Online Class: Precalculus 101
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Course Description
Calculus is a mathematical tool that is required in a variety of scientific, technical, and other professional fields. Because it is a higherlevel area of math, many people think it is a subject that they can never understand. Unfortunately, such an attitude limits an individual's career choices, particularly in a technologyfocused society. This course provides a bridge between algebra and calculus, guiding students through the underlying mathematical concepts needed to understand and appreciate calculus. The course reviews real and complex numbers, functions, and equations and inequalities. It then goes into some detail on specific types of functions, such as polynomials, exponentials, and logarithms. It also provides a derivation of the principles of trigonometry on the basis of simple righttriangle and circle geometry. After reviewing vectors, polar coordinates, and conic sections, the material sets up calculus proper by examining limits as well as sequences and series.
The final lessons of the course use the basic principles of algebra to derive the two key tools of calculus: differentiation (the derivative) and integration (the integral). At the end of this course, students will be prepared to study calculus in greater depth, further investigating and applying derivatives and integrals to solve a variety of math, physics, and other problems.
 Completely Online
 SelfPaced
 Instructor Feedback
 6 Months to Complete
 24/7 Availability
 Start Anytime
 PC & Mac Compatible
 Android & iOS Friendly
 Accredited CEUs
Learning Outcomes
By successfully completing this course, students will be able to:
 Define, identify and demonstrate use of real and complex numbers.
 Define, identify and demonstrate use of functions.
 Define, identify and demonstrate use of equations and inequalities.
 Define, identify and demonstrate use of polynomials and rational functions.
 Define, identify and demonstrate use of exponential and logarithmic functions.
 Define, identify and demonstrate use of trigonometric functions.
 Define, identify and demonstrate use of vectors.
 Define, identify and demonstrate use of polar coordinates.
 Define, identify and demonstrate use of conic sections.
 Define, identify and demonstrate use of limits, sequences, and series.
 Define, identify and demonstrate use of derivatives and integrals, and
 Demonstrate mastery of lesson content at levels of 70% or higher.
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Course Lessons
Lesson 1  Real and Complex Numbers
In this lesson, we begin the process of setting a foundation for understanding calculus by looking briefly at real and complex numbers. These are the sets of values that we will be studying at length in this course. 21 Total Points
 Lesson 1 Video
 Review 3 Articles: Definition of Absolute Value; Interval Notation; Number sense
 Complete Assignment: Introduction
 Complete: Lesson 1 Exam
Lesson 2  Functions I
Having introduced the real and complex number sets in the previous lesson, we now begin to look in depth at series of operations on numbers, or more particularly, numbers and variables. 20 Total Points
 Lesson 2 Video
 Review Article: Independent and Dependent Variables
 Complete: Lesson 2 Exam
Lesson 3  Functions II
Having defined functions in the previous lesson, we now look in more detail at the characteristics of functions. These concepts are critical and will underlie the remainder of this course. 20 Total Points
 Lesson 3 Video
 Review Article: Composition of two functions
 Complete: Lesson 3 Exam
Lesson 4  Equations and Inequalities
Having looked in detail at functions, the course now turns to equations and inequalities: two mathematical expressions that relate different algebraic relations involving numbers, variables, or both. 20 Total Points
 Lesson 4 Video
 Complete: Lesson 4 Exam
Lesson 5  Polynomials and Rational Functions I
Having looked in general at characteristics of functions and their relationship to equations and inequalities, we now turn to a common class of functions, polynomials, and their close cousins, rational functions.x` 20 Total Points
 Lesson 5 Video
 Review Article: Graphing the Rational Function
 Complete: Lesson 5 Exam
Lesson 6  Polynomials and Rational Functions II
In the previous lesson, we defined and discussed some characteristics of polynomials and rational functions. In this lesson, we will look at these functions in slightly more depth. 20 Total Points
 Lesson 6 Video
 Review 2 Articles: How to Solve Higher Degree Polynomials; Rational Functions and Asymptotes
 Complete: Lesson 6 Exam
Lesson 7  Exponential and Logarithmic Functions
This lesson turns away from polynomials (and their close cousins, rational functions) and looks at another type of function: exponential and logarithmic functions. We consider the basic rules of exponents and logarithms and apply them to simple functions. 20 Total Points
