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Algebra Glossary A-Z

Have fun by learning Algebra Terminology.

absolute valueThe distance from the origin to the coordinate x.
absolute value of a complex numberThe absolute value of a complex number a + bi is the square root of a square plus b square.
additive inversesPairs of real number that have the sum 0.
additive inverse of a matrixFor each matrix A, there is a matrix -A(the additive inverse of A), such that A + (-A) = Z.
algebraic expressionsExpressions that are made up of variables, numbers, grouping sym- bols, operation signs, and exponents.
amplitudeHalf the difference between the maximum and minimum values of a periodic function.
angle or depressionAn angle that measures between 0' and 90' formed by a horizontal ray and a ray from the observer to the object observed below.
angle of elevationAn angle that measures between 0 and 90 formed by a horizontal ray and a ray from the observer to the object observed above.
arithmetic meanThe sum of the num- bers in a set divided by the number of numbers in the given set.
arithmetic meansTerms of an arithmetic se- quence that are between two given terms.
arithmetic sequenceFor each positive inte- ger n, the sequence with the first term a, and nth term a, is an arithmetic sequence if and only if an = a1 + (n - 1)d.
arithmetic seriesThe indicated sum of the terms of an arithmetic sequence.
asymptotes (of a hyperbola)The lines within which the branches of the hyperbola lie, and which are approached by the branches as |x| increases.
augmented matrixThe coefficient matrix for a system of linear equations with a final column included for the constants of the equations.
axis of symmetryA line in the plane of a graph such that the part of the graph on one side of the line is a reflection of the part on the other side.
biased -sampleA sample that is not random.
binomialA polynomial with two terms.
boundary conditionAn extreme value in an inequality problem. Solutions will be less than or greater than that value.
center of a circleThe point in a circle from which the distance to any point on the circle is a constant.
center of an ellipseThe intersection of the axes of symmetry.
central tendency of a set of numbersA number considered to be the most typical or representative of that set.
circleThe set of all points in a plane such that the distance (radius) from a given point (center of the circle) is constant.
circular functionsPeriodic functions related to the unit circle.
closureA set of numbers is closed under an operation if combining any two elements in the set by that operation yields a number in the set.
coefficientThe constant factor of a monomial.
common ratioThe common ratio is a constant.
complement of an eventEvent A is a com- plement of event B with respect to sample spaceS if and only if A and 8 include all outcomes of S, and A and B have no outcomes in common.
completing the squareA method used to solve a quadratic equation in which a number is added to both sides of the equation so that one side is a perfect square.
complex conjugateFor all real numbers a and b, a + bi and a - bi are complex conjugates.
complex fractionA fraction that has frac- tions in either the numerator or the denominator or both.
complex numberA number of the form a + bi, where a and b are real numbers and i is the imaginary unit.
components or an ordered pairThe individual numbers in an ordered pair.
compound inequalityA sentence linking two conditions with "and" or "or". At least one of the conditions is an inequality.
conic sectionA curve that has a sec- ond-degree equation and is defined in terms of the distance of its points from fixed points and/or lines. This includes circles, parabolas. ellipses and hyperbolas.
conjugateTwo binomials of the form (a + Nt/b) and (a - N/b). where a and b are rational numbers.
consistent system of equationsA system that has at least one solution.
constantA number or a polynomial of degree 0.
constant differenceThe difference be- tween successive terms in a sequence
constant of inverse variationThe number k in the inverse variation Y = K/X.
constant linear functionA function whose equation can be written in the form y = b and whose graph is a horizontal line.
constant term of a polynomialThe term a which can be considered the coefficient of x.
constant term of a quadratic equationThe term c in the form V = ax- + bx + r.
constant of variationThe number k in the direct variation y = kx or in the inverse variation Y = K/X.
continuousA polynomial function whose graph is smooth without "jumps".
convergeIf there is a real number that is the value of the infinite series, the series converges.
convex polygonal regionA region that has a polygon with no "indentations" as a boundary.
coordinateThe number associated with a particular point on a number line.
coordinate axesTwo perpendicular lines selected in a plane.
coordinates of a pointThe numbers of an ordered pair.
correlation coefficientA number between - I and + I which is a measure of the dispersion of data points about a regression line.
corresponding elements of matricesFor two matrices with the same dimensions. the elements in the same row and the same column.
cubic polynomialA polynomial of degree 3.
cycleThe graph of a periodic function through one fundamental period.
decreasing functionfunction such that for any numbers a and b in the domain. if a > b. then f(a) < f(b).
