GRE Math Glossary
Diagonal
A line segment that connects two nonadjacent vertices in any polygon. In the following rectangle, AC and BD are diagonals:
Diameter
A line segment that joins two points on a circle and passes through the center of the circle
Point
A location in a plane or in space that has no dimensions.
Polynomial
A mathematic expression consisting of more than two terms. 2x^2 + 4x + 4 is a simple quadratic equation, and also a polynomial.
Ratio
A mathematical comparison between two quantities. A ratio of 1 to 5, for example, is written as either 1/5 or 1:5.
Inequality
A mathematical expression that shows that two quantities are not equal. For example, 2x < 8 is an inequality that means that 2x is less than 8. Likewise, 3a > 17 is an inequality that means that 3a is greater than 17.
Distributive Property
A mathematical property observed when an expression involves both addition and multiplication. The distributive property is expressed as a(b + c) = ab + ac, where the variable a is distributed to the variables b and c.
Like Terms
Terms that contain the same variable raised to the same power. For example, 3x^2 and 10x^2 are like terms that can be combined to get 13x^2. Also, -x and 4x are like terms that can be combined to get 3x.
Interior Angle
The angle inside two adjacent sides of a polygon. The sum of the interior angles in a triangle is always 180 degrees.
Arithmetic Mean (see Average)
The average of a group of values. Calculate the arithmetic mean by dividing the sum of all of the values in the group by the total count of values in the group
Denominator
The bottom part of a fraction. For example, in the fraction 3/ 4 , 4 is the denominator.
Midpoint
The center point of a line segment. To find the midpoint of a line given two points on the line, use the formula
Slope
The change in y-coordinates divided by the change in x-coordinates from two given points on a line. The formula for slope is m = (y2 - y1)/ (x2 - x1) , where (x1,y1) and (x2,y2) are the two given points. For example, the slope of a line that contains the points (3,6) and (2,5) is equivalent to (6-5)/ (3-2) , or 1/1 , which equals 1.
Circumference
The distance around a circle. The circumference of a circle is equal to pi times the diameter (pi d). The formula for the circumference of a circle can also be expressed as 2(pi)r, because the diameter, d, is twice the radius, r.
Perimeter
The distance around any shape or object.
Radius
The distance from the center of a circle to any point on the circle, as shown below in the following circle with center:
Point-slope Form
The equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.
Frequency Distribution
The frequency with which a data value occurs in any given set of data.
System of Equations
A group of two or more equations with the same set of unknowns. In solving a system of equations, try to find values for each of the unknowns that will satisfy every equation in the system.
Perimiter of a Square
4s, where s is the length of a side
Triangle
A closed plane figure having three sides and three angles.
Polygon
A closed plane figure made up of at least three line segments that are joined. For example, a triangle, a rectangle, and an octagon are polygons.
Line Segment
A figure representing two points on a line and all of the points in between, as shown in the following figure:
Pentagon
A five-sided figure
Percent
A fraction whose denominator is 100. The fraction 25/100 is equal to 25% and can also be expressed as 0.25.
Rational Number
A fraction whose numerator and denominator are both integers and the denominator does not equal 0.
Associative Property
A mathematical property whereby the grouping of numbers being added or multiplied can be changed without changing the sum or the product. The associative property of multiplication can be expressed as (a X b) X c = a X (b X c). Likewise, the associative property of addition can be expressed as (a + b) + c = a + (b + c).
Commutative Property
A mathematical property whereby the order of numbers being added or multiplied can be changed without changing the sum or the product. The commutative property of addition is expressed as a + b = b + a. Likewise, the commutative property of multiplication is expressed as a X b= b X a, or ab = ba.
Proportion
A mathematical statement indicating that one ratio is equal to another ratio. For example, 1/5 = x/20 is a proportion.
Volume
A measure of space or capacity of a three-dimensional object. The formula for the volume of a rectangular solid is V = lwh, where l = length, w = width, and h = height.
FOIL Method
A method of multiplying two binomials, such as (x + 2) and (x + 3), according to the following steps: Multiply the FIRST terms together: (x)(x) = x^2 Multiply the OUTSIDE terms together: (x)(3) = 3x Multiply the INSIDE terms together: (2)(x) = 2x Multiply the LAST terms together: (2)(3) = 6 Now, combine like terms to get x^2 + 5x + 6
Square
A number multiplied by itself. Squaring a negative number yields a positive result. For example, -2^2 = 4.
