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Content for Algebra I/II and Precalculus and Trig.?

  1. May 9, 2014 #1
    I'm wondering if someone who is experienced can list all the content that a person should have mastered in the subjects of Algebra I/II and Precalculus and Trig.

    I completed College Algebra at community college just this past year and I'm going to be taking Precalc./Trig this upcoming year. I just want to make sure that I have everything down that I need to know. Our instructor, despite being nice and helpful, didn't cover everything in our book and I'm not even sure exactly whether there are official topics designated for each area. For example, we didn't do logarithms in my College Algebra class, but my friend's class had them.

    I'm just wondering if there is a standard set of topics that go with each class that students should know whether or not the book or instructor actually covers them. Thanks everyone.
     
  2. jcsd
  3. May 9, 2014 #2

    symbolipoint

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    Precalculus is a heavy combination of College Algebra and Trigonometry. If you did not cover all essential parts (whatever those are) in your College Algebra course, then you should see again what you still need to cover in your PreCalculus course. Trigonometry should also be available as a separate course and more complete than as done in your PreCalculus course.

    I recommend checking any common College Algebra textbook to know what the contents should be for College Algebra; and also check a good Trigonometry book to know what is or should be the contents of a Trigonometry course. I ALSO RECOMMEND reviewing what you missed on logarithms and log and exp functions on your own before enrolling in your PreCalculus course.


    Some of the absolutely necessary contents of College Algebra are these:
    Linear and quadratic relationships, inequalities, absolute value; as an intense review of intermediate algebra;
    Polynomial Functions and their graphs;
    Rational Functions and their graphs;
    Conic Sections, ..
    Inverses of Functions;
    Exponential and Logarithmic Functions;
    Functions for the Domain of Whole Numbers (sequences and series);
    Applications for several of the above listed topics.
    Limits of Functions (which is why College Algebra is included in Pre-Calculus);
    Other assorted topics sometimes including binomial theorem, linear algebra/linear systems
     
  4. May 9, 2014 #3

    462chevelle

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    Trig necessities are

    Right angle relationships
    Unit circle
    radian measure
    graphs of trig functions
    identities.. lots and lots of identities.
    sum and difference
    pythagorean
    half angle
    double angle
    reciprocal
    Solving trig equations
    Obliques (law of sines and cosines)
    Vectors
    Polar coordinates and complex numbers. Demoivres method.
     
  5. May 10, 2014 #4

    verty

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    @OP:
    I think you'll get the most relevant advice if you list the topics in your textbook so we can say which are more important and which are less so or which can be left for later.
     
  6. May 10, 2014 #5

    IGU

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    The Art of Problem Solving precalculus book table of contents tells you what a good class would cover.
     
  7. May 11, 2014 #6
    Hi, verty

    I'll have to come back to this thread a bit later (busy weekend!), but for now I can give you all my College Algebra book name and ISBN: :smile:

    Intermediate Algebra (by Charles McKeague)
    ISBN-13: 978-0495384977

    I haven't picked up my Precalculus and Trig. book yet, but it's definitely listed in the school bookstore. I'll have to try to look through it when I get the chance.

    I'll be back soon guys. Thanks so much again! Also, feel free to give recommendations for readings and books in these topics. If they're cheap enough or are just like the best of the best, then I may be willing to buy one this summer. :thumbs:
     
  8. May 11, 2014 #7

    symbolipoint

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    College Algebra is much more advanced than Intermediate Algebra. Intermediate Algebra is a subset of the contents of College Algebra. You have three months now before the autumn semester begins. You should get any good College Algebra or Precalculus book NOW and study the course on your own, before the next semester begins, to prepare yourself for your autumn term in Precalculus.
     
  9. May 11, 2014 #8

    verty

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    Ok, this book seems to use matrices from early on which I find a little strange. Matrices in a book where completing the square is found in chapter 8? Cramer's rule in an appendix?

    From what I can see, it looks to be set at a good level for intermediate algebra although some topics are advanced. So you'd want to learn everything from chapters 1-11 but with a few exceptions. Matrices you should probably just skip altogether; the different quotient is not going to mean much until you learn about limits; and quadratic inequalities are a little complicated, I would place them last in order of topics to learn from this book. I suppose you'll have learn most of what is left already in class, so perhaps just learn the few remaining topics? The rest you can learn when you get there, I think.
     
  10. May 11, 2014 #9

    462chevelle

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  11. Oct 11, 2014 #10
    My precalculus course did not even offer conic sections. So conic sections is not something I would worry about. Even in Calculus 2 we completely skipped Hyperbolic functions
     
  12. Oct 11, 2014 #11

    Rocket50

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    It really depends on the course level. However, as stated above, try the AoPS book contents or Sullivan's book.
     
  13. Oct 11, 2014 #12
    The art of problem solving is not a book I would recommend. I bought that textbook before, and needless to say the explanations were terrible. Sometimes I felt like the instructions for certain problems were too vague, and the end goal was not clear. Then there were certain chapters on topics that most of my TAs never even heard about. For someone who is just starting to study precalculus/alegbra/trig, the AOPS books are not for you. Just find a regular text somewhere, and start from chapter 1.
     
  14. Oct 11, 2014 #13

    Rocket50

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    In this case, it is only to check out a list of topics.

    The explanations are actually quite good, as they show why it works.

    As for covering extra topics, they do it because those topics are covered on major math contests.
     
  15. Oct 11, 2014 #14
    I did not find their explanations that good, but as I have stated earlier these text are for people who are preparing for mathematical competitions, meaning people who already have a solid foundation in mathematics, not someone just trying to self-learn with almost zero foundation. It is like telling a person with no knowledge of analysis that they take spivak for their first calculus course.
     
  16. Oct 11, 2014 #15

    Rocket50

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    Uh... Quite a people take Spivak as their first calculus course. But yes, I agree that these books cater mainly towards people training for mathematical competitions. However, I had little interest in those contests and still managed to use the books (much more fruitfully than the regular school textbooks).
     
  17. Oct 11, 2014 #16
    I tend be skeptical of people when they state such things about taking spivak as their first calculus course. Most of the time, they had some AP-BC calculus that allowed them to take such a course. Very few will actually understand what to do in spivak's book without some sort of training in proofs and analysis. I do not debate that there are some incredibly gifted people out there, but most of time when someone mentions spivak, they are just parroting what someone else told them.
     
  18. Oct 11, 2014 #17

    symbolipoint

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    Conic Sections needs to be included in both Intermediate Algebra and in College Algebra.
     
  19. Oct 11, 2014 #18
    I do not think that they do, or my precalculus class would have covered them. Also my college algebra classes we did not even include them. If you are making a statement, then I don't see the harm in including them.
     
  20. Oct 11, 2014 #19

    symbolipoint

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    One must study conic sections as a part of staying aligned with the study of the natural or physical sciences, engineering, or as for a major field in mathematics.
     
  21. Oct 11, 2014 #20

    462chevelle

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    we studied conic sections in college algebra. we didnt cover matrices though. the last thing we covered was log and exponential functions
     
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