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Prerequisites and setbacks

  1. Jul 9, 2005 #1
    I just got back from the University of Florida freshman preview, and I ended up with a schedule that I wasn't quite expecting. I found out that I failed the AP Calculus (got a 2 even though I made a valiant attempt at it and tried as hard as I could) and had the same effect on the University's Calculus Readiness Assessment (which mainly tested precalculus). Now I have to retake MAC 1147 (college precalculus).

    I have to admit that my precalculus skills are rather sketchy. It wasn't exactly my fault though (but I frequently blame myself for it), because halfway through my junior year in high school our precalculus teacher left to Venezuela due to instabilities in their government and he had to fix a few things there. We were left with a substitute who didn't exactly know what to do, and I tried to learn on my own (with limited success).

    Even though I tried as hard as I could, and worked extremely hard in my calculus class (and outside of it) and did well in the class (and in the countywide calculus competition), it still didn't cut it by the time the APs came. I'm one of the few people I know so far who gets excited about topics like calculus, to the point of staying afterschool just to learn more and learning calculus after the AP calculus exam, so this entire series of events came as sort of a crushing blow.

    So now I am set back an entire semester, can't even get on track for a physics major in the first place because of this. Am I making a big deal out of this.. or is this a common thing? I find it difficult to digest because I have always known myself as being extremely dedicated towards my studies, and very enthusiastic about learning topics like math or physics (yet I never really got a decent chance in high school), taken a calc class in high school, only to take a giant step back in college and take precalc....

    I don't know... perhaps the extra practice provided by that class will help build a better foundation so that I won't be struggling as much by the time I get to harder courses like Calc 3, along with some of the other physics classes I will be taking in the future.

    It just feels very discouraging having to take steps backward just because my old high school didn't prepare me enough.

    edit: Should I try to get into the Calculus 1 course, or will I be setting myself up for failure?
    Last edited: Jul 9, 2005
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  3. Jul 9, 2005 #2
    I suggest taking a college pre-calculus course. That will help you hone your skills in algebra and mathematical thinking.
  4. Jul 9, 2005 #3
    There's also the option of boning up on your precalculus skills until the rest of the summer. Do you know what you are weak at in precalc? Do you know why you scored badly on the AP exam? Did you take any practice AP exams beforehand (one of the official ones)? It would be very useful to figure out what the problem is in more detail.
  5. Jul 9, 2005 #4
    many students who get even 5s on the AP Calc exam end up taking Calc 1 and 2 over again anyway. It is not that big of a setback.
  6. Jul 9, 2005 #5

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    Is it too late to jump into a summer session pre-calc class at your university? I was thinking you could do that, and then go back and retake the readiness test and still take Calc 1 in the Fall.
  7. Jul 9, 2005 #6
    If you're willing to put that level of work into things, I would imagine that you would be fine in the long run. You might have to spend an extra semester catching up, but there's nothing wrong with that if you're doing what you enjoy.
  8. Jul 9, 2005 #7


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    In my opinion, you learn the "real" math in College, instead of High School's watered down version (i am especially refering to Calculus), it'll probably be better for you to retake Precalculus, and there's nothing wrong with that.

    I remember when i started the University, i retook Precalculus, and i even thought i knew a lot of what was covered, i ended up learning a few algebra "tricks" i didn't know, which has been useful for the later maths and physics courses, i've already taken. Motai, and if you're really interested i bet the teacher could recommend some books for you to look at, which has a more advanced treatment of algebra and trigonometric (Basicly what Precalculus is all about)
  9. Jul 9, 2005 #8


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    I would say it's a common thing: I've heard many a rant about students being poorly prepared for math classes (I've never taught myself, but when I tutored, some of the problems some people had were downright embarassing), even if they did well in High School.

    If you're really willing to work at it, I don't see why you shouldn't be able to catch up before classes, or even brush up on your algebra and logical thinking skills while you're taking Calc. (But keep in mind that will probably be a lot of work!)
  10. Jul 9, 2005 #9
    I was a math TA at my school, Georgia Tech, this past year, and I was astounded at some of the huge gaps that existed in people taking differential equations, even after a year of college math.

