# Calculus pre-reqs



## pepsivanilla93 (Dec 8, 2012)

I recently purchases an algebra book for self review with the intention of progressing through geometry and trig to gain a head start on calculus. My goal is to test into a calculus class with the college placement tests. Now my question for you all is: what are the most important parts of algebra, geometry, and trig that are fundamental for calculus? Basically, what topics in those subsets should I spend the most time on/do extra problems with? I appreciate any and all advice. Thanks!


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## jbking (Jun 4, 2010)

Graphs of functions would be the main area I'd suggest as there are a few parts of Calculus that do a lot with functions whether that be computing derivatives, integrals or limits. Another thought is to consider something like https://www.khanacademy.org/ that can offer free practice tests within Calculus that may be of use.


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## pepsivanilla93 (Dec 8, 2012)

jbking said:


> Graphs of functions would be the main area I'd suggest as there are a few parts of Calculus that do a lot with functions whether that be computing derivatives, integrals or limits. Another thought is to consider something like https://www.khanacademy.org/ that can offer free practice tests within Calculus that may be of use.


Wow, the link you posted looks incredible. I will definitely spend some time with their practice tests. Thank you much!


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## jbking (Jun 4, 2010)

Essays on the Calculus would be my secondary suggestion though scroll to the bottom for the courses on Calculus. Some of the material is presented in a humorous manner though the Math is pretty solid.


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## pepsivanilla93 (Dec 8, 2012)

Thank you for the calculus site as well. I do prefer a book on calculus so I can take it with me, but that's not to say that your link won't provide a good companion. The .pdf's of the lecture look really nice though. I've already downloaded them :happy:.


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## fihe (Aug 30, 2012)

jbking said:


> Graphs of functions would be the main area I'd suggest as there are a few parts of Calculus that do a lot with functions whether that be computing derivatives, integrals or limits. Another thought is to consider something like https://www.khanacademy.org/ that can offer free practice tests within Calculus that may be of use.


absolutely. I'm currently taking a calculus class, and the limits and derivatives make heavy use of functions, which I find are easier to understand if they are graphed. you will also need to know basic algebra, when you are given a polynomial in the limit and need to simplify it.


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## FlightsOfFancy (Dec 30, 2012)

algebra and geometry is really all you need tbqmfh.

Don't skimp on the algebra at all. You need that #1. You will find that a derivative/integral is nothing more than shortcuts/fine-tuning of algebraic concepts.

Geometry - know basics of how shapes are the way they are. Know the basic tenets, but you don't have to know much about the proofs of such.

Trig - all trig identities, but these are normally given.

your main friend is algebra.


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## pepsivanilla93 (Dec 8, 2012)

FlightsOfFancy said:


> algebra and geometry is really all you need tbqmfh.
> 
> Don't skimp on the algebra at all. You need that #1. You will find that a derivative/integral is nothing more than shortcuts/fine-tuning of algebraic concepts.
> 
> ...


That's what I thought about algebra. Given that I'm reviewing it I found it necessary to have it mastered in the wake of my near-fail pre-calculus class. As for geometric proofs, my teacher actually never taught that to us. So I have no idea how proofs work, but if they're not essential for say applications of calculus to chemistry or physics, then I'm not all that interested in learning them. Are they even useful for calculus at all? Even when you get to higher up calculus classes?
@huesos I know what you mean about understanding functions. I have the basics down (input, output) from my college algebra class, and I remember extensive use of them in pre-calculus. Overall, functions are probably going to dominate my study time when it comes to algebra, along with mastering the basics such as exponential equations and fractions/division.


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## goodgracesbadinfluence (Feb 28, 2011)

You definitely need to review your algebra! Make sure you know how to factor, combine like terms, and simplify expressions. Study logarithm expansion and contraction rules and also the exponential functions. Learning what equations look like on the graph doesn't hurt either. I'd review y=x, y=x^2, y=x^3, y=sinx, y=cosx, and y=e^x to start out with. You need to know about limits, and that might not be in a normal algebra book. Limits are the very first new thing you learn in calculus, at least in my experience.