Irrational Number
A number that cannot be exactly expressed as the ratio of two integers. For example, pi (~3.14) is an irrational number.
Exponent
A number that indicates the operation of repeated multiplication. A number with an exponent is said to be "raised to the power" of that exponent. For example, 2^3 indicates 2 raised to the power of 3, which translates into 2 X 2 X 2. In this instance, 3 is the exponent.
Absolute Value
A number's distance on the number line from 0, without considering which direction from 0 the number lies. Therefore, absolute value will always be positive.
Coordinate Plane
A plane, typically defined with the coordinates x and y, where the two axes are at right angles to each other. The horizontal axis is the x-axis, and the vertical axis is the y-axis, as shown in the following figure:
Rectangle
A polygon with four sides (two sets of congruent, or equal sides) and four right angles. All rectangles are parallelograms.
Arc
A portion of the circumference of a circle, as shown in the following figure: The complete arc of a circle has 360°.
Parallelogram
A quadrilateral in which the opposite sides are of equal length and the opposite angles are equal, as shown below: The sum of the angles in a parallelogram is always 360 degrees.
Function
A set of ordered pairs where no two of the ordered pairs has the same x-value. In a function, each input (x-value) has exactly one output (y-value). For example, f(x) = 2x + 3. If x = 3, then f(x) = 9. For every x, only one f(x), or y, exists.
Hexagon
A six-sided figure, shown below:
Line
A straight set of points that extends into infinity in both directions, as shown in the following figure:
Congruent
A term describing any shapes or figures, including line segments and angles, that have the same size or measure.
Perpendicular
A term describing two distinct lines whose intersection creates a right angle. Two lines are perpendicular if and only if the slope of one of the lines is the negative reciprocal of the slope of the other line. In other words, if line a has a slope of 2, and line b has a slope of -1/2 , then the two lines are perpendicular.
Collinear
A term referring to points that pass through or lie on the same straight line.
Parallel
A term that describes two distinct lines that lie in the same plane and do not intersect. Two lines are parallel if and only if they have the same slope. For example, the two lines with equations 2y = 6x + 7 and y = 3x + 14 have the same slope (3) (see Point-slope Form).
Equilateral Triangle
A triangle in which all of the sides are congruent and each of the angles equals 60 degrees.
Isosceles Triangle
A triangle in which two sides have the same length.
Set
A well-defined group of numbers or objects. For example, {2, 4, 6, 8} is the set of positive even whole numbers less than 10.
PEMDAS
An acronym that describes the correct order in which to perform mathematical operations. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. It should help you to remember to do the operations in the correct order, as follows: P First, do the operations within the parentheses, if any. E Next, do the exponents, if any. M, D Next, do the multiplication or division, if any. A, S Next, do the addition or subtraction, in order from left to right, if any.
Acute Angle
An angle less than 90 degrees
Right Angle
An angle that measures 90 degrees.
Obtuse Angle
An angle that measures greater than 90 degrees and less than 180 degrees
Sequence
An arithmetic sequence is one in which the difference between one term and the next is the same. For example, the following sequence is an arithmetic sequence because the difference between the terms is 2: 1, 3, 5, 7, 9. A geometric sequence is one in which the ratio between two terms is constant. For example, the following sequence is a geometric sequence because the ratio between the terms is 1/2 : 16, 8, 4, 2, 1, 1/2
Octagon
An eight-sided figure
Fraction
An expression that indicates the quotient of two quantities. For example, 2/3 is a fraction, where 2 is the numerator and 3 is the denominator.
Improper Fraction
An integer combined with a fraction. For example, 2 1/2 is an improper fraction (see also Mixed Number).
Quadrilateral
Any four-sided polygon with four angles. A parallelogram, a rectangle, a square, and a trapezoid are all examples of quadrilaterals.
Prime Number
Any number that can only be divided by itself and 1. That is, 1 and number itself are the only factors of a prime number. For example, 2, 3, 5, 7, and 11 are prime numbers.
Real Number
Any rational or irrational number, used to express quantities, lengths, amounts, and the like. All real numbers correspond to points on the number line. All real numbers except zero are either positive or negative.
Divisible
Capable of being divided, usually with no remainder. For example, 6 is divisible by 2, because when 6 is divided by 2, the result is 3 with no remainder.
