Algebra Trigonometry: Equations and Inequalities

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Build a Strong Foundation of Mathematics to Start a Successful Career in Mathematics, Engineering or Science.

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- 20 hours on-demand video
- 1 Article
- 1 Supplemental Resource
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What Will I Learn?

- Have a practical understanding of all the concepts discussed in the course and apply most of them in your day-to-day life.
- Have the necessary knowledge and skills to start the next course in the series. At the end of the series, the student will have a strong foundation of calculus.

Requirements

- You need to be able to access the course lectures via any device connected to the Internet, e.g., a computer, iPad, etc.
- You must have completed at least 7th grade to have the underlying mathematical skills.
- You also need to have completed "Algebra Trigonometry Prerequisites", the previous course in this series or have a fairly good understanding of the topics discussed therein.

Description

This course is the second stepping stone in **a series of 29 courses** that will take your on a **successful and exciting journey of Mathematics all the way up to Calculus**. Nonetheless, **the course can be taken individually as well**. The **textbook** used in this course is **"Algebra and Trigonometry" from the OpenStax College**. This course covers the second chapter of the book.

**This course covers** the following topics:

- Cartesian Coordinate System
- Linear Equations in One Variable
- 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

As described in the introduction video, this course can also be used in combination with a series of other courses that will take you all the way to calculus. If you'd like to have an overview of our mathematics road map, please read our "Mathematics" page on the "Great IT Courses" website.

Thank you for learning with Great IT Courses!

Who is the target audience?

- This course is for you if you are planning a career in Engineering, Programming, Science, etc. where you'd need a strong foundation in Mathematics.
- This course is also for you if you are changing careers and need to use the discussed concepts in your future career, for example as a computer programmer.

Compare to Other Trigonometry Courses

Curriculum For This Course

96 Lectures

20:10:39
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General Course Information - Important
6 Lectures
26:50

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!

Preview
04:34

Here, you'll learn how you can download the course textbook and find the curriculum related to this course in the book.

Preview
04:17

In this video, you'll learn how to make progress in this course, how to use the resources, etc. to get the best results.

Preview
05:14

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.

Preview
06:20

In this video, we show a way and request you to use the rating and evaluation system on Udemy constructively.

Preview
05:02

Here, you'll find our Imprint and our Terms of Service related to this course.

Preview
01:23

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The Rectangular Coordinate Systems and Graphs
11 Lectures
01:43:49

Cartesian Coordinate System Explanation

Preview
11:09

Plotting Points in a Rectangular Coordinate System

07:47

Graphing an Equation in Two Variables by Plotting Points

11:32

Exercise – Graphing an Equation in Two Variables by Plotting Points

08:13

How to Use a graphing utility like a desktop software program or a graphing calculator to draw the graph of a function

Graphing Equations with a Graphing Utility

08:48

How to calculate the x- and y-intercepts of a function

Finding x- and y-intercepts of a graph

06:15

Calculate the x-intercept and y-intercept of a function. Use them to draw the graph.

Exercise - Finding x- and y-intercepts of a graph

07:53

Distance Formula Derivation

Distance Formula

14:09

Use the Distance Formula to calculate the distance between two points

Exercise - Distance Formula

08:09

Learn the Midpoint Formula and how it’s been derived.

Midpoint Formula Derivation

12:14

Midpoint Formula Exercises

Exercise – Midpoint Formula

07:40

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Linear Equations in One Variable
19 Lectures
04:53:36

Learn how you can apply linear equations to your day-to-day life

Linear Equations Introductions

10:59

Identity, Conditional and Inconsistent Linear Equations

Linear Equations in One Variable

15:12

Learn how to solve an equation in order to find the solution set of the equation

Solving an Equation on One Variable

17:45

Learn how to solve a rational equation finding an LCD

Solving a Rational Equation

19:32

Exercise – Solving Rational Equations

16:06

Solving Rational Equations with Binomial in Denominator

17:37

Learn how to identify the excluded values of rational expressions

Rational Equations Excluded Values

10:43

Exercise - Rational Equations Excluded Values

15:40

Learn about slope, y-intercept and the general form of the equation of a straight line

Equation of Straight Lines Introduction

15:38

Slope of a Straight Line

15:09

Exercise - Slope of a Straight Line

12:50

Point-Slope Form Formula of a Straight Line

16:53

Exercise – Point-Slope Form Formula of a Straight Line

14:30

How to Write the Equation of a line in standard form and exercises

Standard Form of a Line

14:11

How to write the equation, draw the graph and calculate the slope of Horizontal and vertical lines

Horizontal and Vertical Lines

17:07

The slope of perpendicular lines are the negative reciprocal of each other - Proof

Perpendicular Lines and their Slopes

17:43

Parallel and Perpendicular Lines and their Slopes – Concept and Example

Parallel and Perpendicular Lines and their Slopes

14:22

Watch the first part of the exercise in the previous video. A continuation of the last video

