Factor Theorem
Using the Factor Theorem to factor a polynomial function given one zero
Using the Rational Zeros Theorem to find all possible rational zeros
The Fundamental Theorem of Algebra and the Number of Zeros Theorem
Writing Polynomial Functions Given Zeros and a Point
Conjugate Zeros Theorem
Descartes' Rule of Signs
Intermediate Value Theorem
Boundedness Theorem
Find the upper and lower bounds for zeros of a polynomial function
Solving nonlinear systems of equations
Conic Sections: Parabolas - Focus and Directrix
Conic Sections: Ellipses - Finding the Foci and Graphing
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
Sets, Subsets, Venn Diagrams
Union of Two or More Sets
Intersection of Two or More Sets
The Binomial Theorem
Counting Theory
Combinations
Permutations
Probability
Angles in Trigonometry
Complementary and Supplementary Angles
Working with Degrees, Minutes, and Seconds
Converting between Decimal Degrees and Degrees, Minutes, and Seconds
Determine if two angles are coterminal angles
Finding angle measures for similar triangles
Finding side lengths for similar triangles
Finding the Trigonometric Function Values of an Angle
Finding the Trigonometric function Values of an Angle Given a Point on the Terminal Side
Finding Trigonometric Function Values Given One Value and the Quadrant
Finding Trigonometric Function Values Based on Pythagorean Identities
Finding Trigonometric Function Values Based on Quotient Identities
Finding Trigonometric Function Values of Acute Angles
Writing Trigonometric Functions in Terms of its Cofunction
Solving Trigonometric Equations Using Cofunction Identities
Reference Angles
Finding Trigonometric Function Values of Non-Acute Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values Using a Calculator
Finding Missing Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan
Solving Right Triangles
Solving Word Problems with angles of elevation
Solving Word Problems with 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
Defining the Six Trigonometric Functions Using the Unit Circle
Solving Trigonometry Word Problems that Involve Linear and Angular Speed
Graphing Sine and Cosine
Graphing Function Transformations of Sine and Cosine
Finding the Amplitude, Period and Phase Shift for Trigonometric Functions
Using the Fundamental Identities to find missing Trigonometric Ratios
Using the Fundamental Identities to rewrite Trigonometric Expressions
Verifying Trigonometric Identities
Sum and Difference Identities for Sine, Cosine, and Tangent
Finding sin(A + B), cos(A + B), and tan(A + B)
Finding sin(A - B), cos(A - B), and tan(A - B)
Finding Trigonometric Function values using Double-Angle Identities
Working with Product-to-Sum and Sum-to-Product Identities
Working with Half-Angle Identities
Evaluating Inverse Trigonometric Functions
Graphing Inverse Trigonometric Functions
Finding the Composition of Inverse Trigonometric Functions
Solving Trigonometric Equations Using Linear Methods
Solving Trigonometric Equations by Factoring
Solving Trigonometric Equations by Squaring/Square Roots
Solving Trigonometric Equations Using Identities
Solving Trigonometric Equations Using the Quadratic Formula
Solving Trigonometric Equations with Half-Angles
Solving Trigonometric Equations with Multiple Angles
Solving Trigonometric Equations Involving Inverse Trigonometric Functions
The Law of Sines (ASA)
The Law of Sines (SAA)
The Area of a Triangle using Sine (SAS)
The Law of Sines Ambiguous case (SSA)
The Law of Cosines (SAS), (SSS)
The Area of a Triangle using Heron's Formula
Finding the Component Form of a Vector
Finding the Magnitude of a Vector
Finding the Direction Angle of a Vector
Finding the Sum (resultant) of Two Vectors
Multiplying a Vector by a Scalar
How to Find the Unit Vector
How to Write a Linear Combination of Unit Vectors
How to Find the Dot Product
How to Find the Angle Between Two Vectors
How to Determine if Two Vectors are Orthogonal
How to Add Two Complex Numbers Graphically
Find the Trigonometric (Polar) Form of a Complex Number
Convert a Complex Number between the Rectangular Form and Polar Form
Multiplying Complex Numbers in Polar Form
Dividing Complex Numbers in Polar Form
Product and Quotient Theorems
De Moivre's Theorem
Powers of Complex Numbers in Polar Form
Roots of Complex Numbers in Polar Form
Solving Equations Using Roots of Complex Numbers
The Polar Coordinate System
Plotting Polar Coordinates on the Polar Grid
Converting Between Polar Coordinates and Rectangular Coordinates
Writing Polar Coordinates in Multiple Forms
Finding the Distance Between Two Polar Points
Converting Linear Equations Between Rectangular and Polar Forms
Graphing Lines on the Polar Coordinate Plane
Converting Circles from Polar to Rectangular Form
Graphing Circles on the Polar Grid
Finding the Inclination of a Line
Finding the Angle Between Two Lines
Finding the Shortest Distance Between a Point and a Line
Who this course is for:
- Students who need a complete understanding of Advanced Algebra
- Students currently enrolled in a College Level Algebra Course
- Students currently enrolled in a Pre-Calculus Course
- Students who need to master Algebra in order to fully prepare for Calculus
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