# Calculus CLEP Free Study Guide Name of Exam: Calculus CLEP

Number of Questions: 44

Time Limit: 90 Minutes

ACE Recommended Passing Score: 50

Cost: \$80 + Sitting Fee (Usually no more than \$20) at your testing site. Military can take CLEPs for free with Tuition Assistance. Check with your Educational Officer!

Difficulty 1-5 : 4
(One being the easiest, and five being the hardest)

### Exam Description:

The Calculus CLEP covers the material usually taught in a one semester college Calculus course. You will be expected to already understand college algebra, geometry, trigonometry, and analytic geometry.

Important! - There is an on-screen graphing calculator included that you will need for the second portion of this exam. CollegeBoard recommends that you download a free 30 day trial of the graphing calculator along with a tutorial in order to become familiar with its use. You can find that here

You will need to know how to do the following with the above calculator:

• Generate a table of values for a function
• Find numerical solutions to equations
• Perform calculations to include exponents, logarithms, roots, and trigonometric values
• Find zeros of functions
• Find minima/maxima of functions
• Graph functions and analyze the graphs
• Find points of intersection of graphs of functions

### Personal Thoughts:

If the idea of me teaching someone Precalculus was funny, then the idea of me teaching Calculus is downright hysterical. Ask me what a maxima is and I'm going to point you towards the nearest Nissan dealer.

As before, I wouldn't even know where to begin with explaining each topic. Using the same format as we did for Precalculus, I'm going to list the material covered on this exam, and then show you some resources that you can use to brush up on them.

### Exam breakdown:

According to the College Board website, the Calculus CLEP is broken down as follows:

50% Differential Calculus Integral Calculus Limits

### Areas of Study

Hold up! Check out the official list of topics for this exam which you can find here. It's in PDF form and they have some examples that I couldn't list below because

1) I still haven't figured out how type fractions and

2) I have no idea what they are so I'm loathe to mistype something.

The examples may or may not help you out. I just don't know enough about Calculus to know for sure, so I'm including them here.

#### Differential Calculus(50% of the Calculus CLEP )

The Derivative

• Definitions of the derivative
• Derivatives of elementary functions
• Derivatives of sums, products, and quotients to include tan x and cot x
• Derivative of a composite function - chain rule
• Implicit differentiation
• Derivative of the inverse of a function to include arc sin x and arc tan x
• Higher order derivatives
• The corresponding characteristics of graphs of f, f', and f"
• Statement of the Mean Value Theorem with applications and graphical illustrations
• Relation between differentiability and continuity
• The use of L’Hospital’s Rule - both quotient and indeterminate forms

Applications of the Derivative

• Slope of a curve at a point
• Tangent lines and linear approximation
• Curve sketching
• Increasing and decreasing functions
• Tangent lines and linear approximation
• Relative and absolute maximum and minimum points
• Concavity
• Points of inflection
• Extreme value problems
• Velocity and acceleration of a particle moving along a line
• Average and instantaneous rates of change
• Related rates of change

#### Integral Calculus(40% of the Calculus CLEP )

Antiderivatives and Techniques of Integration

• The concept of antiderivatives
• Basic integration formulas
• Integration by substitution (the use of identities and change of variable)

Applications of Antiderivatives

• Distance and velocity from acceleration with initial conditions
• Solutions of y' = ky and applications to growth and decay

The Definite Integral

• Definition of the definite integral as the limit of a sequence of Riemann sums and approximations of the definite integral using areas of rectangles (that hurt my head just typing it)
• Properties of the definite integral
• The Fundamental Theorem

Applications of the Definite Integral

• Average value of a function on an interval
• Area - to include the area between curves
• Other (such as - accumulated change from a rate of change)

#### Limits(10% of the Calculus CLEP )

• Statement of properties such as - Limit of a constant, Sum, Product, or Quotient
• Limit calculations to include limits involving infinity

### Recommended Free Study Resources

I wish there were as many free resource for Microeconomics as there are for the Calculus CLEP! See any of the below free study resources to find the above topics. All of them are worth the time to review. Between the resources in the below list, you should be covered for the material on this exam.

Calculus.org - Simple, but a great resource with links to everything you could want to know about Calculus.

HippoCampus - Calculus

MIT - Calculus - Fall 2005

Koofers - Calculus I, II, and III videos

Northern State University Online Tutorials

Shoreline Community College - Math videos including calculus

Math Tools

Wolfram Math World - Calculus

### Recommended bargain-priced study resources

Always check your library first! You may be able to find some of these for free. You don't have to buy the officially recommended resources all the time. If you're the type of person that prefers to study from a textbook source however, then please see below.

I'm going completely off recommendations on this topic because I haven't used these myself.

Calculus for Dummies - Just my style of book on this subject! The fact that it has 4.5 stars after 72 reviews doesn't hurt either!

Calculus Workbook For Dummies (Dummies Series) - A companion book to the one above. Walks you through some of the more common problems contained within.

CLEP Calculus w/ CD-ROM (REA) - Just in case you are more comfortable studying with REA, though I'd still probably go with the above two based solely on reviews.

The Standard Deviants - Calculus DVD Pack (Conquer Calculus 1 & 2) - A video option for the Calculus CLEP takers.

The Calculus 1 & 2 Tutor - 2 DVD Set! - 8 Hour Course! - Learn By Examples! - Another video study option that seems to be getting rave reviews. Eight hours of Calculus. Good Lord!

InstantCert Academy - Calculus Thread - It's in the free portion of the forums, so you can take a look at this without being a subscriber. They have some additional resources in there as well. Unfortunately, there's really no specific exam feedback for the Calculus CLEP. Be the first to start the thread!

If you don't know what InstantCert is, then click here for the scoop as well as a discount code: **InstantCert Academy**

You'll find an InstantCert link for every exam here if that gives you an idea of the amount of information they have available. It's an outstanding resource.

### Closing Thoughts

I shouldn't have a headache from just describing math.. right? There seems to be a ton of great resources out there for the Calculus CLEP if you're already reasonably familiar with it. If you're looking for an easier place to start, perhaps you should give the free Precalculus CLEP study guide a try. Either way, my hat's off to you for giving this one a shot. I have no doubt that with the proper study, you can do it!

Best of luck!

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