APPENDIX B

Glossary of GRE
Math Terms
T

his glossary includes many of the concepts tested on the GRE Quantitative
section. We recommend that you thoroughly review difficult mathematicalconcepts, and refer to this glossary as necessary during your preparation.

AAbsolute 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.
Acute Angle An angle less than 90 degrees.
Adjacent Angle Either of two angles having a common side and common
vertex. For example, in the following figure, angles a and b are adjacent angles:

ab

Arc

A portion of the circumference of a circle, as shown in the following figure:
BArc BCACThe complete arc of a circle has 360°.

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Appendix B: Glossary of GRE Math Terms
Area The number of square units that covers the shape or figure. Following arethe formulas for the area of some common figures:• Square: side (s) squared (s2)• Rectangle: length (l) times width (w) (l  w)
• Circle: pi () times the radius (r) squared (r2)
1 b  h)• Triangle: one half the base (b) times the height (h) (__2

Arithmetic Mean (see Average) The average of a group of values. Calculate thearithmetic mean by dividing the sum of all of the values in the group by the total
count of values in the group. For example, the average of the 3 test scores 82%,83%, and 87% is equivalent to (82  83  87) divided by 3; 252  3  84.
Associative Property A mathematical property whereby the grouping ofnumbers being added or multiplied can be changed without changing the sumor the product. The associative property of multiplication can be expressed as(a  b)  c  a  (b  c). Likewise, the associative property of addition can beexpressed as (a  b)  c  a  (b  c).
Average (see Arithmetic Mean) The arithmetic mean of a group of values.
Calculate the average by dividing the sum of all of the values in the group by thetotal count of values in the group. For example, the average of the 3 test scores
82%, 83%, and 87% is equivalent to (82  83  87) divided by 3; 252  3  84.
B–C
Base In geometry, the bottom of a plane figure. For example, in the right triangle
that follows, AC is the base:BAC

In algebra, the base is the number that is raised to various powers. For example,
23 indicates a base of 2 raised to the power of 3.

Circumference The distance around a circle. The circumference of a circle isequal to pi times the diameter (d). The formula for the circumference of a circle
can also be expressed as 2r, because the diameter, d, is twice the radius, r.
Collinear A term referring to points that pass through or lie on the same straightline.

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441

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, thecommutative property of multiplication is expressed as a  b  b  a, or ab  ba.
Complementary Angles Two angles for which the sum is 90 degrees.
Congruent A term describing any shapes or figures, including line segments
and angles, that have the same size or measure. For example, in the triangle
below, sides AB and BC are congruent, and angles A and C are congruent:B

101050°50°
CACoordinate 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 thex-axis, and the vertical axis is the y-axis, as shown in the following figure:y(0, 0)x

You can locate any point (x,y) on the coordinate plane by an ordered pair ofnumbers. The ordered pair (0,0), where the x and y axes meet, is the origin.

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Appendix B: Glossary of GRE Math Terms
The coordinate plane is divided into four quadrants, as shown in the following
figure:y+4
3
2
1–x–4–3–2

–1

1

2

3x+

4–1
–2
–3
–4–yDDecimal 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 thedigits are tenths, hundredths, thousandths, and so on.
3,Denominator The bottom part of a fraction. For example, in the fraction __4
4 is the denominator.

Diagonal A line segment that connects two nonadjacent vertices in any polygon.
In the following rectangle, AC and BD are diagonals:
BCA

D

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443

Diameter A line segment that joins two points on a circle and passes throughthe center of the circle, as shown in the following figure, where AB is thediameter:

AB

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.
Divisible Capable of being divided, usually with no remainder. For example, 6 isdivisible by 2, because when 6 is divided by 2, the result is 3 with no remainder.
E–F
Equilateral Triangle A triangle in which all of the sides are congruent and eachof the angles equals 60 degrees.
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, 23 indicates 2 raised to the power of 3, which translates into2  2  2. In this instance, 3 is the exponent.
Factor One of two or more expressions that are multiplied together to geta product. For example, in the equation 2  3  6, 2 and 3 are factors of 6.
Likewise, in the equation x2  5x  6, (x  2) and (x  3) are factors.
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)  x2
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 x2  5x  6Fraction An expression that indicates the quotient of two quantities.
2 is a fraction, where 2 is the numerator and 3 is the denominator.
For example, __3Frequency Distribution The frequency with which a data value occurs in any
given set of data.