    The lesson you should take from this is that it doesn't matter if you got an A in a class or a C in the class; if you actually LEARNED the stuff in the class, in the long run you're better off. You have to know the stuff in a class to progress, so just don't forget it after final exams are over.
  11. Jul 9, 2005 #10


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    since you say your precalculus skills are weak, i think you should be glad to take precalculus, since otherwise you will be hung out to dry in a setting you are not ready for.

    in my experience (over 26 years teaching college calculus), I have almost never met a high school student, with AP calc or not, who should skip first year college calculus.

    certainly nothing taught in most high schools covers as much ground and in the depth that my calculus course does.

    as to precalculus, if you do not know the addition laws for sin and cos, and the definitions of sin and cos, the meaning of radian measure, and the areas of rectangles, triangles, and parallelograms, and the areas and volumes of spheres, cones, and cylinders, and the properties of isosceles and equilateral triangles, and pythagoras' theorem, as well as basic algebra such as the "root factor" theorem (that r is a root of a polynomial iff x-r is a factor), and the quadratic formula, you definitely need precalc too.

    it would also help a lot if you have seen proofs of some of the basic theorems of algebra and geometry, because college courses are about why, and when to do do things, not just how to carry out mechanical procedures.

    by the way the one primary cause of lack of success in college calculus is poor algebra skills.
  12. Jul 9, 2005 #11
    If I were you I would just take pre-calculus again.

    I re-took pre-calculus and trig the summer before I started college just to guarantee that I would make it into calc 1 the following fall. Later that summer I got my ap scores back and I managed a 3 on the ap calc exam. I decided to skip calculus 1 and ended up with what students called a difficult teacher for calculus 2; moreover, I spent a large amount of time practicing the homework problems for calculus 2, and got an A in the class, and learned a lot of algebra in the class too. One thing that was interesting is that the first month of calculus 2 was covered in ap calculus in high school.
  13. Jul 9, 2005 #12
    I wasn't able to respond earlier because a hurricane literally came through the area. That and I hit backspace and I lost the post that I wrote an hour earlier (which was really long).

    It wasn't my intention to skip 1st year college calculus. My main objective was to get into college calculus in the first place, and I guess I'm not good enough at that.

    As far as the assessment went, I got a 16 (a 20 was needed) and the 4 questions I missed dealt with advanced trigonometric manipulation (the questions were tricky on a scale that I didn't see in HS).

    I already know all of that (though the cubic root factor escapes me at the moment). The things I don't know: vectors, product identities, product-sum identities, triple-angle formulas, among others. Though I said that my precalculus was weak, it wasn't that weak. It just didn't get me through what I needed to get through.

    I tried so hard to get to the point where I could take college calculus. I put forth a tremendous effort in HS calculus class, staying afterschool, learning after the AP test, so that I could know the fundamental why's behind the theories of calculus... and now I cannot even take calculus at this point.

    That, I have to say, is the main source of my frustration at this point.
  14. Jul 9, 2005 #13


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    Motai, don't feel frustrated, even thought i was strong at precalculus, i retook it, and it was an easy A for me (i must say i ended up in a pretty well position on the nationwide math olympics in my country for High Schools), but the teacher did teach me new stuff, especially proofs, so i didn't think i wasted my time. Finally, when i got into "calculus", i did pretty well.
  15. Jul 9, 2005 #14
    You're saying you only got 4 questions wrong? You needed to get a perfect score, in other words (20 - 16 = 4)? That doesn't sound quite right to me.

    These assessment tests are not foolproof, and in my experience, there's usually some leeway and the bar is not set at perfection. So if you're failing this exam, chances are you need to learn the material much better.

    However, if advanced trigonometric manipulation is really your only weakness, then you might want to study up on this for the rest of the summer, and skip undergrad precalc.

    If you are having problems with AP-level calculus, you're going to have problems with your physics courses down the line because the math is more difficult, so it's important not to cut any corners.
  16. Jul 9, 2005 #15
    I made it clear when I drafted the original reply (which is now gone), but there were 25 questions.

    I had no prior knowledge that I had to take this exam (being away on vacation), and took the exam at 10:00 PM after a long day. Fatigue was a factor, and the constant stress of having to take such a thing after not staying in practice. But yes, I failed. It is probably going to be a long string of failures if things like this keep happening to me.

