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College Mathematics CLEP
Free Study Guide
Name of Exam: College Mathematics CLEP
Number of Questions: 60
Time Limit: 90 Minutes
ACE Recommended Passing Score: 50
Practice Test Available?: Yes - Click here
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 : 3
(One being the easiest, and five being the hardest)
Alternatives: ALEKS Intermediate Algebra
Exam Description:
The College Mathematics CLEP covers the knowledge you would learn in college without having any advanced mathematics requirements for your degree. It will test you on Functions and their graphs, equations, real number system, probability, statistics (of the easy sort) and data analysis.
The College Mathematics CLEP will touch on Logarithms, Algebra, and Geometry, but these do not make up the majority of the exam.
Personal Thoughts:
This is the CLEP that I always recommend people to start with if they haven't touched math in a while. Most of the test covers material that you probably learned in high school. If math usually makes you break into cold sweats (just like me) then it's a great way to get your feet wet. You will probably need to review a few of the topic on this exam to re-famaliarize yourself with the terminology. We'll cover all that below.
Something to take note of - The College Mathematics CLEP is worth six credits, but most colleges will not count this towards a math requirement on a business degree. If your degree has a "Quantitative Analysis" or "College Algebra" requirement, then you'll need to check with your advisor on whether these credits will apply. If they don't, then usually these six credits will instead be applied towards your general electives or social sciences requirements.
Six elective credits is still six credits towards a degree, and this exam is a good practice run for the more intensive College Algebra CLEP. Let's look at what to expect on the College Mathematics CLEP.
Exam breakdown:
According to the College Board website, the College Mathematics CLEP exam is broken down as follows:
Types of questions:
| 50% | Solving the given, routine problems |
|---|---|
| 50% | Solving non-routine problems that require you to understand concepts as well as their application. (Multi-step problems) |
What those questions will cover:
| 25% | Probability and Statistics |
|---|---|
| 20% | Functions and their Graphs |
| 20% | Real Number System |
| 15% | Additional Algebra and Geometry topics |
| 10% | Logic |
| 10% | Sets |
Areas of Study
I'm still experimenting with the best way to cover the needed material, so we're going to try something new for this study guide. I'll break down the percentages above with the topics that fall under each category. This should allow you to decide what you need help with, and only study those areas in which you feel a little weak. Less wading through masses of resources, and more targeted studying.
If you like this style, please let me know via the "Contact Us" form. The end goal here is to give you the information in the most helpful manner.
Alright, here we go:
Probabilities and Statistics
(25% of the College Mathematics CLEP)
- Permutations and Combinations (Counting Problems) - This isn't difficult, just know the formulas and when to apply each. Remember- Permutations are used when the order of the items (groups, people, chairs, whatever) matters. Combinations are used when you just want to know how many different ways of doing something there are.
- Probability - You'll probably get a few of these on the exam, so know how to get the answers. The sample questions in the tutorial match closely with what I saw on my own CLEP. Know this and you'll have the probability questions beat.
- Mean, Median, Mode, and Range - Easy stuff here, just remember:
- Mean = Average (Sum of numbers divided by amount of numbers)
- Median = The middle number once they've been put in numerical order. Example - 1, 2, 3, 4, 5 The Median would be "3" (See the link for what to do for even amounts of numbers)
- Mode = Number that occurs most often in the list
- Range = Difference between largest and smallest values (Highest number - lowest number = Range)
- Standard Deviation - This is the simplest link I could find to describe Standard Deviation and it still sounds like gibberish to me. It truly isn't that complicated.
The steps for finding the Standard Deviation are:
- Get the Mean (Average) of the number set (list of numbers)
- Subtract each number in the set from the Mean (#1 minus Average, #2 minus Average, etc)
- Square each of those numbers
- Average the set of squared numbers (This gets you the Variance)
- Find the square root of the Variance (This gets you the Standard Deviation)
Functions and their Graphs
(20% of the College Mathematics CLEP)
- Properties of Functions - This is the most straightforward lesson on functions and their graphs that I've found. CoolMath is another site that tries a more elementary style of teaching. Use whichever fits your learning style more closely.
