Math 104: Calculus
 Course type: Selfpaced
 Available Lessons: 105
 Average Lesson Length: 8 min

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

Watch a preview:
chapter 1 / lesson 1What is a Function: Basics and Key Terms
Course Summary
Our Calculus course is a quick and affordable way to earn transferable college credits in math. With our engaging and fun video format, our expert instructors make even the most challenging topics easy to understand and enjoyable to learn.To Start This Course Today
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Lesson 1  What is a Function: Basics and Key Terms

Lesson 2  Graphing Basic Functions

Lesson 7  Exponentials, Logarithms & the Natural Log

Lesson 8  Slopes and Tangents on a Graph

Lesson 9  Equation of a Line Using PointSlope Formula

Lesson 10  Horizontal and Vertical Asymptotes

Lesson 11  Implicit Functions

Go to chapter Graphing and Functions

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Lesson 1  Continuity in a Function

Lesson 2  Discontinuities in Functions and Graphs

Lesson 3  Regions of Continuity in a Function

Lesson 4  Intermediate Value Theorem: Definition

Go to chapter Continuity

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Lesson 1  How to Solve Visualizing Geometry Problems

Lesson 2  How to Calculate the Volumes of Basic Shapes

Lesson 4  Trigonometry: Sine and Cosine

Lesson 5  Trigonometry and the Pythagorean Theorem

Go to chapter Geometry and Trigonometry

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Go to chapter Using Scientific Calculators

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Lesson 1  Using a Graph to Define Limits

Lesson 2  Understanding Limits: Using Notation

Lesson 3  OneSided Limits and Continuity

Lesson 4  How to Determine the Limits of Functions

Lesson 5  Understanding the Properties of Limits

Lesson 6  Squeeze Theorem: Definition and Examples

Go to chapter Limits

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Lesson 1  Velocity and the Rate of Change

Lesson 2  Slopes and Rate of Change

Lesson 3  What is the Mean Value Theorem?

Lesson 5  Derivatives: The Formal Definition

Lesson 6  Derivatives: Graphical Representations

Lesson 7  What It Means To Be 'Differentiable'

Go to chapter Rate of Change

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Lesson 1  Using Limits to Calculate the Derivative

Lesson 2  The Linear Properties of a Derivative

Lesson 10  Calculating Higher Order Derivatives

Lesson 11  How to Find Derivatives of Implicit Functions

Go to chapter Calculating Derivatives and Derivative Rules

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Lesson 1  Graphing the Derivative from Any Function

Lesson 2  Non Differentiable Graphs of Derivatives

Lesson 5  Concavity and Inflection Points on Graphs

Lesson 9  What is L'Hopital's Rule?

Lesson 10  Applying L'Hopital's Rule in Simple Cases

Lesson 11  Applying L'Hopital's Rule in Complex Cases

Go to chapter Graphing Derivatives and L'Hopital's Rule

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Lesson 1  Linearization of Functions

Lesson 3  What is Newton's Method?

Lesson 5  Optimization and Differentiation

Lesson 6  Optimizing Simple Systems

Lesson 7  Optimizing Complex Systems

Go to chapter Applications of Derivatives

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Lesson 1  Summation Notation and Mathematical Series

Lesson 4  What is the Trapezoid Rule?

Lesson 5  How to Find the Limits of Riemann Sums

Lesson 6  Definite Integrals: Definition

Lesson 8  Linear Properties of Definite Integrals

Lesson 9  Average Value Theorem

Lesson 10  The Fundamental Theorem of Calculus

Lesson 11  Indefinite Integrals as Anti Derivatives

Lesson 12  How to Find the Arc Length of a Function

Go to chapter Area Under the Curve and Integrals

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Lesson 1  Calculating Integrals of Simple Shapes

Lesson 5  How to Solve Integrals Using Substitution

Lesson 7  Using Integration By Parts

Lesson 10  Understanding Trigonometric Substitution

Lesson 12  How to Solve Improper Integrals

Go to chapter Integration and Integration Techniques

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Lesson 1  Integration and Dynamic Motion

Go to chapter Integration Applications

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Lesson 1  Differential Notation in Physics