degree of a monomialThe sum of the exponents of the variables.
degree of a polynomialThe degree of the term (or terms) of highest degree.
dependent eventsTwo events A and B are dependent if and only if (A and then B) * P(A) - P(B).
dependent systemA system whose gr-aphs coincide and that has infinitely many solutions.
dependent variableIf the value of a de- pends on the value of b, or if a is usually defined in terms of b, a is called the dependent variable. and it is graphed on the vertical axis.
depressed equationThe equation Q(x) = 0. where Q(x) is the quotient when a polynomial has been divided by a factor (x - r).
descending orderA polynomial is written in descending order when the term with highest de- gree is written first, followed by the term with next highest degree second, and so on.
determinantA real number represented by a square array of numbers.
determinant of a matrixThe determinant of a matrix is the determinant with the same corre- sponding elements.
dimensions of a matrixThe number of rows and the number of columns.
direct variationTwo variables are said to vary directly if and only if there is a constant of variation or (constant of proportionality) k. k ¹ 0. such that y = kx.
directed networkA network that indicates the direction of flow on each arc.
directrixA line used in the definition of a conic section.
discriminantThe expression b2 - 4ac of the quadratic formula that determines several characteristics of the roots of a quadratic equation.
dispersionA measure of how closely a set of data are clustered about the mean.
distance formulaFor points P1(X1, Y1) and P2(Y1, Y2), P1P2 = Ö (X2-X1)^2 + (Y2-Y1)^2.
divergeIf there is no real number that is the value of an infinite series, the series diverges.
domain of a relationThe set of first components of the ordered pairs in the relation.
double rootTwo roots that are alike
eccentricityA ratio used in some definitions of conic sections.
ellipseThe set of all points in a plane such that the sum of the distances (focal radii) from two given points (foci) is constant.
ellipsisA symbol indicating that the pattern-continues in a sequence.
equivalent transformationA transformation that results in an equation equivalent to the original.
eventA subset of a sample space.
explicit definitionA definition used to state the relationship between a term t. of a sequence and the number n of that term.
exponential equationAn equation with the variable in an exponent.
exponential functionFor all real numbers x and for all positive numbers b, b ¹ 1, the equation y = b^x defines an exponential function with base b.
factorial notalionFor each positive integer n, n! = n(n - 1)(n - 2) ... 3 x 2 x 1. Also,0! = 1.
fieldA set of numbers with two operations that has the closure, commutative, associative, identity, and inverse properties for addition and multiplication and distributive for multiplication over addition.
finite sequenceA sequence that has a last term.
fitted lineThe line that best approximates the graph of the relationship between two vari- ables, if that relationship is nearly linear.
focusThe fixed point or points (foci) used to define a conic section.
fractional equationAn equation with a vari- able in the denominator of a fraction.
functionA relation in which each element of the domain is paired with exactly one element of the range.
function notationRepresenting any number in the range of the function f as f(x). in which x is the corresponding number in the domain.
geometric meanThe square root of the product of two numbers. It is also called the mean proportional.
geometric meansThe terms of a geometric sequence between two given terms.
geometric sequenceFor each positive integer n, and for each real number r, r ¹ 0, the sequence with the first term a, and nth term a. is a geometric sequence if and only if a. = a1r^n-1.
geometric seriesThe indicated sum of the terms of a geometric sequence.
greatest common factorThe common factor that is a multiple of each common factor.
greatest integer functionA step function that pairs a real number with the greatest integer that is less than or equal to the real number.
half lifeThe length of time it takes half of an amount of radioactive material to decay.
harmonic meanIn a set of n numbers. n divided by the sum of the reciprocals of the number.
hyperbolaThe set of all points in it plane such that the absolute value of the difference of the distances (focal radii) from two given points (foci) is constant.
hypotenuseThe longest side of a right triangle. It is opposite the right angle.
identityAn equation that is true for all elements of its domain.
identity elementA number which added to or multiplied times any number in a set yields that same number in the set.
identity propertiesThere are real numbers 0 and I such that for each real number a, a + 0, 0 + a = a and a x 1 = 1 x a = a.
imaginary numberA complex number that is not real.
inconsistent system of equationsA system with no soiution.
increasing functionA function such that for any numbers a and b in the domain. if a > b, then f(a) > f(b).
independent eventsTwo events not affected by each other. Two events A and B are independent if and only if P(A and then B) P(A) x P(B).
independent variableIf the value of a depends upon the value of b, or if a is usually defined in terms of b, b is called the independent variable, and it is graphed on the horizontal axis.
