CLEP Calculus

[calculess]

Sorry to bump such an old thread, but this has some really good info, and like another poster, I also felt it was better to add to this one than create a new one. I took the Calculus CLEP within the last few days and wanted to share my 2 cents on it. Info from this thread/forum helped me in prepping for it, so hopefully my info can also be of some contribution.

Just some quick background info about me though. I actually took Calculus I almost 15 years ago in HS and earned a "C", so to say my Calc skills were rusty would be a major understatement. I was even shakier with my Trig, so I knew passing the CLEP would be a challenge. For the record, I consider me to be of slightly average intelligence: no more, no less. This assessment is based on my SATs and academic record. So basically what I'm saying is, I'm not a genius nor math whiz, so if I can pass the CLEP (I earned a 74), then anyone can with the right preparation.

Now with regard to the preparation...

1. Several people in this thread have mentioned the need to do as many problems as possible. This is probably the most critical aspect of learning Calc, and it's one I neglected back in HS. However, the most efficient way to go about this for this purpose is NOT to do every random problem in a textbook (not saying you CAN'T succeed with this approach, but it's not the most efficient for passing the CLEP IMO).

It seems like all CLEP questions follow a particular mold, so you want to spend your time doing problems that are posed in a similar fashion to the questions on the CLEP. For this, the REA book and AP prep books are invaluable. I used "Multiple Choice Questions in Preparation for the AP Calculus (AB) Examination" by David Lederman (which has 240 questions with solution key), but I'm sure there are plenty of other similar resources.
Between the REA book, the Lederman book, and the sample exam that you buy for 10 bucks from College Board (*cough* price gouging), you should have almost 400 CLEP-style questions at your disposal. DO them all (multiple times), and UNDERSTAND them all.

Keep in mind though, based on the REA book and the particular CLEP exam I took, things like volumes of revolution, Newton's Method, and integration by parts that are on the AB AP don't seem like they're on the CLEP. By the time you're prepped enough to pass the CLEP though, these kinds of problems should be very trivial to solve anyway, but it's still one less thing you have to concentrate on.

2. The CLEP (and AP) focuses on the underlying principles of Calculus. Whether you can find a derivative or integral of some explicit function in some mechanical fashion is NOT what the CLEP tests you on (you could probably teach a 10-YO how to mechanically find a derivative or integral of polynomials within 5 minutes). At most, there were probably 3-4 questions on my particular CLEP that were this quick/easy, and they were probably put there as "freebie"/"warm-up" points.

The CLEP (and AP) seems to put tons of emphasis on the notion of continuity, the Mean Value Theorem, the limit definitions of derivatives, the relationship between f(x)/f'(x)/f''(x), and the Fundamental Theorem of Calculus. The funny thing about a lot of these theorems/concepts is that they seem to emphasize things that are mind-numbingly obvious, but you need to understand (mathematically) what they're actually saying and be able apply them mathematically, which aren't so trivial to do without practice.

Here's an example of a question on the actual CLEP I took (numbers might be different though):

------------------

Given f(x) below on [0, (pi/2)], find all x values, if any, where f(x) is discontinuous:

f(x) = {
0 when x < 0;
sin(x) when 0 <= x < (pi/4);
cos(x) when (pi/4) <= x < (pi/2);
1 when x >= (pi/2)
}

-------------------

This was on a non-calculator section btw. Obviously you have to know your basic sin(x) and cos(x) values (more on that below), but it also helps if you know what the exact requirements for continuity at a point are and how to evaluate a limit from the left and right.

As mentioned, the application of the Mean Value Theorem is another concept the CLEP I took seemed to hammer away on. Intuitively, the MVT says at some point in an interval containing a continuous curve, the instantaneous rate of change (i.e.; derivative) will equal (at least once) the average rate of change. Mathematically, it says the tangent line at some point will equal (at least once) the secant line (drawn from the endpoints of the interval). Understand the MVT intuitively, graphically, and formulaically because all three forms will probably show up on the exam (as in my case).