 Lesson 7 Video
 Review 2 Articles: LOGARITHMIC AND EXPONENTIAL FUNCTIONS; Solving Equations Using Logarithms
 Complete: Lesson 7 Exam
Lesson 8  Trigonometric Functions I
We now consider another class of functions called trigonometric ("trig") functions. These functions are useful in a variety of contexts involving triangles and circles. This lesson considers the origin of these functions in right triangles and looks at so 20 Total Points
 Lesson 8 Video
 Review 2 Articles: Basic Trigonometry Rules; Right Triangle Trig Calculator
 Complete: Lesson 8 Exam
Lesson 9  Trigonometric Functions II
In the previous lesson, we reviewed the origin of trigonometric functions in the context of right triangles. Interestingly, however, trig functions also have applicability to circles. The present lesson will focus on circles and the relationship of circle 20 Total Points
 Lesson 9 Video
 Review Article: The Trigonometry of Circles
 Complete: Lesson 9 Exam
Lesson 10  Trigonometric Functions III
In this lesson, we will look at a few more aspects of trigonometry, including trigonometric identities and inverse trigonometric functions. 20 Total Points
 Lesson 10 Video
 Review 2 Articles: Inverse Trigonometric Functions; Table of Trigonometric Identities
 Complete: Lesson 10 Exam
Lesson 11  Vectors I
In this lesson, we introduce a new quantity: the vector. Vectorsunlike simple numbers (scalars) that have only a magnitudehave both a magnitude (length) and direction. We will explore how to represent vector quantities, as well as how to add and subtr 20 Total Points
 Lesson 11 Video
 Complete: Lesson 11 Exam
Lesson 12  Vectors II
In the previous lesson, we introduced vectors as quantities with a magnitude and direction. In this lesson, we look more deeply into vectors to flesh out some of the concepts introduced previously. 20 Total Points
 Lesson 12 Video
 Review 3 Articles: Algebraic Representation of Vectors; Unit Vector; Vector Addition and Scalar Multiplication
 Complete: Lesson 12 Exam
Lesson 13  Polar Coordinates
In this lesson, we introduce a new type of coordinate system: polar coordinates. Polar coordinates are one example of the many alternative coordinate systems that can be devised; these alternatives can greatly simplify certain problems. 20 Total Points
 Lesson 13 Video
 Complete: Lesson 13 Exam
Lesson 14  Conic Sections I
In this lesson, we introduce conic sections and show how they are related to cross sections of a cone (hence their name). The basic characteristicsalgebraic and graphicalof two conic sections are discussed in detail: circles and parabolas. The next less 20 Total Points
 Lesson 14 Video
 Complete: Lesson 14 Exam
Lesson 15  Conic Sections II
This lesson continues our examination of conic sections, focusing specifically on ellipses and hyperbolas. The end of the lesson presents a practical way of relating all the conics we have studied thus far by way of the motion of celestial objects. 20 Total Points
 Lesson 15 Video
 Review Article: Conic Sections
 Complete: Lesson 15 Exam
Lesson 16  Limits
In this lesson, we introduce limits, a topic fundamental to understanding differentiation and integrationtwo critical aspects of calculus. Limits are generally intuitive, but a solid ability to use them is important to the remainder of the course. 20 Total Points
 Lesson 16 Video
 Review 2 Articles: Basic Limit Laws; Calculating Limits
 Complete: Lesson 16 Exam
Lesson 17  Sequences and Series
The current lesson switches our focus slightly to look briefly at sequences and series. These mathematical constructs play an important role in calculus and other branches of mathematics. 20 Total Points
 Lesson 17 Video
 Review Article: Introduction to Series
 Complete: Lesson 17 Exam
Lesson 18  Introduction to Derivatives
Having covered all the necessary mathematical background, the final two lessons of the course turn to two fundamental concepts in calculus: the derivative and the integral. Although we will not go into great depth on these subjects, we will show how they 20 Total Points
 Lesson 18 Video
 Review Article: Introduction of Derivatives
 Complete: Lesson 18 Exam
Lesson 19  Introduction to Integrals
In the previous lesson, we covered one of two major aspects of calculus: the derivative. For this closing lesson to the course, we will look briefly at the other of these two concepts: the integral. 100 Total Points
 Lesson 19 Video
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 Complete: The Final Exam
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Course Title:
Precalculus 101
Course Number:
9770456
Languages:
English  United States, Canada and other English speaking countries
Course Type:
General Education
Grading Policy:
Earn a final grade of 70% or higher to receive an online/downloadable CEU Certification documenting CEUs earned.
Assessment Method:
Lesson assignments and review exams
Duration:
Continuous: Enroll anytime!
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