# Miscellaneous Math Knowledge

By Brian D.

As with any exam that tests mathematical knowledge, you’re going to need to know the basics. These include topics like exponents, factors, etc. Here we will be doing a brief review of the basic information that you should know for this test, and many others in general.

### Laws of Exponents

Here is how exponents are typically represented in a problem.

ab

a represents the base and b represents the exponent.

·      The base is the number that is being multiplied.

·      The exponent is the number of times the base is multiplied by itself.

If you have a negative exponent, then it simply means that you need to convert it to fractional form, in which the numerator is always 1 and the denominator is the base raised to the exponent with a positive sign rather than a negative sign.

If you have a base with a fractional exponent, then the first thing you do is put the base raised to the fraction’s numerator under a radical sign. The radical will be raised to the denominator’s root. So to sum it up, the numerator goes under the radical sign and the denominator goes outside.

If you’re presented with a situation in which you’re asked to multiple numbers that have the same base but different exponents, then what you do is add the exponents while keeping the base the same. On the other hand, if the exponents are the same but the bases are different, then you will not be able to multiple them this way. You’ll either have to use a calculator or use the specific circumstances to find a way short of manually multiplying the numbers (not only will that be time consuming but also very prone to mistakes).

The same above applies to division of bases with exponents. Instead of adding the exponents (if applicable) you subtract them.

If you have an entire fraction raised to an exponent, then you simply raise both the numerator and denominator to that exponent.

If you have a term nested in parentheses raised to a power, then you raise every term within those parenthesis raised to that power. For instance:

(XY)n = XnYn

But if there are no parenthesis, then you do not raise the entire term to that power

XYn! = XnYn

### Factor Trees

Factor trees are a visual method of determining factors and ultimately, prime factors. This is not recommended because it is time consuming. In the time used to draw an entire tree (especially for larger numbers), you could have been solving other problems that present a greater challenge or require more attention. You should use this only if you do not feel comfortable with (prime) factorization because you have the multiple choice working to your advantage, if you plug in rather than spending the time to do the problem the long way.

If you do decide to use factor trees, then you simply find factors of the specified number and keep on doing that until you have only prime numbers and 1. When nothing more can be further simplified, then you have your prime factors. If the number at the top of the tree cannot be further simplified however, then it is already a prime number.

# SAT Graphs

Graphs on the SAT are not the most complex parts of the exam. However, there are still many things that can go wrong here, and caution should be exercised. Don’t be the one to screw up on these question types!

Analyze the data first, go into the question with some idea of what information is available to you and what isn’t. If you free up some time doing these generally easy questions, you will have more time to work on more challenging questions.

You don’t want to spend an unnecessary amount of time on these types of questions, especially if they’re easy.

Save time by eliminating options as you figure out the only remaining possible answer. Sometimes you won’t even need to work all the way to the end! Save some time for the next question.