Also, a couple Fundamental Theorem of Calculus problems will probably show up on your exam, too, and they'll probably be posed in this fashion (with actual symbols though lol):

-----------------------------

Evaluate:

(d/dx)(integral of some nasty function from 0 to x)

or

(d/dx)(integral of some nasty function from x to 0)

or

(d/dx)(integral of some nasty function from 0 to (1 + x^3))

or

(integral from a to b of ((d/dx) of some nasty function))

----------------------

I think I had the second example on my particular exam (answer is negative of said nasty function in terms of x). The third requires the (implicit) use of the chain rule due to the (1 + x^3) term. There was actually a really tricky one that popped up on my exam, but I can't recall it right now. I'll update if I remember.

You should also be very familiar with how to split up definite integrals. Another problem on my exam:

--------------------------------------------

Given:

integral of f(x) from 0 to 9 = 12
integral of f(x) from 0 to 5 = 8
integral of f(x) from 2 to 9 = 6

Find integral of f(x) from 2 to 5.

--------------------------------------------

Also, you need to be very proficient with looking at graphs of f(x), f'(x), or f"(x), and determining what's going on with the others. For example: "f'(x) (not f"(x)) is shown with points A, B, C, D, and E. Find all points of concavity."

Hmm, what else? Know L'Hopital's Rule as I had a couple of those on my exam. Also on my exam, regarding "word" problems: 1 related rates prob involving volume/radius of a sphere (very standard stuff), 1 exponential decay prob involving a leaking oil tanker (lol), and 1 frustrating (at the time) volume max prob, which is identical to the following but with different numbers:

Math Forum - Ask Dr. Math

3. Know your basic trig. Know what sin(x) and cos(x) look like graphically. Know that tan(x) is sin(x)/cos(x), sec(x) is 1/cos(x), etc. Know that sin(x)^2 + cos(x)^2 = 1. Also know the values of sin(x), cos(x), and tan(x) for [0, (pi/2)], and know their zeros and periods. The CLEP WILL expect you to know this stuff.

4. Know ln (natural log) like the back of your hand. Know that ln(a*b) = lna + lnb. Know that ln(a/b) = lna - lnb. Know that ln(a^b) = b*lna. Know the derivative and integrals of a^x are (a^x)*lna and (a^x)/lna, respectively. These were ALL on my particular exam. There were a few problems where the answer was in a specific form (e.g.; 2ln2 instead of ln4), so know your ln properties.

5. You have approximately 2 minutes per question. There are 44 questions on my exam, and my particular breakdown was 27 in the non-calculator part and 17 in the calculator part (not sure if they're all the same). Note that only like 5 problems actually required me to use a calculator on my particular exam, and out of those, I believe only two required me to graph anything (the others required resolving some nasty numbers to match an answer).

6. IMO the actual CLEP exam was quite a bit faster to work through (though not necessarily easier) than the practice problems found in the REA book and the sample exam from College Board. (The actual CLEP was way easier than the AP practice probs though.)

Even though I routinely struggled to finish the practice exams in any of the books under the hour and a half time constraint (even when it was the third or fourth time I was doing the same exam lol), on the actual CLEP I finished the first part with about 7 minutes to spare, and the second part with about 10 minutes to spare.

7. With regard to #5 and #6, as frustrating as it may be, understand that the CLEP is measuring your test-taking prowess, as well as your Calculus knowledge. It makes no allowances for stupid arithmetic or transcription mistakes, routinely including likely "benign" (i.e.; non-Calculus-related) wrong answers as a choice.

That's why I think #1 (not only practicing, but practicing the "right" kind of problems) is so important. In order to minimize the likelihood of making silly mistakes (and maximize the likelihood of you getting to all the questions) on the actual exam, the whole process needs to become almost visceral in nature, and I think you can get there through familiarity with the form of the questions. In my honest opinion, you really don't have time to "think", or even read, on the CLEP. If you're not scribbling away the instant the new page pops up, you're too slow.

8. Finally, for a layman's explanation of the concepts of Calculus, I highly, highly, highly recommend "The Calculus Lifesaver" by Adrian Banner. The book is 700 pages long, but the way he presents the material appeals to one's common sense and intuition.

Good luck!

P.S. Unfortunately, even after the CLEP exam, you never get to find out which problems you got wrong (nor obviously how to do any you may have struggled with). Actually, you aren't even told how MANY you got wrong... The formula the computer uses to calculate your score is apparently even more secret and convoluted than the formula for the BCS.

