Review Sheet for Math Quiz 2, Maestro Summer Program 2016
Colorado State University, Pueblo

It would be a good idea to be comfortable with the problems from the math worksheets you did this week. Those worksheets covered a lot of the algebra/arithmetic of powers and applied models using exponential growth and decay. The material discussed in class on Thursday was not in any worksheets, so here are some practice problems you might look at for that. Just to summarize the content we've done in the last week, here are the topics:
  1. Equations for exponential growth and decay. The base of the exponent. The initial condition (starting value).
  2. Rules for manipulating powers.
    1. If $a$ is any real number and $n$ is a natural number, $a^n=\overbrace{a\cdot\dots\cdot a}^{n\textrm{ times}}$.
    2. If $a$, $x$, and $y$ are any real numbers, then $\left(a^x\right)^y=a^{x\cdot y}$.
    3. If $a$ is any real number and $p$ and $q$ are any integers, then $a^{p/q}=\sqrt[q]{a^p}$, as long as the root is defined (so: if $a$ is positive this always works, or if $a$ is negative and $q$ is odd, ...).
    4. If $a$, $x$, and $y$ are real numbers, then $a^x\cdot a^y = a^{x+y}$.
    5. If $a$ and $x$ are two real numbers, then $a^{-x}=\frac{1}{a^x}$.
    6. If $a$, $x$, and $y$ are real numbers, then $a^x/a^y = a^{x-y}$.
    7. If $a$ is any non-zero real number, then $a^0=1$.
  3. Differnt kinds of numbers:
    1. natural numbers, $\NN=\{1,2,3,\dots\}$.
    2. integers, $\ZZ=\{\dots,-3,-2,-1,0,1,2,3,\dots\}$
    3. rational numbers, $\QQ=\{p/q,\textrm{ where }p\textrm{ and }q\textrm{ are integers, and }q\neq0\}$.
    4. real numbers, $\RR$, all the numbers corresponding to points on the number line
    5. irrational numbers, the real numbers which aren't rational, like $\sqrt{2}$.
    6. complex numbers, $\CC$, all numbers which can be written in the form $a+bi$, where $a$ and $b$ are real and $i$ is the imaginary unit which satisfies $i^2=-1$. The $a$ here is called the real part and the $bi$ is the imaginary part.
  4. Arithmetic with complex numbers — multiplication by FOILing like crazy, addition and subtraction just by grouping terms, and division by using the method which turns the denominator into a real number.
You may bring one page of notes to the test. It may have anything you like on it — equations, defintions, examples, poetry, diagrams — but should be written in your own handwriting. You must hand in your page of notes with your test.