Lesson 4  Related Rates: The Draining Tank Problem

Go to chapter Differential Equations
Course Format:
Math 104 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.
The course is completely selfpaced. Watch lessons on your schedule whenever and wherever you want. When you're ready, take the final exam.
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 104:
 A nongraphing, scientific calculator
 One sheet of blank scratch paper
 Pen or pencil
Items NOT Allowed on Study.com Proctored Exam for Math 104:
 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 calculus course and recommended it for college credit. To earn credit, follow these steps:
 Identify if you need a calculus 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 104 by watching videos, taking short quizzes and completing practice exams.
 Contact our expert instructors if you ever have questions.
 Take the creditgranting Math 104 exam on our site.
 Transfer credit to your school!
Study Schedule for Math 104: Calculus
You can easily break up this course into short chunks to make it easier to study when it's convenient for you. Since each video lesson is 510 minutes long, you can study in small segments or for long bursts. The study schedule below gives you an estimate of approximately how long it will take for you to complete the course.
Study Frequency  When You'll Be Ready for the Exam 

3 hours a day; 3 days a week  1 week 
2 hours a day; 3 days a week  2 weeks 
1 hour a day; 3 days a week  3 weeks 
Who's It For?
This calculus course is designed for students who want to save time and money while completing their college education. If you're currently in college and need to pass Math 104 or planning to attend and want a jump start on your degree, this course is for you. When you complete the final exam at the end of the course, you'll have real college credit that can be easily transferred to your college.
The course will teach you about polynomials, factoring, rate of change, differential equations, higherorder derivatives and even how to use a scientific calculator. Skip the lectures, books and semester of completing homework. Start mastering the basics of calculus today.
Prerequisites
There are no prerequisites for this course, but many students choose to complete Math 103: Precalculus prior to Math 104: Calculus.
Why It Works:
 Efficient: Short videos focus on the needtoknow Math 104 topics.
 Comprehensive: From basic function terminology to ubiquity in physics, this course covers the breadth of calculus.
 Convenient: Study on your laptop, tablet or phone. Learn calculus wherever you go!
 Learn Your Way: Each video lesson combines visuals, professional audio and complete transcripts to teach you in different ways.
 Expert Instructors: Learn from math experts who make topics clear, interesting and fun!
Course Topics
Category  Objectives 

Graphing and Functions  Learn to graph basic functions, inverse functions and functions of functions. Discover ways to determine the equation of a line using pointslope formula and to recognize vertical and horizontal asymptotes. 
Continuity  Examine continuity in a function, discontinuities in functions and graphs, and regions of continuity in a function. Define intermediate value theorem with examples and applications. 
Geometry and Trigonometry  Get practice in visualizing geometry programs and calculating the volume of basic shapes. See how to use the Pythagorean Theorem and graph sines and cosines. 
Using Scientific Calculators  Study how to solve equations and understand trigonometry functions on a scientific calculator. 
Limits  Explore ways to determine the limits of functions and use a graph to define limits. Study the properties of limits and the squeeze theorem, with examples. 
Rate of Change  See how motion can define the rate of change, define and graph the Mean Value Theorem and explain how it relates to Rolle's Theorem. Define and graph derivatives. 
Calculating Derivatives and Derivative Rules  See how the rules of differentiation can be used to calculate derivatives, calculate derivatives of exponential equations, and find derivatives of implicit functions. Examine derivatives of polynomial equations, derivatives of trigonometric functions, higherorder derivatives, derivatives of inverse trigonometric functions, and linear properties of a derivative. 
Graphing Derivatives and L'Hopital's Rule  Understand L'Hopital's Rule and be able to apply it in simple and complex cases. Learn how to graph the derivative from any function and how to show maximum and minimum values and points on a graph. 
Applications of Derivatives  Study the estimation of function values with linearization. Understand Newton's method and be able to use it to find roots of equations. 
Area Under the Curve and Integrals  Learn about summation nation, Riemann sums and how to use them, average value theorem, definite integrals, indefinite integrals as antiderivatives, and linear properties of definite integrals. Learn to determine the arc length of a function and to explain the trapezoid rule. 
Integration and Integration Techniques  Find out how to calculate the integrals of simple shapes, the indefinite integrals of polynomials, the integrals of trigonometric functions, and the integrals of exponential functions. See how to solve improper integrals and ways to use trigonometric substitutions to solve integrals. 
Integration Applications  Explore the connection between integration and dynamic motion, and learn to determine simple areas with root finding and integration. See how to figure out volumes by using single integrals. 
Differential Equations  Learn about differential notation in physics, separation of variables to solve system differential equations, and calculating rate and exponential growth. Study related rates through the draining tank problem and the distance between moving points problem. 
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 104: Calculus 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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