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Algebra Vocabulary-1st Semester

AB
absolute valuethe distance from zero on a number linea number is.
adding integersintegers with the same sign, add their absolute value. Give the result the same sign as the integers. Integers with different signs, subtract the lesser absolute value from the greater absolute value. Give the result the same sign as the
addition property of inequalityFor all numbers a, b, and c, the following is true: 1. If a > b, then a + c > b + c. 2. If a < b, then a + c < b + c.
addition property of equalityFor any numbers a, b, and c, if a = b, then a + c = b + c.
additive identityFor any number a, a + 0 = 0 + a = a.
additive inverse propertyFor any number a, a + (-a) = 0.
algebraic expressionAn expression consisting of one or more numbers and variables along with one or more arithmetic operations.
associative propertyFor any numbers a, b, and c, (a + b) + c = a + (b + c) and (ab)c = a(bc).
axesTwo perpendicular number lines that are used to locate points on a coordinate plane.
baseIn an expression of the form x^ n it is x.
best-fit lineA line drawn on a scatter plot that passes close to most of the data points.
binomialThe sum of two monomials.
coefficientThe numerical factor in a term.
commutative propertyFor any numbers a and b, a + b = b + c and ab = ba.
comparison propertyFor any two numbers a and b, exactly one of the following sentences is true. a < b a = b a > b.
complex fractionIf a fraction has one or more fractions in the numerator or denominator.
compound inequalityTwo inequalities connected by "and" or "or".
consecutive integersIntegers in counting order.
constantsMonomials that are real numbers.
coordinateThe number that corresponds to a point on a number line.
coordinate planeThe plane containing the x- and y-axes.
cross productsWhen two fractions are compared, the products of the terms on the diagonals.
defining the variableRepresenting one of the unspecified numbers in a problem.
degree of a monomialthe sum of the exponents of its variables.
degree of a polynomialthe degree of the term of the greatest degree.
dependent variableThe variable in a function whose value is determined by the independent variable.
distributive propertyFor any numbers a, b and c: 1. a(b + c) = ab + ac and (b + c)a = ba + ca. 2. a(b - c) = ab - ac and (b - c)a = ba - ca.
dividing rational numbersThe quotient of two rational numbers having the same sign is positive. The quotient of two rational numbers having different signs is negative.
division property of inequalityFor all numbers a, b, and c the following is true: 1. If c is positive and a < b, then a/c < b/c, and if c is positive and a > b, then a/c > b/c. 2. If c is negative and a < b, then a/c > b/c and if c is negative and a > b, then a/c < b/c.
division property of equalityFor any numbers a, b, and c, with c not equal to 0, if a = b, then a/c = b/c.
domainthe set of all first coordinates from the ordered pairs in a relation.
elementA member of a set.
equationA mathematical sentence that contains an equals sign, =.
equation in two variablescontains two unknown values.
equivalent equationsEquations that have the same solution.
equivalent expressionsExpressions that denote the same number.
evaluateTo find the value of an expression when the values of the variables are known.
exponentIn an expression of the form x^n, it is n.
factorsIn a multiplication expression, the quantities being multiplied.
family of graphsincludes graphs and equations of graphs that have at least one characteristice in common.
FOIL methodTo multiply two binomial find the sum of the products of F: the first terms, O: the outside terms, I: the inside terms, and L: the last terms.
formulaAn equation that states a rule for the relationship between certain quantities.
functionA relation in which each element of the domain is paired with exactly one element of the range.
functional notationthe equation y = x + 5 is written as f(x) = x + 5.
graphTo draw, or plot, the points named by certain numbers or ordered pairs on a number line or coordinate plane, respectively.
horizontal axisThe horizontal line in a graph that represents the independent variable.
identityAn equation that is true for every value of the variable.
independent variableThe variable in a function whose value is subject to choice is the independent variable. The independent variable affects the value of the dependent variable.
inequalityA mathematical sentence havin the symbols <, < or equal to, >, or > or equal to.
integersThe set of numbers represented as {..., -3, -2, -1, 0, 1, 2, 3, ...}
intersectionthe set of elements common to both A and B.
irrational numbersA number that cannot be expressed in the form a/b, where a and b are integers and b does not equal 0.
like termsTerms that contain the same variables, with corresponding variables with the same power.
linear equationAn equation whose graph is a line.
linear functionAn equation whose graph is a nonvertical line.
monomiala number, a variable, or a product of a number and one or more variables.
multi-step equationsequations that need more than one operation to solve them.
multiplicative identityFor any number a, (a)(1) = (1)(a) = a.
multiplicative inverseFor any nonzero number a/b, where a, b are not equal to 0, there is exactly one number b/a such that (a/b)(b/a) = 1.
multiplication property of inequalityFor all numbers a, b, and c, the following is true: 1. If c is positive and a < b, then ac < bc, c is not equal to 0 and if c is positive and a > b, then ac > bc, c is not equal to 0. 2. If c is negative and a < b, then ac > bc, c is not equal to 0 and
multiplicatve property fo -1The product of an number and -1 is the additive inverse. -1(a) = -1 and a(-1) = -a.
multiplicative property of equalityFor any numbers a, b and c, if a = b, then ac = bc.
multiplicative property of zeroFor any number a, (a)(0) = (0)(a) = 0.
