with CEU Certificate*
Beginner to Intermediate Algebra is intended for students who need to gather a basic understanding of how to perform Algebra operations. This course will benefit current students and adult learners who need to know how to perform basic Algebra operations which involve simplifying, factoring, or solving equations in the form of inequalities, fractions, exponents and word problems.
Even from their childhood days, most people have at least a basic grasp of arithmetic: addition and subtraction of numbers, for instance. As we master these basic operations, we begin to search for a more systematic and rigorous understanding of the behavior of numbers (particularly, sets of numbers) and functional relationships. This search is where we make the step from arithmetic to algebra. Algebra is the systematic study of numbers (or, more generally, quantity) and their relationships at an abstract level. By studying algebra, you can acquire the ability to analyze the relationships between numbers generally, rather than simply between particular numbers. These abilities pave the way for understanding other areas of mathematics such as trigonometry and calculus.
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Lesson 1 – Algebra Terms and MotivationThis lesson will introduce you to the essential terminology of algebra as well as the reasons why studying algebra is important and helpful.
Lesson 2 – The Set of Real NumbersNow that you have gained a grasp of the essential purpose of and some of the important terms used in algebra, we can move on to study the subject in more depth.
Lesson 3 – Algebraic OperationsIn this lesson, you will learn (or review) how to perform addition, subtraction, multiplication, and division in the context of algebra.
Lesson 4 – FunctionsOnce you have mastered the basic concepts associated with functions, you will then have all the tools you need to get into the more complicated (and more fun) aspects of algebra.
Lesson 5 – Linear EquationsThis lesson will introduce you to linear equations, including their properties, graphs, and solutions.
Lesson 6 – Linear InequalitiesA slight twist on the concept of a linear equation is the linear inequality. Linear inequalities, instead of equating two functions, relate two functions in terms of their relative magnitudes.
Lesson 7 – Systems of Linear EquationsThis lesson will teach you how to solve so-called systems of linear equations using substitution and will extend your understanding beyond simple equations in two dimensions to equations in many dimensions.
Lesson 8 – Systems of Linear InequalitiesAs with systems of linear equations, we can also handle systems of linear inequalities.
Lesson 9 – Solving Word Problems IThis lesson, then, will teach you some basic skills for dealing with problems that can arise in the real world.
Lesson 10 – Polynomial FunctionsThis lesson, then, will teach you some basic skills for dealing with problems that can arise in the real world.
Lesson 11 – Exponential and Logarithmic FunctionsNow that we have covered polynomials, we will look at a special class of functions that differ quite drastically: logarithmic and exponential functions.
Lesson 12 – Polynomial Functions IIIn this lesson, we will learn how to find solutions to higher-degree polynomial equations.
Lesson 13 – Application of Algebra to GeometryIn this lesson, we will apply what we've learned about algebra to the study of geometry. If you've carefully followed the course up to this point, much of what is discussed here should hold no surprises for you.
Lesson 14 – Application of Algebra to Statistics and ProbabilityAlthough this lesson assumes some prior knowledge of probability and statistics, the concepts presented from these areas are relatively simple and understandable.
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Learning OutcomesBy successfully completing this course, students will be able to:
- Identify and define Algebra terms.
- Identify Real Numbers.
- Perform basic Algebraic Operations.
- Identify and create Algebra Functions.
- Identify and solve Linear Equations.
- Identify and solve Linear Inequalities.
- Identify and solve Algebra Word Problems.
- Identify and solve Polynomial Functions.
- Identify and solve Exponential and Logarithmic Functions, and
- Demonstrate mastery of lesson content at levels of 70% or higher.
|Lesson 1 Assignment||Assignment||15|
|Lesson 1 – Algebra Terms and Motivation||Exam||10|
|Lesson 2 Assignment||Assignment||15|
|Lesson 2 – The Set of Real Numbers||Exam||10|
|Lesson 3 Assignment||Assignment||15|
|Lesson 3 – Algebraic Operations||Exam||11|
|Lesson 4 Assignment||Assignment||15|
|Lesson 4 – Functions||Exam||10|
|Lesson 5 Assignment||Assignment||25|
|Lesson 5 – Linear Equations||Exam||10|
|Lesson 6 Assignment||Assignment||15|
|Lesson 6 – Linear Inequalities||Exam||11|
|Lesson 7 Assignment||Assignment||15|
|Lesson 7 – Systems of Linear Equations||Exam||10|
|Lesson 8 Assignment||Assignment||15|
|Lesson 8 – Systems of Linear Inequalities||Exam||10|
|Lesson 9 Assignment||Assignment||15|
|Lesson 9 – Solving Word Problems I||Exam||10|
|Lesson 10 Assignment||Assignment||15|
|Lesson 10 – Polynomial Functions||Exam||10|
|Lesson 11 Assignment||Assignment||15|
|Lesson 11 – Exponential and Logarithmic Functions||Exam||10|
|Lesson 12 Assignment||Assignment||15|
|Lesson 12 – Polynomial Functions II||Exam||9|
|Lesson 13 Assignment||Assignment||15|
|Lesson 13 – Application of Algebra to Geometry||Exam||9|
|Lesson 14 Assignment||Assignment||15|
|Lesson 14 – Application of Algebra to Statistics and Probability||Exam||9|
|The Final Exam||Exam||46|
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