absolute valuethe value of a number without regard to its sign
Addition Property of Equality

allows us to add the same amount to both sides of an equation: For all real numbers a, b, and c, if a = b, then a + c = b + c

Addition Property of Identity

states that any number plus zero equals that number: For all real numbers a, a + 0 = a

Additive Inverse Property

states that every real number added to its additive inverse (or opposite) will equal zero: For all real numbers a, a + (-a) = 0; also called Inverse Property of Addition

algebrathe branch of mathematics that deals with operations on sets of numbers and relationships between them
area modela graphic representation of a multiplication problem, in which the length and width of a rectangle are the factors and the area is the product
Associative Property of Addition

states that numbers in an addition sequence can be added in any order, and the value of the expression will not change: For all real numbers a, b, and c, (a + b) + c = a + (b + c)

Associative Property of Multiplication

states that numbers in a multiplication sequence can be multiplied in any order, and the value of the expression will not change: For all real numbers a, b, and c, (ab)c = a(bc)

axis of symmetrya line of symmetry for a graph—it divides a figure or graph into halves that are the mirror images of each other
base

the value that is raised to a power when a number is written in exponential notation.  In the term 53, 5 is the base and 3 is the exponent.

binomial

a sum of two monomials, such as 3x2 + 7

boundary linea line that represents the edge of a linear inequality: if points along the boundary line are included in the solution set, then a solid line is used; if points along the boundary line are not included in the solution set, then a dashed line is used
bounded regionthe set of solutions that are true for all of the linear inequalities under consideration
coefficienta number that multiplies a variable
combinationsgroupings in which the order of members does not matter
common denominatora number that is a multiple of all of the denominators in a group of fractions
Commutative Property of Addition

states that when two values are added together, changing their order does not affect their sum: For all real numbers a and b, a + b = b + a

Commutative Property of Multiplication

states that when two values are multiplied together, changing their order does not affect their product: For all real numbers a and b, ab = ba

completing the square

the process of changing a polynomial of the form  into a perfect square trinomial , or

compound eventan event with more than one outcome
conclusionthe part of a logical statement that provides the result or consequences of the hypothesis—In a statement “If x then y”, the conclusion is y.
conjecturea statement that attempts to make a conclusion but has not been proved true or false
constant of proportionalitythe constant in a proportional function equation; it describes the ratio or proportional relationship of the independent and dependent variables—also called the constant of variation or the rate of change
constant of variationthe constant in a proportional function equation; it describes the ratio or proportional relationship of the independent and dependent variables—also called the rate of change or the constant of proportionality
continuous patterna pattern made of uninterrupted or connected values or objects
coordinate plane

a plane in two dimensions, containing the x- and y-axes, used to map ordered pairs in the form (x, y)

coordinates

a pair of numbers that identifies a point on the coordinate plane—the first number is the x-value and the second is the y-value

counterexamplea situation that provides evidence that a logical statement is false
counting numbersalso called natural numbers, the numbers 1, 2, 3, 4, ...
deductive reasoninga form of logical thinking that uses generalizations to draw specific conclusions based on a series of logical steps, deductive reasoning may use rules, laws, and theories to support or justify a conjecture
dependent eventstwo or more events for which the occurrence of one affects the probability of the other(s)
dependent valuea value or variable that depends upon the independent value
dependent variablea value or variable that depends upon the independent value
discrete patterna pattern made of separate and distinct values or objects
discrete valuesvalues that change in increments (not continuously)
discriminant

the expression b2 – 4ac under the radical in the quadratic formula; the expression can be used to determine the number of real roots the quadratic equation has

Distributive Property

states that the product of a number and a sum equals the sum of the individual products of the number and the addends: for all real numbers a, b, and c, a(b + c) = ab + ac

Division Property of Equality

allows us to divide both sides of an equation by the same amount: For all real numbers a, b, and c, if a = b and c is not 0, then

domainthe set of all possible inputs of a function which allow the function to work
elimination methoda method of solving a system of equations by adding or subtracting equations in order to eliminate a common variable
equally likelyhaving the same likelihood of occurring, such that in a large number of trials, two equally likely outcomes would happen roughly the same number of times
equationa statement that describes the equality of two expressions by connecting them with an equals sign
eventa collection of possible outcomes, often describable using a common characteristic, such as rolling an even number with a die or picking a card from a specific suit
event spacethe set of possible outcomes in an event: for example, the event “rolling an even number” on a die has the event space of 2, 4, and 6
examplea situation that suggests a logical statement may be true
excluded valuea value for a variable that is not allowed in an expression, such as a variable in a rational expression that would make the denominator equal zero
exponent

the value that indicates the number of times another value is multiplied by itself in exponential notation. The exponent, also called the power, is written in superscript. In the term 53, 5 is the base and 3 is the exponent.

