MA120: Applied College Algebra | Saylor Academy

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COURSE INTRODUCTION

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Time: 36 hours

Free Certificate

In this course, you will explore intermediate-level algebraic operations and learn how algebraic methods are used in real-world applications. Topics include systems of linear equations and inequalities, quadratic equations, exponential and logarithmic functions, and operations with rational expressions. Using algebra involves graphing functions and relating functions' properties to their graphs. You will apply these skills to create mathematical models for word problems. Each unit will include many application problems that will draw on your knowledge of the concepts presented in that unit. This course requires prior knowledge of basic algebra.
- Select activity Course Syllabus
  
  Course Syllabus Page
Unit 1: 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 many of the sections in this unit as you move through the course. For some, this material may be repeated, 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 5 hours.
- Select activity Unit 1 Learning Outcomes
  
  Unit 1 Learning Outcomes Page
- 1.1: Solving Linear and Rational Equations in One Variable
  - Select activity Solving Linear Equations in One Variable
    
    Solving Linear Equations in One Variable Book
    
    Students must
    
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  - Select activity Solving Linear Equations Practice
    
    Solving Linear Equations Practice Book
    
    Students must
    
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  - Select activity Applications of Linear Equations
    
    Applications of Linear Equations Book
    
    Students must
    
    View
  - Select activity Rational Equations
    
    Rational Equations Book
    
    Students must
    
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  - Select activity Rational Equations Practice
    
    Rational Equations Practice Book
    
    Students must
    
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- 1.2 Quadratic, Radical, and Absolute Value Equations
  - Select activity Complex Numbers
    
    Complex Numbers Book
    
    Students must
    
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  - Select activity Solve Quadratic Equations by Factoring
    
    Solve Quadratic Equations by Factoring Book
    
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  - Select activity Solving Quadratic Equations Practice
    
    Solving Quadratic Equations Practice Book
    
    Students must
    
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  - Select activity Solve Quadratic Equations Using the Square Root Property
    
    Solve Quadratic Equations Using the Square Root Property Book
    
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  - Select activity Using the Quadratic Formula and the Discriminant
    
    Using the Quadratic Formula and the Discriminant Book
    
    Students must
    
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  - Select activity Equations That Are Quadratic in Form
    
    Equations That Are Quadratic in Form Book
    
    Students must
    
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  - Select activity Absolute Value Equations
    
    Absolute Value Equations Book
    
    Students must
    
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  - Select activity Absolute Value Equations Practice
    
    Absolute Value Equations Practice Book
    
    Students must
    
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  - Select activity Radical Equations
    
    Radical Equations Book
    
    Students must
    
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  - Select activity Radical Equations Practice
    
    Radical Equations Practice Book
    
    Students must
    
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- 1.3: Linear Inequalities
  - Select activity Using Interval Notation and Properties of Inequalities
    
    Using Interval Notation and Properties of Inequalities Book
    
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  - Select activity Solve Simple and Compound Linear Inequalities
    
    Solve Simple and Compound Linear Inequalities Book
    
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  - Select activity Solve Simple and Compound Linear Inequalities Practice
    
    Solve Simple and Compound Linear Inequalities Practice Book
    
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  - Select activity Absolute Value Inequalities
    
    Absolute Value Inequalities Book
    
    Students must
    
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- Unit 1 Assessment
  - Select activity Unit 1 Assessment
    
    Unit 1 Assessment Quiz
    
    Students must
    
    Receive a grade
Unit 2: Introduction to Functions
The study of functions is one of the main focuses of this course. In this unit, you will be introduced to 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 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, and you will practice graphing the many different types of functions we will focus on throughout the course. Pay close attention to this unit as it builds the foundation for most of the course. Enjoy your study of functions!

