abscissa: the distance along the horizontal axis in a coordinate graph.
absolute value: the numerical value when direction or sign is not considered. The symbol for absolute value is ∣ ∣.
additive axiom of equality: if a = b and c = d, then a + c = b + d.
additive axiom of inequality: if a > b, then a + c > b + c.
additive inverse: the opposite (negative) of a number. Any number plus its additive inverse equals 0.
algebra: arithmetic operations using letters and/or symbols in place of numbers.
algebraic expressions: expressions composed of letters to stand for numbers.
algebraic fractions: fractions using a variable in the numerator and/or denominator.
ascending order: basically, when the power of a term increases for each succeeding term.
associative property: grouping of elements does not make any difference in the outcome. Only true for multiplication and addition.
axioms of equality: basic rules for using the equal sign.
binomial: an algebraic expression consisting of two terms.
braces: grouping symbols used after the use of brackets. Also used to represent a set. { }
brackets: grouping symbols used after the use of parentheses. [ ]
canceling: in multiplication of fractions, dividing the same number into both a numerator and a denominator.
cartesian coordinates: a system of assigning ordered number pairs to points on a plane.
closed half-plane: a half-plane that includes the boundary line and is graphed using a solid line and shading.
closed interval: an interval that includes both endpoints or fixed boundaries.
closure property: when all answers fall into the original set.
coefficient: the number in front of a variable. For example, in 9x, 9 is the coefficient.
common factors: factors that are the same for two or more numbers.
commutative property: order of elements does not make any difference in the outcome. Only true for multiplication and addition.
complex fraction: a fraction having a fraction or fractions in the numerator and/or denominator.
composite number: a number divisible by more than just 1 and itself (such as 4, 6, 8, 9, . . . ). 0 and 1are not composite numbers.
conjugate: the conjugate of a binomial contains the same terms, but the opposite sign between them. (x + y) and (x − y) are conjugates.
coordinate axes: two perpendicular number lines used in a coordinate graph.
coordinate graph: two perpendicular number lines, the x axis and the y axis, creating a plane on which each point is assigned a pair of numbers.
coordinates: the numbers that correspond to a point on a coordinate graph.
cube: the result when a number is multiplied by itself twice. Designated by the exponent 3 (such as x3).
cube root: the number that when multiplied by itself twice gives you the original number. For example, 5 is the cube root of 125, which is symbolized as 
.
denominator: everything below the fraction bar in a fraction.
descending order: basically, when the power of a term decreases for each succeeding term.
direct variation: when y varies directly as x or y is directly proportional to x.
discriminant: the value under the radical sign in the quadratic formula. [b2 − 4ac]
distributive property: the process of distributing the number on the outside of the parentheses to each number on the inside. a(b + c) = ab + ac
domain: the set of all first coordinates from the ordered pairs in a relation.
element: a member of a set.
empty set: a set with no members (a null set).
equal sets: sets that have exactly the same members.
equation: a balanced relationship between numbers and/or symbols. A mathematical sentence.
equivalent sets: sets that have the same number of members.
Euler circles: a method of pictorially representing sets.
evaluate: to determine the value or numerical amount.
exponent: a numeral used to indicate the power of a number.
extremes: outer terms.
factor: to find two or more quantities whose product equals the original quantity.
finite: countable. Having a definite ending.
F.O.I.L. method: a method of multiplying binomials in which first terms, outside terms, inside terms, and last terms are multiplied.
function: a relation in which each element in the domain is paired with exactly one element in the range.
graphing method: a method of solving simultaneous equations by graphing each equation on a coordinate graph and finding the common point (intersection).
half-open interval: an interval that includes one endpoint, or one boundary.
half-plane: the region of a coordinate graph on one side of a boundary line.
identity element for addition: 0. Any number added to 0 gives the original number.
identity element for multiplication: 1. Any number multiplied by 1 gives the original number.
imaginary numbers: square roots of negative numbers. The imaginary unit is i.
incomplete quadratic equation: a quadratic equation with a term missing.
indirect variation or inverse variation: when y varies indirectly as x or y is indirectly proportional to x. That is, as x increases, y decreases and as y increases, x decreases. Also referred to as inverse or indirect proportion.
inequality: a statement in which the relationships are not equal. The opposite of an equation.
infinite: uncountable. Continues forever.
integer: a whole number, either positive, negative, or zero.
