CLEP College Algebra - Algebra 2

CLEP College Algebra - Algebra 2

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Section 1

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Relation

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Section 1

(51 cards)

Relation

Front

Any set of ordered pairs

Back

formula

Front

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

Back

Literal Equation

Front

An equation that contains two or more variables

Back

Associative

Front

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

Back

Vertical-Line Test

Front

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

Back

X-Intercept

Front

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

Back

Direct Variation

Front

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

Back

Identity

Front

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

Back

Compound Inequality

Front

A pair of inequalities combined by the words and or or

Back

Correlation Coefficient

Front

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

Back

Inconsistent System

Front

A system of equations or inequalities that has no solution

Back

rational numbers

Front

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

Back

like radical terms

Front

radical terms having the same radicand and index.

Back

infinite set

Front

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

Back

Simplified Expression/Function

Front

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

Back

Independent Variable

Front

The input of a function

Back

Rational Numbers

Front

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

Back

Y-Intercept

Front

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

Back

extraneous solution

Front

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

Back

Range

Front

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

Back

empty set

Front

a set with no elements.

Back

Domain

Front

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

Back

opposite

Front

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

Back

power

Front

an expression that represents repeated multiplication of the same factor

Back

Dependent Variable

Front

The output of a function

Back

finite set

Front

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

Back

absolute value

Front

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

Back

algebraic expression

Front

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

Back

System of Equations

Front

A set of equations in the same variables

Back

Commutative

Front

changes order, but the statement remains the same

Back

Distributive

Front

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

Back

Consistent System

Front

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

Back

Slope-Intercept Form

Front

y=mx+b

Back

reciprocal

Front

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

Back

Function

Front

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

Back

integers

Front

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

Back

whole numbers

Front

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

Back

radical symbol

Front

the symbol used to denote a root

Back

interval notation

Front

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.

Back

variable

Front

a letter that is used to represent one or more numbers

Back

natural numbers

Front

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

Back

Rationalizing the denominator

Front

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.

Back

radicand

Front

a number or expression under a radical sign

Back

Standard Form

Front

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

Back

identity

Front

a statement that equates two equivalent expressions

Back

element

Front

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

Back

Irrational Numbers

Front

Numbers whose decimal part does not terminate or repeat

Back

Inverse

Front

equals 0

Back

principal root

Front

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

Back

like term

Front

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

Back

Section 2

(51 cards)

opposite/additive inverse

Front

-a is the opposite/additive inverse of a

Back

simplify

Front

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/, +-

Back

equivalent

Front

equal for every value of each variable they contain

Back

reciprocal/multiplicative inverse

Front

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

Back

Grouping symbols

Front

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

Back

open sentence

Front

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

Back

algebraic expression

Front

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

Back

evaluation an expression/finding the value of

Front

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

Back

base

Front

the repetitive factor 3 is the base of 3^4

Back

origin

Front

the graph of 0

Back

equivalent equations

Front

equations that have the same solution set

Back

irrational numbers

Front

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

Back

quotient

Front

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

Back

product

Front

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

Back

Constant Term

Front

Term with a variable

Back

equation

Front

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

Back

absolute value

Front

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

Back

value of a numeral expression

Front

12 is the value of 3x4

Back

values of a variable

Front

what the variable could symbolize

Back

Exponent

Front

The number of times the base is multiplied

Back

is greater than

Front

>

Back

similar terms/like terms

Front

terms that contain the same variable factors

Back

terms

Front

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

Back

formula

Front

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

Back

exponent

Front

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

Back

domain/replacement set

Front

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

Back

inequality

Front

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

Back

difference

Front

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

Back

solution/root

Front

any value of the variable that makes an open sentence true

Back

unique field number

Front

only that number has the properties

Back

power

Front

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

Back

Base

Front

Number or factor that's being exponent times

Back

solution set

Front

the set of all solutions of an open sentence

Back

constant

Front

the fixed numbers in an equation or formula

Back

Variable

Front

A letter that is used to represent a number or numbers

Back

sum

Front

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

Back

solve an equation

Front

to change/transform it into a simple equivalent equation

Back

identity

Front

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

Back

numeral expression

Front

a symbol or group of symbols used to represent a number

Back

field

Front

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

Back

numeral

Front

a simplified version of a numeral expression (a number)

Back

variable

Front

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

Back

Term

Front

Expression with a variable

Back

is less than

Front

<

Back

Power

Front

Repeated times of the same number or factor

Back

inequality symbol

Front

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

Back

graph

Front

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

Back

empty/null set

Front

a solution set with no members

Back

Reciprocal

Front

Multiplicative inverse of a non zero number

Back

coordinate

Front

a real number paired with a point on the number line

Back

Section 3

(52 cards)

Point-Slope Form

Front

Y2-Y1=m(x2-x1)

Back

Absolute Value

Front

Distance from zero

Back

direct variation

Front

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

Back

Absolute Value Function

Front

F(x)=|x|

Back

Distributive Property

Front

a(b+c)=ab=ac

Back

Independent Variable

Front

X

Back

Extraneous Solution

Front

A solution that doesn't satisfy the original equation

Back

Slope, Rate of Change

Front

rise over run

Back

Parallel

Front

same slope

Back

Coefficient

Front

A Numerical factor of a term

Back

Extraneous Solution

Front

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

Back

Slope-Intercept Form

Front

Y=mx+b

Back

Domain

Front

Everything X can be

Back

Standard Form

Front

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

Back

Translation

Front

Shift left or right, up or down on a graph

Back

Irrational Numbers

Front

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

Back

Best Fitting Line

Front

A line closest to all data points

Back

Linear Function

Front

Constant rate of change and each input has exactly 1 output

Back

Direct Variation

Front

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

Back

Coefficient

Front

Number in front of a variable

Back

PEMDAS

Front

Order of operations

Back

Identity Property

Front

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

Back

Relation

Front

Pairing of inputs and outputs

Back

Positive Correlation

Front

Positive slope on a scatter plot

Back

Inverse Property

Front

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

Back

Dependent Variable

Front

Y

Back

Whole Numbers

Front

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

Back

Vertex

Front

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

Back

Integers

Front

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

Back

Reflection

Front

Flip over X or Y axis

Back

Correlation Coefficient

Front

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

Back

Transformation

Front

Changes graphs shape, size or position

Back

Perpendicular

Front

negative reciprocal slope

Back

Range

Front

Everything Y can be

Back

Negative Correlation

Front

Negative slope on a scatter plot

Back

Compound Inequality

Front

Two inequalities joined by and "or" or

Back

Function

Front

Every input has exactly 1 output

Back

Associative Property

Front

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

Back

Function Notation

Front

f(x)=

Back

Equivalent Expressions

Front

Two expressions that equal each other

Back

Formula

Front

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

Back

Natural Numbers

Front

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

Back

Term

Front

A Variable,a number or the product of those

Back

Compound Inequality

Front

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

Back

Parent Function

Front

Most basic function shared in a family

Back

Like Terms

Front

Same variable, same exponent

Back

Variable

Front

Letter that represents a number

Back

Commutative Property

Front

a+b=b+a ab=ba

Back

Rational Numbers

Front

All numbers that can be written as quotients of integers.

Back

inverse variation

Front

indirect variation -power of two number is a constnat -xy=k -x1=y2(partners are diagonal) -x1/x2=y2/y1

Back

Section 4

(52 cards)

rational numbers

Front

can be written as quotients of integers but can be written as decimals that terminate or repeat

Back

exponent

Front

in a power, the number of times the base is used as a factor.

