Algebra I Glossary

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 (xy) 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 [img id:59962].

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 [img id:59963].

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.

x-axis the horizontal axis in a coordinate graph.

x-coordinate the first number in the ordered pair. Refers to the distance on the x-axis (the abscissa).

y-axis the vertical axis in a coordinate graph.

y-coordinate the second number in the ordered pair. Refers to the distance on the y-axis (the ordinate).