[desuu]

Wow! Awesome post, calculess. That's a ton of great information.

I still haven't taken the calculus CLEP, but I'm going to! It's on a laundry lists of exams that are coming up (GRE, language exams, etc.), so it's going to be a busy summer.

If anybody else has recently taken the calculus CLEP exam, please contribute your experience.

edit: I just realized that I posted this thread over two years ago. Not only that, but, in the original post, I wanted to take the exam in two months. I can't believe how quickly time has gone by. Oh well! But, really, I do plan on taking the exam in a few months.

[calclep]

I just passed the calculus CLEP a few hours ago! I scored a 65. I'm so glad I found this forum. This thread specifically is the reason I passed. I would like to contribute by sharing my experience with the CLEP in chronological order so that I cover the details of my experience instead of repeating information that is found easily on the CollegeBoard website. I am sure someone who is looking to take the Calculus Clep will appreciate the small details, and perhaps relate to some of them.

BACKGROUND WITH CLEP:

I was introduced to the CLEP 5 months ago. I decided to switch from business to engineering, and suddenly the "business math" courses I was enrolled in were worthless. I knew bits and pieces of many subjects, but there was no way my college would let me take on the course load I needed to get back on track, and it was too late to sign up for classes towards a new major. It looked like I was stuck until summer. Fortunately the CLEP offered a solution, and I was thrilled to discover that I could use what I had learned in my business math courses for quick and cheap credit towards my new major!

Soon after learning about CLEP I took the College Algebra (scored a 70) and Pre-calculus (scored a 66) CLEP tests without much trouble. I haven't been out of high school very long and I only needed a quick review to pass. Calculus was a different story, and I had never even heard of a "derivative" until 3 months ago. I had signed up for an online self-paced "business calculus" course which basically means "calculus without trigonometry". I learned some of the material, but I would need to learn a lot on my own.

Through acquainting myself with the world of "self-study", I discovered this thread. The possibility of getting credit through ACE/ALEKS/StraighterLine went out the window the first time I asked my advisor about it, and got a blank stare, followed by a confused look from the head of advising, and ending with an unfulfilled promise to "look into it" and get back to me. CLEP was the ideal method.


STUDYING:

I was not familiar with studying for CLEP. All I knew was that if you had taken a class before then you should be able to pass the test. I tried Thinkwell Calculus for 2 weeks, but I felt that it was not the fastest method to passing CLEP if you've already been exposed to some calculus. If you are new to calculus, be prepared for lectures by a professor who single-handedly proves that math isn't all that bad. He can make calculus video lectures almost fun to watch, and that's saying something.

My major weak point was trig, so I got a subscription to ALEKS for trigonometry. It was nice and tedious, which was perfect for learning the basics of a subject I had avoided for so long. Its a slow but effective way to prepare for calculus if you are lacking in a specific area.

REA STUDY GUIDE

Last week I took the advice of the geniuses in this thread and bought the "REA CLEP Calculus" study guide w/CD. I cant begin to describe how helpful it was. I hardly studied the book, honestly, I stuck almost exclusively to the practice tests except for a few references to learn more about integrals, "trapezoidal approximation of an integral" and Riemann sums since I had not learned them. This guide is essential because the questions are similar to the CLEP, and it gives you an in-depth understanding of the CLEP topics with functions that are "meatier" than the ones I encountered on the actual test. It is more complicated, and that's a good thing.

My study plan consisted of completing the first practice test, viewing my results, and working to understand the explanations for the problems I missed. Once I felt comfortable with the explanations, I took the test again. I concluded with the second practice test last night, and scored a 60, but I did not review the test due to time constraints. It is important to note that I never managed to complete either practice test in 1.5 hours. I tend to get stuck on a problem and instead of moving to the next one, I insist on at least getting an answer that matches one of the available choices. Needless to say, that behavior didn't help on the actual CLEP test.