Back

describing functions

Front

-ordered pairs -mapping -rule(tells what to do to x in order to get y) -graph

Back

addition property of equality

Front

add the same number to each side

Back

algebraic expression

Front

expression with a variable

Back

commutative property of multiplication

Front

ab=ba

Back

closure property of addition

Front

a+b is a real number

Back

inverse property of multiplication

Front

aX(1/a)=1, a = 0

Back

table of values

Front

-chose x values -substitute x -slove for y -plot points -connect lines

Back

domain

Front

set of the 1st coordinate(x) -allows values of the independant clause

Back

joint variation

Front

involves three or more variables(direct variation)

Back

linear equation

Front

an equation that can be written in the form ax+b=0 where a and b are constants and a=0

Back

coefficient

Front

the product of a number and a variable

Back

composite function

Front

g(f(x)) -replace the x in g(x) with the function f to get a new function

Back

x and y intercepts solving equations

Front

-let y=0 -solve for x -let x=0 -solve for y -plot points -connect line

Back

opposite

Front

additive inverse (exp. subtraction is the opposite of addition)

Back

identity property of addition

Front

a+0=a, 0+a=a

Back

verticle line test

Front

draw a verticle line anywhere(everywhere) if it crosses the graph in one place, the graph is a function

Back

identity property of multiplication

Front

aX1=a, 1Xa=a

Back

reciprocal

Front

multiplicative inverse (exp. of any nonzero number b is 1/b)

Back

numerical expression

Front

consists of numbers, operations, and grouping symbols

Back

point-slop form

Front

y-b=m(x-a)

Back

irrational numbers

Front

cannot be written as quotients of integers and cannot be written as decimals that terminate or repeat

Back

variable

Front

letter that is used to represent one or more numbers

Back

evaluate funtion

Front

replace the x and calculate y -f(x) is the same as y

Back

inverse property of addition

Front

a+(-a)=0

Back

terms

Front

in an expression that can be written as a sum, the parts added together are called terms

Back

slop intercept form

Front

y=mx+b -b is the y-intercept

Back

order of operations

Front

Please Excuse My Dear Aunt Sally

Back

rate of change

Front

change in y divided by the change in x -slope

Back

number line

Front

a graph of real numbers that are graphed on a line in increasing money from left to right

Back

power

Front

expression formed by repeated multiplication of the same factor

Back

equation

Front

a statement that two expressions are equal

Back

base

Front

in a power, the factor

Back

relation

Front

set of ordered pairs -each number is a coordinate -1st coordinate is x(abscissa) -2nd coordinate is y(ordinate)

Back

subtraction property of equality

Front

subtract the same number from each side

Back

distributive property

Front

a(b+c)=ab+ac

Back

multiplication property of equality

Front

multiply each side by the same nonzero number

Back

closure property of multiplication

Front

ab is a real number

Back

inverse of a function

Front

any relation that swaps the dependant and independant variable -new relation may or may not be a function

Back

associative property of multiplication

Front

(ab)c=a(bc)

Back

slop of a line

Front

-change in y is the differnece in y coordinates (vertical change) -change in x is diffrence in x coordinates(horizontal change) -slop is the same of any 2 points

Back

y-intercept

Front

line crosses the y-axis -(0,b) -let x=0 to solve for y

Back

associative property of addition

Front

(a+b)+c=a+(b+c)

Back

parrallel

Front

lines that have same slop -slopes are negative reciprocals

Back

function

Front

set of ordered pairs in which no first coordinate is not repeated

Back

x-intercept

Front

line crosses x-axis -(x,0) -let y=0 to solve for x

Back

commutative property of addition

Front

a+b=b+a

Back

disjunction

Front

has "or" -ex. x id less than, or euql to five

Back

range

Front

set of 2nd coordinates(y) -resulting value of the dependant varible

Back

Section 5

(52 cards)

Compound Inequality

Front

has word and/or in it

Back

associative property

Front

(a+b)+c=a+(b+c)

Back

verbal model

Front

an equation written in words before numbers

Back

union

Front

the graph of a compound inequality containing 'or' is the union of the solution sets of the two inequalities

Back

algebraic expression

Front

expressions that contain at least one variable

Back

distance formula

Front

d=rt

Back

Union

Front

OR <=-=>

Back

temperature formula

Front

F=9/5C+32

Back

Set-Builder Notation

Front

{x|x>7}

Back

area of a triangle

Front

A=1/2bh

Back

absolute value

Front

a number's distance from 0 on the number line l x l

Back

intersection

Front

the graph of a compound inequality containing 'and' is the intersection of the solution sets of the two inequalities

Back

Circumference of a circle

Front

C=2(pi)r

Back

Area of a trapezoid

Front

A=1/2(b1+b2)h

Back

identity property

Front

a+0=a=0+a

Back

division property of equality

Front

divide each side by the same nonzero number

Back

Formula

Front

Something that relates quantitites to calculate things

Back

Trichotomy Property

Front

a=b, a>b, a<b

Back

Area of a rectangle

Front

A=lw

Back

reflexive property

Front

for any real numbera: a=a ex: -7+n=-7+n

Back

element of a set

Front

item in a set

Back

Algebraic Expressions

Front

Minimum of a variable

Back

irrational numbers

Front

real numbers that are not rational ex: square root of 5, pi

Back

Empty Set

Front

{ } No Solution

Back

Variables

Front

symbols

Back

set-builder notation

Front

the solution of an inequality can be expressed by using this ex: {x1x>9}

Back

open sentence

Front

a mathamatical sentence containing one or more variables

Back

compound inequality

Front

consists of two inequalities joined by the word 'and' or the word 'or'

Back

commutative property

Front

a+b=b+a

Back

Area of a circle

Front

A= r(pi)r

Back

set

Front

collection of items called elements

Back

Order of Operations

Front

PEMDAS

Back

Interval Notation

Front

(7, infinity)

Back

rational numbers

Front

can be expressed as a ratio m/n where m and n are integers and n is not 0

Back

Open Sentence

Front

Sentence using < or > sign

Back

Solution

Front

Replacement that makes a sentence true

Back

subset

Front

a set whose elements all belong to another set

Back

distributive property

Front

a(b+c)=ab+ac and (b+c)a=ba+ca

Back

Absolute Value

Front

Distance from 0 on the number line

Back

Perimeter of a rectangle

Front

P=2l+2w

Back

Intersection

Front

AND <-=->

Back

formula

Front

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

Back

symmetric property

Front

for all real numbers a and b, if a=b then b=a ex: if 3=5x-6, then 5x-6=3

Back

substitution property

Front

if a=b, then a may be replaced by b and b may be replaced by a ex: if (4+5)m=18, then 9m=18

Back

Equation

Front

Sentence containing an = sign

Back

trichotomy property

Front

aka the property of order for any two real numbers a and b, exactly one of the following is true: a<b a=b a>b

Back

absolute value

Front

how far away a number is from zero

Back

transitive property

Front

for all real numbers a, b, and c if a=b and b=c, then a=c ex: if 2x+1=5x-8, then 2x+1=5x-8

Back

empty set

Front

the solution for an equation with no solution, symbolized by { } or 0 with /

Back

inverse property

Front

a+(-a)=0=(-a)+a

Back

Section 6

(51 cards)

zero

Front

neither positive nor negative

Back

parent function

Front

simplest function defining characteristics of the family

Back

translation

Front

or "slide" moving each point in a figure the same distance same direction

Back

subtraction

Front

x-y means x+(-y)

Back

function

Front

relation in which the domain is never repeated

Back

closure

Front

real numbers are closed under addition and under multiplication (x+y is unique and real) (xy is unique and real)

Back

function notation

Front

equation satisying the definition of a function

Back

scientific notation

Front

method of writing numbers by using powers of ten

Back

multiplicative inverse

Front

1/x=(x*1/x=1)

Back

additive identity

Front

zero is, x+0=x if x is a real number

Back

positive numbers

Front

numbers greater than 0

Back

symmetry

Front

if x=y then y=x

Back

reflection

Front

transformation that flips a figure across a line called line of reflection

Back

division

Front

x-y=x*1/y

Back

imaginary numbers

Front

square roots of negative numbers, have no points on the number line

Back

integers

Front

whole numbers and their opposites

Back

transformation

Front

s change in posiion, size shaoe of a figure

Back

independent variable

Front

input x is independant

Back

compression

Front

pushing points towards y-axis

Back

infinite set

Front

unlimited, or infinite number of elements.

