Algebra Trigonometry: Equations and Inequalities

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Course Description

Algebra Trigonometry: Equations and Inequalities is the second course in a series of 29 courses in mathematics offered by Great IT Courses to help you master your mathematics.

Topics Covered in Algebra Trigonometry: Equations and Inequalities

Topics covered in this course are: 

  • Cartesian Coordinate System
  • Linear Equations - Models and Applications
  • Complex Numbers 
  • Quadratic Equations
  • Other Types of Equations like polynomial, radical, absolute value equations and equations in quadratic form and involving rational exponents and rational equations

Watch Sample Course Videos on Youtube

In order to watch a few sample lectures of this course on Youtube, please follow the link below. It will take you to the relevant Youtube playlist.

Course Curriculum

Section 1 - Course General Information

Section 1 - Course General Information

 Instructor Introduction  Here, we'll introduce your instructor in this course and Great IT Courses to you. We'll also introduce some other ways like Facebook, Google+, etc. to connect with us!​
 Course Curriculum  Here, you'll learn how you can download the course textbook and find the curriculum related to this course in the book.​
 How to Use This Course In this video, you'll learn how to make progress in this course, how to use the resources, etc. to get the best results.​ 
 Road Map  In this video, you'll learn how you can use this course in combination with the other courses in this series to build a strong foundation all the way up to calculus.​
 Feedback  In this video, we show a way and request you to use the rating and evaluation system on Udemy constructively.​
 Terms of Service  Here, you'll find our Imprint and our Terms of Service related to this course.​
Section 2 - The Rectangular Coordinate System and Graphs

Section 2 - The Rectangular Coordinate System and Graphs

Cartesian Coordinate System  Cartesian Coordinate System Explanation
 Plotting Points in a Rectangular Coordinate System  -
 Graphing an Equation in Two Variables by Plotting Points  -
 Exercise – Graphing an Equation in Two Variables by Plotting Points  -
 Graphing Equations with a Graphing Utility  How to Use a graphing utility like a desktop software program or a graphing calculator to draw the graph of a function
 Finding x- and y-intercepts of a graph  How to calculate the x- and y-intercepts of a function
 Exercise - Finding x- and y-intercepts of a graph  Calculate the x-intercept and y-intercept of a function. Use them to draw the graph.
 Distance Formula  Distance Formula Derivation
 Exercise - Distance Formula  Use the Distance Formula to calculate the distance between two points
 Midpoint Formula Derivation  Learn the Midpoint Formula and how it’s been derived.
 Exercise – Midpoint Formula  Midpoint Formula Exercises
Section 3 - Linear Equations in One Variable

Section 3 - Linear Equations in One Variable

 Linear Equations Introductions  Learn how you can apply linear equations to your day-to-day life
 Linear Equations in One Variable  Identity, Conditional and Inconsistent Linear Equations
 Solving an Equation on One Variable Learn how to solve an equation in order to find the solution set of the equation 
 Solving a Rational Equation  Learn how to solve a rational equation finding an LCD
 Exercise – Solving Rational Equations  -
 Solving Rational Equations with Binomial in Denominator  -
Rational Equations Excluded Values   Learn how to identify the excluded values of rational expressions
 Exercise - Rational Equations Excluded Values  -
 Equation of Straight Lines Introduction Learn about slope, y-intercept and the general form of the equation of a straight line
 Slope of a Straight Line  -
Exercise - Slope of a Straight Line -
Point-Slope Form Formula of a Straight Line -
Exercise – Point-Slope Form Formula of a Straight Line -
Standard Form of a Line How to Write the Equation of a line in standard form and exercises
Horizontal and Vertical Lines How to write the equation, draw the graph and calculate the slope of Horizontal and vertical lines
Perpendicular Lines and their Slopes The slope of perpendicular lines are the negative reciprocal of each other - Proof 
Parallel and Perpendicular Lines and their Slopes Parallel and Perpendicular Lines and their Slopes – Concept and Example
Exercise - Parallel and Perpendicular Lines and their Slopes Watch the first part of the exercise in the previous video. A continuation of the last video
Equation of a Line Parallel or Perpendicular to a Given Line -
Section 4 - Linear Equations, Models and Applications

