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  • Compound Inequality

    A pair of inequalities combined by the words and or or

    Correlation Coefficient

    A number represented by the variable r, where -1≤r≤1, that describes how closely points in a scatter plot cluster around the least-squares line

    Direct Variation

    The equation y=kx describes a direct variation, where y varies directly as x, k is the constant of variation, and k≠0

    Literal Equation

    An equation that contains two or more variables

    Simplified Expression/Function

    An expression/function that has had all like terms combined and all the parentheses have been removed

    Slope-Intercept Form

    y=mx+b

    Standard Form

    Ax+By=C, where A and B are not both 0

    X-Intercept

    The x-coordinate of the point where the graph crosses the x-axis

    Y-Intercept

    The y-coordinate of the point where the graph of a line crosses the y-axis

    Dependent Variable

    The output of a function

    Independent Variable

    The input of a function

    Domain

    The set of possible values for the first coordinate of a function

    Range

    The set of possible values for the second coordinate of a function

    Rational Numbers

    Numbers that can be expressed as the quotient of two integers, where the denominator is not equal to zero

    Irrational Numbers

    Numbers whose decimal part does not terminate or repeat

    Relation

    Any set of ordered pairs

    Function

    A relation in which, for each first coordinate, there is exactly one corresponding second coordinate

    Vertical-Line Test

    If a vertical line crosses the graph of a relation in more than one point, the relation is not a function

    Consistent System

    A system of equations or inequalities that has at least one solution

    Inconsistent System

    A system of equations or inequalities that has no solution

    System of Equations

    A set of equations in the same variables

    Commutative

    changes order, but the statement remains the same

    Associative

    changes the grouping of parentheses, but the numbers do not move

    Identity

    Adding a 0, and multiplying by 1 - it does nothing

    Inverse

    equals 0

    Distributive

    2(4x-3) = 8x - 6

    element

    a value in a set or matrix; also called an entry.

    empty set

    a set with no elements.

    finite set

    a set with a definite, or finite, number of elements.

    infinite set

    a set with an unlimited, or infinite, number of elements.

    interval notation

    a way of writing the set of all real numbers between two endpoints. The symbols [ and ] are used to include an endpoint in an interval, and the symbols ( and ) are used to exclude an endpoint from an interval.

    like radical terms

    radical terms having the same radicand and index.

    principal root

    the positive square root of a number, indicated by the radical sign.

    radical symbol

    the symbol used to denote a root

    radicand

    a number or expression under a radical sign

    Rationalizing the denominator

    Rationalizing the denominator is a method of rewriting a fraction by multiplying by another fraction that is equivalent to 1 in order to remove radical terms from the denominator.

    opposite

    additive inverse; the ______ of any number "b" is "−b"

    reciprocal

    multiplicative inverse; the _______ of any nonzero number "b" is "1/b"

    formula

    an equation that relates two or more quantities, usually represented by variables

    like term

    terms that have the same variable parts; also called constant terms

    identity

    a statement that equates two equivalent expressions

    variable

    a letter that is used to represent one or more numbers

    extraneous solution

    an apparent solution that must be rejected because it does not satisfy the original equation

    absolute value

    the __________ of a number "x", represented by the symbol "l x l", is the distance the number is from 0 on a number line

    algebraic expression

    an expression that consists of numbers, variables, operations, and grouping symbols; also called variable expression

    power

    an expression that represents repeated multiplication of the same factor

    natural numbers

    {1,2,3...}(counting numbers)

    whole numbers

    {0,1,2,3...}

    integers

    {-3,-2,-1,0,1,2,3...}

    rational numbers

    numbers such as 5/3, 7/9, that result when an integer is divided by a non zero integer

    irrational numbers

    numbers such as √12, √52 (non-repeating, not rational)

    coordinate

    a real number paired with a point on the number line

    graph

    a point on a number line that is paired with a real number

    origin

    the graph of 0

    is less than

    <

    is greater than

    >

    absolute value

    The distance a number is from zero on a number line. ALWAYS POSITIVE

    numeral expression

    a symbol or group of symbols used to represent a number

    numeral

    a simplified version of a numeral expression (a number)

    value of a numeral expression

    12 is the value of 3x4

    equation

    A sentence formed by placing a "=" between two expressions (called the sides of of the equation) it is true if both sides have the same value

    inequality symbol

    one of the symbols less than (<), greater than (>), less than or equal to ( <= ) or greater than or equal to ( >= )

    inequality

    A sentence formed by placing an inequality symbol between the two expressions

    sum

    the result of adding numbers, called the terms
    21 is the sum of 6+15

    terms

    numbers that are added together
    6 and 15 are the terms of 6+15=21

    difference

    the result of subtracting one number from another
    2 is the difference of 8-2

    product

    the result of multiplying numbers, called factors
    3 and 5 are the factors of the product 15 in 3 x 5 = 15

    quotient

    the result of dividing one number by the other
    7 is the quoteint of 35/5= 7

    power

    product of of equal factors first power = 3^1,
    second power = 3^2

    base

    the repetitive factor
    3 is the base of 3^4

    exponent

    tells the number of times the base is a factor
    (the little number on the top)