Back

irrational numbers

Front

cannot be expressed exactly as a ratio of two integers, but are real numbers

Back

transitivity

Front

x=y and y=z then x=z

Back

range

Front

output or Y

Back

natural numbers

Front

positive integers or counting numbers

Back

distributivity

Front

multiplication distributes over addition (x(y+z) = xy+xz

Back

associativity

Front

addition and multiplication of real numbers is (x+y)+z = x + (y+z)

Back

relation

Front

pairing of unput and output values

Back

radicals

Front

involve square root, cube root, etc... of integers

Back

digits

Front

numbers from which the numerals are made

Back

finite set

Front

has a definite, or finite, number of elements

Back

stretch

Front

pulling all points away from y-axis

Back

empty set

Front

set containing no elements

Back

additive inverse

Front

adding the opposite (x+(-x)=0)

Back

real numbers

Front

have points on the number line

Back

complex numbers

Front

form of a+bi, a and b are real i is equal to sqrt of -1

Back

rational numbers

Front

can be expressed exactly as a ratio of two integers

Back

multiplicative identity

Front

one is, 1*x=x for real numbers

Back

negative numbers

Front

numbers less than 0

Back

radicand

Front

The number expression under the radical symbol

Back

principal root

Front

the radical symbol indicates both the positive and negative square root of a number

Back

reflexive property

Front

if x is a real number, the x=x

Back

roster notation

Front

elements of a set listed between braces

Back

non-integers

Front

fractions, numbers between the integers

Back

interval notation

Front

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

Back

commutativity

Front

addition and multiplications of real numbers are x+y=y+x xy=yx

Back

like radical terms

Front

sqare roots that have the same radicand

Back

domain

Front

input or X

Back

set builder notation

Front

uses the propertied of the elements in a set to define the set

Back

trichotomy

Front

either x<y, x>y, or x=y

Back

dependent variable

Front

depends on inout value of function example: f(x)

Back

Section 7

(52 cards)

polynomial

Front

a monomial or a sum of monomials

Back

Quotient Property

Front

(a^m)/(a^n)= a^m-n

Back

Distributive Property

Front

a(b+c)= ab+ac

Back

absolute value

Front

The distance a number is from zero on a number line

Back

Associative Property

Front

(a+b) +c= a+ (b+c)

Back

algebraic expression

Front

an expression with one or more variables

Back

open sentence

Front

an equation with one or more variables

Back

Product Property

Front

a^m *a^n= a^m+n

Back

Additive Inverse Property

Front

a+(-a)=0

Back

power

Front

an expression that represents repeated multiplication of the same factor

Back

Power of a Product

Front

(ab)^m= a^m*b^m

Back

Power of a Quotient

Front

(a/b)^m= (a^m)/(b^m)

Back

no solution

Front

The answer to a contradiction is:

Back

empty set

Front

set with no elements: zero or {}.

Back

Zero Property

Front

(ab)^0= 1

Back

Commutative Property

Front

a+b=b+a

Back

Multiplicative Inverse

Front

a*(1/a)= 1

Back

Power Property

Front

(a^m)^n= a^m*n

Back

Interval Notation

Front

Used to express sets of real numbers. An open interval is expressed as (a,b) is the set of real numbers not including a and b. a and b are endpoints of the interval. But if written [a,b], the set does include a and b.

Back

radicant

Front

number under the radical

Back

coefficient

Front

number in front of a variable

Back

set-builder notation

Front

The expression of a solution set of an inequality

Back

union

Front

The graph of two or more inequalities containing or >

Back

compound inequailty

Front

two inequalities joined by and or or

Back

set

Front

a collection of items, called elements.

Back

Negative Property

Front

b^-n= 1/(b^n)

Back

subset

Front

a set whose elements all belong to another set.

Back

equation

Front

a mathematical sentence that shows that two expressions are equal

Back

Closure Property

Front

a∈W, b∈W then a+b∈W

Back

empty set

Front

the solution set for and equation that doesn't have a solution

Back

degree

Front

the sum of the exponents of the variables of a monomial

Back

trinomial

Front

a polynomial with three unlike terms

Back

constant

Front

a term that does not contain a variable

Back

monomial

Front

an expression with only one term

Back

rational numbers

Front

numbers that can be written as fractions, including terminating and repeating decimals, and integers

Back

like terms

Front

Expressions that contain the same variables to the same power

Back

irrational numbers

Front

A real number that isn't rational that doesn't terminate or repeat

Back

variable

Front

symbols used to represent unknown quantities x, y

Back

principle root

Front

√16 = 4←

Back

real numbers

Front

all numbers we use in everyday life

Back

Roster Notation

Front

finite: {8,9,12} a definite # of elements. infinite: {1,2,3,4...} unlimited # of elements.

Back

intersection

Front

The graph of a compound inequality that contains and

Back

Sets of Numbers

Front

1. natural numbers (bold N) {1,2,3,4,5...} 2. whole (bold W) {0,1,2,3,4...} 3. Integers (bold Z) {-3,-2,-1, 0, 1...} 4. Rational (bold Q) {3/4, 1/2, 1/4, 7/8} 5. Irrational {√2, √8, ∏, -√3} 6. Real (bold R)

Back

Additive Identity Property

Front

a+0=a

Back

multiplication property of -1

Front

-1*x=-x

Back

Multiplicative Identity Property

Front

a*1=a

Back

order of operations

Front

PEMDAS

Back

radical

Front

Back

multiplication property of 0

Front

if xy=0 then x=0 or y=0

Back

Set Builder Notation

Front

ex. {x⎮3<x<8, x∈R

Back

Section 8

(50 cards)

subtraction property of equality

Front

if a = b, then a - c = b - c

Back

Constant Function

Front

f(x)=c D: (-∞, ∞) R: [c]

Back

property of opposites of a sum

Front

-(a+b) = -a + (-b)

Back

definition of subtraction

Front

a - b = a + (-b)

Back

vertical translation

Front

change the y-values to their opposite. move x-value up or down.

Back

Square Root

Front

F(x)= √x D: [0, ∞) R: [0, ∞)

Back

Quadratic

Front

f(x)= x^2 D: (-∞, ∞) R: [0, ∞)

Back

Stretch

Front

I. Vertical -change y. L(x)= af(x) |a|>1 II. Horizontal- change x. n(x)=f(1/b(x)) |b|>1...ex: horizontal stretch by 4-> n(x)= ((1/4)x)^2

Back

multiplicative property of -1

Front

a*-1 = -a -1*a = -a

Back

distributive property of division

Front

(a+b)/c = a/c + b/c (must have a monomial in denominator - does not work for the reciprocals of the above)

Back

closure field property of real numbers

Front

a + b and ab are unique real numbers

Back

Function

Front

for every input there is ONE unique output. the first coordinate is never repeated.

Back

the absolute value of the product of of 2 or more numbers is the product of their absolute values

Front

|ab| = |a| * |b|

Back

Transformation

Front

changes the position size or shape of the figure .

Back

multiplicative property of 0

Front

a*0 = a 0*a = 0

Back

Linear

Front

f(x)= x D: (-∞, ∞) R: (-∞, ∞)

Back

horizontal translation

Front

change the x-values to their opposite. move x-value right or left.

Back

One-to-One Function

Front

a function in which the x- and y-values can NOT repeat.

