Algebra 1, 2, & 3 - Intermediate & College Level Course

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Algebra Review - Slope, Graphing Linear Equations, Exponents, Factoring, Solving Quadratic Equations, & Radicals

Best Seller

753 students enrolled

What Will I Learn?

- At the end of my course, students will be able to understand the basic fundamentals and principles of algebra.

Requirements

- Students will need a basic understanding of the principles of math such as addition, subtraction, multiplication, and division.

Description

This course is designed for university students taking intermediate algebra and college algebra and high school students taking algebra 1, algebra 2, or algebra 3.

Here is a list of topics covered in this course:

1. Basic Arithmetic - Addition, Subtraction, Multiplication, and Division

2. Fractions Review

3. Solving Linear Equations

4. Order of Operations

5. Absolute Value Functions & Inequalities

6. Graphing Linear Equations Using Slope & The Y-Intercept

7. Polynomials

8. Factoring

9. Systems of Linear Equations

10. Quadratic Equations

11. Rational Expressions

12. Radical Expressions

13. Complex Imaginary Numbers

14. Exponential and Logarithmic Functions

15. Functions

16. Conic Sections

17. Arithmetic and Geometric Sequences

Who is the target audience?

- high school and college students including adults returning to college.

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Curriculum For This Course

227 Lectures

20:51:11
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Introduction
1 Lecture
01:00

Welcome to Algebra. In this course, we will cover topics such as solving linear equations, graphing quadratic functions, and simplifying radical and rational expressions just to name a few. My recommendation is to work through each example problem in the videos. This will help to boost your algebra skills in the long run which will help you to do well in higher level math courses.

Preview
01:00

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Basic Arithmetic - Addition, Subtraction, Multiplication, and Division
9 Lectures
27:14

This lesson shows you how to add two numbers mentally by the use of a number line.

Preview
03:05

This lesson explains how to subtract two numbers mentally using a number line.

Subtracting Two Numbers Using a Number Line

03:17

This lesson explains how to add two large numbers on paper without the use of a calculator.

Adding Two Large Numbers

02:32

This lesson explains how to subtract two large numbers on paper without using a calculator.

Subtracting Two Large Numbers

02:56

This video explains the concept of multiplication using repeated addition.

Understanding The Concept of Multiplication

02:52

This lesson focuses on the relationship between multiplication and division.

Understanding Division and Multiplication

02:44

This lesson explains how to multiply two large numbers without using a calculator.

Multiplying Two Large Numbers

03:36

This video explains how to divide two numbers using long division.

Long Division

02:04

This 5 question multiple choice video quiz will test your knowledge on the basic principles of addition, subtraction, multiplication, and division. Make sure to pause the video to work on the problem first before viewing the solution.

Basic Arithmetic Video Quiz

04:08

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Fractions Review Tutorial
9 Lectures
33:39

This video provides a simple technique for adding and subtracting two fractions.

Adding and Subtracting Two Fractions

01:40

This lesson explains how to add and subtract three fractions by finding the common denominator. Keep in mind, you can only add or subtract fractions if they all share the same denominator.

Adding and Subtracting Three Fractions

04:52

This lesson explains how to multiply fractions which can be done by multiplying the numerators and denominators of each fraction separately.

Multiplying Fractions

02:21

This lesson shows you how to divide fractions using a technique known as "Keep Change Flip!"

Dividing Fractions

03:00

This video discusses how to simplify complex fractions by clearing away the small fractions that are part of the larger fraction.

Preview
02:56

This lesson explains how convert mixed numbers into improper fractions and how to convert improper fractions to mixed numbers.

Interconverting Mixed Numbers and Improper Fractions

03:44

This lesson explains how to convert fractions into decimals using long division.

Converting Fractions To Decimals

03:37

This video tutorial provides a simple way to convert decimals to fractions.

Decimals to Fractions

03:36

This 4 question multiple choice video quiz will test your knowledge of fractions and decimals.