Completing this unit should take you approximately 4 hours.
- Select activity Unit 2 Learning Outcomes
  
  Unit 2 Learning Outcomes Page
- 2.1: Notation and Basic Functions
  - Select activity The Rectangular Coordinate System and Graphs
    
    The Rectangular Coordinate System and Graphs Book
    
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  - Select activity Defining and Writing Functions
    
    Defining and Writing Functions Book
    
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  - Select activity Properties of Functions and Basic Function Types
    
    Properties of Functions and Basic Function Types Book
    
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- 2.2: Properties of Functions and Describing Function Behavior
  - Select activity Finding the Domain of a Function Defined by an Equation
    
    Finding the Domain of a Function Defined by an Equation Book
    
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  - Select activity Finding the Domain of a Function Define by an Equation Practice
    
    Finding the Domain of a Function Define by an Equation Practice Book
    
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  - Select activity Finding Domain and Range from Graphs
    
    Finding Domain and Range from Graphs Book
    
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  - Select activity Finding Domain and Range from Graphs Practice
    
    Finding Domain and Range from Graphs Practice Book
    
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  - Select activity Graphing Piecewise-Defined Functions
    
    Graphing Piecewise-Defined Functions Book
    
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  - Select activity Graphing Piecewise-Defined Functions Practice
    
    Graphing Piecewise-Defined Functions Practice Book
    
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  - Select activity Calculate the Rate of Change of a Function
    
    Calculate the Rate of Change of a Function Book
    
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  - Select activity Determine Where a Function Is Increasing, Decreasing, or Constant
    
    Determine Where a Function Is Increasing, Decreasing, or Constant Book
    
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  - Select activity Increasing and Decreasing Functions Practice
    
    Increasing and Decreasing Functions Practice Book
    
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- Unit 2 Assessment
  - Select activity Unit 2 Assessment
    
    Unit 2 Assessment Quiz
    
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    Receive a grade
Unit 3: Algebraic Operations on Functions
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 important foundational unit in College Algebra, 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 equation, domain, and range of the function. In subsequent 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.
- Select activity Unit 3 Learning Outcomes
  
  Unit 3 Learning Outcomes Page
- 3.1: Composite Functions
  - Select activity Creating and Evaluating Composite Functions
    
    Creating and Evaluating Composite Functions Book
    
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  - Select activity Creating and Evaluating Composite Functions Practice
    
    Creating and Evaluating Composite Functions Practice Book
    
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  - Select activity Creating and Evaluating Composite Functions Practice II
    
    Creating and Evaluating Composite Functions Practice II Book
    
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  - Select activity Finding the Domain of a Composite Function
    
    Finding the Domain of a Composite Function Book
    
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- 3.2: Transformations
  - Select activity Graphing Functions Using Vertical and Horizontal Shifts
    
    Graphing Functions Using Vertical and Horizontal Shifts Book
    
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  - Select activity Graphing Functions Using Vertical and Horizontal Shift Practice
    
    Graphing Functions Using Vertical and Horizontal Shift Practice Book
    
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  - Select activity Graphing Functions Using Reflections
    
    Graphing Functions Using Reflections Book
    
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  - Select activity Graphing Functions Using Reflections Practice
    
    Graphing Functions Using Reflections Practice Book
    
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  - Select activity Determining Whether a Function Is One-to-One
    
    Determining Whether a Function Is One-to-One Book
    
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  - Select activity Graphing Functions Using Stretches and Compressions
    
    Graphing Functions Using Stretches and Compressions Book
    
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  - Select activity Compressing and Stretching Graphs Practice
    
    Compressing and Stretching Graphs Practice Book
    
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  - Select activity Compressing and Stretching Graphs Horizontally Practice
    
    Compressing and Stretching Graphs Horizontally Practice Book
    
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- 3.3: Inverse Functions
  - Select activity Inverse Functions
    
    Inverse Functions Book
    
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  - Select activity Inverse Functions Practice
    
    Inverse Functions Practice Book
    
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- Unit 3 Assessment
  - Select activity Unit 3 Assessment
    
    Unit 3 Assessment Quiz
    
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    Receive a grade
Unit 4: 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 rate of change. One of the most important key characteristics of a linear function is its rate of change. If you continue past College Algebra to 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, and we can build a model using a linear function to represent its behavior and make predictions.
Completing this unit should take you approximately 2 hours.
- Select activity Unit 4 Learning Outcomes
  