indexThe number represented by n in nÖb.
index of summationThe variable used in sigma notation.
infinite geometric seriesA geometric series with an infinitely large number of terms.
infinite sequenceA sequence that does not have a last term.
interquartile rangeThe difference between the upper and lower quartiles of a set of numbers.
inverse functionsFunctions and g are inverse functions if and only if f(g(x)) = g(f(x)) =x for all numbers x in the domains of both f and 9.
inverse of a relationRelation B is the inverse of relation A if it consists of the inverses of the individual ordered pairs in relation A.
inverse variationTwo quantities x and y vary inversely if and only if there is a constant k. k ¹ 0, such thatY = K/X.
irrational numberA real number that is not a rational number, i.e. cannot be expressed as the quotient of two integers.
latus chordA segment whose endpoints are on a parabola. which passes through the focus, and is parallel to the directrix.
leading coefficientThe coefficient of the term of a polynomial with the highest degree.
like termsTerms that contain identical vari- ables with identical exponents.
linear combinationAn equation that is formed by adding multiples of two equations together.
linear equation in two variablesAn equation of the form y = mx + b.
linear functionA function is a linear function if and only if its domain is the set of all real numbers and its equation can be written in the form y = mx + b.
linear polynomialA polynomial of degree 1.
linear programmingA branch of mathematics based on the maximum-minimum property.
linear term of a quadratic equationThe term bx in an equation of the form y = ax^2+ bx + c.
literal equationAn equation in which con- stants are represented by letters.
logarithmic equationAn equation involving logarithms of expressions containing variables.
logarithmic functionFor all positive real numbers x and b, b ¹ 1, there is a real number v such that v = logbx if and only if x = b^x
lowest terms (simplest form)A fraction is expressed in lowest terms when its numerator and denominator have no common factors other than 1 or - 1.
main diagonal of a square matrixThe diagonal from the upper left to the lower right.
major axisThe longer axis of an ellipse.
mappingAn association from the elements of the domain to the elements of the range.
matrix matricesA rectangular array of numbers arranged in Tows and columns.
maximum valueThe Y-coordinate of the vertex of the graph of a quadratic function that opens downward.
meanThe sum of a set of numbers divided by the number of numbers in the set.
mean absolute deviationThe average absolute deviation from the mean for a set of numbers.
mean proportionalThe geometric mean between two numbers.
medianThe middle number in a set of numbers arranged in order.
midpointThe point on a segment that is equidistant from the endpoints.
midpoint formulaIf the coordinates of point A are (x1,y1) and the coordinates of point B are (x2,y2), then the coordinates of the midpoint of segment AB are {(x1+x2)/2, (y1+y2)/2}
minimum valueThe y-coordinate of the vertex of the graph of a quadratic function that opens upward.
minor of an elementThe determinant that remains after the row and column containing the element have been deleted.
minor axisThe shorter axis of an ellipse.
modeThe number that occurs most often in a set of numbers.
monomialA constant (a number), a variable, or a product of constants and/or variables.
multiplicative inverse (or reciprocals)Pairs of real numbers that have the product 1.
multiplicative identity matrixA square matrix with I's on the main diagonal (upper lcft to lower right) and other entries 0.
mutually exclusive eventsTwo events A and B are mutually exclusive if and only if they have no outcomes in common.
natural logarithmsBase-e logarithms
negative exponentsFor each nonzero number a and for each positive integer n, a^-n = 1/a^n.
negative reciprocalsTwo numbers having a product of - 1.
negative square rootThe negative of the principal square root.
negative square root functionThe function with the equation y= -Öx
networkA set of points (vertices) connected by arcs.
nonequivalent transrormationA transformation that results in an equation not equivalent to the original.
nonlinear systemA system of two or more equations at least one of which is nonlinear.
normal distributionA specific bell-shaped algebraic function approximated by many frequency distributions.
oppositesTwo numbers whose sum is zero. Also called additive inverses.
ordered pairA pair of numbers that identifies the location of a particular point on a graph.
ordered triples (X, Y, Z)The set that is the solution of an equation in three variables.
origin (on a graph)The point of intersection of the coordinate axes. It is designated (0. 0).
origin (on a number line)The point on the number line associated with zero.
outcomeThe result of an experiment
parabolaThe set of all points in a plane that are the same distance from a point (focus) as they are from a given line (directrix). it is the graph of a quadratic function having a U shape.
parallel linesLines that have equal slopes.
partial sum of a seriesThe sum of a finite number of terms of the series.
