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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
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.
This lesson shows you how to add two numbers mentally by the use of a number line.
This lesson explains how to subtract two numbers mentally using a number line.
This lesson explains how to add two large numbers on paper without the use of a calculator.
This lesson explains how to subtract two large numbers on paper without using a calculator.
This video explains the concept of multiplication using repeated addition.
This lesson focuses on the relationship between multiplication and division.
This lesson explains how to multiply two large numbers without using a calculator.
This video explains how to divide two numbers using long division.
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.
This video provides a simple technique for adding and subtracting two fractions.
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.
This lesson explains how to multiply fractions which can be done by multiplying the numerators and denominators of each fraction separately.
This lesson shows you how to divide fractions using a technique known as "Keep Change Flip!"
This video discusses how to simplify complex fractions by clearing away the small fractions that are part of the larger fraction.
This lesson explains how convert mixed numbers into improper fractions and how to convert improper fractions to mixed numbers.
This lesson explains how to convert fractions into decimals using long division.
This video tutorial provides a simple way to convert decimals to fractions.
This 4 question multiple choice video quiz will test your knowledge of fractions and decimals.
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.
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.
This lesson focuses on solving linear equations that contain parentheses. The distributive property will be useful in this situation.
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.
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.
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.
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.
This lecture focuses on the order of operations as it relates to addition and subtraction.
This video focuses on the order of operations with regard to multiplication and division.
This lesson focuses on examples of simplifying expressions using mixed operations of multiplication, division, addition, and subtraction.
This video focuses on simplifying expressions that contain exponents. Exponents are a representation of repeated multiplication.
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.
This lesson provides examples with fractions. The principles of PEMDAS still apply here.
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.
This short lecture explains how to graph ordered pairs (x,y) on a x-y coordinate system.
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.
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.
This lesson explains how to graph horizontal and vertical lines.
This lecture explains how to determine the slope between two points. Examples include fractions as well.
This video explains how to determine if the two lines are parallel, perpendicular, or neither by comparing the slopes of the two lines.
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.
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.
This lesson explains how to write linear equations of parallel lines. Parallel lines share the same slope.
This lesson explains how to write linear equations of perpendicular lines. Perpendicular lines have slopes that are negative reciprocals of each other.
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.
This video quiz contains 10 multiple choice questions that covers the lessons found in this section.
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.
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.
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!
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.
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.
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.
This lecture explains how to graph systems of linear inequalities and where to shade the appropriate region to represent the solution of the system.
This video quiz contains 4 multiple choice questions that covers the first four lectures of this section.
This lesson explains when you should add, subtract, or multiply two exponents together.
This lesson contains more examples of simplifying expressions by adding, subtracting or multiplying exponents.
This lecture explains how to change a negative exponent into a positive exponent in order to simplify an algebraic expression.
This lesson provides many examples of simplifying algebraic expressions with multiple variables many of which contain negative exponents.
This lecture explains how to identify a monomial, binomial, and a trinomial.
This lesson will help you to identify the leading coefficient of a polynomial as well as its degree.
This video will help you to identify the degree of a polynomial with multiple variables such as X and Y.
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.
This lesson explains how to multiply two binomials together using the foil method.
This lecture shows you how to multiply a monomial by a trinomial.
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.
This video explains how to multiply two trinomials together using a technique similar to the foil method.
This lesson explains how to divide a polynomial by a monomial. Long division is not needed for this lesson.
This video explains how to divide a polynomial by a binomial using long division.
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.
This 2nd free response video quiz is simply a continuation of the first one.
This video explains how to factor the GCF or Greatest Common Factor.
This video explains how to factor a polynomial with 4 terms by grouping.
This video explains how to factor trinomials when the leading coefficient is 1.
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.
This lesson explains how to factor perfect square trinomials in the form A^2 + 2AB + B^2 which is equivalent to (A+B)^2.
This video explains how to factor differences of perfect squares using the formula A^2 - B^2 = (A + B)(A - B).
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)
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.
This lecture explains how to solve equations by factoring.
This video quiz contains a few free response questions that covers the lessons found in this section.
This lesson helps you to determine if an ordered pair is a solution to a system of two linear equations.
This lecture explains how to solve a system of two linear equations using the elimination method.
This video tutorial shows you how to solve a system of two linear equations using the substitution method.
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.
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.
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.
This lecture discusses how to solve systems of equations by graphing. The solution is the point where the two graphs intersect.
This lecture explains how to solve a system of three equations using the elimination method also known as the addition method.
This video provides an investment word problem that explains how to write a system of equations and to solve it at the same time.
This lecture explains how to solve total value word problems using a system of equations.
This free response video quiz covers all the topics in this section.
I started my education career by tutoring students right after high school and into college receiving a BA in Chemistry. The request that I usually receive were hard core topics like Algebra, Geometry, Trigonometry, Precalculus, Calculus, General Chemistry, Physics, and Organic Chemistry.
Over time, I learned which teaching methods are most effective for helping students to not only understand the material but to retain it and to apply it during an exam to boost their score. Now, I focus more on creating videos and online courses that help not just students in my locality but students worldwide who might be struggling with this course.
Best Regards,
Julio G.