  Unit 4 Learning Outcomes Page
- 4.1: Linear Functions
  - Select activity Representations of Linear Functions
    
    Representations of Linear Functions Book
    
    Students must
    
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  - Select activity Interpreting Slope as a Rate of Change
    
    Interpreting Slope as a Rate of Change Book
    
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  - Select activity Interpreting Slope as a Rate of Change Practice
    
    Interpreting Slope as a Rate of Change Practice Book
    
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  - Select activity Writing and Interpreting an Equation for a Linear Function
    
    Writing and Interpreting an Equation for a Linear Function Page
    
    Students must
    
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  - Select activity Writing Equations of Lines Practice
    
    Writing Equations of Lines Practice Book
    
    Students must
    
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  - Select activity Graphing Lines Practice
    
    Graphing Lines Practice Book
    
    Students must
    
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  - Select activity Parallel and Perpendicular Lines
    
    Parallel and Perpendicular Lines Book
    
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- 4.2: Modeling with Linear Functions
  - Select activity Building Linear Models from Words
    
    Building Linear Models from Words Book
    
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  - Select activity Modeling a Set of Data with Linear Functions
    
    Modeling a Set of Data with Linear Functions Page
    
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- 4.3: Fitting Linear Models to Data
  - Select activity Finding the Line of Best Fit
    
    Finding the Line of Best Fit Book
    
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  - Select activity Graphing Calculator
    
    Graphing Calculator Book
    
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- Unit 4 Assessment
  - Select activity Unit 4 Assessment
    
    Unit 4 Assessment Quiz
    
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    Receive a grade
Unit 5: Polynomial Functions
Polynomial functions include quadratic functions, which may be familiar to you from past math courses. In this unit, we will continue 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 complicated algebra.
Completing this unit should take you approximately 4 hours.
- Select activity Unit 5 Learning Outcomes
  
  Unit 5 Learning Outcomes Page
- 5.1: Quadratic Functions
  - Select activity Understanding How the Graphs of Parabolas Are Related to Their Quadratic Functions
    
    Understanding How the Graphs of Parabolas Are Related to Their Quadratic Functions Page
    
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  - Select activity Vertex and Zeros of a Quadratic Function Practice
    
    Vertex and Zeros of a Quadratic Function Practice Book
    
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  - Select activity Finding the Domain and Range of a Quadratic Function
    
    Finding the Domain and Range of a Quadratic Function Page
    
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  - Select activity Determining the Maximum and Minimum Values of Quadratic Functions
    
    Determining the Maximum and Minimum Values of Quadratic Functions Book
    
    Students must
    
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- 5.2 Power and Polynomial Functions
  - Select activity Power Functions
    
    Power Functions Book
    
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  - Select activity Power Functions Practice
    
    Power Functions Practice Book
    
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  - Select activity Polynomial Functions
    
    Polynomial Functions Book
    
    Students must
    
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- 5.3 Graphs of Polynomial Functions
  - Select activity Identify the x-Intercepts of Polynomial Functions with Factorable Equations
    
    Identify the x-Intercepts of Polynomial Functions with Factorable Equations Book
    
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  - Select activity x-Intercepts of Polynomial Functions Practice
    
    x-Intercepts of Polynomial Functions Practice Book
    
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  - Select activity Graphing Polynomial Functions
    
    Graphing Polynomial Functions Book
    
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  - Select activity Graphing Polynomial Functions Practice
    
    Graphing Polynomial Functions Practice Book
    
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- 5.4 Dividing Polynomials
  - Select activity Use Long Division to Divide Polynomials
    
    Use Long Division to Divide Polynomials Book
    
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  - Select activity Long Division to Divide Polynomials Practice
    
    Long Division to Divide Polynomials Practice Book
    
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  - Select activity Use Synthetic Division to Divide Polynomials
    
    Use Synthetic Division to Divide Polynomials Book
    
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- 5.5 Finding Roots of Polynomial Functions
  - Select activity Three Techniques for Evaluating and Finding Zeros of Polynomial Functions
    