Section 4 - Linear Equations, Models and Applications

Linear Equations Models and Applications    Learn How you can use Linear equations to model and solve real world problems
How to Set Up a Linear Equation to Solve a Real World Problem  Learn all the necessary steps to set up a linear equation to solve a real world problem, draw the graph and analyze the graph of the equation 
Setting up Linear Equations   Learn how to turn an English word problem into a mathematical linear equation to solve for the unknown
 Exercise – Setting Up a Linear Equation (Part 1 of 2)  Learn how you can set up linear equations to compare two cellphone packages from two different providers against different sets of monthly talk time duration.
 Exercise – Setting Up a Linear Equation (Part 1 of 2) Learn how you can set up linear equations to compare two cellphone packages from two different providers against different sets of monthly talk time duration. 
Exercise - Setting Up a Linear Equation   A speed time distance situation to set up a two linear equations and solve for the unknowns
 Exercise - Setting Up a Linear Equation  Two length volume situations to set up linear equations and solve for unknowns
Section 5 - Complex Numbers

Section 5 - Complex Numbers

Brief Categorization of Real, Imaginary and Complex Numbers Learn how real numbers, imaginary numbers and complex numbers are categorized and related to one another
Imaginary Numbers, Complex Numbers and “i” Learn what Imaginary and complex numbers are, what the difference between imaginary and real numbers is and where you can apply “i”
Expressing an Imaginary Number in Standard Form learn how you can write any imaginary number (sqrt(-9)) in standard form (a + bi) 
How to Plot a Complex Number on the Complex Plane Learn how you can plot the real and imaginary parts of a complex number in a complex plane graphically
Adding and Subtracting Complex Numbers -
Multiplying Complex Numbers  Learn how you can calculate the product of a real number and a complex number and the product of two complex numbers
Dividing Complex Numbers Learn how to divide complex numbers by finding the complex conjugate of the denominator and multiply it into both the numerator and denominator of the original expression
Exercise – Dividing Complex Numbers Learn how to divide complex numbers by finding the complex conjugate of the denominator and perform the division
Simplifying Powers of “i” Learn the cyclic nature of the powers of “i”. Additionally, learn how you can solve large powers of “i” using the cyclic nature
Exercise – Simplifying the Powers of “i” Learn how you can simplify the powers of “i” in four different ways
Section 6 - Quadratic Equations

Section 6 - Quadratic Equations

Quadratic Equations Introduction Learn what quadratic equations are, how to factorize them, the difference between an equation and an expression, Zero-product Property and how to solve a quadratic equation to find the roots or the x-intercepts
Graphs of Quadratic Equations Learn what the roots of a quadratic equation mean in terms of the graph of the function
Solving Quadratic Equations by Factoring Learn How to solve quadratic equations by factoring them into two simple linear expressions
Solving Quadratic Equations - Difference of Squares Rule Learn how you can solve quadratic equations using a² – b² = (a – b) (a + b) Formula
Solving Quadratic Equations - Grouping Learn how to rewrite quadratic equations to get four term so you can group each to term together and simplify
Solving a Higher Degree Quadratic Equation - Factoring Learn how to write a higher degree quadratic equation having term like x³ in terms of normal quadratic equations and then find the roots of the simpler quadratic equation
Solving a Quadratic Equation - Square Root Property Learn how you can solve a quadratic equation in which the x term in not present using a simple square root applied to both sides of the equation
Exercise – Solving a Quadratic Equation Using Square Root Property Learn how you can solve a quadratic equation in which the x term in not present using a simple square root applied to both sides of the equation
Solving Quadratic Equations - Completing the Square Learn how you can write quadratic equations in the form of perfect squares ( a + b ) ² = a² + 2ab + b² and then apply the square root property to both sides of the equation to solve for x.
Exercise - Solving Quadratic Equations by Completing the Square(Part 1 of 2)  Learn how you can write quadratic equations in the form of perfect squares ( a + b ) ² = a² + 2ab + b² and then apply the square root property to both sides of the equation to solve for x.
Exercise - Solving Quadratic Equations by Completing the Square(Part 2 of 2)  Learn how you can write quadratic equations in the form of perfect squares ( a + b ) ² = a² + 2ab + b² and then apply the square root property to both sides of the equation to solve for x.
Exercise - Solving Quadratic Equations by Completing the Square Learn how you can write quadratic equations in the form of perfect squares ( a + b ) ² = a² + 2ab + b² and then apply the square root property to both sides of the equation to solve for x.
Quadratic Formula Derivation Learn what the quadratic formula is and how you can derive it.
Exercise – Solving Quadratic Equations using Quadratic Formula Learn how you can solve quadratic equations using the quadratic formula by substituting the values of a, b and c into the formula.
Discriminant of a Quadratic Equation Learn the four different cases that could happen in a quadratic equation based on its discriminant for example if the equation is going to have two rational solutions, two irrational solutions, etc.
Exercise - Discriminant of a Quadratic Equation Learn how you can calculate the discriminant of any quadratic equation and predict how many solution of type real or complex you’re going to have based on the discriminant.
Pythagorean Theorem and Solving Quadratic Equations Learn how you can calculate the lengths of a right triangle using the Pythagorean theorem and the techniques you have learned for solving quadratic equations
Section 7 - Other Types of Equations