    Sometimes I wonder if dedication and sheer enthusiasm for the subject at hand is enough to get me through. Perhaps not.

    I never said I was having problems with the course itself, I didn't. I may have had difficulties in the AP test itself, but that is a different matter entirely. I actually enjoyed the course a great deal, so I find it to my dismay that I won't be able to take the college level course in the fall.
  17. Jul 10, 2005 #16
    Dedication and perserverence can definitely make a big difference. If you have the patience and given your enthusiasm for the subject matter, you might want to wait until you have at least 2 or 3 years of college under your belt before giving up on math and science. But switching majors after your third year would probably mean staying in school for an extra year or two.

    I would say that if you are having problems with the AP test, that is a more objective measure of your current level of calculus ability than whatever your grade or performance was in your high school class or even some county exam. Unless of course you have some fairly decent excuse for your performance.
  18. Jul 10, 2005 #17
    I skipped a quarter of calc due to my AP test scores. BAD IDEA. I jumped into integrals, and thought "ok, I know what's going on", but a lot of the stuff was new. The notation was TOTALLY different than in HS, since it wasn't watered down anymore.

    Also, my trig blows. I barely passed the class and still struggle with it. If you can, retake it. It will help a LOT in the long run.

  19. Jul 10, 2005 #18
    I'm not going to give up anytime soon. This minor setback (and probably others in the future no doubt) will probably mean that I will have to stay an extra year in school, but I guess that shouldn't be too bad (which I heard is the norm for science/engineering majors).

    I need to find out exactly what caused me problems on the AP test, but right now I don't have anything to work with. Since it is generally recommended to retake the precalc course, I might as well use the review and clear up some loose ends before I get into the heavier stuff. This means that I will be starting from the bottom and building my way up, but at least I'll be getting a stronger foundation to build up the rest of the maths. Better to be safe and wait a little bit than to be hasty and rush into unknown territory.

    Thanks for all your help everyone :smile:, I never realized how little high school courses "prepared" me, and this will be a good opportunity for me to get my feet wet in college.
  20. Jul 10, 2005 #19
    As I mentioned previously - a good diagnostic would be your performance on previous AP exams. It's been a while, but I remember that I ordered old, actual AP exams from ETS and practiced on those before taking the real exam.

    It also might be worthwhile to dig around the web for precalc/calc course material at various colleges. Sometimes they put their old problems sets and exams up, and even the solutions.
  21. Jul 10, 2005 #20


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    it is very hard to determine, from tests or otherwise, where a student should be placed. your basic argument seems to be that you do know precalculus but did poorly on the test through the fault of unusual circumstances.

    now i feel honesty bound to say, that my experience teaches that 99% of all students who say that are wrong, that indeed they do not know precalculus at all well, and would be well off taking it again. Remember you missed 9 out of 25 questions, which is a D, on a test of material considerably more elementary than calculus.

    the idea that you should only be measured on material you bone up on the night before, and not on what you actually carry around with you all the time, ready for instant use, is at odds with college expectations.

    However i cannot be sure this statistical data applies to you, not having even met you.

    so lets assume you are right and that you do not need precalculus. then i cannot imagine that you cannot talk your way into the calculus cousre by actually meeting with the profeesor and convincing him/her that you do know the material.

    either request to retest the placement material, or just talk to someone and essentially take an oral exam.

    this happens all the time. schools definitely do want to place everyone correctly. you need to be talking to your school rather than to us.

    for example when i was a student i blew off honors calculus class and got a D- in it, and then got kicked out of school for a year. a semester after i returned i determined to get back into the honors sequence and at the end of spring went to the professor teaching the second year honors course in the fall, and asked him what i really needed to know from the cousre i had essentially failed. he told me some topics on topology of the real line, compactness etc..., which it then went and learned on my own over the summer from an advanced calculus book by david widder. i then got a B+ followed by an A- in the advanced honors calc course, and got into grad school and eventually, after other mishaps and recoveries, became a professional mathematician.

    good luck.
    Last edited: Jul 10, 2005
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