Chapter : Systems Of Linear Equations And Inequalities
3.1 Solving Systems of Linear Equations by the Graphing Method
3.2 Solving Systems of Linear Equations by the Substitution Method
3.3 Solving Systems of Linear Equations by the Addition Method
Problem Recognition ExercisesSolving Systems of Linear Equations
3.4 Applications of Systems of Linear Equations in Two Variables
3.5 Linear Inequalities and Systems of Linear Inequalities in Two Variables
3.6 Systems of Linear Equations in Three Variables and Applications
3.7 Solving Systems of Linear Equations by Using Matrices
Unit : Introduction To Conic Sections
Conic sections are made by taking particular slices of a cone. The slices we will study include ellipses, hyperbolas, and parabolas. You will have studied parabolas in the context of functions previously in the course, but these parabolas are different because they are not functions. Read on to learn more!
Completing this unit should take you approximately 2 hours.
Saylor Direct Credit Exam
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Unit : Exponential And Logarithmic Functions
Welcome to the final unit on functions. In this unit, you will learn about exponential and logarithmic functions. Exponential functions are often used to model the behavior of populations and the growth of an investment or debt. You will learn the characteristics of an exponential function and become proficient at graphing them given key components. In addition to exponential functions, you will learn about the logarithmic function. The logarithmic function is the inverse of the exponential, and we will explore the relationship between the two.
Completing this unit should take you approximately 3 hours.
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Unit : Equations And Inequalities
In this unit, you will learn important terminology and characteristics of linear equations, inequalities, and their graphs. Additionally, we will cover how to solve general linear equations in one variable, literal equations, and compound inequalities. You will also explore how to graph linear equations and inequalities in two variables on a coordinate plane, learn how to solve systems of two or three linear equations, and apply these skills to realworld applications. You may want to refer to this unit as you move through the course. For some, this material may be a repeat, and you will be able to move quickly. For others, it may have been a long time since you practiced the concepts in this unit, and taking the time to become fluent with solving and graphing equations and inequalities will pay off later in the course.
Completing this unit should take you approximately 4 hours.
Chapter : Linear Equations In Two Variables And Functions
2.1 Linear Equations in Two Variables
2.2 Slope of a Line and Rate of Change
2.3 Equations of a Line
Problem Recognition ExercisesCharacteristics of Linear Equations
2.4 Applications of Linear Equations and Modeling
2.5 Introduction to Relations
Problem Recognition ExercisesCharacteristics of Relations
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Unit : Linear Functions
In this unit, you will explore linear functions in depth. Linear functions are a great place to start our indepth exploration of functions because they are fairly straightforward to master, and many people have learned about them in past math courses. In our discovery of linear functions, we will work with tables, equations, graphs, and words to describe the behavior and key characteristics of linear functions. You will also learn about an important concept called the rate of change. One of the most important key characteristics of a linear function is its rate of change. If you continue on to study calculus, you will learn about the rate of change in depth. In addition to the rate of change, you will discover that some observable phenomena behave linearly. We can build a model using a linear function to represent their behavior and make predictions.
Completing this unit should take you approximately 2 hours.
Unit : Exponential And Logarithmic Equations
Now that you know all about exponential and logarithmic functions, you can learn how to solve equations that involve them. You will use the properties of logarithms and exponentials and the fact that they are inverses to solve equations. You will also explore some applied problems involving exponential and logarithmic equations. Finally, you will learn to fit exponential and logarithmic models to data.
Completing this unit should take you approximately 3 hours.
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Unit : Rational Functions
In this unit, you will apply what you have learned about functions to rational functions. Rational functions are based on the toolkit reciprocal functions and have many interesting characteristics. You will apply similar skills and techniques for defining intercepts and end behavior of polynomial functions to rational functions. By the end of this unit, you will be proficient in defining the local behavior and end behavior of a polynomial function and drawing the graph of a polynomial function given its characteristics.
Completing this unit should take you approximately 2 hours.
Unit : Introduction To Functions
The study of functions is one of the main focuses of this course. In this unit, we will introduce the definition of a function and the special notation used to write equations for functions of two variables. You may find some of the material is familiar if you have already learned about plotting points on the cartesian coordinate plane and writing equations of lines. You will be introduced to a toolkit of functions early in the unit that we will use throughout most of the course, so pay close attention to the characteristics and notation used to define them. You will practice defining important characteristics of functions such as the domain and range. You will practice graphing the many different types of functions that we will focus on throughout the course. Pay close attention to this unit, as it builds the foundation for the course. Enjoy your study of functions!
