Some Advice - What do I really need to know?

[Tim67]

So, I hated math in high school, and thus did very poorly in it when I even went at all. Lately, though, I've been reading up more on it and doing some on my own, and find I quite like it and find it very interesting, it was just taught very poorly, also I'm in my secondish semester of college and I've switched my major to economics, something sort of math-intensive. I'm a bit behind since I have a VERY poor math background, and just following the regular course of classes will take quite a while, so I'm trying to study independently so I can jump up to Calculus I or II next semester. I've got some Calculus study guides and used textbooks to learn from, but before that, I want to know what precalculus topics I REALLY need to know to move forward?

Obviously trigonometry, but what type of algebra should I REALLY know like the back of my hand? For example, do I really need to have a good knowledge of synthetic division, etc to be successful in studying and attending calculus courses? I want to just do a quick review/self-study of the important precalculus topics that will be important for understanding and learning calculus itself before I really get in it. If someone could give me a list of the most important precalculus concepts to go over, I would really appreciate it.

Thanks.
(hope this is the right forum for this, seems it)

 

[capandbells]

Finding equations of lines given either two points or a point and a slope.
Solving quadratic equations (completing the square, quadratic formula, factoring, etc.)
Solving systems of linear equations
Exponential and logarithmic functions, in particular you should know the properties of logarithms well (this isn't algebra, but precalculus courses cover it and you should know it)
Rational expressions and polynomial division
Functions (adding, subtracting and especially composition of functions)Basically you should be really familiar with all the "rules" of algebra: the various ways you can manipulate an equation "legally." I tutor a lot of people in Calc I, and the biggest problem I see is people taking wrong algebraic steps (e.g., (x + 4)^2 = x^2 + 16, etc.) or missing the answer because of an algebraic step they didn't know was allowed. If someone hands you a quadratic (or linear, for that matter) equation and it has real roots, you should be able to find them. I don't remember what synthetic division is and I'm a junior physics major, if that says anything, but you will need to know how to divide polynomials. I may have left some stuff out (and if I remember more I'll post it), but this is the minimum of what you will need to know.

 

[Angry Citizen]

I'd also familiarize yourself with limits, and series/summation, and matrices as well. You should know what synthetic division is (it's not that hard). You don't make use of it much after you learn the power, chain, product, and quotient rules, but the first few weeks of calculus I will be much easier if you know how to synthetically divide.

I'm in calculus I right now, and I can tell you for a fact that if you don't know square root manipulation like the back of your hand, you will have issues. ESPECIALLY learn how and when to multiply by conjugates (you'll need it when you study limits in-depth). But definitely understand slope, and how to find equations of lines (you'll be doing that A LOT when you're working with derivatives).