Back

definition of division

Front

a/b = a * 1/b b does not = 0 and ab E R

Back

Restriction on Domain

Front

1. Never have zero in the denominator. 2. Radicant ≥ 0.

Back

Compression

Front

I. Vertical- m(x)=af(x) 0<|a|<1 II. Horizontal- p(x) = f(1/b (x)...ex: p(x)= x^2 horizontal comp. by 1/3= p(x) = f(3x)^2

Back

rule for addition if a is positive and b is negative and | a | < | b |

Front

a + b = - ( | b | - | a | )

Back

rule for addition if a and b are both negative numbers

Front

a + b = - ( | a | + | b | )

Back

addition property of equality

Front

if a = b, then a + c = b + c

Back

1 positive and 1 negative numbers' products are

Front

negative

Back

Parent Functions

Front

constant, linear, cubic, quadratic, absolute value, square root.

Back

distributive field property of real numbers

Front

a(b+c) = ab + ac

Back

property of reciprocals field property of real numbers

Front

a * 1/a = 1

Back

How do you determine if a set is closed under addition?

Front

If you take any number in the set and add it to another number in the set and get an answer as number in the set, the set is closed under addition.

Back

substitution field property of real numbers

Front

if a = b, then a + c = b + c

Back

2 positive or 2 negative numbers' products are

Front

positive

Back

identity field property of real numbers

Front

a + 0 = a a * 1 = a

Back

Relation

Front

any pairing of an input(domain) with the output(range).

Back

reflexive property of equality

Front

a = a

Back

the quotient of 2 positive or 2 negative numbers is

Front

positive

Back

symmetric property of equality

Front

if a = b, then b = a

Back

Cubic

Front

f(x)= x^3 D: (-∞, ∞) R: (-∞, ∞)

Back

Reflection

Front

I. across x-axis. change y-value. j(x)= -f(x) II. Across y-axis. change x-value. j(x)= f(-x)

Back

the quotient of 1 positive and 1 negative number is

Front

negative

Back

Absolute value

Front

f(x)= |x| D: (-∞, ∞) R: [0, ∞)

Back

property of opposite products

Front

-ab = b(-a) -ab = (-a)b

Back

transitive property of equality

Front

if a = b and b = c, then a = c

Back

Is a relation a function?

Front

y^even is NOT a function...why? ex: y^2= x+3 (1, 2) (1, -2) |y| is NOT a function...why? ex: |y|=3x+2 (5,√17) (5, −√17)

Back

How do you determine if a set is closed under multiplication?

Front

If you take any number in the set and multiply it by another number in the set and get an answer as a number in the set, then the set is closed under multiplication.

Back

to divide by a fraction,

Front

multiply by its reciprocal

Back

commutative field property of real numbers

Front

a + b = b + a ab = ba

Back

associative field property of real numbers

Front

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

Back

multiplication property of equality

Front

if a = b, then ac = bc

Back

rule for addition if a is positive and b is negative and | a | > | b |

Front

a + b = | a | - | b|

Back

property of opposites field property of real numbers

Front

a + (-a) = 0

Back

Section 9

(52 cards)

Inverse Property of Multiplication

Front

a ⋄ 1/a = 1, a ≠ 0 *Answer is ALWAYS 0 because you multiply by the reciprocal

Back

Infinite set

Front

A set having an unlimited number of members

Back

Finite set

Front

a set with a definite number of elements

Back

Substitution POE

Front

If a = b, then b may be substituted for a in an expression to obtain an equivalent expression

Back

Intersection

Front

Symbol: upside down U definition: overlap

Back

element

Front

one individual number/unit in a set

Back

Commutative Property of Multiplication

Front

ab = ba *Order of numbers/variables doesn't effect the answer

Back

Inverse Property of Addition

Front

a + (-a) = 0 *Answer is ALWAYS 0 because you add by the opposite

Back

Distributive Property

Front

a(b + c) = ab + ac

Back

Variable

Front

a quantity that can assume any of a set of values

Back

subset

Front

symbol: c definition: a part of a set including the set itself, all elements, and zero

Back

Commutative Property of Addition

Front

a + b = b + a *Order of numbers/variables doesn't effect the answer

Back

Origin

Front

the point of intersection of coordinate axes

Back

irrational numbers

Front

symbol: I definition: any number that cannot be written as a fraction example: square root -2, pi

Back

Empty set

Front

Set containing no elements

Back

whole numbers

Front

symbol: W definition: any counting number that is positive or negative excluding 0

Back

integers

Front

symbol: Z definition: any counting number that is positive or negative including 0

Back

Transitive Property of Inequalities

Front

If a ≤ b and b ≤ c, then a ≤ c

Back

imaginary numbers

Front

definition: any number that is not real example: square root -1

Back

Identity Property of Addition

Front

a + 0 = a, 0 + a = a *a value is never changed

Back

Opposites

Front

two numbers that have the same absolute value but have different signs

Back

Division POE

Front

If a = b and c ≠ 0, then a/c = b/c

Back

Closure Property of Multiplication

Front

ab is a real number

Back

Addition Property of Inequalities

Front

If a ≤ b, then a + c ≤ b + c

Back

Set

Front

Collection of elements

Back

Multiplication Property of Inequalities

Front

If a ≤ b and c > 0, then ac ≤ bc If a ≤ b and c < 0, then ac ≥ bc Watch out when c is negative

Back

Subset

Front

a set whose members are members of another set

Back

natural numbers

Front

symbol: N definition: any positive whole number

Back

Algebraic expression

Front

A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Back

Subtraction Property of Inequalities

Front

If a ≤ b, then a - c ≤ b - c

Back

value of a numerical expression

Front

the number represented by the equation

Back

What does absolute value usually represent?

Front

a distance

Back

Set

Front

a group of numbers

Back

Division Property of Inequalities

Front

If a ≤ b and c > 0, then a/c ≤ b/c If a ≤ b and c < 0, then a/c ≥ b/c Watch out when c is negative

Back

Subtraction POE

Front

If a = b, then a - c = b - c

Back

Interval notation

Front

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 endpoint from an interval

Back

Closure Property of Addition

Front

a + b is a real number

Back

Identity Property of Multiplication

Front

a ⋄ 1 = a, 1⋄ a = a *a value is never changed

Back

grouping symbols

Front

(parenthesis) {braces} [brackets] ____ fraction bar l absolute value bars l

Back

Multiplication POE

Front

If a = b, then ac = bc

Back

Associative Property of Addition

Front

(ab)c = a (bc) *Grouping doesn't effect the answer

Back

Roster notation

Front

the elements of a set are listed between braces

Back

rational numbers

Front

symbol: Q definition: any number that can be written as a fraction example: 2/3, 2.3, 23

Back

real numbers

Front

symbol: R definition: any number that is not imaginary

Back

substitution

Front

an expression that can be replaced by another expression that represents the same value

Back

Associative Property of Addition

Front

(a + b) + c = a + (b + c) *Grouping doesn't effect the answer

Back

Set-builder notation

Front

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."

Back

Union

Front

symbol: U definition: everything together

Back

domain

Front

anything that the variable can be

Back

Element

Front

one of four substances thought in ancient and medieval cosmology to constitute the physical universe

Back

Section 10

(51 cards)

discrete graph

Front

a graph whose points are not connected.

Back

Opposite of a Product

Front

-(ab) = - a ⋄ b = a ⋄ (-b) [Only for multiplication, has to end up negative if the numbers are positive to begin with]

Back

Reflexive POE

Front

a = a [*Reflexive sounds like reflection]

Back

continuous graph

Front

a graph of a line or a smooth curve

Back

Multiplication by Negative one

Front

-1⋄ a = - a

Back

Multiplication by Zero

Front

0 ⋄ a = 0

Back

independent variable

Front

the input value;the values make up the domain

Back

Opposite of a Difference

Front

-(a - b) = b - a [or -a +b] [Only with subtraction]

Back

Irrational Numbers

Front

A number that cannot be expressed in the form a/b, where a and b are both integers Ex. .0101110101000..., √2, pi, √3 etc.

