Yang Kuang

Functions can be categorized in many different ways. Here, you see functions in terms of the operations being performed. Here, though, you see classifications that work for all the many types of functions. If you know that a function is even or odd or one-to-one, then you know how the function can be applied and whether it can be used as a model in a particular situation.

As you work through pre-calculus, adopting certain tasks as habits can help prepare your brain to tackle your next challenge: calculus. In this article, you find ten habits that should be a part of your daily math arsenal. Perhaps you’ve been told to perform some of these tasks since elementary school — such as showing all your work — but other tricks may be new to you.

Every good thing must come to an end, and for pre-calculus, the end is actually the beginning — the beginning of calculus. Calculus includes the study of change and rates of change (not to mention a big change for you!). Before calculus, everything was usually static (stationary or motionless), but calculus shows you that things can be different over time.

Here you find some pretty amazing curves that are formed from some pretty simple function equations. The trick to drawing these polar curves is to use radian measures for the input variables and put the results into a polar graph. A polar graph uses angles in standard positions and radii of circles; it’s not your usual rectangular coordinate system.

When you study pre-calculus, you are crossing the bridge from algebra II to Calculus. Pre-calculus involves graphing, dealing with angles and geometric shapes such as circles and triangles, and finding absolute values. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations.

Gaussian elimination is probably the best method for solving systems of equations if you don't have a graphing calculator or computer program to help you.The goals of Gaussian elimination are to make the upper-left corner element a 1, use elementary row operations to get 0s in all positions underneath that first 1, get 1s for leading coefficients in every row diagonally from the upper-left to the lower-right corner, and get 0s beneath all leading coefficients.

A binomial is a polynomial with exactly two terms. Multiplying out a binomial raised to a power is called binomial expansion. Your pre-calculus teacher may ask you to use the binomial theorem to find the coefficients of this expansion. Expanding many binomials takes a rather extensive application of the distributive property and quite a bit of time.

Polar coordinates are an extremely useful addition to your mathematics toolkit because they allow you to solve problems that would be extremely ugly if you were to rely on standard x- and y-coordinates. In order to fully grasp how to plot polar coordinates, you need to see what a polar coordinate plane looks like.

You can use both polar coordinates and Cartesian (x, y) coordinates (also known as rectangular coordinates) at any time to describe the same location on the coordinate plane. Sometimes you'll have an easier time using one form, and for this reason it's important to know how to change between the two. Cartesian coordinates are much better suited for graphs of straight lines or simple curves.