    Grouping symbols

    ( ) [ ] or ---- (division bar)

    simplify

    replace it with its most simplest symbol having the same value
    1) substitution can be used
    2) order of operations can be used (grouping symbols, exponents and roots, x/, +-

    variable

    a symbol used to represent a number (a, x, y)

    domain/replacement set

    the set that the variable belongs to (whole, natural rational sets...)

    values of a variable

    what the variable could symbolize

    algebraic expression

    a numerical expression, a variable, sum, difference, product, quotient that contains one or more variables

    evaluation an expression/finding the value of

    the process of replacing each variable in an expression by a value and simplifying it

    field

    a set of numbers (real numbers a types of field)

    unique field number

    only that number has the properties

    opposite/additive inverse

    -a is the opposite/additive inverse of a

    reciprocal/multiplicative inverse

    the value a number can by multiplied by to get to 1
    the reciprocal of A would by 1/A

    equivalent

    equal for every value of each variable they contain

    similar terms/like terms

    terms that contain the same variable factors

    open sentence

    an equation or inequality that contains a variable such as
    2t - 1=5

    solution/root

    any value of the variable that makes an open sentence true

    solution set

    the set of all solutions of an open sentence

    equivalent equations

    equations that have the same solution set

    solve an equation

    to change/transform it into a simple equivalent equation

    empty/null set

    a solution set with no members

    identity

    an equation that is satisfied by all values of the variable
    6s-9=6s-9

    formula

    an equation that states a relationship between 2 or more variables
    h= -16t^2+vt

    constant

    the fixed numbers in an equation or formula

    Reciprocal

    Multiplicative inverse of a non zero number

    Power

    Repeated times of the same number or factor

    Exponent

    The number of times the base is multiplied

    Base

    Number or factor that's being exponent times

    Variable

    A letter that is used to represent a number or numbers

    Term

    Expression with a variable

    Constant Term

    Term with a variable

    Coefficient

    Number in front of a variable

    Like Terms

    Same variable, same exponent

    Equivalent Expressions

    Two expressions that equal each other

    Formula

    An equation that relates two or more quantities. Has an equal sign

    Compound Inequality

    Two inequalities joined by and "or" or

    Absolute Value

    Distance from zero

    Extraneous Solution

    A solution that doesn't satisfy the original equation

    Relation

    Pairing of inputs and outputs

    Domain

    Everything X can be

    Range

    Everything Y can be

    Function

    Every input has exactly 1 output

    Independent Variable

    X

    Dependent Variable

    Y

    Linear Function

    Constant rate of change and each input has exactly 1 output

    Function Notation

    f(x)=

    Slope, Rate of Change

    rise over run

    Parallel

    same slope

    Perpendicular

    negative reciprocal slope

    Parent Function

    Most basic function shared in a family

    Slope-Intercept Form

    Y=mx+b

    Standard Form

    Ax+By=C, no fraction, no negative x value

    Point-Slope Form

    Y2-Y1=m(x2-x1)

    Direct Variation

    Y=Kx, linear, always goes through (0,0)

    Positive Correlation

    Positive slope on a scatter plot

    Negative Correlation

    Negative slope on a scatter plot

    Correlation Coefficient

    numerical value between -1 and 1. Tells strength of relationship of two variables

    Best Fitting Line

    A line closest to all data points

    Absolute Value Function

    F(x)=|x|

    Vertex

    Highest or lowest point on a graph, written as an ordered pair

    Transformation

    Changes graphs shape, size or position

    Translation

    Shift left or right, up or down on a graph

    Reflection

    Flip over X or Y axis

    Natural Numbers

    The set of numbers 1, 2, 3, 4, ... Also called counting numbers.

    Whole Numbers

    Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...

    Integers

    Natural numbers,their opposites, and zero..-2,-1,0,1,2..Etc

    Rational Numbers

    All numbers that can be written as quotients of integers.

    Irrational Numbers

    Numbers that cannot be expressed as a ratio of two integers. Their decimal expansions are nonending and nonrepeating. Also not perfect squares.

    Variable

    Letter that represents a number

    PEMDAS

    Order of operations

    Term

    A Variable,a number or the product of those

    Coefficient

    A Numerical factor of a term

    Compound Inequality

    A pair of inequalities joined by "and" or "or"

    Extraneous Solution

    A solution of an equation derived from an original equation that is not a solution of the original solution

    Inverse Property

    a + (-a) = 0
    a times 1/a = 1

    Identity Property

    a + 0=a
    a times 1 = a
    0 + a = a
    1 times a = a

    Commutative Property

    a+b=b+a
    ab=ba

    Associative Property

    (a+b)+c=a+(b+c)
    (ab)c=a(bc)

    Distributive Property

    a(b+c)=ab=ac

    direct variation

    linear function where y-intercept is 0
    -y=mx
    -m is a constant of variation(use k rather than m)
    -y varies directly as x
    -y/x=k