In a problem involving data that is normally distributed, the Z-score is how many standard deviations from the mean that a sample data value lies. For example, if the standard deviation is 10 and the mean is 20, then a data value of 25 is 5 units from the mean and 5/10, which is 1/2 standard deviation away from the mean. The Z-score is then 0.5.

Statistics involves the study of data that is collected. The data is analyzed, presented and interpreted in various ways such as numerically and graphically. The two primary methods used to analyze the data are descriptive statistics and inferential statistics. Mean and standard deviation are examples of descriptive statistics. Inferential statistics involves data that has errors in observation or sample variation.

The surface area of a cylinder is the area of the two bases, both circles plus the area of the part in the middle. Think of a soda can, generally cylindrical in shape. That part that you hold around middle of the can, if you could peel off the put flat, would be a rectangle. You can also think of it as the height of the cylinder times the circumference of the top or bottom. So a formula could be 2Pi(r)^2 (area of top and bottom) plus h(2Pi)(r) , area of the part around the middle.

Odds can be thought of as a chance of an event occurring. Suppose you know there are 8 possible outcomes, each equally likely. The odds or any one happening are 1 in 8. It can also be represented as a ratio, in which case it is the one chance that the event occurs and seven that is does not occur, written as 1:7, and it is said that odds are "1 to 7"

Real numbers are all rational and irrational numbers which include whole numbers, repeating decimals and non-repeating decimals. Non-real numbers are known as "imaginary" numbers. The square root of negative numbers, which will come up as an "error" on most calculators are imaginary numbers. The square root of -1, is known as "i" and imaginary numbers can be part of the complex number which has a real an imaginary part. And example of a complex number is 2 + i.

Suppose we want to solve an equation such as x^3 + 2x^2 -3x + 6 = 0. We can use the rational root theorem to find the possible rational roots and then use synthetic division to find a root. After we find a root, we will have a quadratic equation left to solve to obtain the other roots. This can be quite tedious. With a graphing calculator, you can solve this equation by seeing where the graph of the equation crosses the x-axis. These points are the solutions to the equation. If you have multiple equations, the solutions are the intersection points of the graphs.

Quotient rule for differentiation:

derivative of f(x)/g(x) = [g(x)f'(x)- f(x)g'(x)]/g(x)^2

Product rule for differentiation:

derivative of f(x)g(x) = f(x)g'(x) + g(x)f'(x)

Chain rule

derivative of f(x)^2 is

2f(x)f'(x)

in general

derivative of f(x)^n is

n(f(x))^(n-1)f'(x)

Remember that "natural log of x", written as "lnx" is really log (base e) x where "e" is approximately 2.718.  You see the used of "e" in exponential growth and decay, also interest compounded continuously A=Pe^(rt) where A is the amount, P is the initial investment, r is the interest rate and t is the time in years.

When solving a system of equations by substitution, remember to remove the one variable and replace it with a quantity equal to that variable. For example, suppose the system is x = 2y + 3 and 3x + 4y = 16.

You can solve this system by substituting 2y+3 for x in the second equation. The second equation becomes 3(2y+3) + 4y = 16. Now we can solve for y.

6y + 9 + 4y = 16

10y = 7

y = 7/10

To solve for x, substitute 7/10 for y in the first equation. That gives us

x = 2(7/10) + 3

x = 14/10 + 3

x = 4.4