PreCalculus Review: Essential Topics for Quick Success

[Opus_723]

I thought maybe this should go in the Precalc Learning Materials section, but since I can't post there this seems like the next best fit. If I've picked the wrong forum, I apologize in advance.

I need a quick review of everything leading up to Calculus. From basic algebra up, essentially (Obviously not TOO basic, like 2x = 4 and such, but still, I want to be thorough). It's been a long time since I've used any of this, but I would like to review it all as quickly as possible in order to take a Calculus class.

So my question is: what essential topics do I need to review before taking Calculus? If I were to compile a list for review, what would be the bare bones, structural version? I would like to review all of this as soon as possible, so I'd like to go through all of the absolutely necessary topics first, and then fill in the gaps with any time left over. Links to resources would be great, but not necessary as I can always peruse through the resources forum later.

Thanks.

 

[lisab]

You're going to want to be very fluent in algebra. The exercises where you're presented with a big hairy equation and the instruction says, "Simplify" - those, you want to be able to power right through.

Trig, and trig identities, will be important too.

 

[contramundum]

radicals and rational exponents, factoring, exponential functions, log functions, graphs of functions, inequalities, and the things lisab mentioned.

 

[HeLiXe]

Hi Opus,

I had to do this recently. I reviewed algebra-precalc in one month and I am in calculus I w/analytic geometry now. I used Nathaniel Max Rock's books in google. There are loads of exercises. He provides minimal answers and some of the answers are wrong, but the instruction is good and direct, so I was able to go through it fairly quickly.

I still have them in my favorites so here are the links:
http://books.google.com/books?id=xS...resnum=4&ved=0CDsQ6AEwAw#v=onepage&q&f=false"

http://books.google.com/books?id=oT...resnum=5&ved=0CEMQ6wEwBA#v=onepage&q&f=false"

http://books.google.com/books?id=iA...e=gbs_ge_summary_r&cad=0#v=onepage&q&f=false"

http://books.google.com/books?id=Xk...resnum=1&ved=0CDEQ6wEwAA#v=onepage&q&f=false"

The way he teaches trig annoys me though, so I used various sites for trig, but I do not have them in my faves. So far in calculus I, I've found that Algebra I&II and trigonometry have been useful. Particularly factoring polynomials, understanding logarithms, and understanding sin, cos, tan, cot, sec, csc. Not to mention algebra is generally essential for working out problems, etc. The topics we've covered thus far in calculus are limits, derivatives, differentiation, special functions (trigonometric, logarithmic, exponential), computational techniques, and implicit differentiation. We still have a lot more to go so I'm sure there are other important things to focus on that I am not mentioning.

 

[HeLiXe]

Also this guy's lectures on conic sections are good to supplement Rock's equations and problems.
http://www.yaymath.org/Videos.html

 

[QuarkCharmer]

There is an amazing trig short-course here...
http://www.clarku.edu/~djoyce/trig/
that quickly covers it in a good amount of detail. I read through that and then covered some problems from other random sites around the internet with no issue. If you run across a list of problems to improve your factoring skills let me know!

 

[jeremmed77]

You should start with learning college algebra, followed by trigonometry. I think you should try khanacademy.org out. On the website, they have online lectures that can teach you some of the concepts of algebra/trigonometry (They also have calculus on there). Unfortunately, the algebra and trig on khan academy is not the same as college level, but it will be good to look at before jumping right into the college level stuff.