RTCNTC said:
If you were to make a list of 10 important precalculus topics that students should know very well, what would they be?
Let me start by saying word problems. All students going into Calculus 1 should be able to answer Algebra 1 and 2 applications. Can you name 9 other important precalculus topics? I would like to have a list of 10, if possible.
Algebra, Algebra, and more Algebra - including Theory of Algebra and so-called "College Algebra". If you can't Complete the Square to derive the Quadratic Formula, you haven't done nearly enough. If you can't QUICKLY plot a line on a Cartesian Coordinate system or write the equation of a line in four or five different ways, practice some more.
Geometry - Constructions, Theorems. Nothing better for knowing what makes sense and what doesn't. This WILL organize your brain.
Analytic Geometry, but not just Conic Sections. Throw in Rational Functions (They may be part of "College Algebra", I suppose.) Functions in general. Two-dimensional spatial orientation will save you.
Trigonometry - More than you think. Memorize. Manipulate. Get a good handle on it. Don't forget Polar Coordinates!
To a lesser extent - Matrices and Linear Algebra. This will help you foresee some things that will be important and cause you to wonder about systems, rather than just individual functions.
To a lesser extent - A broad classification of "Discrete Mathematics" and "Finite Mathematics". This can be an odd collection of things. There is more going on, here, than you might think.
To a lesser extent - Static Physics. Some general idea of some of the applications of the calculus will serve you well. This will help you appreciate calculus-based physics.
To a lesser extent - Financial Mathematics, Theory of Interest. If nothing else, this should warm you up to Geometric Series. This will also prep you for early applications of differential equations. This will also force you to be more organized.
To a lesser extent - Number Theory. If nothing else, like Geometry, this will make you use your brain in a way with which you may not be accustomed. it will broaden your horizons.
Sorry, only made it to 9, but my classifications were not all that distinct. Some are downright muddled. Anyway, if you nail down these things - make them second nature - you can spend your time on the calculus, rather than on reviewing what should have been listed as prerequisite.