    Three Techniques for Evaluating and Finding Zeros of Polynomial Functions Book
    
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  - Select activity Using the Fundamental Theorem of Algebra and the Linear Factorization Theorem
    
    Using the Fundamental Theorem of Algebra and the Linear Factorization Theorem Book
    
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- Unit 5 Assessment
  - Select activity Unit 5 Assessment
    
    Unit 5 Assessment Quiz
    
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    Receive a grade
Unit 6: Rational Functions
In this unit, you will apply what you have learned about functions to rational functions. Rational functions are based on the reciprocal functions in the toolkit, and they 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.
- Select activity Unit 6 Learning Outcomes
  
  Unit 6 Learning Outcomes Page
- 6.1: Characteristics of Rational Functions
  - Select activity End Behavior and Local Behavior of Rational Functions
    
    End Behavior and Local Behavior of Rational Functions Book
    
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  - Select activity End Behavior and Local Behavior of Rational Function Practice
    
    End Behavior and Local Behavior of Rational Function Practice Book
    
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  - Select activity Domain and Range of Rational Functions
    
    Domain and Range of Rational Functions Book
    
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  - Select activity Zeros of Rational Functions
    
    Zeros of Rational Functions Book
    
    Students must
    
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- 6.2: Finding Asymptotes of Rational Functions
  - Select activity Vertical and Horizontal Asymptotes of Rational Functions
    
    Vertical and Horizontal Asymptotes of Rational Functions Book
    
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  - Select activity Vertical and Horizontal Asymptotes of Rational Function Practice
    
    Vertical and Horizontal Asymptotes of Rational Function Practice Book
    
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- 6.3: Graphs and Equations of Rational Functions
  - Select activity Graphing Rational Functions
    
    Graphing Rational Functions Book
    
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  - Select activity Graphing Rational Functions Practice
    
    Graphing Rational Functions Practice Book
    
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- Unit 6 Assessment
  - Select activity Unit 6 Assessment
    
    Unit 6 Assessment Quiz
    
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    Receive a grade
Unit 7: Exponential and Logarithmic 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 again learn the basic 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 in this unit. The logarithmic function is the inverse of the exponential, and the relationship between the two will be explored.
Completing this unit should take you approximately 4 hours.
- Select activity Unit 7 Learning Outcomes
  
  Unit 7 Learning Outcomes Page
- 7.1: Introduction to Exponential Functions
  - Select activity Properties of Exponential Functions
    
    Properties of Exponential Functions Book
    
    Students must
    
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  - Select activity Equations of Exponential Functions
    
    Equations of Exponential Functions Page
    
    Students must
    
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  - Select activity Financial Applications of Exponential Functions
    
    Financial Applications of Exponential Functions Book
    
    Students must
    
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- 7.2: Graphs of Exponential Functions
  - Select activity Characteristics of Graphs of Exponential Functions
    
    Characteristics of Graphs of Exponential Functions Book
    
    Students must
    
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  - Select activity Transformations of Graphs of Exponential Functions
    
    Transformations of Graphs of Exponential Functions Book
    
    Students must
    
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  - Select activity Graphing Exponential Functions Practice
    
    Graphing Exponential Functions Practice Book
    
    Students must
    
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- 7.3: Introduction to Logarithmic Functions
  - Select activity Convert Between Logarithmic and Exponential
    
    Convert Between Logarithmic and Exponential Book
    
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  - Select activity Convert Between Logarithmic and Exponential Practice
    
    Convert Between Logarithmic and Exponential Practice Book
    
    Students must
    
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  - Select activity Common and Natural Logarithms
    
    Common and Natural Logarithms Book
    
    Students must
    
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- 7.4: Graphs of Logarithmic Functions
  - Select activity Characteristics of Graphs of Logarithmic Functions
    
    Characteristics of Graphs of Logarithmic Functions Book
    
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  - Select activity Transformations of Graphs of Logarithmic Functions
    
    Transformations of Graphs of Logarithmic Functions Book
    
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  - Select activity Graphing Logarithmic Functions Practice
    
