College Algebra Chapter 1 Study Guide

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 Exercises-Solving 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.

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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 real-world 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 Exercises-Characteristics of Linear Equations

2.4 Applications of Linear Equations and Modeling

2.5 Introduction to Relations

Problem Recognition Exercises-Characteristics 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 in-depth 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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The following course materials are required for Math 112:

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Free Algebra Study Guide With Videos

Intermediate Algebra

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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 Exercises-Equations 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 Exercises-Identifying 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 Exercises-Operations on Rational Expressions

5.5 Solving Rational Equations

Problem Recognition Exercises-Rational Equations versus Expressions

5.6 Applications of Rational Equations and Proportions

Variation

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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 Exercises-Quadratic 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 Exercises-Recognizing 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 Exercises-Identifying Graphs of Functions

8.5 Properties of Logarithms

8.6 The Irrational Number e and Change of Base

Problem Recognition Exercises-Logarithmic 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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