Back

Linear Equations

Front

has only addition, subtraction, and multiplication as operators of a variable and a constant. The variable has 1 as an exponent.

Back

function

Front

a mathematical relation such that each element of the domain is paired with exactly one element of the range.

Back

dimensional analysis

Front

the process of carrying units throughout a computation

Back

vertical line test

Front

a method to determine if a graph is a function or not

Back

Ordered Pair

Front

A pair of numbers that can be used to locate a point on a coordinate plane

Back

Opposite

Front

Also known as the additive inverse. When the sum of the opposite and the original number is added the sum is zero. Ex. The opposite of A is -A

Back

equivalent equations

Front

two equations that have the same solution

Back

Natural Numbers

Front

1,2,3... ✩Only positive numbers, and NO zero

Back

Whole Numbers

Front

0,1,2,3... ✩Only positive numbers and zero, NO fractions

Back

formula

Front

a rule for the relationship between certain quantities

Back

mapping

Front

Illustrates how each element of the domain is paired with an element in the range

Back

Quadrant

Front

any of the four areas into which a plane is divided by two orthogonal coordinate axes

Back

Rational Numbers

Front

Any number that can be written in the form a/b, where both a and b are integers and b ≠ 0 Ex. 5/8 , .75, 4, - 2/3 etc. -Some repeating and terminating decimals can be rational numbers

Back

Real Numbers

Front

All numbers

Back

range

Front

the set of second coordinates of the ordered pairs of a relation.

Back

Opposite of an Opposite

Front

-(-a) = a [If a is a positive number, then the answer will be positive as well]

Back

Integers

Front

...-3,-2,-1,0,1,2,3... ✩Negative and positive numbers including zero, NO fractions

Back

multi-step equation

Front

an equation that requires more than one step to solve

Back

ratio

Front

a comparison of two numbers by division

Back

percent of change

Front

the ratio of the change in an amount to the original amount expressed as a percent

Back

Absolute Value

Front

A number's distance from zero. The value is always positive

Back

proportion

Front

an equation stating two ratios are equal

Back

Transitive POE

Front

If a = b and b = c, then a = c

Back

Symmetric POE

Front

If a = b, then b = a

Back

solve an equation

Front

to find the value of the variable that makes the equation true

Back

Reciprocal

Front

Also known as the multiplicative inverse, the inverse of a nonzero number Ex. The reciprocal of 4 is 1/4

Back

Addition POE

Front

If a = b, then a + c = b + c

Back

Whole Numbers

Front

0,1,2,3... ✩Only positive numbers and zero, NO fractions

Back

function notation

Front

replacing the y with the symbol f(x)

Back

domain

Front

the set of first coordinates of the ordered pairs of a relation.

Back

one-to-one function

Front

a function where each element of the range is paired with exactly one element of the domain.

Back

relation

Front

A set of ordered pairs

Back

identity

Front

equations that are true for all values of the variables

Back

Definition of Subtraction

Front

a - b = a + (-b)

Back

Opposite of a Sum

Front

-(a + b) = - a + (- b) [Only with addition]

Back

scale model

Front

a three-dimentional reproduction of an item that has been reduced or increased in size proportionally

Back

rate

Front

the ratio of two measurements having different units of measure

Back

Definition of Division

Front

a ÷ b = a/b = a ⋄ 1/b, b≠0

Back

Distributive Property for Subtraction

Front

a(b - c) = ab - ac

Back

Cartesian Coordinate Plane

Front

a plane divided into four quadrants by the intersection of the x-axis and the y-axis at the origin

Back

dependent variable

Front

the output value; the values make up the range.

Back

Section 11

(52 cards)

Parameter

Front

a determining or characteristic element; a factor that shapes the total outcome; a limit, boundary

Back

Linear Function

Front

a function in which the graph of the solutions forms a line

Back

Dependent Variable

Front

a factor that can change in an experiment in response to changes in the independent variable

Back

Vertex

Front

The point in a function where the function reaches a min or a max

Back

Linear Inequality

Front

an inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line

Back

Relation

Front

A set of ordered pairs

Back

domain

Front

set of input values

Back

dependent variable

Front

the output variable, depends on the value of the input variable

Back

Standard Form

Front

ax+by=c

Back

range

Front

set of output values

Back

Absolute Value Function

Front

a function written in the form y = /x/, and the graph is always in the shape of a v

Back

x-intercept

Front

The x-coordinate of the point where a line crosses the x-axis.

Back

perpendicular

Front

slope = - reciprocal

Back

Scatter Plot

Front

a graph with points plotted to show a possible relationship between two sets of data.

Back

Mapping Diagram

Front

a way to show a relation that links elements of the domain with cooresponding elements of the range

Back

Independent Variable

Front

variable that is changed in an experiment

Back

output

Front

y

Back

Direct Variation

Front

y=kx

Back

weighted average

Front

the sum of the product of the number of units and the value per unit divided by the sum of the number of units, represented by M

Back

y-intercept

Front

the y-coordinate of the point where the line crosses the y-axis.

Back

function notation

Front

using f(x) to represent the dependent variable of a function. basically y

Back

slope

Front

the change in y over the change in x m y1-y2 over x1-x2 rise over run

Back

Translation

Front

A transformation that "slides" each point of a figure the same distance in the same direction.

Back

VLT

Front

vertical line test

Back

Stretch

Front

Multiplies all y values by the same factor greater than 1

Back

Point slope form

Front

Y-Y1=m(x-x1)

Back

equation in two variables

Front

an equation that contains two variables

Back

input

Front

x

Back

Function Notation

Front

an equation in the form of 'f(x)=' to show the output value of a function, f, for an input value x

Back

Vertical Line Test

Front

a method to determine if a graph is a function or not

Back

Shrink

Front

Reduces y values by a factor between 1-0

Back

relation

Front

a mapping or pairing of input values with output values

Back

parallel

Front

slope = the same

Back

linear function

Front

can be written as y=mx+b where m and b are constants (x has to be to the first power)

Back

Function

Front

A relation which one element from the domain is paired with range

Back

Transformation

Front

An operation that moves or changes a geometric figure in some way to produce a new figure

Back

unit rate

Front

a rate that tells how many of one item is being compaired to 1 of another item

Back

Range

Front

The y-coordinates of the set of points on a graph. Also, the y-coordinates of a given set of ordered pairs.

Back

Linear Equation

Front

an equation whose graph is a straight line

Back

function

Front

a relation for which each input has exactly one output

Back

Constant of Variation

Front

the number k in equations of the form y=kx

Back

Slope

Front

the steepness of a line, equal to the ratio of a vertical change to the corresponding horizontal change

Back

Trend Line

Front

a line that approximates the relationship between the data sets of a scatter plot

Back

Domain

Front

The set of x-coordinates of the set of points on a graph; the set of x-coordinates of a given set of ordered pairs. The value that is the input in a function or relation.

Back

HOY VIXN

Front

-horizontal directional 0 slope y=k equation -vertical directional x=k equation no slope

Back

independent variable

Front

the input variable

Back

Slope Intersept Form

Front

the equation of a line in the form of y=mx+b, where m is the slope and b is the y intersept

Back

Parent Function

Front

The simplest function in a family; all functions in the family are transformations of it

Back

-horizontal directional 0 slope y=k equation -vertical directional x=k equation no slope

Front

HOY VIXN

Back

Reflection

Front

A transformation that "flips" a figure over a mirror or reflection line.