    Graphing Logarithmic Functions Practice Book
    
    Students must
    
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- 7.5: Properties of Logarithmic Functions
  - Select activity Properties of Logarithms
    
    Properties of Logarithms Book
    
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  - Select activity Expanding and Condensing Logarithms
    
    Expanding and Condensing Logarithms Book
    
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  - Select activity Logarithms Rules Practice
    
    Logarithms Rules Practice Book
    
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- Unit 7 Assessment
  - Select activity Unit 7 Assessment
    
    Unit 7 Assessment Quiz
    
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    Receive a grade
Unit 8: Exponential and Logarithmic Equations
Now that you know all about exponential and logarithmic functions, you can build on your knowledge and learn skills 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 how to fit exponential and logarithmic models to data.
Completing this unit should take you approximately 3 hours.
- Select activity Unit 8 Learning Outcomes
  
  Unit 8 Learning Outcomes Page
- 8.1: Solving Exponential Equations
  - Select activity Using Like Bases to Solve Exponential Equations
    
    Using Like Bases to Solve Exponential Equations Book
    
    Students must
    
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  - Select activity Exponential Equations Practice
    
    Exponential Equations Practice Book
    
    Students must
    
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  - Select activity Solving Exponential Equations Using Logarithms
    
    Solving Exponential Equations Using Logarithms Book
    
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  - Select activity Exponential Equations Using Logarithms Practice
    
    Exponential Equations Using Logarithms Practice Book
    
    Students must
    
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- 8.2: Solving Logarithmic Equations
  - Select activity Using the Definition of a Logarithm to Solve Logarithmic Equations
    
    Using the Definition of a Logarithm to Solve Logarithmic Equations Book
    
    Students must
    
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  - Select activity Exponential Equations Practice II
    
    Exponential Equations Practice II Book
    
    Students must
    
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  - Select activity Solving Applied Problems Using Exponential and Logarithmic Equations
    
    Solving Applied Problems Using Exponential and Logarithmic Equations Book
    
    Students must
    
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  - Select activity Exponential Model Word Problems Practice
    
    Exponential Model Word Problems Practice Book
    
    Students must
    
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- 8.3: Exponential and Logarithmic Models
  - Select activity Models of Exponential Growth and Decay
    
    Models of Exponential Growth and Decay Book
    
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  - Select activity Half-Life Practice
    
    Half-Life Practice Book
    
    Students must
    
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  - Select activity Using Logistic Growth Models
    
    Using Logistic Growth Models Book
    
    Students must
    
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- 8.4: Fitting Exponential and Logarithmic Models to Data
  - Select activity Use Data to Build a Logarithmic Model
    
    Use Data to Build a Logarithmic Model Book
    
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  - Select activity Use Data to Build a Logistic Model
    
    Use Data to Build a Logistic Model Page
    
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- Unit 8 Assessment
  - Select activity Unit 8 Assessment
    
    Unit 8 Assessment Quiz
    
    Students must
    
    Receive a grade
Unit 9: Systems of Equations and Inequalities
Systems of equations are very useful when exploring the relationship between two or more things. For example, a business's profit depends on both the cost to produce goods or services and the money it brings in from selling those goods or services. You will be introduced to methods for solving systems and interpreting the solution when you find one. Additionally, you will be introduced to methods for graphing systems of inequalities that include combinations of linear and quadratic equations. You will use the skills you have learned from working with linear and quadratic functions and graphing and solving linear inequalities to master the topics in this unit.
Completing this unit should take you approximately 3 hours.
- Select activity Unit 9 Learning Outcomes
  
  Unit 9 Learning Outcomes Page
- 9.1: Systems of Linear Equations in Two Variables
  - Select activity Introduction to Systems of Linear Equations
    
    Introduction to Systems of Linear Equations Page
    
    Students must
    
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  - Select activity Algebraic Methods for Solving Systems in Two Variables
    
    Algebraic Methods for Solving Systems in Two Variables Book
    
    Students must
    
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  - Select activity Substitution Method Practice
    