Adjacent Angle
Either of two angles having a common side and common vertex. For example, in the following figure, angles 1 and 2 are adjacent angles:
Perimeter of a Rectangle
Equivalent to 2l + 2w, where l is the length and w is the width.
Reciprocal
Given a number, n, the reciprocal is expressed as 1 over n, or 1/n . The product of a number and its reciprocal is always 1. In other words, 1/3 X 3/1 = 3/3 , which is equivalent to 1.
Square Root
Given a number, n, the square root is written as sqrt n , or the non-negative value a that fulfills the expression a^2 = n. For example, the square root of 5 is expressed as sqrt5 , and (sqrt5)^2 = 5.
Base
In geometry, the bottom of a plane figure. In algebra, the base is the number that is raised to various powers. For example, 2^3 indicates a base of 2 raised to the power of 3.
Integer
Integers include both positive and negative whole numbers. Zero is also considered an integer
Factor
One of two or more expressions that are multiplied together to get a product. For example, in the equation 2 X 3 = 6, 2 and 3 are factors of 6. Likewise, in the equation x^2 + 5x + 6, (x + 2) and (x + 3) are factors.
Greatest Common Factor (GCF)
The largest number that will divide evenly into any two or more numbers. For example, 1, 2, 4, and 8 are all factors of 8; likewise, 1, 2, 3, and 6 are all factors of 6. Therefore, the greatest common factor of 8 and 6 is 2.
Hypotenuse
The leg of a right triangle that is opposite the right angle. The hypotenuse is always the longest leg of a right triangle
Probability
The likelihood that an event will occur. For example, Jeff has three striped and four solid ties in his closet; therefore, he has a total of seven ties in his closet. He has three chances to grab a striped tie out of the seven total ties, because he has three striped ties. So, the probability of Jeff grabbing a striped tie is 3 out of 7, which can also be expressed as 3:7, or 3/7
Number Line
The line on which every point represents a real number. On a number line, numbers that correspond to points to the right of zero are positive, and numbers that correspond to points to the left of zero are negative. For any two numbers on the number line, the number to the left is less than the number to the right.
Median
The middle value of a series of numbers when those numbers are in either ascending or descending order. In the series (2, 4, 6, 8, 10) the median is 6. To find the median in an even set of data, find the average of the middle two numbers. In the series (3, 4, 5, 6) the median is 4.5.
Area
The number of square units that covers the shape or figure.
Mode
The number that appears most frequently in a series of numbers. In the series (2, 3, 4, 5, 6, 3, 7) the mode is 3, because 3 appears twice in the series and the other numbers each appear only once in the series
y-intercept
The point at which a line crosses the y-axis in the (x,y)-coordinate plane.
Decimal
The point that separates values less than 1 from those greater than 1. In our number system, digits can be placed to the left and right of a decimal point. Place value refers to the value of a digit in a number relative to its position. Starting from the left of the decimal point, the values of the digits are ones, tens, hundreds, and so on. Starting to the right of the decimal point, the values of the digits are tenths, hundredths, thousandths, and so on.
Quotient
The result of division.
Least Common Denominator (LCD)
The smallest multiple of the denominators of two or more fractions. For example, the least common denominator of 3/4and 2/5 is 20.
Least Common Multiple (LCM)
The smallest number that any two or more numbers will divide evenly into. For example, the common multiples of 3 and 4 are 12, 24, and 36; 12 is the smallest multiple, and is, therefore, the least common multiple of 3 and 4.
The perimeter of a triangle
The sum of the lengths of the sides.
Numerator
The top part of a fraction. For example, in the fraction 3/4 , 3 is the numerator.
Pythagorean Theorem
This theorem applies only to finding the length of the sides in right triangles, and states that c^2 = a^2 + b^2, where c is the hypotenuse (the side opposite the right angle) of a right triangle and a and b are the two other sides of the triangle.
Similar Triangles
Triangles in which the measures of corresponding angles are equal and the corresponding sides are in proportion, as shown in the following figure:
Special Triangles
Triangles whose sides have special ratios.
Complementary Angles
Two angles for which the sum is 90 degrees.
Area of a rectangle
length (l) times width (w) l x w
Area of a triangle
one half base times height
Area of a circle
pi times the radius (r) squared
Area of a square
side (s) squared (s^2)
The perimeter of other polygons
the sum of the lengths of the sides.
Slope-intercept Equation
y = mx + b, where m is the slope of the line and b is the y-intercept (that is, the point at which the graph of the line crosses the y-axis).