pascal's triangleA triangular arrangement of numbers in which each number is the sum of the two numbers above it in the preceding row.
perfect square trinomialThe square of a binomial. with the form a2 ± 2ab + b2.
periodic functionA function y=f(x) is periodic if and only if there is a real number p such that for each x in the domain of f. f(x + p)=f(x).
permutationAn arrangement of a number of objects in a definite order
perpendicular linesLines with slopes that are negative reciprocals.
point matrixA 2 x 1 matrix whose ele- ments are the coordinates of a point.
point-slope formIf (x1, y1) is a point on the line y = mx + b. then y - y1 = m(x - xl) is the point-slope form of the equation
polynomialA monomial or the sum of monomials.
polynomial functionA function P whose values are defined by a polynomial.
power functionFunctions with equations of the form y = x^n, with it a positive integer.
prime factorizationA representation of a number as the product of its prime factors.
principal cube rootThe one real-number cube root of a real number.
principal square rootThe positive square root, denoted by
principle square root functionThe function with the equation Ö
probability of an eventThe ratio of the number of outcomes in the event to the number of outcomes in the sample space.
pure imaginary numberAny number of the form ai. where a is real.
pure quadratic equationA quadratic equation with no x-term.
quadrilateralA quadrilateral is a polygon with four sides.
rational numberA number that can be expressed as the quotient of two integers.
rationalizing the denominatorThe process of changing an irrational denominator to a rational one.
real numbersThe set of all rational and irrational numbers.
reciprocalsPairs of real numbers that have the product 1. Also known as mulliplicarive inverses.
regression lineA fitted line determined by a specific algebraic technique.
relationA set of ordered pairs.
repeating decimalA decimal in which a digit or a group of digits repeats forever, e.g. 0.66666 ... or 0.846846846 ... .
repetendThe portion of a repeating decimal that repeats.
restrictionsThe set of possible values for the variables for which an expression is real, or for which it is defined.
resultantThe sum of two vector.
row matrixA matrix with one row.
sample spaceThe set of all possible outcomes of an experiment.
scalarThe real number that is a factor in scalar multiplication.
scalar multiplicationFor any scalar c, number, and any m x n matrix A with elements aij, the product of c and A is the in m x n matrix whose elements are caij.
scientific notationThe product of a power of 10 and a number greater than or equal to 1 and less than 10.
second-order determinantA determinant with two rows and two columns.
sequenceA function dcfined on the positive integers or a subset of consecutive positive integers starting with 1.
seriesThe indicated sum of the terms of a sequence.
set-builder notationA mathematical sentence that "builds" the set by selecting the elements that belong to the set.
sigma notationExpresses the sum of a series.
slope-intercept formThe form Y = mx + b of a linear equation in two variables. The slope is m and the y-intercept is b.
solving a triangleFinding all the unknown measures of a triangle.
square matrix of order nA matrix with n rows and n columns.
square rootIf x^2 = y. then x is a square root of y.
step functionA function whose graph resembles a staircase.
subsetA set all of whose elements are elements in a larger set.
standard scores (or --scores)An expression for each value in a frequency distribution in terms of the number of standard deviations it is above or below the mean.
substitutionA method of solving systems of equations by replacing one variable with another variable or variable expression that is equal to it.
systemA set of equations having the same variables.
terms of a sequenceThe numbers in a sequence.
theoremA statement that has been proven to be true.
third-order determinantA determinant with three rows and three columns.
transformation matrixA matrix used for multiplying a point matrix to give a new point matrix.
translationA transformation made by substitutions that shift each point of a given graph to a different location without changing the shape of the graph.
trinomialA polynomial with three terms.
unit circleA circle with center at the origin and with a radius of one unit.
value of a seriesThe simplified sum of a series.
variableA symbol, usually a letter, that represents, and may be replaced by, any number from a particular set of numbers.
vectorsMatrices with either one row or one column.
vertex of a parabolaThe point on a parabola midway between the focus and the directrix.
vertical-line testIf no vertical line intersects a graph of a relation more than once, then the re- lation is a function.
vertices of an ellipseThe endpoints of the major and minor axes.
vertices of a hyperbolaThe two points in which a hyperbola is intersected by the line through the two focus points.
vinculumThe bar over the radicand.
wrapping functionThe function that maps the real numbers onto the points of the unit circle.
x-axisThe horizontal axis.
y-axis:The vertical axis.
y-intercept of a graphThe y-coordinate of the point at which a line crosses the Y-axis.
zero matrixAn m x n matrix whose elements are all zero. It is denoted Z m x n or just Z.

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