Knowing the Test
Part of what I do is help students leverage the limitations of the exam to their advantage. This is done because I know how these test questions are created and written as well as some of the limitations put on the questions. For example, the Pythagorean theorem is fair game on the SAT (x^2 + y^2 = z^2) and this can be a computational and time intensive problem. However, the SAT usually limits itself to integer solutions on this type of problem and I know from the number theory class I took in college that there are only a set number of "Pythagorean triples" (a set of three integers that can solve the above equation) If you know that and you are given two of the numbers you immediately know the third number in the set. This saves massive amounts of time and leaves more time to work on other questions.
This is the type of understanding and additional tricks I bring to the table as well as being able to teach the traditional methods of doing well on the math section of the SAT.