Multiple Choice Video Quiz

07:53

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Solving Linear Equations
8 Lectures
32:30

This lesson explains how to solve simple linear equations in one step using addition and subtraction. The purpose of solving an equation is to find the value of x. To do this, rearrange the equation until the variable 'X' is by itself on one side of the equation.

Solving Linear Equations By Addition and Subtraction

02:36

Solving Linear Equations Using Multiplication and Division

03:06

This lesson focuses on solving linear equations with X variables on both sides of the equation. In this situation, move all x variables to one side of the equation and move all constants (non-variables) to the other side of the equation and solve.

Solving Linear Equations With Variables on Both Sides

04:24

This lesson focuses on solving linear equations that contain parentheses. The distributive property will be useful in this situation.

The Distributive Property - Solving Equations With Parentheses

04:18

This lesson focuses on solving linear equations that contain fractions. The first thing I would recommend doing is to clear away all fractions by multiplying every term on both sides of the equation by the common denominator of all fractions in the equation.

Preview
05:35

This video explains how to solve linear equations with fractions using cross multiplication. You should cross multiply whenever you have two fractions separated by an equal sign and nothing else.

Solving Equations With Fractions Using Cross Multiplication

01:44

This video explains how to solve linear equations containing decimals. For equations containing decimals rounded to the tenth place, you should multiply every term in the equation by ten to remove all decimals from the equation. For equations containing decimals rounded to the hundredth place, you should multiply all terms by 100.

Solving Linear Equations With Decimals

03:31

This free response video quiz contains 5 questions. Pause the video and work on solving each equation and then unpause it to see the solution.

Free Response Video Quiz

07:16

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Order of Operations
7 Lectures
19:45

This lecture focuses on the order of operations as it relates to addition and subtraction.

PEMDAS - Addition and Subtraction

01:17

This video focuses on the order of operations with regard to multiplication and division.

Preview
03:01

This lesson focuses on examples of simplifying expressions using mixed operations of multiplication, division, addition, and subtraction.

Order of Operations With Addition, Subtraction, Multiplication and Division

03:15

This video focuses on simplifying expressions that contain exponents. Exponents are a representation of repeated multiplication.

Operations With Exponents

02:32

This lesson contains examples of simplifying expressions with parentheses and exponents using order of operations. PEMDAS represents the order of operations. Parentheses and Exponents have the highest priority followed by multiplication and division and then addition and subtraction.

Order of Operations With Parentheses & Exponents

03:09

This lesson provides examples with fractions. The principles of PEMDAS still apply here.

Order of Operations Within Fractions

02:14

This free response video quiz contains 4 example problems. Don't forget to pause the video and work out each example before viewing the solution.

Free Response Video Quiz

04:17

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Graphing Linear Equations
12 Lectures
01:13:45

This short lecture explains how to graph ordered pairs (x,y) on a x-y coordinate system.

Graphing Ordered Pairs

02:43

This lecture explains how to graph linear equations in slope-intercept form or y=mx+b form. It includes an example with a fractional slope. First, plot the y-intercept (B) on the y-axis and then use the slope (m) to find the next point. The slope is the ratio of rise over run. A slope of 2 which is equal to 2/1 means you should go up 2 units (rise) starting from the y-intercept and then travel 1 unit to the right (run) to get the next point on the graph.

Graphing Linear Equations In Slope-Intercept Form

06:05

This lecture explains how to graph linear equations in standard form or Ax + By = C form. The best way to graph it is by finding the x and y intercepts of the function and plotting those points.

Graphing Linear Equations In Standard Form

03:11

This lesson explains how to graph horizontal and vertical lines.

Graphing Horizontal and Vertical Lines

01:55

This lecture explains how to determine the slope between two points. Examples include fractions as well.

Finding The Slope Between Two Points

05:21

This video explains how to determine if the two lines are parallel, perpendicular, or neither by comparing the slopes of the two lines.

Are The Two Lines Parallel, Perpendicular, or Neither?

03:58

This lecture explains how to write the linear equation in point-slope form, slope-intercept form, and standard form given a point and the slope of the line.