    Substitution Method Practice Book
    
    Students must
    
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  - Select activity Addition Method Practice
    
    Addition Method Practice Book
    
    Students must
    
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  - Select activity Multiplication with Addition Method Practice
    
    Multiplication with Addition Method Practice Book
    
    Students must
    
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  - Select activity Analyzing the Solution to a System in Two Variables
    
    Analyzing the Solution to a System in Two Variables Book
    
    Students must
    
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  - Select activity An Application of Systems in Two Variables
    
    An Application of Systems in Two Variables Page
    
    Students must
    
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- 9.2: Systems of Linear Equations in Three Variables
  - Select activity Solve Systems with Three Variables
    
    Solve Systems with Three Variables Book
    
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  - Select activity Classify Solutions to Systems with Three Variables
    
    Classify Solutions to Systems with Three Variables Page
    
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  - Select activity Writing Systems of Equations as Matrices
    
    Writing Systems of Equations as Matrices Page
    
    Students must
    
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  - Select activity Equations as Matrices Practice
    
    Equations as Matrices Practice Book
    
    Students must
    
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- 9.3: Systems of Nonlinear Equations
  - Select activity Algebraic Methods for Solving Systems of Nonlinear Equations
    
    Algebraic Methods for Solving Systems of Nonlinear Equations Book
    
    Students must
    
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  - Select activity Nonlinear Inequalities
    
    Nonlinear Inequalities Page
    
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- Unit 9 Assessment
  - Select activity Unit 9 Assessment
    
    Unit 9 Assessment Quiz
    
    Students must
    
    Receive a grade
Unit 10: Introduction to Conic Sections
Conic sections are made by taking very specific slices of a cone. The slices we will study include ellipses, hyperbolas, and parabolas. You have previously studied parabolas in the context of functions 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 3 hours.
- Select activity Unit 10 Learning Outcomes
  
  Unit 10 Learning Outcomes Page
- 10.1: Ellipses
  - Select activity Writing Equations of Ellipses in Standard Form
    
    Writing Equations of Ellipses in Standard Form Book
    
    Students must
    
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  - Select activity Equations of Ellipses Practice
    
    Equations of Ellipses Practice Book
    
    Students must
    
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  - Select activity Graphing Ellipses
    
    Graphing Ellipses Book
    
    Students must
    
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  - Select activity Graphing Ellipses Practice
    
    Graphing Ellipses Practice Book
    
    Students must
    
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- 10.2: Hyperbolas
  - Select activity Writing Equations of Hyperbolas
    
    Writing Equations of Hyperbolas Book
    
    Students must
    
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  - Select activity Writing Equations of Hyperbolas Practice
    
    Writing Equations of Hyperbolas Practice Book
    
    Students must
    
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  - Select activity Writing Equations of Hyperbolas Centered at the Origin Practice
    
    Writing Equations of Hyperbolas Centered at the Origin Practice Book
    
    Students must
    
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  - Select activity Graphing Hyperbolas
    
    Graphing Hyperbolas Book
    
    Students must
    
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- 10.3: Parabolas
  - Select activity Parabolas Centered at the Origin
    
    Parabolas Centered at the Origin Book
    
    Students must
    
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  - Select activity Parabolas Not Centered at the Origin
    
    Parabolas Not Centered at the Origin Book
    
    Students must
    
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  - Select activity Graphing Parabolas Practice
    
    Graphing Parabolas Practice Book
    
    Students must
    
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- Unit 10 Assessment
  - Select activity Unit 10 Assessment
    
    Unit 10 Assessment Quiz
    
    Students must
    
    Receive a grade
Unit 11: Introduction to Sequences and Series
Finally, you will be introduced to the basics of defining, notating, and evaluating sequences and series. You will explore arithmetic and geometric sequences and series, and you will also be able to distinguish between them when you are finished.
Completing this unit should take you approximately 2 hours.
- Select activity Unit 11 Learning Outcomes
  
  Unit 11 Learning Outcomes Page
- 11.1: Sequences and Their Notations
  - Select activity Sequences Defined by an Explicit Formula
    
