A few months ago we sent you some key math vocabulary words. Understanding math terms is essential for acing the math sections of the ACT and SAT. Please e-mail us if you missed the first math vocabulary newsletter and would like us to send it to you. Here are some more important terms:
CONSTANT
A constant means an unchanging number, like 3, as opposed to a variable, like x.
Warning! The SAT will often use a letter to stand for a constant. For example:
“The population of hummingbirds t years after 1980 can be given by the equation 5000t + k, where k is a constant.”
However, notice the difference between t (a variable) and k (a constant). t stands for the number of years after 1980, so you could plug in different numbers for t depending on what year you were interested in.
k, on the other hand, is always the same number. This would be a perfect opportunity to use Picking Numbers: replace k with a number of your choice to make the question more straightforward.
INTEGER
A whole number, such as -5 or 18.
Yes, integers may be positive or negative. And don’t forget zero, especially on hard questions!
RATIONAL NUMBER
This one’s confusing. There are several correct definitions. Just remember that ALL of the following are rational numbers:
(a) Any fraction (that includes integers – remember, 3 is the same as 3/1)
(b) Any repeating decimal (such as 0.4545454545…)
(c) Any terminating decimal (i.e. any decimal that stops at some point)
You may ask, “What’s left?” The only non-rational (irrational) numbers are decimals that go on forever with no apparent pattern, such as π = 3.141592653… or √2 = 1.4142135…
nth TERM
Once in a while, the SAT will ask about a sequence of numbers, such as the following:
4, 7, 10, 13, 16, . . .
“The first term of the above sequence is 4, and each term after the first is three more than the preceding term. Which of the following expressions represents the nth term of the sequence?”
The letter n refers to a number’s place in the sequence. For example, 16 is the 5th term, so n = 5.
Whenever you’re working with sequences and the “nth term” is mentioned, it’s a good idea to write a row for n on top, like this:
n: 1 , 2 , 3 , 4 , 5 , 6 , 7 , etc
S: 4, 7, 10, 13, 16, 19, 22, etc.
UNITS DIGIT
For its own nefarious reasons, the SAT prefers to say “units digit,” even though every student learns this concept as “the ones place.”
In the number 452, the “units digit” is 2.
BONUS: Even vs. Positive
I know you know what an even number is, and I know you know what a positive number is.
However, time after time, SAT students at every level get the two mixed up. This is probably because even numbers and positive numbers are both “nice” kinds of numbers. Just be aware of this phenomenon and be extra alert whenever you see one of these key words mentioned.