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## pepsivanilla93 (Dec 8, 2012)

Thank you all for your help so much! I pose one further question. What would be the correct order of precedence in my study of mathematics? Should I go: Algebra>Geometry>Advanced Algebra>Trigonometry>Pre-calculus>Calculus? Should I combine basic and advanced algebra into one unit of study. Should I omit, say, pre-calculus? Thank you in advance.


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## L'Empereur (Jun 7, 2010)

You can probably skip PreCal.


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## Orion (Jan 25, 2011)

pepsivanilla93 said:


> I recently purchases an algebra book for self review with the intention of progressing through geometry and trig to gain a head start on calculus. My goal is to test into a calculus class with the college placement tests. Now my question for you all is: what are the most important parts of algebra, geometry, and trig that are fundamental for calculus? Basically, what topics in those subsets should I spend the most time on/do extra problems with? I appreciate any and all advice. Thanks!


What type of calculus are you thinking of taking? My University has 3 levels: Math, Engineers and Biological Science (kind of a catch all). I took the math major calc I and it was heavier on geometry. Calc II I took at the engineer level and that was trig heavy.


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## pepsivanilla93 (Dec 8, 2012)

Orion said:


> What type of calculus are you thinking of taking? My University has 3 levels: Math, Engineers and Biological Science (kind of a catch all). I took the math major calc I and it was heavier on geometry. Calc II I took at the engineer level and that was trig heavy.


I didn't realize there were different varieties. It will be science based calculus, so I'm not quite sure. Perhaps you could fill me in? Physical sciences, chemistry and physics. In college I plan to at least go through Calc I & II.


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## bellisaurius (Jan 18, 2012)

Algebra is all about the factoring. Once you can reorganize and simplify equations as easily as you move words around a sentence, you're golden. Trig is all about the identities, understand those and the rest is easy.


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## Orion (Jan 25, 2011)

pepsivanilla93 said:


> I didn't realize there were different varieties. It will be science based calculus, so I'm not quite sure. Perhaps you could fill me in? Physical sciences, chemistry and physics. In college I plan to at least go through Calc I & II.


Hard to say, you seem to have a good work ethic so I would hate to under-judge your abilities. If physics is your thing, then you will be taking the math majors calc, plus a whole bunch of other math classes. Some disciplines of chemistry do not differ much from physics, so I would suggest take the hardest math for that as well. If the biological sciences are your thing, then just take the lowest level calc, those generally will allow you to take the harder math classes later if you so desire. 

If you are good at math, then take as much as you can, it is one of the few proven ways I know of to separate oneself from the masses.


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## bellisaurius (Jan 18, 2012)

Orion said:


> If you are good at math, then take as much as you can, it is one of the few proven ways I know of to separate oneself from the masses.


and since things tend to get graded on bell curves, there's minimal downside risk in terms of grading.


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## Orion (Jan 25, 2011)

bellisaurius said:


> and since things tend to get graded on bell curves, there's minimal downside risk in terms of grading.


That is true but not accurate. If you can't handle the math in a more difficult class, then the curve will not help you. Quality institutions also limit the grade padding. Tests are curved less these days as the internet allows anyone that tries a little to get 100% on homework assignments.


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## pepsivanilla93 (Dec 8, 2012)

Orion said:


> Hard to say, you seem to have a good work ethic so I would hate to under-judge your abilities. If physics is your thing, then you will be taking the math majors calc, plus a whole bunch of other math classes. Some disciplines of chemistry do not differ much from physics, so I would suggest take the hardest math for that as well. If the biological sciences are your thing, then just take the lowest level calc, those generally will allow you to take the harder math classes later if you so desire.
> 
> If you are good at math, then take as much as you can, it is one of the few proven ways I know of to separate oneself from the masses.


I appreciate your giving me this information and your compliment on my work ethic. I've been a very good math student (my favorite class after science) and with that I believe I should prepare myself for the math based calculus courses. Can you give any examples of what may differ from a math based course to a general "biology course"?


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## Orion (Jan 25, 2011)

Nope, I never took the general calc classes. Find a website for a large University that offers multiple levels of calc, read the course descriptions for each.


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## angularvelocity (Jun 15, 2009)

I'm in grad school and am taking undergrad calc II at Berkeley for a refresher. It is heavy trig based. I wish I knew my trig identities and how they relate to each other better. It would've made this class a lot easier.


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