Back

Section 12

(50 cards)

slope intercept form

Front

y=mx+b m=slope b=y-intercept

Back

Ray

Front

a half line; the portion of a line on one side of a fixed point on the line.

Back

y=ax

Front

direct variation a=constant of variation y varies directly with x

Back

Slope-intercept form

Front

one form of writing the equation of a line - (y=mx+b)

Back

subtract from input

Front

translate graph right

Back

relation

Front

a mapping, or pairing, of input values with output values; can be represented by ordered pairs, a table, a graph, or a mapping diagram

Back

transformation

Front

a change to a function

Back

slope

Front

the ratio of vertical change (the rise) to horizontal change (the run) for a nonvertical line passing through the points (x₁, y₁) and (x₂, y₂), the ________ is m=(y₂ - y₁)/(x₂ - x₁)

Back

change sign of input

Front

reflect over y-axis

Back

trend line

Front

approximates the relationship between the variables, or data sets, of a scatter plot

Back

Curve

Front

the path traced by a moving point; an unbroken connection of points.

Back

dependent variable

Front

the output variable in an equation in two variables; in y=3x+5, the __________ is y

Back

independent variable

Front

the input variable in an equation in two variables; in y=3x+5, the __________ is x

Back

≤ < less than (or equal to)

Front

shade down

Back

y=k

Front

horizontal line 0 slope

Back

Variable

Front

a letter used to represent a number

Back

weak

Front

correlation when data points are loosely packed

Back

Like Terms

Front

terms whose literal components represent the same number regardless of the numbers used to replace the variables

Back

dilation

Front

changes the size of a graph by stretching or compressing

Back

add to output

Front

translate graph up

Back

perpendicular lines have _____ _____ slopes

Front

negative reciprocal

Back

piecewise functions

Front

a function determined by at least 2 equations, each of which applies to a different part of the functions domain restricted domain

Back

translation

Front

shifting or sliding a function up, down, left, right

Back

scatter plot

Front

a graph that relates two sets of data by plotting the data as ordered pairs

Back

≥ > greater than (or equal to)

Front

shade up

Back

point slope form

Front

(y-y1)=m(x-x1) m=slope (x1, y1)= point

Back

parent

Front

simplest function form in a set that forms a family

Back

2-intercept form

Front

x y - + - = 1 a b a= x-intercept b = y-intercept

Back

Line Segment

Front

part of a line that consists of two end points and all points between them

Back

x=k

Front

vertical line no slope

Back

Constant Term

Front

a quantity whose value does not change

Back

best fit

Front

line that gives the most accurate model of related data (two words)

Back

strong

Front

correlation when data points are tightly packed

Back

axis of symmetry

Front

vertical line; x=h; separates graph of absolute value function into two equal, but mirrored, parts

Back

multiply by value bigger than 1

Front

vertically stretch graph

Back

parallel lines have _____ slopes

Front

same

Back

subtract from output

Front

translate graph down

Back

Point

Front

A location in space with no physical size

Back

add to input

Front

translate graph left

Back

rate of change

Front

a comparison of how much one quantity changes, on average, relative to the change of another quantity

Back

standard form

Front

ax+by=c a, b, c are integers

Back

Slope

Front

the ratio of the change in the y coordinate to the change in the x coordinate from a point on a line to any other point on a line

Back

change sign of output

Front

reflect over x-axis

Back

multiply by fraction between 0 and 1

Front

vertically compress graph

Back

correlation coefficient

Front

r; tells the strength of the correlation

Back

reflection

Front

a flip; it changes the sign of the input or the output

Back

LIne

Front

a straight curve that has no ends, or extends indefinetly in two opposite directions.

Back

vertex

Front

single maximum or minimum point of an absolute value function; (h,k)

Back

function

Front

a relation for which each input has exactly one output; if any input of a relation has more than one output, the relation is not a function

Back

absolute value

Front

function that has a V-shaped graph; y=a|x-h|+k; a is the slope of the right branch; has symmetry and one vertex; can open up or down

Back

Section 13

(52 cards)

Similar Triangles

Front

Two triangles whose angles have equal measures

Back

Proportion

Front

an equation or other statement that indicates that two ratios equal

Back

Transversal

Front

a line that cuts or intersects one or more other lines in the same plane

Back

Factor

Front

one of two or more expressions that are multiplied to form a product

Back

Substitution Axiom

Front

equal quantities may always be substituted for one another

Back

Rational Expression

Front

an algebraic expression written in the form of a fraction

Back

Scale Factor

Front

a multiplying factor relating the corresponding lengths of a given geometric shape to its enlarged or reduced counterpart. A scale factor of 1 denotes congruence.

Back

1st Property of a Parallelogram

Front

The sides opposite each other have equal lengths

Back

1st Major Rule of Algebra

Front

the same quantity can be added to both sides of an equation without changing the solution to the equation

Back

commutative axiom for addition

Front

a+b=b+a

Back

identity axiom of addition

Front

a+0=a

Back

Exterior Angles

Front

the angles outside the parallel lines

Back

Formula of Tangent

Front

TOA: Opposite over adjacent

Back

Pythagorean Theorem

Front

the area of a square drawn on the hypotenuse of a right triangle equals the sum of the areas of the squares drawn on the other two sides

Back

Corresponding Angles

Front

angles located in matching positions when two lines are cut by a transversal.

Back

Unit Multipliers

Front

a ratio of named numbers whose value is 1; this ratio is used to convert unit measurements( for example to convert feet to inches or feet to miles)

Back

associative axiom for addition

Front

(a+b)+c=a+(b+c)

Back

1st Property of a Rhombus

Front

a rhombus is a parallelogram whose four sides have equal lengths

Back

Product of Square roots rule

Front

If m and n are nonnegative real numbers then the square root of m times the square root of n equals the square root of m time n and the square root of m times n equals the square root of m times the square of n

Back

identity axiom of multiplication

Front

a(1)=a

Back

Area of a triangle

Front

one half base times height

Back

Congruent

Front

identical in all characteristics

Back

Formula of Sine

Front

SOH: Opposite over hypotenuse

Back

Corresponding Sides

Front

corresponding sides are the sides opposite equal angles in similar triangles; the ratios of the lengths of corresponding sides in similar triangles are equal

Back

3rd Property of a Rhombus

Front

the diagonals of a rhombus are perpendicular bisectors of each other

Back

Monomial

Front

a polynomial of one term

Back

Quadratic Equation

Front

a one variable polynomial equation whose degree is 2

Back

Binomial

Front

a polynomial of two terms

Back

4th Property of a Parallelogram

Front

The diagonals bisect each other

Back

Scientific Notation

Front

a method of writing a number as a product of a decimal number and a power of 10

Back

Denominator-Numerator Rule

Front

the denominator and the numerator of a fraction may be multiplied by the same non-zero quantity without changing the value of the fraction

Back

additive inverse axiom

Front

a+-a=0

Back

Radical

Front

an expression for taking the root of a quantity indicated by the symbol

Back

Alternate Angles

Front

angles on opposite sides of a transversal

Back

Formula of Cosine

Front

CAH: Adjacent over hypotenuse

Back

Inscribed Angle

Front

an angle inside a circle with its vertex on the circle whose measure equals half the measure of the intercepted arc

Back

2nd Property of a Rhombus

Front

The diagonals of a rhombus bisect the angles of the rhombus

Back

3rd Property of a Parallelogram

Front

The sum of the measures of any two consecutive angles is 180 degrees

Back

Interior Angles

Front

the angles between parallel lines

Back

distributive axiom for multiplication over addition

Front

a(b+c)=ab+ac

Back

Parallelogram

Front

a quadrilateral that has two pairs of parallel sides

Back

Trinomial

Front

a polynomial of three terms

Back

commutative axiom for multiplication

Front

ab=ba

Back

2nd Property of a Parallelogram

Front

The angles opposite each other have equal measures

Back

2nd Major Rule of Algebra

Front

every term on both sides of an equation can be multiplied or divided by the same quantity( except zero) without changing the solution to the equation.