exponential function

a nonlinear function in which the independent value is an exponent in the function, as in y = abx

exponential notation

a condensed way of expressing repeated multiplication of a value by itself. Exponential notation consists of a base and an exponent. In the exponential term 53, 5 is the base and 3 is the exponent. This is a shorthand way of writing 5 5 5. Also called exponential form.

extraneous solutiona solution that results from solving an equation that is not a valid solution in the original equation
factor

for any number x, the numbers that can be evenly divided into x are called factors of x. For example, the number 20 has the factors 1, 2, 4, 5, 10, and 20.

factored form of a polynomiala polynomial written as a product of factors, and each non-monomial factor has no common factors in its terms
factorial

an abbreviated way of writing a product of all whole numbers from 1 to a given number, indicated by that number followed by an exclamation point, as in 3! = 3 • 2 • 1

factoring

the process of breaking a number down into its multiplicative factors. Every number x has at least the numbers 1 and x as factors.

formulaa type of equation—usually reserved for multi-variable equations that describe a well-known or often repeated calculation
functiona kind of relation in which one variable uniquely determines the value of another variable
Fundamental Counting Principlea way to find the number of outcomes in a sample space by finding the product of the number of outcomes for each element
generalizethe process of using observations of specific events to make statements or conjectures about more general situations
greatest common factorthe largest number or expression that will divide a number or expression exactly
greatest common factor (GCF)the largest factor that two numbers have in common
grouping techniquea factoring technique involving finding common factors among groups of terms rather than among all of terms
half-planeon a coordinate plane, the shape of the region of possible solutions generated by a single inequality
hypotenusethe side opposite the right angle in any right triangle—the hypotenuse is the longest side in a right triangle
hypothesisthe part of a logical statement that provides the premise on which the conclusion is based—In a statement “If x then y,” the hypothesis is x.
independent eventstwo or more events for which the occurrence of one does not affect the probability of the other(s)
independent valuea value or variable that changes or can be manipulated by circumstances
independent variablea value or variable that changes or can be manipulated by circumstances
inductive reasoninga form of logical thinking that makes general conclusions based on specific situations, inductive reasoning takes the path of observation to generalization to conjecture
inequality

a math sentence that defines a range of numbers; inequalities contain the symbols <, ≤, >, or ≥

inputthe independent variable of a function—input determines output
integersthe numbers …, -3, -2, -1, 0, 1, 2, 3,…
intercepta point where a line meets or crosses a coordinate axis
intercept form of a quadratic equation

written as y = a(xp)(xq), where the x-intercepts are p and q

inverse function

a nonlinear function in which the reciprocal of the independent variable times a constant equals the dependent variable, as in

Inverse Operationsoperations that undo or cancel one another, such as addition/subtraction and multiplication/division
Inverse Property of Addition

states that every real number added to its additive inverse (or opposite) will equal zero: for all real numbers a, a + (-a) = 0; also called Additive Inverse Property

Inverse Property of Multiplication

states that any number multiplied by 1 over that number equals 1: For all real numbers a, ; also called Multiplicative Inverse Property

irrational numbers

numbers between integers that cannot be written as a ratio of integers (that is, as  where p and q are both integers), the decimal representation of an irrational number is non-repeating and non-terminating

justifyprovide a logical argument for a conclusion or conjecture
least common denominatorthe smallest number or expression that is a multiple of all the denominators in a group of fractions or rational expressions
least common multiplethe smallest number or expression that is a multiple of a group of numbers or expressions
legin a right triangle, one of the two sides creating the right angle
like terms

two or more monomials that contain the same variables raised to the same powers, regardless of their coefficients. For example, 2x2y  and -8x2y are like terms because they have the same variables raised to the same exponents.

