Math 105: Precalculus Algebra
 Course type: Selfpaced
 Available Lessons: 102
 Average Lesson Length: 8 min

Eligible for Credit: Yes
Earn transferable credit by taking this course for credit.

Watch a preview:
chapter 1 / lesson 1Writing & Evaluating Algebraic Expressions for TwoDimensional Geometric Figures
Course Summary
Take our Math 105: Precalculus Algebra course to quickly earn transferable college credits in math. Taught by expert instructors, this selfpaced course offers an affordable path to college credit through a series of engaging video lessons, selfassessment quizzes, practice exams and more.To Start This Course Today
Try it free for 5 days

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Go to chapter Mathematical Modeling

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Lesson 1  What is a Linear Equation?

Lesson 5  How to Write a Linear Equation

Lesson 6  Equation of a Line Using PointSlope Formula

Lesson 7  What is an Inequality?

Lesson 8  How to Graph 1 and 2Variable Inequalities

Lesson 9  Graphing Inequalities: Practice Problems

Lesson 10  What is a System of Equations?

Lesson 11  How Do I Use a System of Equations?

Go to chapter Linear Equations & Inequalities

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Lesson 1  What is a Parabola?

Lesson 5  How to Complete the Square

Lesson 6  Completing the Square Practice Problems

Go to chapter Quadratic Functions

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Lesson 3  How to Add and Subtract Rational Expressions

Lesson 5  How to Solve a Rational Equation

Lesson 6  Horizontal and Vertical Asymptotes

Go to chapter Rational Expressions and Functions

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Lesson 3  How to Divide Polynomials with Long Division

Go to chapter Polynomial Functions of a Higher Degree

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Lesson 1  What is an Absolute Value?

Lesson 2  How to Evaluate Absolute Value Expressions

Lesson 3  How to Solve an Absolute Value Equation

Lesson 4  Solving Absolute Value Practice Problems

Go to chapter Absolute Value Equations & Inequalities

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Lesson 1  What is an Imaginary Number?

Lesson 3  How to Divide Complex Numbers

Go to chapter Complex Numbers

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Lesson 1  Circles: Area and Circumference

Lesson 4  How to Use The Distance Formula

Lesson 5  How to Use The Midpoint Formula

Go to chapter Geometry Basics

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Lesson 1  What is a Function: Basics and Key Terms

Lesson 3  Graphing Basic Functions

Lesson 4  What Is Domain and Range in a Function?

Lesson 7  Discontinuities in Functions and Graphs

Lesson 8  How to Graph Piecewise Functions

Lesson 10  Transformations: How to Shift Graphs on a Plane

Go to chapter Functions Overview

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Lesson 2  How to Compose Functions

Lesson 6  Inverse Functions

Go to chapter Function Operations

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Lesson 4  Even & Odd Functions: Definition & Examples

Go to chapter Graph Symmetry

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Lesson 1  What Is an Exponential Function?

Lesson 2  Exponential Growth vs. Decay

Lesson 5  What is a Logarithm?

Lesson 6  How to Evaluate Logarithms

Lesson 7  Writing the Inverse of Logarithmic Functions

Lesson 8  Exponentials, Logarithms & the Natural Log

Lesson 10  Logarithmic Properties

Lesson 11  Practice Problems for Logarithmic Properties

Lesson 12  How to Solve Logarithmic Equations

Lesson 14  How to Solve Exponential Equations

Go to chapter Exponential and Logarithmic Functions

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Lesson 1  Velocity and the Rate of Change

Lesson 2  Slopes and Rate of Change

Lesson 3  Derivatives: The Formal Definition

Go to chapter Introduction to the Derivative
Course Format
Math 105 consists of short video lessons that are organized into topical chapters. Each video is approximately 510 minutes in length and comes with a quick quiz to help you measure your learning. At the end of each chapter, you can complete a chapter test to see if you're ready to move on or have some material to review. Once you've completed the entire course, take the practice test to see if you're ready to earn credit. Use the study tools in the course to prepare for your final exam.
The course is completely selfpaced. Watch lessons on your schedule whenever and wherever you want. When you're ready, take the final exam.
Course Outcomes
Upon completion of the course, you will be able to:
 Write and solve mathematical modeling equations, including those pertaining to cost, determination, economic equilibrium and relating a 2dimensional figure's side lengths, perimeter and area.
 Evaluate linear equations, 1 and 2variable inequalities and systems of equations.
 Factor and solve quadratic equations, including solving by utilizing the quadratic formula.
 Complete operations involving rational expressions and solve rational equations.
 Complete operations involving polynomials, including factoring polynomials using the remainder, factor and rational zero theorems as well as synthetic division.
 Evaluate absolute value expressions and solve and graph absolute value equations and inequalities.
 Complete operations involving complex numbers and graph complex numbers on the complex plane.
 Graph different types of functions, including inverse functions, square root functions, cube root functions and functions of functions.
 Detect symmetry graphically, numerically and algebraically.
 Evaluate logarithms, including rewriting logarithmic equations in exponential form, graphing logarithmic functions and identifying a logarithmic function's vertical asymptote, domain and range.
 Define and utilize the derivative, including demonstrating its relationship to the rate of change.
Grading Policy
Your grade for this course will be calculated out of 150 points. The minimum score required to pass and earn real ACE college credit for this course is 105 points, or an overall course grade of 70%. The table below shows the assignments you must complete and how they'll be incorporated into the overall grade.
Assignment  Possible Points 