- Graphing Functions Part 1 - This is the best list of the most common graphs I've seen.
- Graphing Functions Part 2
- Domain and Range - Covers both topics well. You can find another tutorial about Domain and Range **Here**
- Composition of Functions
- Inverse Functions - I only had one or two questions that covered this on my version of the College Mathematics CLEP.
Real Number System
(20% of the College Mathematics CLEP)
- Prime and composite numbers - Ah, back to the simple stuff!
- Factoring
- Rational and Irrational Numbers - You'll probably be asked to identify whether a number is Rational or Irrational.
- Absolute Values
- Open and Closed Intervals - Know that ( , ) is open, [ , ] is closed, and that [ , ) and ( , ] is half-closed. Know how to plug numbers into those brackets when given a line diagram.
Additional Topics from Algebra and Geometry
(15% of the College Mathematics CLEP)
- Complex Numbers - I had perhaps three or four questions dealing with complex numbers. They were all covered in this tutorial.
- Logarithms - Very few questions dealing with logarithms on my exam. As long as you have a general understanding, you should be fine.
- Geometry - Learn these formulas by heart if you don't know them already. You'll probably be asked to find the area/perimeter/volume on at least two or three questions of the College Mathematics CLEP.
- Pythagorean Theorem - My exam didn't ask me for the theorem itself, rather it expected me to use it to answer other problems.
- Solving Linear Equations - Basic algebra. I used CoolMath to refresh myself on this subject as well as to practice Solving Inequalities.
- Fundamental Theorem of Algebra, the Remainder Theorem, and the Factor Theorem - I don't remember any of this on my exam and I think I would have remembered if asked, because my head would have exploded soon thereafter. Maybe I was lucky? If you understand this, great. If not, take a look at the links and may you have more luck than I.
Logic
(10% of the College Mathematics CLEP)
- Truth Tables - I had none of these on my own College Mathematics CLEP. Your experience may vary.
- Conjunctions, Disjunctions, Implications, and Negations - Make sure you know the symbols. That's all that was really required of me on my exam. I think I had one question on this? No more than two.
- Conditional Statements - A simple concept that gets complicated very quickly. Don't stress over this, just understand the If..Then basics.
- Converse - The link deals with logic, but the same applies to any equation.
- Inverse
- Contraposition - This link goes over the preceeding two topics as well. Go ahead and read the full article if time allows.
- Hypothesis - Skip down a few sentences to where it talks about the use in mathematical logic.
- Conclusions - It actually links to another place, but it explains conclusions in this article (and you need to understand logical consequence as well).
- Counterexamples - A nice explanation of this term.
Sets
(10% of the College Mathematics CLEP)
- Definition of Sets - Just a quick overview for those not familiar with the concept.
- Unions, Intersections, and Subsets - As always, know the symbols to understand what the exam is asking you.
- How to read Venn Diagrams - Didn't have any of these either on my College Mathematics CLEP, but it's on the Collegeboard list so here we are.
- Cartesian Product - This one's beyond me, so I went with the most detailed source I could find. I didn't get asked anything about this on my own CLEP (Thankfully).
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.
Review for the CLEP General Mathematics (Review for the Clep General Mathematics Examination)
InstantCert Academy - College Mathematics Specific Exam Feedback - Four pages of in-depth study resources and after-action reports. If you're a subscriber, I would check it out.
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
If you read the above Areas of Study and are starting to have second thoughts about the College Mathematics CLEP, just wait a second and hear me out. If I would have read the CollegeBoard website before taking the exam I probably wouldn't have taken it either. I think Collegeboard intentionally tries to make it sound scary.
I'd highly suggest you study everything that I've listed above. If you know all of it walking into the exam, then I can almost certainly guarantee that you'll pass. If you don't know absolutely everything, then that's okay too. Checkmark the ones that you don't know and skip them. Answer all of the ones you do know and then come back. An educated guess is better than no answer at all. After all is said and done, I think you'll be pleasantly surprised at how well you do. After all, I passed. ;)
The College Mathematics CLEP is worth six credits, so it's worth pursuing. Hit those websites/books and make it happen!
Best of luck!
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