linear equationan equation that describes a straight line
linear functiona function with a constant rate of change and a straight line graph
linear inequality

an inequality represented in a form equivalent to Ax + By > C, where the symbol > could also be <, ≤, or ≥

logical argumenta series of statements, each verifiable as true, that lead to a conclusion
logical statementa statement that allows drawing a conclusion or result based on a hypothesis or premise
mathematical sequencean ordered list of numbers or objects
monomial

a number, a variable, or a product of a number and one or more variables with whole number exponents, such as -5,  x, and 8xy3

multi-step equationan equation that requires more than one step to solve
Multiplication Property of Equality

allows us to multiply both sides of an equation by the same amount: For all real numbers a, b, and c, if a = b, then ac = bc

Multiplication Property of Identity

states that any number times 1 equals that number: For all real numbers a, a 1 = a

Multiplicative Inverse Property

states that any number multiplied by 1 over that number equals 1: For all real numbers a, ; also called Inverse Property of Multiplication

natural numbersalso called counting numbers, the numbers 1, 2, 3, 4, …
nonlinear functiona function with a variable rate of change that graphs as a curved line
nonrepeating decimalsnumbers whose decimal parts continue without repeating, these are irrational numbers
nonterminating decimalsnumbers whose decimal parts continue (with non-zero digits) forever, these decimals can be rational (if they repeat) or irrational (if they are nonrepeating)
numeric constanta quantity that has a known, fixed value
operationa mathematical procedure, such as addition, subtraction, multiplication, and division
outcomea result of a trial
outputthe dependent variable of a function—output is determined by input
overgeneralizea logical mistake caused by basing a generalization on inadequate evidence or observation or by making too broad a conjecture, such as generalizing a pattern seen only in whole numbers to all real numbers
parabolaa U-shaped graph which is produced by a quadratic equation
parallel lines

lines that have the same slope and different y-intercepts

partial productsa method of multiplication in which each factor is split into a sum of its parts. Every part of one factor is multiplied by every part of the other factor, then these partial products are added together. For example, (5)(23) = (5)(20 + 3) = 5(20) + 5(3) = 100 + 15 = 115
perfect square

any of the squares of the integers. Since 12 = 1, 22 = 4, 32 = 9, etc., 1, 4, and 9 are perfect squares

perfect square trinomial

a trinomial that is the product of a binomial times itself, such as r2 + 2rs + s2 (from (r + s)2), and r2 – 2rs + s2 (from (rs)2)

permutationsgroupings in which the order of members matters
perpendicular lineslines that have opposite reciprocal slopes
point-slope formula

a form of linear equation, written as, where m is the slope and (x1, y1) are the co-ordinates of a point

polynomial

a monomial or sum of monomials, like 4x2 + 3x – 10

polynomial functions

a monomial or sum of monomials, like y = 4x2 + 3x – 10

power

a way of describing the exponent in exponential notation. We can say the base is raised to the power of the exponent.  For example we read x5 as “x raised to the 5th power.”

power of a power

raising a value written in exponential notation to a power as in (x2)3

prime factora factor that has no factors but 1 and itself. For example, 2 is a prime factor of 12 because its only factors are 1 and 2, while 6 is not a prime factor of 12 because it has more factors than 1 and 6 (i.e. 2 and 3).
prime factorizationthe process of breaking a number down into its prime factors
prime numbera whole number for which the only factors are 1 and the number itself
prime trinomiala trinomial that cannot be factored using integers
probabilitya measure of how likely it is that something will occur
product of powersmultiplication of two or more values in exponential form that have the same base—the base stays the same and the exponents are added
Properties of Inequalitya set of rules for inequalities that describe how addition, subtraction, multiplication, or division can be applied to both sides of an inequality in order to produce an equivalent inequality
Property of Equalitystates that the equality of an equation is maintained when both sides have the same value added, subtracted, multiplied, or divided
proportional functiona function in which the input times a constant equals the output
Pythagorasa Greek philosopher and mathematician who lived in the 6th Century BC
Pythagorean Theorem

the formula used to relate the lengths of the sides in any right triangle

quadratic equation

an equation that can be written in the form ax2 + bx + c = 0 where a ¹ 0. When written as y = ax2 + bx + c the expression becomes a quadratic function.

quadratic formula

the formula  ; it is used to solve a quadratic equation of the form

quadratic function

a function of the form y = ax2 + bx + c where a is not equal to zero

quotient of powersdivision of two or more values in exponential form that have the same base—the base stays the same and the exponent in the denominator is subtracted from the exponent in the numerator
radical

the math symbol , used to denote the process of taking a root of a quantity

radical equationan equation that contains a variable within a radical term
radical expression

a quantity that contains a term with a radical, as in

radicandthe number under the radical symbol
raised to a power

a way of describing the exponent in exponential notation. We can say the base is “raised to the power” of the exponent.  For example we read x5 as “x raised to the 5th power.”