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Function A set of ordered pairs where no two of the ordered pairs has the samex-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.
G–H–I
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 factorof 8 and 6 is 2.
Hexagon A six-sided figure, shown below:

Hypotenuse The leg of a right triangle that is opposite the right angle. For
example, in the right triangle in the following figure, BC is the hypotenuse:
BAC

The hypotenuse is always the longest leg of a right triangle.
1 is an
Improper Fraction An integer combined with a fraction. For example, 2__2
improper fraction (see also Mixed Number).

Inequality A mathematical expression that shows that two quantities are notequal. 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.
Integer Integers include both positive and negative whole numbers. Zero is also
considered an integer.
Interior Angle The angle inside two adjacent sides of a polygon. The sum of theinterior angles in a triangle is always 180 degrees.
Irrational Number A number that cannot be exactly expressed as the ratio oftwo integers. For example,  (3.14) is an irrational number.
Isosceles Triangle A triangle in which two sides have the same length.

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445

J–L
Least Common Denominator (LCD) The smallest multiple of the denominators
3 and __
2of two or more fractions. For example, the least common denominator of __45
is 20.
Least Common Multiple (LCM) The smallest number that any two or morenumbers 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.
Like Terms Terms that contain the same variable raised to the same power. Forexample, 3x2 and 10x2 are like terms that can be combined to get 13x2. Also, x
and 4x are like terms that can be combined to get 3x.
Line A straight set of points that extends into infinity in both directions, as
shown in the following figure:lLine Segment A figure representing two points on a line and all of the points inbetween, as shown in the following figure:y(1, 3)(7, 3)
xM–N
Median The middle value of a series of numbers when those numbers are ineither 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 twonumbers. In the series (3, 4, 5, 6) the median is 4.5.
Midpoint The center point of a line segment. To find the midpoint of a liney 1  y2 ][ x1  x2 ], [________
given two points on the line, use the formula ________.
22Mixed Number A number that combines an integer with a fraction. Mixed
1 is a mixed number.
numbers are also called Improper Fractions; 1__2446

Appendix B: Glossary of GRE Math Terms
Mode The number that appears most frequently in a series of numbers. In theseries (2, 3, 4, 5, 6, 3, 7) the mode is 3, because 3 appears twice in the series andthe other numbers each appear only once in the series.
Number Line The line on which every point represents a real number. On anumber 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.
3, 3 is theNumerator The top part of a fraction. For example, in the fraction __4numerator.

O–P
Obtuse Angle An angle that measures greater than 90 degrees and less than 180degrees.
Octagon An eight-sided figure, shown as follows:

Parallel A term that describes two distinct lines that lie in the same plane anddo 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 thesame slope (3) (see Point-slope Form).
Parallelogram A quadrilateral in which the opposite sides are of equal lengthand the opposite angles are equal, as shown below:
85145°

35°
535°

145°
8The sum of the angles in a parallelogram is always 360 degrees.

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447

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.

Pentagon A five-sided figure, shown as follows:

Percent A fraction whose denominator is 100. The fraction 25/100 is equal to25% and can also be expressed as 0.25.
Perimeter The distance around any shape or object. Following are the formulas
for the perimeter of some common figures:• The perimeter (P) of a rectangle is equivalent to 2l  2w, where l is thelength and w is the width.
• The perimeter (P) of a square is 4s, where s is the length of a side.
• The perimeter (P) of other polygons is the sum of the lengths of the sides.
• The perimeter (P) of a triangle is the sum of the lengths of the sides.

