Names of Numbers used by the SAT: #1 INTEGER

The SAT Math problems are all word problems; it is imperitive that you understand the meaning of the words being used.

Here is a beginning to the list of Math Vocubulary that you MUST be able to understand:
Integer; Rational Number; Factor; Multiple; Product; Sum - not to mention all of the many Geometry terms used. This gives me a great idea for a Sat Math Vocab list.

Lets start with the #1 math word on the SAT: INTEGER

Integer: 1 : any of the natural numbers, the negatives of these numbers, or zero

since natural number is used in the definition, what does it mean:

Natural Number: the number 1 or any number (as 3, 12, 432) obtained by adding 1 to it one or more times : a positive integer

Examples of integers are: -567,-27, -12, -4, -3,-2,-1, 0, 1, 2, 3, 34, 567, etc.

Another way to look at it is that integers are points on a number line. They are NOT fractions, or decimals.

So the SAT uses the word integer in many ways. But one of the most common SAT math questions is what I call the "Consecutive Integer"

Here is an example:
The sum of two consecutive integers is 11, what is the value of the least?

There are only two numbers that solve this problem, 5 & 6; 5 + 6 = 11. 5 is the correct answer choice (6 will be one of the choices as well, just in case you did not read the entire question).

To solve any of these with algebra, you make one integer n. The "consecutive" means the next number, so the next number is n+1. Your equation is then:

n + (n+1) = 11; solve for n.
2n + 1 = 11
2n = 10
n = 5

That would be an easy problem (the math is broken into easy, medium & hard); a medium problem throws some twists into the verbage.

MEDIUM

The sum of two consecutive odd integers is 47 less than their product. What is the value of the smallest integer

The key here is that "odd" requires you to add 2 to n, instead of just one. They are consecutive & odd, like 3 & 5.

Here is the set up:

n + (n+2) = n*(n+2) - 47

simplify:

2n + 2 = n^2 + 2n - 47

n^2 - 49 = 0

(n-7)(n+7) = 0; n is either 7 or - 7

lets check our work

7+9 = 7*9 - 47

16 = 63 - 47

16 = 16 check

(note: -7 does not work here, because -16 does not equal positve 16; but don't worry our friends at the College Board will have - 16 as an answer choice).

This also would make a great "grid-in" or officially the "student response" where you have no multiple choice answers and have to come up with the answer on your own. There are 10 of these on the SAT.