Back

Product

Front

the number or quantity obtained by multiplying two or more numbers together

Back

3rd Major Rule of Algebra

Front

the denominator and the numerator of an expression can be multiplied or divided by the same non zero quantity without changing the value of the expression. Only the form of the expression is changed.

Back

associative axiom for multiplication

Front

(ab)c=a(bc)

Back

Reciprocal

Front

for any non-zero real number, the number in inverted form. For example, the reciprocal of 3 is 1/3 and the reciprocal of 3/4 is 4/3

Back

Remote Interior Angles

Front

the two remaining interior angles of a triangle given one interior angle

Back

Section 14

(52 cards)

Feasible Region

Front

the intersection of the inequalities

Back

Consistent Dependent

Front

∞, all points on the line, the lines coincide

Back

identity

Front

an equation that is true for all values of the variable

Back

Bounded

Front

when the feasible region is a polygon

Back

formula

Front

a literal equation that states a rule for a relationship among quantities

Back

Unbounded

Front

when the feasible region is NOT a polygon

Back

direct variation

Front

slope k is constant y=kx

Back

eight

Front

How many different ways can 3 planes intersect?

Back

Constraints

Front

the inequalities

Back

domain

Front

set of all inputs, x coordinates of the ordered pairs

Back

transitive property of equality and order

Front

if a=b, and b=c, then a=c

Back

proportion

Front

a statement that 2 ratios are equal

Back

deductive reasoning

Front

the process of using logic to draw conclusions

Back

addition property of order

Front

if x>y, then x+a>y+a

Back

solution of an equation

Front

a value or values that make the equation true

Back

range

Front

set of all outputs, y coordinates of the ordered pairs

Back

symmetric axiom of equality

Front

if a=b, then b=a

Back

linear function

Front

a function whose graph is a line

Back

multiplication property of -1

Front

a(-1)=-a

Back

Ax+By=C

Front

standard form of a linear equation

Back

multiplication property of equality

Front

if x=y, then xa=ya

Back

y=mx+b

Front

slope intercept form

Back

addition property of equality

Front

if x=y, then x+a=y+a

Back

linear function

Front

y=mx+b

Back

equivalent equations

Front

equations that have the same solution set

Back

Linear Programming

Front

the process of finding the maximum and minimum value of a function for a region defined by inequalities

Back

rate

Front

a ration that compares 2 quantities measured in different units

Back

literal equation

Front

an equation that contains two or more variables

Back

ratio

Front

a comparison of 2 numbers or quantities

Back

function

Front

a relation in which each element of the domain is paired with exactly one element in the range

Back

multiplication property of order

Front

if x>y, then xa>ya

Back

constant of variation

Front

when x and y are variables k=y/x

Back

unit rate

Front

in which the 2nd quantity in the comparison is one unit

Back

Substitution

Front

What would be better in this situation (substitution or elmination)? 3w+2d=192, d=2w-13

Back

relation

Front

set of pairs of input and output values. can be written as an ordered pair

Back

Trace

Front

The line at which a plane intersects with a coordinate plane is called a ________.

Back

Inconsistent

Front

No solutions, parellel (don't intersect)

Back

Elimination

Front

What would be better in this situation (substitution or elmination)? 3w+d=14, 3w-2d=9

Back

percent

Front

a ratio that compares a number to 100

Back

Consistent Independent

Front

One solution, intersect at one point

Back

y-y1=m(x-x1)

Front

point slope form

Back

multiplicative inverse axiom

Front

a(1/a)=1

Back

cross products

Front

in the statement a÷b = c÷d bc and is this.

Back

reflexive axiom of equality

Front

a=a, x=1

Back

y-y/x-x

Front

slope formula

Back

y=3x+2

Front

linear equation, represents linear function

Back

solution set

Front

the set of all solutions of a particular problem

Back

definition of division

Front

a/b=a(1/b)

Back

definition of subtraction

Front

a-b=a+-b

Back

equation

Front

a mathematical statement that 2 expressions are equal

Back

Section 15

(50 cards)

best-fitting line

Front

line that lies closest to all the data point

Back

Slope

Front

The ratio of the vertical change to a corresponding horizontal change

Back

scale factor

Front

the multiplier used on each dimension to change one figure into a similar figure

Back

correlation coefficient

Front

denoted by r

Back

Slope-intercept form

Front

y=mx+b

Back

Linear Function

Front

A function whose graph is a line

Back

Point-Slope form

Front

y-y1=m(x-x1)

Back

constant of variation

Front

non-zero constant a

Back

Parent Function

Front

The simplest function in a group of functions with common characteristics

Back

Scatter Plot

Front

A graph that relates two different sets of data by plotting the data as ordered pairs

Back

Linear Inequality

Front

An inequality in two variables whose graph is a region of the coordinate plane that is bounded by a line

Back

y-intercept

Front

y-coordinate where the graph intersects the y-axis

Back

function notation

Front

f(x)=mx+b

Back

Vertical-line test

Front

Used to determine whether the relation has at least one element of the domain paired with more than one element of the range

Back

Slope

Front

A measure of the steepness of a line.

Back

rate of change

Front

how much one quantity changes in relation to how much another quantity changes

Back

Function

Front

A relation in which each element of the domain is paired with exactly one element in the range

Back

parallel

Front

two lines on a plane that do not intersect

Back

direct variation

Front

y=ax

Back

Vertex

Front

The point where a function reaches a maximum or a minimum

Back

x-intercept

Front

x coordinate of a point where a graph crosses the x axis/ y coordinate of this point is zero

Back

Mapping Diagram

Front

Links the elements of the domain with corresponding elements of the range

Back

standard form

Front

Ax + By=C, where A, B, and C are not decimals or fractions, where A and B are not both zero, and where A is not a negative

Back

Translation

Front

An operation that shifts a graph horizontally, vertically, or both

Back

y intercept

Front

The y coordinate of the points where a graph intersects the y-axis.

Back

Trend Line

Front

A line that approximates the relationship between the data sets of a scatter plot

Back

Constant of Variation

Front

The value of K in direct variation

Back

parent function

Front

most basic family function

Back

Linear Function

Front

A function that can be written in the form of y=mx+b, where x is the independant vairable and m and b are real numbers. It's graph is a line

Back

Absolute Value Function

Front

A function of the form f(x)=|mx+b|+c

Back

Indirect Measurement

Front

A method of measurement that uses formulas, similar figures, and/or proportions

Back

Correlation

Front

A measure of the strength and direction of the relationship between two variables or data sets

Back

Relation

Front

A set of pairs of input and output values

Back

slope-intercept form

Front

y=, an equation written in the form y=mx+b is in slope-intercept form. The graph is a line with slope m and y-intercept b.

Back

point-slope form

Front

y-y1 = m(x-x1), where m is the slope and (x1,y1) is the point the line is passing through.