    Sequences Defined by an Explicit Formula Book
    
    Students must
    
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  - Select activity Sequences Defined by a Recursive Formula
    
    Sequences Defined by a Recursive Formula Book
    
    Students must
    
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- 11.2: Arithmetic Sequences
  - Select activity Write the Terms of an Arithmetic Sequence
    
    Write the Terms of an Arithmetic Sequence Book
    
    Students must
    
    View
  - Select activity Use a Formula for an Arithmetic Sequence
    
    Use a Formula for an Arithmetic Sequence Book
    
    Students must
    
    View
- 11.3: Geometric Sequences
  - Select activity Write the Terms of a Geometric Sequence
    
    Write the Terms of a Geometric Sequence Book
    
    Students must
    
    View
  - Select activity Use a Formula for a Geometric Sequence
    
    Use a Formula for a Geometric Sequence Book
    
    Students must
    
    View
- 11.4: Arithmetic Series
  - Select activity Use the Formula for an Arithmetic Series
    
    Use the Formula for an Arithmetic Series Book
    
    Students must
    
    View
  - Select activity Summation Notation Practice
    
    Summation Notation Practice Book
    
    Students must
    
    View
  - Select activity Use the Formula for a Geometric Series
    
    Use the Formula for a Geometric Series Book
    
    Students must
    
    View
  - Select activity Geometric Series Practice
    
    Geometric Series Practice Book
    
    Students must
    
    View
- Unit 11 Assessment
  - Select activity Unit 11 Assessment
    
    Unit 11 Assessment Quiz
    
    Students must
    
    Receive a grade
Study Guide
- Select activity MA120 Study Guide
  
  MA120 Study Guide Book
Certificate Final Exam
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.
- Select activity MA120: Certificate Final Exam
  
  MA120: Certificate Final Exam Quiz
  
  Students must
  
  Receive a grade
  
  Receive a passing grade
Saylor Direct Credit
Take this exam if you want to earn college credit for this course. This course is eligible for college credit through Saylor Academy's Saylor Direct Credit Program.

The Saylor Direct Credit Final Exam requires a proctoring fee of $5. To pass this course and earn a Proctor-Verified Course Certificate and official transcript, you will need to earn a grade of 70% or higher on the Saylor Direct Credit Final Exam. Your grade for this 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 a maximum of 3 times, with a 14-day waiting period between each attempt.

We are partnering with SmarterProctoring to help make the proctoring fee more affordable. We will be recording you, your screen, and the audio in your room during the exam. This is an automated proctoring service, but no decisions are automated; recordings are only viewed by our staff with the purpose of making sure it is you taking the exam and verifying any questions about exam integrity. We understand that there are challenges with learning at home - we won't invalidate your exam just because your child ran into the room!

Requirements:

Desktop Computer

Chrome (v74+)

Webcam + Microphone

1mbps+ Internet Connection

Once you pass this final exam, you will be awarded a Credit-Recommended Course Completion Certificate and can request an official transcript.

Saylor Direct Credit Exam

This exam is part of the Saylor Direct College Credit program. Before attempting this exam, review the Saylor Direct Credit page for complete requirements.

Essential exam information:

You must take this exam with our automated proctor. If you cannot, please contact us to request an override.

The automated proctoring session will cost $5.

This is a closed-book, closed-notes exam (see allowed resources below).

You will have two (2) hours to complete this exam.

You have up to 3 attempts, but you must wait 14 days between consecutive attempts of this exam.

The passing grade is 70% or higher.

This exam consists of 50 multiple-choice questions.

Some details about taking your exam:

Exam questions are distributed across multiple pages.

Exam questions will have several plausible options; be sure to pick the answer that best satisfies each part of the question.

Your answers are saved each time you move to another page within the exam.

You can answer the questions in any order.

You can go directly to any question by clicking its number in the navigation panel.

You can flag a question to remind yourself to return to it later.

You will receive your grade as soon as you submit your answers.

Allowed resources:

Gather these resources before you start your exam.