COLLEGEBOARD CALCULUS EXAM GUIDE

The next brilliant piece of advice I received was to get the "CLEP Calculus Exam Guide" from CollegeBoard. I worked through the practice questions before getting the REA guide, and took it again after I finished both REA practice tests. The practice questions were confusing at first, but after being exposed to the difficulty level of REA questions, I did better with a raw score of 25. Early this morning I did last minute prep by working through the ones I missed until I got the correct answer, which turned out to be very helpful for the actual test.

This guide is extremely useful because of how similar the questions are to the problems on the actual CLEP test. One thing I found surprising is that I thought I was doing well while working through it, but I ended up missing many questions that were simple once I understood why the answer key was right. Many of the questions in the guide were "tricky" instead of "difficult", and it was a very accurate guide to the kinds of questions that were on the CLEP test. The questions are similar to the test because they focus on the concepts of derivatives and integrals, and the difficulty is closer to the CLEP test than the REA practice tests.


TEST DAY:

I don't recommend cramming, but I mastered most of the relevant CLEP calculus test topics only hours before the exam. reviewing the CollegeBoard exam guide in the morning was very useful. To me it seemed like learning calculus is very slow to begin with, but as things fall into place you can master the topics more quickly. The morning study session was probably the most productive study session in preparation for the test.

THE TEST

I spent an unusual amount of time staring at the simple instructions on how to answer a question so that I could put off the moment when the clock started ticking down. I read that some of you had run into issues with time, and I was getting ready to answer the questions as quickly as possible.

SECTION 1:
After that delay I was thrilled to see how easy the first question was. In fact, the first few questions were all fairly simple. I don't know if the CLEP is designed this way, but I ended up spending the full 2 minutes for the first few easy questions to check and double check my answer to be sure that I would get credit for those (REA gave me the idea that if i got a raw score of 30, I would get the scaled 60 I was aiming for). I should have saved those precious seconds for the later questions, because they gradually got harder.

I ended up skimming through the last 5 questions and making a few guesses. This was the first CLEP where I actually went ahead of the question I was on to make sure I didn't run out of time and have to guess on a question I knew how to solve. I felt I did reasonably well on this section. Based on the ones I solved I would say its even easier than the CollegeBoard Exam Guide

SECTION 2:
The calculator section focused heavily on trig. I was surprised to find that 4-5 of the problems want you to use the calculator to evaluate a trig function for a rounded decimal answer. I didn't find anything like that in the study guides, so it's lucky I stalled on the instructions to learn how to use the calculator. I only used the calculator once on both the Algebra and Pre-calculus CLEP tests, and that was just to check an answer. If you aren't familiar with the CLEP calculator, learn it!

Again I ran into issues with time, but on this section it was because I was stubborn on 2 questions I wasn't sure about, and spent way too long on them when I should have moved on.

After that was the moment of truth. I thought I did well enough while taking the test, but CLEP just LOVES to make you nervous, with a long drawn out process. They even got me on the College Algebra CLEP, when I was sure I did great. The result of the hours you spent studying and the money you just spent to do calculus problems for 90 minutes of your life is only a mouse click away(and then another mouse click away because they want you to be sure). Its a great feeling when it pays off.


CONCLUSION

I realized 2 days ago that I didn't have much time until my testing appointment, and so I accepted a few flaws such as my less-than-perfect grasp of "log", "ln", and "e". I simply practiced how to take the derivatives/anti-derivatives of simple functions using the chain rule, quotient rule, and product rule. It worked well because the CLEP test does not ask you to manipulate one huge complicated function for hours. It tests you over straight forward concepts that can be answered in about 2 minutes.

This past week I spent more of my free time doing calculus problems than I would recommend for any mentally sound person. Ideally I would have taken more time but it was important to test today so that I could take higher math classes over the summer. My biggest fault during my independent study is the huge chunks of time I wasted by missing a problem, refusing to look up how to solve that problem, and hammering away at it until I got the correct answer.

I hope this serves as a reference for someone who is looking at the calculus CLEP to determine their readiness, and give them an idea of what to expect.

Thanks!

[NAP]

Great job! Thank you so much for the feedback!

[Instantaneous]

Hi all!

Yes, this forum is A-mazing! Thank you for all who have posted here because it was all very, very helpful. Seeing that it is becoming some sort of new fad, I myself just passed the CLEP Calculus as well! About one week ago!

