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4 weeks / 6 hours per week

About This Course

It reviews the fundamentals taught in a one-semester college course in calculus. Our lessons are aligned to the content of the CLEP exam, which covers approximately 60% limits and differential calculus and 40% integral calculus. Our goal as creators of this course is to prepare you to pass the College Board's CLEP examination and obtain college credit for free.

"Now more than ever, mathematics is a subject that opens doors-doors to new career opportunities and new intellectual worlds" explains Dr. James Murphy, professor at Johns Hopkins University and instructor of this course.

“Calculus” is a completely self-paced course. It has no prerequisites and it is offered entirely for free.

Course Staff


How is this course organized?

This course is organized into five modules that contain short video lessons, exercises and readings.

All of the course material has been released at once so you can complete it anytime.

What do I need to pass the CLEP exam?

You need to demonstrate understanding of calculus and experience with its methods and applications. Knowledge of preparatory mathematics is assumed, including algebra, geometry, trigonometry, and analytic geometry.

The examination contains 44 questions, in two sections, to be answered in approximately 90 minutes. Please examine our syllabus.

How does this course differ from other CLEP textbooks and traditional courses?

This online course includes a carefully structured series of video lectures and exercises taught by a top quality university professor.




Navigating Through Our Platform

CLEP Program   

Modern States Education Alliance   

Introduce Yourself

1. Limits

1.0 Introduction to Limits   

1.1 Definition of a Limit   

1.2 Computing Basic Limits   

1.3 Continuity   

1.4 Squeeze Theorem   

1.5 Readings

2. Theory of the Derivative

2.0 Introduction to Theory of the Derivative   

2.1 Tangent Lines   

2.2 Definition of Derivative   

2.3 Rates of Change   

2.4 Derivative Rules   

2.5 Higher Order Derivatives   

2.6 Implicit Differentiation   

2.7 L’Hôpital’s Rule   

2.8 Some Classic Theoretical Results   

2.9 Derivatives of Inverse Functions   

2.10 Readings

3. Applications of the Derivative

3.0 Introduction to Applications of the Derivative   

3.1 Plotting with Derivatives   

3.2 Rate of Change   

3.3 Some Physics Problems   

3.4 Readings

4. Theory of the Integral

4.0 Introduction to Theory of the Integral   

4.1 Antidifferentiation   

4.2 Definite Integral   

4.3 Riemann Sums   

4.4 The Fundamental Theorem of Calculus   

4.5 Basic Integral Rules   

4.6 U-Substitutions   

4.7 Readings

5. Applications of the Integral

5.0 Introduction to Applications of the Integral   

5.1 Area Under Curves   

5.2 Average Value   

5.3 Growth and Decay Models   

5.4 Return to Physics   

5.5 Readings

Sample CLEP Questions

Questions 1 - 15

Questions 16 - 30

Questions 31 - 45

Question 46 - 60

Questions 61 - 75

Question 76 - 90

Final Steps

Prof. James Murphy's Recommendation   

Register for the CLEP Exam   

Test Preparation Tips   

How Your Score Is Computed

Learn More