Exercise - Parallel and Perpendicular Lines and their Slopes

14:54

Equation of a Line Parallel or Perpendicular to a Given Line

16:45

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Linear Equations - Models and Application
7 Lectures
01:36:42

Learn How you can use Linear equations to model and solve real world problems

Linear Equations Models and Applications

17:14

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

How to Set Up a Linear Equation to Solve a Real World Problem

19:31

Learn how to turn an English word problem into a mathematical linear equation to solve for the unknown

Setting up Linear Equations

12:04

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)

19:43

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)

09:22

A speed time distance situation to set up a two linear equations and solve for the unknowns

Exercise - Setting Up a Linear Equation

10:25

Two length volume situations to set up linear equations and solve for unknowns

Exercise - Setting Up a Linear Equation

08:23

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Complex Numbers
10 Lectures
01:33:14

Learn how real numbers, imaginary numbers and complex numbers are categorized and related to one another

Brief Categorization of Real, Imaginary and Complex Numbers

10:45

Learn what Imaginary and complex numbers are, what the difference between imaginary and real numbers is and where you can apply “i”

Imaginary Numbers, Complex Numbers and “i”

15:58

learn how you can write any imaginary number (sqrt(-9)) in standard form (a + bi)

Expressing an Imaginary Number in Standard Form

03:08

Learn how you can plot the real and imaginary parts of a complex number in a complex plane graphically

How to Plot a Complex Number on the Complex Plane

05:40

Adding and Subtracting Complex Numbers

06:04

Learn how you can calculate the product of a real number and a complex number and the product of two complex numbers

Multiplying Complex Numbers

11:22

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

Dividing Complex Numbers

13:02

Learn how to divide complex numbers by finding the complex conjugate of the denominator and perform the division

Exercise – Dividing Complex Numbers

07:26

Learn the cyclic nature of the powers of “i”. Additionally, learn how you can solve large powers of “i” using the cyclic nature

Simplifying Powers of “i”

11:16

Learn how you can simplify the powers of “i” in four different ways

Exercise – Simplifying the Powers of “i”

08:33

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Quadratic Equations
17 Lectures
03:49:53

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

Quadratic Equations Introduction

15:01

Learn what the roots of a quadratic equation mean in terms of the graph of the function

Graphs of Quadratic Equations

14:07

Learn How to solve quadratic equations by factoring them into two simple linear expressions

Solving Quadratic Equations by Factoring

11:08

Solving Quadratic Equations - Difference of Squares Rule

04:22

Learn how to rewrite quadratic equations to get four term so you can group each to term together and simplify

Solving Quadratic Equations - Grouping

17:57

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 Higher Degree Quadratic Equation - Factoring

13:14

Solving a Quadratic Equation - Square Root Property

14:33

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

15:23

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.

Solving Quadratic Equations - Completing the Square

17:55

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)

18:13

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)

16:05

Exercise - Solving Quadratic Equations by Completing the Square

11:10

Learn what the quadratic formula is and how you can derive it.

Quadratic Formula Derivation

16:03

Learn how you can solve quadratic equations using the quadratic formula by substituting the values of a, b and c into the formula.

Exercise – Solving Quadratic Equations using Quadratic Formula

08:17

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.

Discriminant of a Quadratic Equation

12:14

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.

Exercise - Discriminant of a Quadratic Equation

15:14

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

Pythagorean Theorem and Solving Quadratic Equations

08:57

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Other Types of Equations
16 Lectures
03:35:28

Learn how you can rewrite expressions involving rational exponents to solve for the variable

Solving Equations Involving Rational Exponents

11:57

Learn how you can rewrite expressions involving rational exponents to solve for the variable

Exercise - Solving Equations Involving Rational Exponents

13:25

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 Equations Containing Polynomials by Factoring

10:31

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

Solving Radical Equations

17:53

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

09:56

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

16:07

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

11:00

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 1 of 2)

19:12

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)

13:41

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

17:57

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

10:09

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 Equations in Quadratic Form

15:41

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.

Exercise - Solving Equations in Quadratic Form

13:36

Learn how to solve equations that containing a binomial like x+5 instead of x as the variable.

Solving an Equation in Quadratic Form Containing a Binomial

08:41

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.

Solving Rational Equations Resulting in a Quadratic

12:40

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

13:02

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Linear Inequalities and Absolute Value Inequalities
10 Lectures
02:31:07

Interval Notation

18:33

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

Exercise – Interval Notation

07:35

Learn about the addition and multiplication properties of inequalities and do a few related exercises

Properties of Inequalities and Exercises

18:54

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.

Solving Inequalities in One Variable Algebraically

15:01

Learn how to solve compound inequalities where you have two inequality signs and variables possibly in more than one part of the inequality

Understanding Compound Inequalities

17:50

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 1 of 2)

19:12

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)

11:08

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

15:01

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 1 of 2)

18:30

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)

Exercise - Solving Absolute Value Inequalities (Part 2 of 2)

09:23

About the Instructor