Blank paper

What should I do before my exam?

Gather these before you start your exam:

A photo I.D. to show before your exam.

A credit card to pay the automated proctoring fee.

(optional) Blank paper and pencil.

(optional) A glass of water.

Make sure your work area is well-lit and your face is visible.

We will be recording your screen, so close any extra tabs!

Disconnect any extra monitors attached to your computer.

You will have up to two (2) hours to complete your exam. Try to make sure you won't be interrupted during that time!

You will require at least 1mbps of internet bandwidth. Ask others sharing your connection not to stream during your exam.

Take a deep breath; you got this!
Course Feedback Survey
Please take a few minutes to give us feedback about this course. We appreciate your feedback, whether you completed the whole course or even just a few resources. Your feedback will help us make our courses better, and we use your feedback each time we make updates to our courses. If you come across any urgent problems, email contact@saylor.org.
- Select activity Course Feedback Survey
  
  Course Feedback Survey URL

COURSE INTRODUCTION

Course Syllabus

Unit 1: Equations and Inequalities

Unit 1 Learning Outcomes

1.1: Solving Linear and Rational Equations in One Variable

Solving Linear Equations in One Variable

Solving Linear Equations Practice

Applications of Linear Equations

Rational Equations

Rational Equations Practice

1.2 Quadratic, Radical, and Absolute Value Equations

Complex Numbers

Solve Quadratic Equations by Factoring

Solving Quadratic Equations Practice

Solve Quadratic Equations Using the Square Root Property

Using the Quadratic Formula and the Discriminant

Equations That Are Quadratic in Form

Absolute Value Equations

Absolute Value Equations Practice

Radical Equations

Radical Equations Practice

1.3: Linear Inequalities

Using Interval Notation and Properties of Inequalities

Solve Simple and Compound Linear Inequalities

Solve Simple and Compound Linear Inequalities Practice

Absolute Value Inequalities

Unit 1 Assessment

Unit 1 Assessment

Unit 2: Introduction to Functions

Unit 2 Learning Outcomes

2.1: Notation and Basic Functions

The Rectangular Coordinate System and Graphs

Defining and Writing Functions

Properties of Functions and Basic Function Types

2.2: Properties of Functions and Describing Function Behavior

Finding the Domain of a Function Defined by an Equation

Finding the Domain of a Function Define by an Equation Practice

Finding Domain and Range from Graphs

Finding Domain and Range from Graphs Practice

Graphing Piecewise-Defined Functions

Graphing Piecewise-Defined Functions Practice

Calculate the Rate of Change of a Function

Determine Where a Function Is Increasing, Decreasing, or Constant

Increasing and Decreasing Functions Practice

Unit 2 Assessment

Unit 2 Assessment

Unit 3: Algebraic Operations on Functions

Unit 3 Learning Outcomes

3.1: Composite Functions

Creating and Evaluating Composite Functions

Creating and Evaluating Composite Functions Practice

Creating and Evaluating Composite Functions Practice II

Finding the Domain of a Composite Function

3.2: Transformations

Graphing Functions Using Vertical and Horizontal Shifts

Graphing Functions Using Vertical and Horizontal Shift Practice

Graphing Functions Using Reflections

Graphing Functions Using Reflections Practice

Determining Whether a Function Is One-to-One

Graphing Functions Using Stretches and Compressions

Compressing and Stretching Graphs Practice

Compressing and Stretching Graphs Horizontally Practice

3.3: Inverse Functions

Inverse Functions

Inverse Functions Practice

Unit 3 Assessment

Unit 3 Assessment

Unit 4: Linear Functions

Unit 4 Learning Outcomes

4.1: Linear Functions

Representations of Linear Functions

Interpreting Slope as a Rate of Change

Interpreting Slope as a Rate of Change Practice

Writing and Interpreting an Equation for a Linear Function

Writing Equations of Lines Practice

Graphing Lines Practice

Parallel and Perpendicular Lines

4.2: Modeling with Linear Functions

Building Linear Models from Words

Modeling a Set of Data with Linear Functions