Writing Linear Equations Given a Point and The Slope In All Three Forms

04:55

This video explains how to write a linear equation in slope intercept form, point-slope form, and in standard form given 2 points found on the line.

Writing Linear Equations Given Two Points

08:21

This lesson explains how to write linear equations of parallel lines. Parallel lines share the same slope.

Writing Linear Equations of Parallel Lines

08:21

This lesson explains how to write linear equations of perpendicular lines. Perpendicular lines have slopes that are negative reciprocals of each other.

Writing Linear Equations of Perpendicular Lines

05:24

This lesson explains how to graph linear equations that are in point slope form. It's not as difficult as it sounds. All you need to graph a line is a point and the slope. You can use the slope to find the additional points after plotting the first point.

Graphing Linear Equations in Point-Slope Form

03:57

This video quiz contains 10 multiple choice questions that covers the lessons found in this section.

Preview
19:34

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Linear Inequalities and Absolute Value Expressions
8 Lectures
54:59

This lesson shows you how to graph linear inequalities on a number line. It explains when you should have an open circle vs a closed circle. It also discusses how to write the solution using interval notation.

Graphing Linear Inequalities on a Number Line

06:03

This lesson focuses on solving linear inequalities including examples with fractions and compound inequalities. The solution is plotted on a number line and expressed using interval notation. Don't forget to change the direction of the inequality sign when multiplying or dividing by a negative number.

Solving Linear Inequalities

06:23

This lecture explains how to solve absolute value equations. When removing an absolute value expression, don't forget to write two equations - a negative and a positive one!

Solving Absolute Value Equations

04:20

This lecture explains how to solve equations that contain absolute value expressions with inequalities. When removing the absolute value expression to solve the equation, write two equation - one positive and one negative and change the inequality sign for the negative equation.

Solving Absolute Value Inequalities

03:55

This lecture explains how to graph absolute value functions using transformations such as vertical shifts, horizontal shifts, and reflections over the x-axis. This video explains how to graph the equation conceptually and contains an example of graphing it using a data table. It also contains a few examples of writing the domain and range of the function in interval notation.

Preview
10:53

This lesson explains how to graph linear inequalities on a x-y coordinate system. It explains how to determine the appropriate region of the graph in which to shade to correctly represent the solution of the inequality.

Graphing Linear Inequalities on a X-Y Coordinate System

07:04

This lecture explains how to graph systems of linear inequalities and where to shade the appropriate region to represent the solution of the system.

Graphing Systems of Linear Inequalities on a X-Y Coordinate System

10:56

This video quiz contains 4 multiple choice questions that covers the first four lectures of this section.

Multiple Choice Video Quiz

05:25

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Polynomials
16 Lectures
01:18:37

This lesson explains when you should add, subtract, or multiply two exponents together.

Introduction to Properties of Exponents

02:18

This lesson contains more examples of simplifying expressions by adding, subtracting or multiplying exponents.

Properties of Exponents - Basic Examples

06:24

This lecture explains how to change a negative exponent into a positive exponent in order to simplify an algebraic expression.

Introduction to Negative Exponents

01:29

This lesson provides many examples of simplifying algebraic expressions with multiple variables many of which contain negative exponents.

Negative Exponents - Basic Examples

11:08

This lecture explains how to identify a monomial, binomial, and a trinomial.

Monomials, Binomials, & Trinomials

03:08

This lesson will help you to identify the leading coefficient of a polynomial as well as its degree.

Identifying The Leading Coefficient and The Degree of a Polynomial

04:44

This video will help you to identify the degree of a polynomial with multiple variables such as X and Y.

Identifying The Degree of a Polynomial With Multiple Variables

02:59

This lesson explains how to add and subtract polynomials. Always distribute the negative sign first when subtracting polynomials to avoid mistakes commonly made by many students in this area.

Adding and Subtracting Polynomials

04:25

This lesson explains how to multiply two binomials together using the foil method.

Multiplying Two Binomials Together

04:25

This lecture shows you how to multiply a monomial by a trinomial.