Section 7 - Other Types of Equations

Solving Equations Involving Rational Exponents Learn how you can rewrite expressions involving rational exponents to solve for the variable
Exercise - Solving Equations Involving Rational Exponents Learn how you can rewrite expressions involving rational exponents to solve for the variable
Solving Equations Containing Polynomials by Factoring Learn how you can factor out some term of the variable in polynomials of degree higher than 2 to find the roots of the equations
Solving Radical Equations Learn how you can solve radical equations by raising both sides of the equation to the index of the radical sign and solve for x
Exercise - Solving Radical Equations Learn how you can solve radical equations by raising both sides of the equation to the index of the radical sign and solve for x
Exercise - Solving Radical Equations With Two Radicals Learn how you can solve radical equations with two radicals by raising both sides of the equation to the index of the radical sign in two steps and solve for x
Exercise - Solving Radical Equations With Two Radicals Learn how you can solve radical equations with two radicals by raising both sides of the equation to the index of the radical sign in two steps and solve for x
Solving Absolute Value Equations (Part 1 of 2) Learn the definition of an absolute value function and how you can use the definition to solve absolute value equations. Also learn what the concept of absolute value refers to and what it practically means on the real number line.
Solving Absolute Value Equations (Part 2 of 2) Learn the definition of an absolute value function and how you can use the definition to solve absolute value equations. Also learn what the concept of absolute value refers to and what it practically means on the real number line.
Exercise - Solving Absolute Value Equations Learn how to solve absolute value equations by analyzing the equation, considering the possible cases for the equation and simplifying the equation accordingly.
Exercise - Solving Absolute Value Equations Learn how to solve absolute value equations by analyzing the equation, considering the possible cases for the equation and simplifying the equation accordingly.
Solving Equations in Quadratic Form Learn how you can rewrite equations in quadratic form usually with a leading term exponent of 4 in the form of a standard quadratic equation and solve for x. 
Exercise - Solving Equations in Quadratic Form Exercise - Learn how you can rewrite equations in quadratic form usually with a leading term exponent of 4 in the form of a standard quadratic equation and solve for x. 
Solving an Equation in Quadratic Form Containing a Binomial Learn how to solve equations that containing a binomial like x+5 instead of x as the variable. 
Solving Rational Equations Resulting in a Quadratic Learn how to solve rational expressions, making changes to them, eliminating the denominators and writing the whole equation in form of a standard quadratic equation. Then you can use the standard techniques you have learned for quadratic equations to solve for x. 
Exercise - Solving Rational Equations Resulting in a Quadratic Learn how to solve rational expressions, making changes to them, eliminating the denominators and writing the whole equation in form of a standard quadratic equation. Then you can use the standard techniques you have learned for quadratic equations to solve for x. 
Section 8 - Linear Inequalities and Absolute Value Inequalities

Section 8 - Linear Inequalities and Absolute Value Inequalities

Interval Notation Learn how you can express inequalities in term on interval notation, number line notation and set-builder notation
Exercise – Interval Notation Learn how you can express a specific set of numbers using the interval notation for example all real numbers greater than or equal to a
Properties of Inequalities and Exercises Learn about the addition and multiplication properties of inequalities and do a few related exercises
Solving Inequalities in One Variable Algebraically Learn how to solve inequalities algebraically by doing addition, subtraction, multiplication and division of different kinds on either side of the inequality as required and express the result in interval notation.
Understanding Compound Inequalities Learn how to solve compound inequalities where you have two inequality signs and variables possibly in more than one part of the inequality
Solving Absolute Value Inequalities (Part 1 of 2)  Learn the meaning of an absolute value inequality, how you can solve it graphically or algebraically and how you can apply the concept to real life problems.
Solving Absolute Value Inequalities (Part 2 of 2)  Learn the meaning of an absolute value inequality, how you can solve it graphically or algebraically and how you can apply the concept to real life problems.
Exercise - Solving Absolute Value Inequalities  Learn how you can calculate all numbers x within a certain distance from a specific number using the concept of absolute value and inequalities.
Exercise - Solving Absolute Value Inequalities (Part 1 of 2) Learn how to solve: “Describe all values x within a distance of 4 from the number 5” and “Given an equation, determine all the x values for which the y values are negative”. (Part 1 of 2)
Exercise - Solving Absolute Value Inequalities (Part 2 of 2) Learn how to solve: “Describe all values x within a distance of 4 from the number 5” and “Given an equation, determine all the x values for which the y values are negative”. (Part 2 of 2)

 

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