Score: 60
Time spent studying: Less than 2 months.

Resources used:
1. Calculus for Dummies
2. REA's Best Test Preparation for the CLEP Calculus
3. CollegeBoard's Official CLEP Calculus Study Guide.

First off, I just want to say: folks, if I can pass this thing, anyone can. I really mean that. Less than two months ago, I was literally at square one. I didn't even know what a limit or a derivative was. This test is not as hard as its reputation has made it seem (as long as you study, study, study).

So here's my story:
In the first month and a half I studied for a few hours or less a day. For the last week or so, I studied for 6-8 hours a day.

Phase I: Calculus for Dummies
I went to the nearest public library and checked out "Calculus for Dummies" by Mark Ryan. For a few weeks, I just read through this book like it was no one's business. I highlighted and wrote things down I thought were important. This book was important for me because it helped me to understand the concepts behind Calculus. The big ideas behind limits, derivatives, and integrals as well as how they are all connected together. (One problem with this book is that you need to skip around because not all of the material in the book is on the CLEP Calculus. For example, integration by parts, infinite series, volumes of weird solids, etc.) However, the "cheat sheet" on the inside cover of this book was extremely helpful. I used this "cheat sheet" to make flashcards of all the derivative and integral rules.

Phase II: REA's Best Test Preparation for the CLEP Calculus
In my personal opinion, this was by far the BEST and most valuable book when it comes to the CLEP Calculus. I honestly think that if you were to study this book alone then you could pass the CLEP Calculus. So it is safe to say that if you know this book inside and out, you will pass.
Note: If it is not in this REA book, it won't be on the test.
For this book, I recommend buying it because you want to have it everywhere you go so that if you have a moment of free time then you can study. I read through this book and highlighted all the concepts and facts I felt were the "big ideas" and "small details.' I did the exercises over and over again. You must read the explanations for the answers to the questions/exercises. [/B] This is probably the most important thing to do. You need to know all the details as to why the answer is what it is. I promise. The most wonderful thing about the REA CLEP Calculus is its practice tests. My advice is to buy the book that includes the CD's. Keep in mind, even though the book itself tells you otherwise, I am telling you that you should read through the entire book and do all the exercises multiple times before you even look at the practice tests. Don't use your notes when you do the practice tests. Take them as if they are real, timed and everything. Remember, after you finish each of them, look at the explanations to the answers!!! From what I can remember, the REA practice tests are [I]EXTREMELY similar to the real CLEP Calculus test. On the first REA practice test I took, I got a 60. On the second REA practice test I took, I got a 58. On the actual CLEP Calculus I got a 60. How crazy is that?

Phase III: CollegeBoard's Official CLEP Calculus Study Guide
The 50 sample questions on this thing is very helpful. But don't waste your $10 bucks. Go to your nearest Borders or Barnes and Noble and just use their copy of the CollegeBoard's huge book for CLEP preparation. And my advice here is to answer the 50 sample questions as if they were a test. Time yourself 90 minutes and answer all 50 sample questions (or as many as you can). Don't use your notes.

Phase IV: The actual CLEP Calculus Test
My biggest problem on the actual test was probably time. On the overall test, I probably guessed on about 10 out of the 45 questions. But on the 35 that I actually answered, I made sure that I had the right answer. So you pretty much have to make a choice: Do you want to race through the test trying to answer all of them right and risk making dumb mistakes? Or do you want to take your time on certain ones that you know that you can do but then run out of time? I obviously chose the second option. I wanted to make sure that I was going to pass. So on the questions I was confident in, I took my time to make sure that I didn't make any mistakes.

The actually content of the test is a bit blurry to me now. I remember there were only about 2-4 optimization/related rates problems on the whole test (both sections). I didn't even try and answer a single one. Those problems take me the longest so I just guessed on them and moved on to easier questions. The test was big on trigonometry so know all your identities. All the questions on the actual test were very, very, very similar to the REA Practice Tests and CollegeBoard's Official Guide sample questions. Almost identical, seriously! Make sure to download the free trial version of the ETS online graphing calculator from the Collegeboard website and get familiar with it. Again, the overall test was not rocket science; that is for dang sure.