intersection of sets: the members that overlap (are in both sets).
interval: all the numbers that lie within two certain boundaries.
inverse relations: relations where the domain and the range have been interchanged—switching the coordinates in each ordered pair.
linear equation: an equation whose solution set forms a straight line when plotted on a coordinate graph.
literal equation: an equation having mostly variables.
means: inner terms.
monomial: an algebraic expression consisting of only one term.
multiplicative axiom of equality: if a = b and c = d, then ac = bd.
multiplicative inverse: the reciprocal of the number. Any number multiplied by its multiplicative inverse equals 1.
negative multiplication property of inequality: reverse the inequality sign when multiplying (or dividing) by a negative number. If c < 0, then a > b if, and only if, ac < bc.
nonlinear equation: an equation whose solution set does not form a straight line when plotted on a coordinate graph.
null set: a set with no members (an empty set).
number line: a graphic representation of integers and real numbers. The point on this line associated with each number is called the graph of the number.
numerator: everything above the fraction bar in a fraction.
numerical coefficient: the number in front of the variable.
open half-plane: a half-plane that does not include the boundary line. If the inequality is a ">" or "<", then the graph is an open half-plane.
open interval: an interval that does not include endpoints or fixed boundaries.
open ray: a ray that does include its endpoint (half line).
ordered pair: any pair of elements (x, y) having a first element x and a second element y. Used to identify or plot points on a coordinate grid.
ordinate: the distance along the vertical axis on a coordinate graph.
origin: the point of intersection of the two number lines on a coordinate graph. Represented by the coordinates (0,0).
polynomial: an algebraic expression consisting of two or more terms.
positive multiplication property of inequality: if c > 0, then a > b if, and only if, ac > bc.
proportion: two ratios equal to each other. For example, a is to c as b is to d.
quadrants: four quarters or divisions of a coordinate graph.
quadratic equation: an equation that could be written Ax2 + Bx + C = 0.
quadratic formula: a method of solving quadratic equations using the formula
radical sign: the symbol used to designate square root.
range: the set of all second (or y) coordinates from the ordered pairs in a relation.
ratio: a method of comparing two or more numbers. For example, a:b. Often written as a fraction, a/b.
real numbers: the set consisting of all rational and irrational numbers.
reducing: changing a numerical or algebraic fraction into its lowest terms. For example, 2/4 is reduced to 1/2, or a/ab is reduced to 1/b.
reflexive axiom of equality: for any number a, a = a.
relation: any set of ordered pairs.
repeating decimal: a decimal fraction that continues forever repeating a number or block of numbers.
roster: a method of naming a set by listing its members.
rule: a method of naming a set by describing its elements.
set: a group of objects, numbers, and so forth.
set builder notation: a formal method of describing a set. Often used for inequalities. For example, {x: x > 1}, which is read "x such that all x is greater than 1."
simplify: to combine several or many terms into fewer terms.
simultaneous equations (system of equations): a set of equations with the same unknowns (variables).
slope of a line: the ratio of the change in y to the change in x in a linear equation (slope = rise/run).
solution set (or solution): all the answers that satisfy the equation.
square: the result when a number is multiplied by itself. Designated by the exponent 2 (such as x2).
square root: the number that when multiplied by itself gives you the original number. For example, 5 is the square root of 25, which is symbolized as 
.
subset: a set within a set.
substitution method: a method of solving simultaneous equations that involves substituting one equation into another.
symmetric axiom of equality: if a = b, then b = a.
system of equations: simultaneous equations.
term: a numerical or literal expression with its own sign.
transitive axiom of equality: if a = b and b = c, then a = c.
transitive axiom of inequality: if a > b and b > c, then a > c. Or if a < b and b < c, then a < c.
trichotomy axiom of inequality: the only possible relationships between two numbers are: a > b, a = b, or a < b.
trinomial: an algebraic expression consisting of three terms.
union of sets: all the numbers in those sets.
universal set: the general category set, or the set of all those elements under consideration.
unknown: a letter or symbol whose value is not known.
value: numerical amount.
variable: a symbol used to stand for a number.
variation: a relationship between a set of values of one variable and a set of values of other variables.
Venn diagram: a pictorial description of sets.
vinculum: a line placed over (sometimes under) a digit or group of digits in a repeating decimal fraction to show which digits are repeating.
whole number: 0, 1, 2, 3, and so on.