Perpendicular A term describing two distinct lines whose intersection createsa right angle. Two lines are perpendicular if and only if the slope of one of thelines is the negative reciprocal of the slope of the other line. In other words,
1, then the two lines are
if line a has a slope of 2, and line b has a slope of __2
perpendicular.
Point A location in a plane or in space that has no dimensions.
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.
Polygon A closed plane figure made up of at least three line segments that arejoined. For example, a triangle, a rectangle, and an octagon are polygons.
Polynomial A mathematic expression consisting of more than two terms.
2x2  4x  4 is a simple quadratic equation, and also a polynomial.

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Appendix B: Glossary of GRE Math Terms
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.
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 inhis 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
3.
is 3 out of 7, which can also be expressed as 3:7, or __7
Proportion A mathematical statement indicating that one ratio is equal tox is a proportion.
1  ___
another ratio. For example, __5 20
Pythagorean Theorem This theorem applies only to finding the length of thesides in right triangles, and states that c2  a2  b2, where c is the hypotenuse(the side opposite the right angle) of a right triangle and a and b are the two othersides of the triangle.
Q–R
Quadrilateral Any four-sided polygon with four angles. A parallelogram, arectangle, a square, and a trapezoid are all examples of quadrilaterals.
Quotient The result of division.
Radius The distance from the center of a circle to any point on the circle, as
shown below in the following circle with center C:

radius (r )C

Ratio A mathematical comparison between two quantities. A ratio of 1 to 5, for
1 or 1:5.
example, is written as either __5
Rational Number A fraction whose numerator and denominator are bothintegers and the denominator does not equal 0.
Real Number Any rational or irrational number, used to express quantities,lengths, amounts, and the like. All real numbers correspond to points on thenumber line. All real numbers except zero are either positive or negative.
1
Reciprocal Given a number, n, the reciprocal is expressed as 1 over n, or __n.
The product of a number and its reciprocal is always 1. In other words,
3  __
3, which is equivalent to 1.
1  ____
3 1 3

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449

Rectangle A polygon with four sides (two sets of congruent, or equal sides) and
four right angles. All rectangles are parallelograms.
Right Angle An angle that measures 90 degrees.
S–T
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 anarithmetic 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
1.
1 : 16, 8, 4, 2, 1, __between the terms is __2
2
Set A well-defined group of numbers or objects. For example, {2, 4, 6, 8} is theset of positive even whole numbers less than 10.
Similar Triangles Triangles in which the measures of corresponding angles areequal and the corresponding sides are in proportion, as shown in the followingfigure:
2240°

40°

6640°

40°

Slope The change in y-coordinates divided by the change in x-coordinates fromy1  y2
two given points on a line. The formula for slope is m  _________xx1  , where (x1,y1) 2and (x2,y2) are the two given points. For example, the slope of a line that contains(6 5)
1, which equals 1.
the points (3,6) and (2,5) is equivalent to _______, or __1(3 2)
Slope-intercept Equation y  mx  b, where m is the slope of the line and b isthe y-intercept (that is, the point at which the graph of the line crosses the y-axis).
Special Triangles Triangles whose sides have special ratios. The following areangle measures and side lengths for special right triangles:

2x45°

60°
xs 2s

30°

45°x 3s30-60-90 Triangle

45-45-90 Triangle

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Square A number multiplied by itself. Squaring a negative number yields a
positive result. For example, 22  4.
Square Root Given a number, n, the square root is written as n , or thenon-negative value a that fulfills the expression a2  n. For example, the squareroot of 5 is expressed as 5 , and   5 2  5.
System of Equations A group of two or more equations with the same set ofunknowns. In solving a system of equations, try to find values for each of theunknowns that will satisfy every equation in the system.
Triangle

A closed plane figure having three sides and three angles.

V–Z
Volume A measure of space or capacity of a three-dimensional object. Theformula for the volume of a rectangular solid is V  lwh, where l  length,w  width, and h  height.
y-intercept The point at which a line crosses the y-axis in the (x,y)–coordinate
plane.