Here are some other resources that might help you:
Khan Academy
Calculus-Help.com: Survive calculus class! - Tutorials for the Calculus Phobe (Limits through Differentiation)
HippoCampus Calculus - AP Calculus AB I - Homework Help
CLEP Calculus Tests
http://www.xtremepapers.me/CLEP/CLEP%20C...0Guide.pdf

If you are even thinking about taking the CLEP Calculus, I say Do it. You have nothing to lose because I really believe you can pass it. Email me if you have any other questions or if I can help you in any other way: Rollerhcky4life@hotmail.com

You guys are all rock-stars. Don't ever give up on your dreams. :imwithstupid:

[letmeout!]

WOW. . . I am so happy that I came across this thread today, seeing that I am scheduled to take the CLEP Calculus exam in less than 48 hours!! Special thanks to calculess, clepcal and Instantaneous for the detailed descriptions of your experiences. While I have found each individual post to be resourceful, I am not sure I am in the "same boat" as any of you.
In short, I should have graduated from a State University on May 13, 2011 with my B.S. - Construction Mgmt degree (2nd Bachelor's actually, I have a B.B.A. from a different State University in a neighboring state) but unfortunately, my department screwed me (we will not go there now...maybe later) and in order to still get my degree by mail next month, they are "letting" me take the CLEP Calculus exam to receive credit that I lack. And by "lack", I mean lack the 3 hour credit somehow with a grand total of 200+ credit hours under my belt. Whatev.
So, here's the deal>>> I took Calculus this last semester, but ended up dropping right at the very last moment because I thought a petition for another class would work, and I wasn't really "in it to win it", if ya know what I mean? Thus, my knowledge of Calculus is pretty fresh, but my question for all of you is this:

[COLOR="Red"]"HOW SAAVY IN PRE-CAL, ALGEBRA, TRIG, ETC. ARE ALL OF YOU CLEP CALCULUS TESTERS THAT HAVE PASSED WITH A 60?
[/COLOR]

Note: I did not take Calculs in High School & obviously I didn't need Cal for my 1st B.B.A. - Computer Info Systems.

I ask this question because my experience thus far with Calculus has not been the Calculus. My problem is that my algebra is VERY rusty, and my trig is rusty too but not as much as the algebra, functions, etc. I have always been what I would refer to as an "A's & B's Math Student" but algebra isn't like learning to "ride a bike". . .learn it once and you can pick it right back up years later. Well, at least not for me.

I find myself sitting here doing Calculus problems, and constantly wasting time googling or referencing an old book on basic algebra, pre-cal skills, so any advice regarding this particular issue in reference to the actual CLEP exam would be EXTREMELY helpful and much appreciated since I am running out of time.

I am SO sick of fighting this University on transfer credits, Post-Baccalaureate policies/procedures, etc. and I just want to be DONE!! Although I said it before, I will say it again: "Never planning on going back to school after this!!!" B.B.A. Degree + B.S. Degree = LET ME OUT!

[valsacar]

Nice, and for those studying for it MIT has some good resources on their Open Courseware page!

[Instantaneous]

Yo "letmeout!"

Sorry for the late reply but I haven't looked at the forum until now. If you are rusty on your pre-caclulus, algebra, etc. the Calculus for Dummies book I mentioned is perfect for you! The entire beginning of the book is dedicated to catching you up with all that old stuff.

But if you have already taken the test, then this post is not worth a crap. Haha. Did you take it yet? How did you do?

[bigticket]

Just passed with 60. Thanks all for their valuable feedback/inputs.

I did complete all ALEKS course earlier hence Calculus was not that difficult. I must have studied for approx. 60 hours.

Here is what I referred.
1) Cracking AP <-- I found this very helpful & relied totally on it.
2) REA <-- Practice test is similar to actual test.

I found REA test little harder and couldn’t complete in stipulated time but on actual exam I could complete both the sections with 10 mins to spare.

Next is Discrete Mathematics.

[Hypa-Link]

Wow this thread is very informative. I didn't pass Calc last semester but spent the whole summer studying, now I'm in the "know what is gonna be on the test phase" because that's how they always get you. I'll be taking mine on Saturday.

So what is the lowest score to pass and what is the maximum?