Multiplying a Monomial By a Trinomial

00:54

This video explains how to multiply a binomial by a trinomial using the foil method. The product of a binomial (2 terms) and a trinomial (3 terms) will produce a polynomial with 6 terms before combining any like terms.

Multiplying a Binomial By a Trinomial

01:31

This video explains how to multiply two trinomials together using a technique similar to the foil method.

Multiplying Two Trinomials Together

02:15

This lesson explains how to divide a polynomial by a monomial. Long division is not needed for this lesson.

Dividing a Polynomial By a Monomial

02:42

This video explains how to divide a polynomial by a binomial using long division.

Long Division: Dividing a Polynomial By a Binomial

07:44

This video quiz contains plenty of examples reviewing the lessons covered in this section. Make sure to pause the video and work out the problem before viewing the solution.

Free Response Video Quiz 1

12:33

This 2nd free response video quiz is simply a continuation of the first one.

Free Response Video Quiz 2

09:58

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Factoring
10 Lectures
46:20

This video explains how to factor the GCF or Greatest Common Factor.

Factoring The GCF

02:42

This video explains how to factor a polynomial with 4 terms by grouping.

Factor By Grouping

02:54

This video explains how to factor trinomials when the leading coefficient is 1.

Preview
03:40

This lecture explains how to factor trinomials when the leading coefficient is not 1. You need to understand how to factor by grouping before watching this lesson.

Factoring Trinomials Ax^2 + Bx + C

03:13

This lesson explains how to factor perfect square trinomials in the form A^2 + 2AB + B^2 which is equivalent to (A+B)^2.

Factoring Perfect Square Trinomials

05:54

This video explains how to factor differences of perfect squares using the formula A^2 - B^2 = (A + B)(A - B).

Factoring Differences of Squares

03:42

This lecture discusses how to factor sums of perfect cubes and differences of perfect cubes. Here are the equations that you need: (A^3 + B^3) = (A + B)(A^2 - AB + B^2) and (A^3 - B^3)(A^2 + AB + B^2)

Factoring Sums and Differences of Cubes

05:18

This lesson contains examples of factoring polynomials with many terms and multiple variables such a and b or x and y. Multiple factoring steps are required to factor the polynomial expressions completely.

Special Challenge Problems

04:19

This lecture explains how to solve equations by factoring.

Solving Equations By Factoring

02:37

This video quiz contains a few free response questions that covers the lessons found in this section.

Free Response Video Quiz

12:01

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Systems of Linear Equations
11 Lectures
01:01:17

This lesson helps you to determine if an ordered pair is a solution to a system of two linear equations.

Determining if an Ordered Pair is a Solution to a System of Equations

02:36

This lecture explains how to solve a system of two linear equations using the elimination method.

Solving Systems of Equations By Elimination

03:48

This video tutorial shows you how to solve a system of two linear equations using the substitution method.

Solving Systems of Equations By Substitution

06:16

This lecture discusses how to solve a system of equations containing fractions. My recommendation is to clear away all fractions by multiplying every term by the common denominator of each fraction in the equation.

Solving Systems of Equations With Fractions

02:43

This lecture discusses how to solve systems of equations with Decimals. Multiply both sides by 10 to eliminate decimals rounded to the tenth place and multiply every term by 100 to eliminate decimals rounded to the hundredth place.

Solving Systems if Equations With Decimals

02:36

This lecture explains how to determine if a solution is consistent, inconsistent, dependent, or independent based on if there's one solution, no solution, or infinitely many solutions.

Consistent or Inconsistent, Dependent or Independent Solution?

07:29

This lecture discusses how to solve systems of equations by graphing. The solution is the point where the two graphs intersect.

Solving Systems of Equations By Graphing

05:14

This lecture explains how to solve a system of three equations using the elimination method also known as the addition method.

System of Equations With Three Variables

04:21

This video provides an investment word problem that explains how to write a system of equations and to solve it at the same time.

Preview
03:26

This lecture explains how to solve total value word problems using a system of equations.

Total Value Word Problem

04:34

This free response video quiz covers all the topics in this section.

Free Response Video Quiz

18:14

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