# Must Know SAT Math Definitions

Here are the most common SAT math definitions that you need to become familiar with. You will see this terminology throughout the SAT math test, so, make sure you understand them completely.

## Average (arithmetic mean)

The average (also called the “mean” or “arithmetic mean”) of a group of numbers is the sum of the numbers divided by the number of numbers. For example, the average of the group of numbers {2, 4, 9} is (2 + 4 + 9)/3 = 5. A typical SAT question might read: “The average of 2, x, 6, and 12 is 7. What is x?” In this case, the average is the sum of the numbers divided by 4. We can write: (2+x+6+12)/4 = 7 ⇒ x+20 = 28 ⇒ x = 8.

## Median

The median of a group of numbers is the number in the middle of the group after the group has been numerically sorted. For example, the median of the numbers {9, 2, 4} is 4, since when sorted, the numbers are {2, 4, 9}, and 4 is in the middle. For groups with an even number of numbers, the median is the average of the two middle numbers. For example, the median of the numbers {1, 1, 2, 4, 4, 9} is (2 + 4)/2 = 3.

## Mode

The mode of a group of numbers is the number or numbers which appear most often (there can be more than one mode for a given group). For example, the mode of the group of numbers* {1, 2, 3, 3, 3, 4, 5, 6, 6, 6, 7, 8, 8}* is both 3 and 6. in terms of You are often asked on the SAT to solve for some variable

*“in terms of”*another variable or variables. For example, if

*, and you are asked to solve for*

**6a + 12b = 3a + 6b − 9c + 15***a*in terms of

*b*and

*c,*then simply solve for a with all other variables and numbers on the other side of the equation. Here, you would get

*so that*

**3a = 15 − 6b − 9c***.*

**a = 5 − 2b − 3c**## Integers

Integers are numbers without a fractional part (and that is why they are often called the whole numbers). Integers include 1, 2, 3, . . . (the counting numbers) along with 0, −1, −2, −3, . . .

## Rational

A rational number is any number that can be written as a fraction: a ratio of two integers. Rational numbers include 1/2, 3/4, 5 (since 5 = 5/1), 22/7, 1/3, and so on. These numbers can always be written as a finite decimal or as an infinite decimal that repeats. For example, 2/5 = 0.4, 7/11 = 0.6363, and 22/7 = 3.142857. Important rational numbers to know from memory as decimals are: 1/2 = 0.5, 1/3 = 0.33, 1/4 = 0.25, 1/5 = 0.2, 2/3 = 0.66, and 3/4 = 0.75.

## Real

The real numbers are all the numbers on the number line, including the integers, the rational numbers, and everything else, which includes, for example, the irrational numbers such as √ 2 and π. Not to be confused with the fake numbers.

## Domain

The domain of a function is all of the possible values that can be used as input to the function, so that the function returns a real value. If the function is written as ** y = f(x)**, the domain is all possible values of x such that y is a real number. For example, the domain of the function

*is all real numbers except for x = 1, since if x = 1, the denominator is 0 and the function “blows up”. The domain of f*

**f(x) = 1/(1 − x)****is all positive real numbers, along with zero.**

*(x) = √ x*## Range

The range of a function is all of the possible values that can be generated (output) by the function. If the function is written as y = f(x), then the domain is all possible values of y. For example, the range of the function f(x) = |x| is all positive real numbers along with 0. Occasionally, “range” is applied to a set of numbers, in which case it means the positive difference between the largest member of the set and the smallest member. For example, the range of the set {6, 8, 1, 4} is 8 − 1 = 7.

## Periodic function

Periodic functions are functions whose values repeat on a regular interval. This regular interval is called the function’s period. In other words, the period of a function is the smallest domain containing a full cycle of the function.

## Chord

A chord is a line segment whose endpoints lie on the circle, but it does not necessarily pass through the center. Therefore, a diameter is always a chord but a chord is not always a diameter.

## Tangent

A line that touches the circle at only one point is called a tangent.

## Secant

An extended line that intersects the circle at two points is called a secant.

## Arc

Any connected part of a circle is called an arc.

## Sector

A region bounded by two radii and an arc lying between the radii is called a sector.

## Segment

A region, not containing the center, bounded by a chord and an arc lying between the chord’s endpoints is called a segment

## Ratios

A ratio is used to compare two quantities. Ratios are typically written in one of three ways – as fractions, as numbers separated by a colon, or as words – , 2 : 3, or 2 to 3.

While we may not realize it, we use ratios every day. For example, when we talk about a vehicle’s rate of travel being 45 mph, we are talking about the ratio of distance traveled to time traveled.

## Exponential Growth

An exponential function with a > 0 and b > 1, represents an exponential growth and the graph of the function rises from left to right.

## Exponential Decay

An exponential function where a > 0 and 0 < b < 1 represents an exponential decay and the graph of the function falls from left to right