Time: 125 hours
In this course, we explore how to use standard mathematical and business formulas, and how to translate verbal descriptions into mathematical equations to establish relationships and create predictions. In the later units, we explore how to use graphs to make these same predictions. You can apply the problem solving strategies we discuss in this course to business, science, and many other fields.
To succeed in this introductory course you should know how to perform operations with real numbers, including negative numbers, fractions, and decimals. Be sure to review RWM101: Foundations of Real World Math if you need a refresher!
First, read the course syllabus. Then, enroll in the course by clicking "Enroll me in this course". Click Unit 1 to read its introduction and learning outcomes. You will then see the learning materials and instructions on how to use them.
In algebra, we use letters to represent numbers in equations. We call these letters variables, because the numbers they represent vary. For example, let’s say your salary is $10 per hour. If you worked two hours, you would be paid $10 × 2, or $20. If you worked five hours you would be paid $10 × 5, or $50. To generalize this we can say that if you work h hours, you will be paid $10 × h.
In this unit, we learn that the properties of numbers also apply to the letters we use in these formulas: you treat variables the same way you treat numbers in calculations. We discuss how to recognize like terms, which you can add and subtract as if they were numbers.
Completing this unit should take you approximately 13 hours.
We use equations everyday without realizing it. Examples include calculating the unit price so we can compare the price of different brands in the grocery store, converting inches into feet (or centimeters into meters), estimating how much time it will take to drive to a destination at a certain speed.
In this unit, we explore formal procedures for solving equations. After reviewing basic math rules, we apply the skills we learned in Unit 1 to simplify the sides of an equation before attempting to solve it and work with equations that contain more than one variable. Because variables represent numbers, we use the same rules to find the specific variables we are looking for.
Completing this unit should take you approximately 15 hours.
Now, let's apply what we learned about solving equations to various types of word problems. To set up the equation, read the word problem carefully to identify the quantity you are being asked to find, the known quantities, and the relationship between them. This is an important skill in algebra since we use algebra to solve many real-world problems.
In this unit, we identify common types of word problems and discuss how to translate these problems into algebraic equations so we can solve them.
Completing this unit should take you approximately 8 hours.
You probably use inequalities, just like equations, in everyday life without thinking about it. Every time you go to the store, you need to decide whether you have enough money to pay for the items you need to purchase. The inequality you need to solve is: your amount of money must be GREATER than the total cost of items.
In this unit, we generalize the procedure we use to solve inequalities. We explore which properties of inequalities are the same and which are different from the properties of equations.
Completing this unit should take you approximately 5 hours.
We use graphs to help visualize how one quantity relates to another. This unit will help you become comfortable with graphing pairs of numbers on the coordinate plane and understand how to use lines to represent equations and relationships.
For example, we can graph how the location of a train depends on when it left the station. If the train is moving at constant speed, the line in the graph is straight. The slope or slant of the line depends on the speed: the greater the speed, the steeper the line. If the line is going up (from left to right), it tells you the distance is growing with time: the train is moving away from the station. If the line is going down, it tells you the distance is decreasing: the train is approaching the station. You can gather a lot of information about the train's journey from just one graph.
Completing this unit should take you approximately 24 hours.
In previous units, we learned that linear equations with one variable generally have one solution. However, linear equations with two variables have an infinite number of solutions. If we pair two linear equations together, we can solve for the pair of numbers that would solve both equations. This is called a system of linear equations. In this unit, we will learn how to solve systems of linear equations.
Completing this unit should take you approximately 14 hours.
As we have seen, in algebra we use variables to represent unknown quantities in equations. Now, let's look at expressions that primarily consist of variables.
The rules that govern operations with expressions come from the properties of operations with numbers, such as the distributive property and the order of operations. In this unit we focus on monomials which are expressions that contain only one term. We learn how to apply rules of exponents, multiply, and divide monomials.
Completing this unit should take you approximately 11 hours.
In this unit, we discuss polynomials, a special type of algebraic expression that contains two or more terms. For example, a polynomial may look like 5x + 2x3 + x2 + 2.
Here we discuss how to recognize, classify, add, subtract, multiply, and divide polynomials, by combining like terms and using the distributive property. We can use these principles to make calculations that pertain to the motion of two or more objects. For example, we can calculate when and where a runner will overtake a competitor, or how much interest you will earn from two or more savings accounts.
Completing this unit should take you approximately 14 hours.
Factoring is multiplication in reverse: rather than multiply two polynomials, you write a given polynomial as a product of two or more different expressions. Factoring is an important tool for solving advanced equations, such as quadratic equations. Quadratic equations occur in problems that involve rectangular objects and their areas, such as planning gardens, framing photographs, carpeting the floors.
Completing this unit should take you approximately 21 hours.
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Take this exam if you want to earn a free Course Completion Certificate.
To receive a free Course Completion Certificate, you will need to earn a grade of 70% or higher on this final exam. Your grade for the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you can take it again as many times as you want, with a 7-day waiting period between each attempt.
Once you pass this final exam, you will be awarded a free Course Completion Certificate.