negative correlationthe values of x and y are related in opposite ways.
negative exponentFor any nonzero number a, and any integer n, a^(-n) is equal to 1/a^n power.
negative numberAny number that is less that zero.
number lineA line with equal distances marked off to represent numbers.
open sentencesMathematical statements with one or more variables, or unknown numbers.
oppositesits additive inverse.
order of operations1. Simplify the expressions inside grouping symbols, such as parentheses, brackets, and braces, and as indicated by fraction bars. 2. Evaluate all powers. 3. Do all multiplications and divisions from left to right. 4. Do all additions and subtractions
ordered pairPairs of numbers used to locate points in the coordinate plane.
originThe point of intersection of the two axes in the coordinate plane.
parallel linesLines in the plane that never intersect. Nonvertical lines that have the same slope.
parent graphThe simplest graph in a family of graphs.
percentis a ratio that compares a number to 100.
percentageThe number that is divided by the base in a percent proportion.
percent of decreaseThe ratio of an amount of decrease to the previous amount, expressed as a percent.
percent of increaseThe ratio of an amount of increase to the previous amount expressed as a percent.
perpendicular linesLines that meet to form right angles.
point-slope formFor any point (x[1], y[1]) on a nonvertical line having slope m, the point-slope form of a linear equation is as follows: y - y[1] = m(x - x[1])
polynomialis a monomial or a sum of monomials.
positive correlationif the values x and y are related in the same way.
powerAn expression of the form x^n
power of a monomialFor any numbers a and b, and any integers m, n, and p, (a^mb^n)^p = a^mpb^np.
power of a powerFor any number a and all integers m and n, (a^m)^n = a^mn.
power of a productFor all numbersa and b, and any integer m, (ab)^m = a^mb^m.
productThe result of multiplication
product of powersFor any number a, and all integers m and n, (a^m)(a^n) = a^(m + n).
quadrantOne of the four regions into which the x- and y- axes separate the coordinate plane.
quotient of powersFor all integers m and n and any nonzero number a, (a^m)/(a^n) = a^(m - n).
rangeThe set of all second coordinates from the ordered pairs in the relation.
ratiois a comparison of two numbers by division.
rational numbersis a number that can be expressed in the form a/b, where a and b are integers and b does not equal to 0.
real numbersThe set of rational number and the set of irrational numbers
reciprocalThe multiplicative inverse of a number.
reflexive property of equalityFor any number a, a = a.
regression lineThe most accurate best-fit line for a set of data, and can be determined with a graphing calculator.
relationa set of ordered pairs.
replacement setA set of numbers from which replacements for a variable may be chosen.
riseThe vertical change in a line.
runThe horizontal change in a line.
scalar multiplicationeach element of a matrix is multiplied by a constant.
scatter plotthe two sets of data are plotted as ordered pairs in the coordinate plane.
scientific notationthe form "a" x 10^n, where 1 less than or equal to "a" < 10 and n is an integer.
setA collection of objects or numbers.
set-builder notationA notation use to describe the members of a set. For example, {y|y<17} represents the set of all numbers y such that y is less than 17.
simplest forman expression having no like terms and no parentheses.
slopeThe ratio of the rise to the run as you move from one point to another along a line.
slope-intercept formAn equation of the form y = mx + b, where m is the slope and b is the y-intercept of a given line.
solutionA replacement for the variable in an open sentence that results in a true sentence.
solution of an equation in two variablesIf a true statement results when the numbers in an ordered pair are substituted into an equation in two variables.
solution setThe set of all replacements for the variable in an open sentence that result in a true statement.
solve an equationmeans to isolate the variable having a coefficient of 1 on one side of the equation.
solving an open sentenceFinding a replacement for the variable that results in a true sentence.
square of a differenceIf an and b are any numbers, (a - b)^2 = a^2 - 2ab + b^2.
square of a sumIf a and b are any numbers, (a + b)^2 = a^2 + 2ab + b^2.
substitution property of equalityIf a = b, thena may be replace by b in any expression.
subtracting integersTo subtract a number, add its additive inverse. For any numbers a and b, a - b = a +(-b).
subtraction property of inequalityFor all numbers a, b, and c, the following are true: 1. if a > b, then a - c > b - c. 2. if a < b, then a - c < b - c.
subtraction property of equalityFor any numbers a, b, and c, if a = b,then a - c = b - c.
symmetric property of equalityFor any numbers a and b, if a = b, then b = a.
termA number, a variable, or a product or quotient of numbers and variables.
transitive property of equalityFor any numbers a, b, and c, if a = b and b = c, then a = c.
trinomialsthe sum of three monomials.
uniform motionWhen an object moves at a constant speed, or rate
variableVariables are symbols that are used to represent unspecified numbers.
vertical axisThe vertical line in a graph that represents the dependent variable.
vertical line testIf any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.
whole numbersis represented by {0,1,2,3,...}.
x-axisThe horizontal number line.
x-coordinateThe first number in an ordered pair.
x-interceptThe coordinate at which a graph intersects the x-axis.
y-axisThe vertical number line.
y-coordinateThe second number in an ordered pair.
y-interceptThe coordinate at which a graph intersects the y-axis.
zero exponentFor any nonzero number a, a^0 = 1.


Ms. Sweeney

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