randomunable to be predicted with certainty
rangethe set of all possible outputs of a function
ratea mathematical way of relating two quantities, which usually are measured in different units
rate of changethe constant in a proportional function equation; it describes the ratio or proportional relationship of the independent and dependent variables—also called the constant of variation or the constant of proportionality
rational equationan equation that contains one or more rational expressions
rational expressiona fraction with a polynomial in the numerator and/or denominator
rational numbers

numbers that can be written as a ratio of integers (that is, as  where p and q are both integers and q ≠ 0)

raya half-line beginning at one point and continuing to infinity
real numbersthe set of numbers that includes both rational numbers and irrational numbers.
reciprocal

a number related to another number in such a way that when they are multiplied together their product is 1.  For example, the reciprocal of 7 is  because ; the reciprocal of  is .  It is also called the multiplicative inverse.

relationthe relationship between variables that change together
repeating decimalsnumbers whose decimal parts repeat a pattern of one or more digits, these are all rational numbers
replacementrestoring a random situation back to its original state after performing an action
right trianglea triangle with one right angle
risevertical change between two points
root

any number x multiplied by itself a specific number of times to produce another number, such that in xn = y, x is the nth root of y – for example, because 23 = 8, 2 is the 3rd (or cube) root of 8

root of an equationany number that makes the equation true when the variable is equal to that number. That is, a solution of the equation.
roots of a quadratic equation

the x-intercepts of the parabola or the solution of the equation

runhorizontal change between two points
sample spacethe set of all outcomes
scientific notation

a convention for writing very large and very small numbers in which a number is expressed as the product of a power of 10 and a number that is greater than or equal to 1 and less than 10 as in 3.2 • 104

simple eventan event with only one outcome
slopethe ratio of the vertical and horizontal changes between two points on a surface or a line
slope formula

the equation for the slope of a line, written as http://www.nrocproto.org/texttabs/slopeformula_files/image001.gif, where m is the slope and (x1, y1) and (x2, y2) are the coordinates of two points on the line

slope-intercept form

a linear equation, written in the form y = mx + b, where m is the slope and b is the y-intercept

slope-intercept formula

a linear equation, written as y = mx + b, where m is the slope and b is the y-intercept

special product

a product resulting from binomial multiplication that has certain characteristics. For example x2 – 25 is called a special product because both its terms are perfect squares and it can be factored into (x + 5)(x –­ 5).

standard form of a linear equation

a linear equation, written in the form Ax + By = C, where x and y are variables and A, B, and C are integers

standard form of a quadratic equation

written as , where x and y are variables and a, b, and c are numbers with a ≠ 0. In the case of a single variable the standard form becomes ax2 + bx + c = 0.

substitution methoda method of solving a system of equations by substituting one quantity in for an equivalent quantity
Subtraction Property of Equality

allows us to subtract the same amount from both sides of an equation: For all real numbers a, b, and c, if a = b, then ac = bc

system of equationsa set of two or more equations that share two or more unknowns
system of inequalitiesa set of two or more inequalities that must hold true at the same time
term

a value in a sequence--the first value in a sequence is the 1st term, the second value is the 2nd term, and so on; a term is also any of the monomials that make up a polynomial

terminating decimalsnumbers whose decimal parts do not continue indefinitely but end eventually, these are all rational numbers
tree diagrama diagram that shows the choices or random outcomes from multiple elements, using branches for each new element
triala random action or series of actions
trinomiala three-term polynomial
variablea symbol that represents an unknown value
vertexthe high point or low point of a parabolic function
vertex form of a quadratic equation

when the quadratic equation is a quadratic function, the vertex form is http://www.nrocproto.org/texttabs/vertexformofaquadraticequation_files/image001.gif, where x and y are variables and a, h, and k are numbers – the vertex of this parabola has the coordinates (h, k)

whole numbersthe numbers 0, 1, 2, 3, …., or all natural numbers plus 0
x-intercept

the point where a line meets or crosses the x-axis

y-intercept

the point where a line meets or crosses the y-axis

Zero Product Property

states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0