Quizzes  50 
Proctored Final Exam  100 
Total  150 
 Quizzes are meant to test your comprehension of each lesson as you progress through the course. You must complete the required quizzes with a score of 80% or higher to earn points toward your final grade and access the proctored final exam. Chapter exams are for selfassessment and do not count toward your final grade.
 The proctored final exam is a cumulative test designed to ensure that you've mastered the material in the course. You'll earn one point for every percentage point you receive on the proctored final. (So if you score an 85% on the final, that's 85 points toward your final grade.)
Items Allowed on Study.com Proctored Exam for Math 105:
 A nongraphing, scientific calculator
 One sheet of blank scratch paper
 Pen or pencil
Items NOT Allowed on Study.com Proctored Exam for Math 105:
 Graphing calculators
 Office programs, web browsers, or any programs other than Software Secure (including Study.com lessons)
 Textbooks (digital or physical)
 Mobile phones, headphones, speakers, TVs, radios
 Notebooks or notes
How It Works:
The American Council on Education (ACE) has evaluated this math course and recommended it for college credit. To earn credit, follow these steps:
 Identify if you need a precalculus algebra course for your degree.
 Check with your registrar to see if your school is one of the 2,000 colleges and universities that accept credit from ACErecommended courses.
 Complete Math 105 by watching videos, taking short quizzes and completing practice exams.
 Contact our expert instructors if you ever have questions.
 Take the creditgranting Math 105 exam on our site.
 Transfer credit to your school!
Prerequisites
There are no prerequisites for this course, but many students choose to complete Math 101: College Algebra prior to Precalculus Algebra.
Course Topics
Category  Objectives 

Mathematical Modeling  Learn how algebraic expressions can be used to describe twodimensional geometric figures and evaluate linear models. Practice using linear systems to find minimum and maximum values, breakeven point and market equilibrium. 
Linear Equations & Inequalities  Find out how to write linear equations in standard and slopeintercept form. Examine the graphs of one and twovariable inequalities and linear systems. 
Quadratic Functions  Identify equations for parabolas written in standard, intercept and vertex forms. Practice using the FOIL method and quadratic formula to factor and solve quadratic equations. Learn to graph quadratic inequalities and systems of quadratic inequalities. 
Rational Expressions & Functions  Perform arithmetic operations with rational expressions. Find out how to graph linear and polynomial rational functions and identify their asymptotes. 
Polynomial Functions of a Higher Degree  Discover the steps involved in adding, subtracting and multiplying polynomials. Learn how to perform long division and synthetic division with polynomials. Explore the applications of the remainder theorem, factor theorem, rational zeros theorem and the fundamental theorem of algebra. 
Absolute Value Equations & Inequalities  Find out what it takes to evaluate, solve and graph absolute value equations and inequalities. Practice performing transformations of an absolute value's graph. 
Complex Numbers  Discover what an imaginary number is before learning how to perform arithmetic operations with complex numbers. Get tips for graphing complex numbers and solving quadratics with complex numbers in the solution. 
Geometry Basics  Explore the formulas for circle area and circumference. Learn how to graph a circle and write the standard form of a circle's equation. Apply the distance and midpoint formulas. 
Functions Overview  Identify a function's domain and range. Find out how to graph basic functions, power functions, radical functions and piecewise functions. 
Function Operations  Examine the steps involved in performing arithmetic operations with functions. Learn to compose functions and work with composite functions, inverse functions and onetoone functions. 
Graph Symmetry  Learn some of the methods used to detect a graph's symmetry. Practice identifying even and odd functions. 
Exponential & Logarithmic Functions  Study the relationship between exponential functions, logarithms and the natural base e. Learn how logarithmic properties and the change of base formula can be used to solve logarithmic equations. Practice graphing these two types of functions. 
Introduction to the Derivative  Discover how velocity and the rate of change are related graphically. 
What to Expect For the Exam
The American Council on Education (ACE) has evaluated this Study.com course and recommended it for college credit. Once you've completed this course, you can take the proctored final exam and potentially earn credit. Follow the steps below to take the exam.
Exam Steps
PreExam Checklist
Before taking the exam, all of the following requirements must be met:
A College Accelerator Study.com membership.  
Completed the entire Math 105: Precalculus Algebra course and achieved 100% Course Progress.  
Not attempted to take this exam within the last three days.  
Have available proctored exams in this month of membership. 
Please complete all of the prerequirements in the PreExam Checklist in order to take the exam.
Start Exam RegistrationExam Process Details
1. Register For Exam
Registering for the exam is simple. First, be sure you meet the system requirements. Next, you'll need to agree to the academic integrity policy. Then just confirm your name and the exam name, and you're ready to go!
2. Download Software Secure
You'll receive an unique access code. Please write this down — you'll need it to take the exam. Then download Software Secure and follow the installation instructions.
3. Take Exam
The exam contains 50  100 multiple choice questions. You will have two hours to complete the exam, so don't start until you're sure you can complete the entire thing. And remember to pace yourself!
4. Get Exam Results
We will send you an email with your official exam results within 1 to 2 weeks.
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