Remember when rationalizing a denominator involving a square root, multiply the numerator and denominator by whatever is under the radical in the denominator.

If the problem is 2/sqrt(3), multiply the numerator and denominator by sqrt(3)/sqrt(3) to get

2sqrt(3)/3.

If the problem involves a cube root, multiply the numerator and denominator by whatever will give you a perfect cube in the denominator.

For example, if the denominator is cube root(3), multiply numerator and denominator by cube root(9). This will make the denominator cube root(27), which equals 3.

Same idea for 4th root, 5th root and so on.

When finding the domain of a function, remember it's all values for the variable where the function is defined.

For example, f(x) = 1/(x - 2), the domain is all real nubmers except for 2. A value of 2 for x makes the denominator 0 and the function undefined.

Be careful with some functions. Make sure everything is simplified before determining the domain. If

f(x) = (x^2 - 16)/(x - 4) it might be tempting to see the denominator and conclue the domain is all real numbers except for 4. But this is incorrect. 

If we factor the numerator, we get (x -4)(x + 4).  The (x - 4) in the numerator will cancel with the (x - 4) in the denominator.

Therefore f(x) = x + 4 and the domain is all real numbers.

When working with formulas involving Pi, sometimes it's easier to just leave the answer in terms of Pi. Othertimes, when needing a specific value for volume or area of a sphere, circle, cylinder for example, it's best to use 3.14 or 22/7 as approximations for Pi. Yes, many people have memorized Pi to a ridiculous number of digits, but for all practical purposes, a few decimal points of Pi will suffice.

Check out the math book as an ebook in pdf form to be viewed on the computer and also as a paperback. 

http://www.lulu.com/spotlight/KKauffman1969

When using matrices to solve a system of three equations in 3 variables x, y and z, write the system as an augmented matrix and use matrix row operations to get the matrix into row-echelon form. We use what is called Gaussian elimination.

When the matrix has 1's along the diagonal from upper left to lower row and 0's underneath the 1's, we can use the value obtained for z and substitute in for z in the second equation to solve for y and then substitute y and z in the first equation to solve for x.

Systems of equations may have none, one or infinitely many solutions. 

When solving for square roots and cube roots, it's very helpful to know many of the perfect squares and perfect cubes.

The first 25 perfect squares are

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625

The first 10 perfect cubes are

1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Knowing these will be very helpful and they aren't hard to memorize.

To find the inverse of a function, substitute y for f(x), then interchange x and y and solve for y.

For example

If f(x) = x + 7, replace f(x) with y to get

y = x + 7

Next interchange x and y to get

x = y + 7

Solving for y we get

x - 7 = y

The inverse is x - 7