PreCalculus CLEP

[Tog]

Hello, everyone. I've been studying for the CLEP Precalculus test.

So far, I've read both "PreCalculus Demystified" and "The Complete Idiot's Guide to PreCalculus." I've also finished quite a bit of REA's "Problem Solvers" (this is a different--and much better--book than the REA CLEP Guide).

Even after completing these books, and feeling comfortable with the material, the official CLEP guide for PreCalculus seems really difficult to me. This includes both the REA guide and the official one that you download directly from the CLEP website. The REA one, in particular, is just mind-blowing hard to me, and the author's explanations are vague.

I have been doing almost nothing but studying for months, so this is getting frustrating. I just want this to be over with, but I am hesitant to take the exam because the study guide just seems to be so difficult, so I am concerned that I am not ready.

I actually postponed the test about 6 weeks ago after being stumped by the official study guide to give myself a chance to "shore up" for the test. After six weeks of additional, *hard*, studying I would say that I understand things a *little* bit better, but at least half of the official material looks like a different subject to me. When I look at the practice tests, I feel like I studied Pre-Algebra, but I am being tested on Algebra II.

I realize that "The Complete Idiot's Guide to PreCalculus" is not the most rigorous book out there, but after reading both that and "PreCalculus Demystified," along with much of the REA "Problem Solvers" book and being comfortable with both, I feel like I should have no problem with most of the questions from the official study guides, but I am really finding a lot of them difficult. Every now and then, the problems seem reasonably easy, but at least a third of them seem extremely difficult, to the point where I can't figure them out even after seeing what the correct answer is and really thinking hard about it.

Has anyone else taken the Precalculus CLEP test here? Did you have this experience? Would you suggest I go ahead and take it, or should I wait until I am completely comfortable with the study guides. I'm just concerned that I will never be completely comfortable with them, and to be honest, I can't really take much more of this.

Nearly ten years ago, I took the College Algebra CLEP test and passed. I remember it being a real nail-biter though. I was sure I had failed until I got my score. I'm worried that I won't get that lucky again.

[Mian]

Perhaps you should try ALEKS instead of doing the CLEP? It would be cheaper too if you could complete it within a couple months.

[Bunbu]

Or you could take the Straighterline class. Judging by the time you've already spent preparing for the CLEP you should be able to pass SL in a couple of weeks. Best thing: Open book exams!

[irnbru]

Which topics or types of questions are you currently having trouble with? If they are challenging at the moment, how much of the syllabus do those topics account for? If you are looking for alternatives, then ALEKS is probably the first port of call. I would recommend you maybe keep ALEKS as a back up option, depending on how your test prep is coming.

If it helps, remember that for a lot of the humanities and social science tests, a person might have a 'gut feeling' for an answer, or have to think a little bit about eliminating options. With the maths tests, a student mostly has to work through a problem, come to a solution, then see if it's one of the options listed. You might not be doing as badly as you feel right now.

[LaceyLady]

It might be an idea to look into ALEKS, if your school accepts ACE credits. Since you have studied a lot already, you should be able to complete the course quickly, maybe even getting 70% on the first or second assessment. And it only costs $20 per month.

Otherwise you could just try the CLEP. Work on the parts that you are having trouble with, then take the test and get it over with. If you studied three books and are comfortable with the material and able to solve all the problems (quickly), you should be able to pass - but don't take my word for it. I have not taken CLEP Precalculus so I cannot offer any advice on it. I passed CLEP College Algebra after studying "College Algebra Demystified" for a little over two months. Then I got discouraged halfway through studying Precalculus and decided to take a course instead.

[Tog]

OK. Here's an example from the study guide:



The answer is 5.28.

After working with some others (people who are engineers, who have taken 3 semesters of Calculus I might add) on this, we've been able figure out that the reason that the answer is 5.28 is because of this:



However, we cannot figure this out how one would determine this mathematically.

To me, this seems awfully difficult and abstract for a Precalculus test. I remember taking Trigonometry in high school, and while I realize that this is not high school anymore, this just seems really out there to me.

[Tog]

I should note that 5.28 = 2pi - 1, so there is a mathematical basis, but I don't know how you would know to get to that point. It seems like a stretch to go from reading that problem and saying "hey I should just add or subtract multiples of pi until I find something that fits into the stated domain"

I guess I'm rambling, but that just seems like a hard question to me.

[Tog]

OK, I actually think I get it now.

Basically, cosine repeats itself every 2pi, so just add or subtract 2pi to whatever the you are given, depending on the domain.

[Tog]

Actually, I take that back. If you add 1 to 2pi, you end up with 7.28, so I guess it's not so clear.

Pardon my rambling.

[irnbru]

Okie, this is a trig question that requires you to know which quadrants are positive for which of the three basic (and the three reciprocal) functions over the period theta = 0 to 2*pi.

You've probably seen the mneumonic ASTC (All Silly Teachers Can) which states that (going anticlockwise) in the first quadrant (0 to pi/2), All basic trig functions are positive. In the second quadrant (pi/2 to pi) only the Sine function is positive, in the third quadrant (pi to 3pi/4) only the Tangent function is positive and in the fourth quadrant (3pi/4 to 2pi) only the Cosine function is positive.

Since we're dealing with the Cosine function, you know it looks like a 'U' anyway; over the four quadrants it is positive to start, then dips under the theta axis and is negative, negative, then comes back up again and is positive.

The question is an equation you have to solve. Remember that theta is just another variable, probably more familiar to you if you think of it as being an 'x'. Cosine is just a function, you can think of it as a 'y' function. The cos(theta)=cos(1) equation is basically y(x)=y(1) but we have to solve for the particular range pi to 2pi.

The cosine function is symmetrical about pi radians (halfway point). We know that cos(1) is less than pi/2 and falls in the first quadrant (positive). So, if we are trying to find the same value of theta somewhere in the third or fourth quadrant, we know it also needs to be in a positive quadrant (this means it will be in the fourth quadrant) and look, the function is symmetrical anyway.

Knowing the cosine function is symmetrical here is probably the easiest way to get to the right answer. The cosine function passes through every horizontal line between y=-1 and y=1 twice between theta= 0 and 2pi - there are definitely two solutions. The first solution is at a distance of 1 radian from the start, the second solution is just back a distance of 1 radian from the 2pi hurdle. 2pi-1 is the right answer.

Calculators are annoying bits of kit and get in the way of a lot of maths. They usually only give you the value of a trigonometric function in the first quadrant. In order to solve this problem, we needed to know the behaviour of the cosine function and how to solve an equation. This gives us the right value of theta (or x, or input) we want in the range we have to find it, i.e. it produces same 'height' later on in the function - but between pi and 2pi. In fact, the same 'height' (or 'y', or output) is hit over and over at cos(1+2kpi) and cos((2pi-1)+2kpi) for every integer k.

Hope this helps

edit (short version): You need to know what the trig functions look like/how they behave. Cos function is symmetrical so the first answer is forward 1 and the second answer is back 1. Unit of counting is radian!