Completing this unit should take you approximately 3 hours.
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Free Algebra Study Guide With Videos
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What Is The Best Study Guide For The Clep College Algebra
The best CLEP College Algebra study guide is the one that keeps you fully motivated. Look for an option thats more interesting than a CLEP College Algebra study book. A system with the techniques described below will give you the inspiration you need.
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Unit : Exponents And Polynomials
In this unit, you will deepen your knowledge of functions by performing algebraic operations on functions and learning how to transform graphs of functions. You will continue to define important characteristics of functions, including domain and range, after performing algebraic operations or transformations on the graphs of functions. This is another fundamental unit, so pay close attention to what kinds of transformations can be performed on the graphs of functions and how they change the key characteristics of the function’s equation, domain, and range. In later units, you will apply the same transformations to the toolkit functions you discovered in Unit 2.
Completing this unit should take you approximately 3 hours.
Chapter : Linear Equations And Inequalities In One Variable
1.1 Linear Equations in One Variable
Problem Recognition ExercisesEquations versus Expressions
1.2 Applications of Linear Equations in One Variable
1.3 Applications of Geometry and Literal Equations
1.4 Linear Inequalities in One Variable
1.5 Compound Inequalities
Problem Recognition ExercisesIdentifying Equations and Inequalities
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Unit : Polynomial Functions
Polynomial functions include quadratic functions, which may be familiar to you from past math courses. In this unit, we will continue the pattern of defining key characteristics of polynomial functions such as the domain and range using equations and graphs. In addition to quadratic functions, the family of polynomial functions includes functions with higher degree exponents. As the degree of a polynomial increases, the algebra required to define its key characteristics such as intercepts and inflection points becomes more and more complicated. You will learn techniques to describe the behaviors of polynomial functions that help us understand them without performing complex algebra.
Completing this unit should take you approximately 4 hours.
Chapter : Rational Expressions And Rational Equations
5.1 Rational Expressions and Rational Functions
5.2 Multiplication and Division of Rational Expressions
5.3 Addition and Subtraction of Rational Expressions
5.4 Complex Fractions
Problem Recognition ExercisesOperations on Rational Expressions
5.5 Solving Rational Equations
Problem Recognition ExercisesRational Equations versus Expressions
5.6 Applications of Rational Equations and Proportions
Variation
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How Do I Study For The Clep College Algebra
The five steps below outline how to study for the CLEP College Algebra exam.
Chapter : Quadratic Equations Functions And Inequalities
7.1 Square Root Property and Completing the Square
7.2 Quadratic Formula
7.3 Equations in Quadratic Form
Problem Recognition ExercisesQuadratic and Quadratic Type Equations
7.4 Graphs of Quadratic Functions
7.5 Vertex of a Parabola: Applications and Modeling
7.6 Polynomial and Rational Inequalities
Problem Recognition ExercisesRecognizing Equations and Inequalities
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Unit : Systems Of Equations And Inequalities
Systems of equations are handy when exploring the relationship between two or more things. For example, the profit a business makes is dependent on both the cost to produce goods or services and the money it brings in from selling those goods or services. We will introduce methods for solving systems and interpreting the solution when you find one. We will also introduce techniques for graphing systems of inequalties that include combinations of linear and quadratic equations. You will use the skills you have learned from working with linear and quadratic functions and from graphing and solving linear inequalities to master the topics in this unit.
Completing this unit should take you approximately 3 hours.
Chapter : Exponential And Logarithmic Functions And Applications
8.1 Algebra of Functions and Composition
8.2 Inverse Functions
Problem Recognition ExercisesIdentifying Graphs of Functions
8.5 Properties of Logarithms
8.6 The Irrational Number e and Change of Base
Problem Recognition ExercisesLogarithmic and Exponential Forms
8.7 Logarithmic and Exponential Equations and Applications
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What Should I Study For The Clep College Algebra Test
Study the following math topics for the CLEP College Algebra Placement test: performing operations with whole numbers, fractions, and decimals reasoning algebraically memorizing the characteristics of basic geometric shapes understanding measurement representing and analyzing data and statistics.
Knowledge And Skills Required
Questions on the College Algebra exam require test takers to demonstrate the following abilities in the approximate proportions indicated:
 Solving routine, straightforward problems
 Solving nonroutine problems requiring an understanding of concepts and the application of skills and concepts
The subject matter of the College Algebra exam is drawn from the following topics. The percentages in parentheses indicate the approximate percentage of exam questions on that topic.
Students will find the online scientific calculator helpful in performing calculations .
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