Back

negative correlation

Front

y decreases as x increases

Back

slope

Front

ratio of rise over run

Back

scatter plot

Front

graph of a set of data pairs

Back

Absolute Value Function

Front

A function whose rule contains absolute value expressions

Back

Direct variation

Front

A linear function defined by an equation of the form y=kx (k is not 0)

Back

Range

Front

All outputs, or y-coordinates, of the ordered pairs

Back

Line of best fit

Front

The line that comes closest to all of the points in a data set

Back

positive correlation

Front

y increases as x decreases

Back

Domain

Front

All inputs, or x-coordinates, of the ordered pairs

Back

Identity

Front

An equation that is true for all values of the variables

Back

perpendicular

Front

two lines intersect to form a ninety degree angle

Back

Rate

Front

A ratio that compares two quantities meausured in different units

Back

Proportion

Front

A statement that two ratios are equal; a/b =c/d

Back

Standard form

Front

Ax+By=C

Back

Dependent Variable

Front

The y-variable

Back

Section 16

(54 cards)

flip the sign

Front

what do you do when you multiply/divide by a negative (inequalities)

Back

Equivalent Equations

Front

equations that have the same solutions

Back

Scale Model

Front

a 3-dimensional model that is similar to a 3-dimensional object

Back

equivalent inequalities

Front

inequalities with the same solution set

Back

conjunction

Front

- 3 ≤ x and x ≤ 4

Back

Unit Analysis

Front

including units for each quantity in a calculation to determine the unit of the answer

Back

Identity

Front

an equation that is true for every value

Back

Multiplication Property of Equality

Front

multiplying each side of an equation by the same number produces equations

Back

and

Front

key word of conjunctions

Back

Addition Property of Equality

Front

to add the same number to each side of an equation

Back

Isolate

Front

using properties of equality and inverse operations to get a variable to a coefficient 1; alone on one side of the equation

Back

Solution of an inequality

Front

a number that produces a true statement when it is substituted for the variable in an inequality

Back

Inverse Opertaions

Front

operations that undo one another

Back

Proportion

Front

an equation that states two ratios are equal

Back

closed circle

Front

(graphing) greater than or equal to/less than or equal to

Back

or

Front

key word of disjunctions

Back

Literal Equation

Front

an equation involving two or more variables

Back

open circle

Front

(graphing) greater than/less than

Back

Values

Front

numbers that one substitutes for the variable

Back

Steps to solving an equation

Front

Get rid of parentheses. Get rid of fractions. Combine like terms. Variables on one side. Everything else on the other. Multiply or divide.

Back

Division Property of Equality

Front

to divide each side of the equation by the same number that produces an equivalent equation

Back

Rate

Front

a ratio of a and b where a and b represent quantities measured in different units

Back

Percent Change

Front

the ratio of the amount of change to the original amount expressed as a percent

Back

Conversion Factor

Front

a ratio of two equivalent measures in different units

Back

disjunction

Front

a sentence formed by joining two sentences with the word OR

Back

compound inequality

Front

conjunction or disjunction

Back

axiom

Front

a statement that is assumed to be true; also called postulate

Back

Similar Figures

Front

two figures that have the same shape but not the same size

Back

hypothesis

Front

a statement that is given or assumed to be true

Back

conjunction

Front

a sentence formed by joining two sentences with the word AND

Back

Cross Product Property

Front

the cross products of a proportion are equal

Back

Scale Drawing

Front

an enlarged or reduced drawing similar to an actual object or place

Back

Subtraction Property of Equality

Front

to subtract the same number from each side of an equation that produces an equivalent equation

Back

y-intercept

Front

The point at which the line crosses the y-axis

Back

Function

Front

Function a rule that establishes a relationship between two quantities called the input and output such that every input has exactly one output.

Back

inequality

Front

x + 4 ≤ 7

Back

Unit Rate

Front

a rate with a denominator of 1

Back

Formula

Front

an equation that states a relationship among quantities

Back

conclusion

Front

a statement that follows logically from the assumptions

Back

Scale

Front

the ratio of any length in a scale drawing to the corresponding actual length

Back

Ratio

Front

the comparison of two quantities by division

Back

Percent Decrease

Front

percent change found when the original amount decreases

Back

Independent Variable

Front

the x-variable

Back

Linear equations

Front

Represents a linear function

Back

disjunction

Front

x ≤ -2 or x ≥ 3

Back

Solution of an equation

Front

A number that when substituted for the variable in an equation, makes the equation a true statement

Back

Cross Products

Front

in a proportion a/b=c/d the products are ad=bc

Back

Percent Error

Front

the ratio of the absolute value of the difference of a measured (or estimated) value and an actual value compared to the actual value expressed as a percent

Back

x-intercept

Front

the point at which a line crosses the x-axis

Back

Relative error

Front

the ratio of the absolute value of the difference of a measured (or estimated) value and an actual value compared to the actual value

Back

Section 17

(53 cards)

Slope-intercept form

Front

y=mx+b y=y-coordinate m=slope x=x-coordinate b=y-intercept

Back

transitive property

Front

if a<b and b<c, then a<c

Back

Greatest Integer Function

Front

A step function written as f(x)=[[x]] where f(x) is the greatest integer less than or equal to x

Back

reflects in the y axis

Front

Which reflection occurs in the equation f(x) = (-x)?

Back

line plot

Front

a # line labeled with a scale that includes all the data and xs above each data point for each time it occurs

Back

graph shifts up 2 units

Front

Describe the translation in lxl +2

Back

comparison property

Front

exactly one of the following statements is true: a>b , a=b , a<b

Back

Point slope form

Front

y-y₁=m(x-x₁)

Back

reflects in the x-axis

Front

Which reflection occurs in the equation f(x) = -1(x)?

Back

vertical shrink

Front

Which transformation occurs in the graph of f(x) = 2lxl?

Back

measures of central tendency

Front

#s that represent the middle value in a set of data. ex: mean, medium and mode

Back

Piecewise Function

Front

A function that is written using two or more expressions

Back

Constant Function

Front

A linear function in the form of f(x)=b

Back

at most/ no more than

Front

< ≤

Back

absolute value function

Front

Which parent function is f(x) = lxl?

Back

proof

Front

a logical reasoning from hypothesis to conclusion

Back

a "v"

Front

What shape does an absolute value function make when graphed?

Back

greater than

Front

absolute value is an OR

Back

Line of Fit

Front

A line that closely approximates a set of data

Back

less than

Front

absolute value is an AND

Back

stem and leaf plot

Front

a system where you separate data into 2 numbers that are used to form a stem and leaf

Back

horizontal shrink

Front

Which transformation occurs in the graph of f(x) = l2xl?

Back

multiplication property

Front

1. if a<b and c is positive, then ac<bc 2. if a<b and c is negative, then ac>bc.

Back

between/ between inclusive

Front

< x < / ≤ x ≤

Back

frequency

Front

how often a piece of data occurs

Back

limit

Front

the number that the output gets closer to the specific x coordinate

Back

theorem

Front

a statement that can be proved

Back

converse

Front

the statement that results from interchanging the hypothesis and the conclusion of an if-then statement

Back

identity function

Front

Which parent function is f(x) = x, passing through all coordinates (a,a), and is the parent function for most linear equations?

Back

Prediction Equation

Front

An equation suggested by the points of a scatter plot that is used to predict other points

Back

addition property

Front

if a<b, then a+c< b+c

Back

probability

Front

the probability of a simple event is a ratio of the # of favorable outcomes for the event to the total # of possible outcomes to the event

Back

compound inequality

Front

two inequalities joined by an AND & OR

Back

graph shifts to the left 2 units

Front

Describe the translation in lx +2l

Back

quadratic function

Front

Which parent function is f(x) = x²?

Back

a parabola (u shape)

Front

What shape does a quadratic function make when graphed?

Back

Scatter Plot

Front

A set of data graphed as ordered pairs in a coordinate plane

Back

at least/ no less than

Front

> ≥

Back

vertical stretch

Front

which transformation occurs in the graph of f(x) = -3lxl?

Back

simple event

Front

a single event

Back

counter example

Front

a single numerical example that makes a statement false

Back

horizontal stretch

Front

Which tranformation occurs in the graph of f(x) = l-3xl?

Back

shrink

Front

What happens when the parent function is multiplied by a value greater than one?

Back

absolute value

Front

on a number line, ⌉a⌉ is the distance between the graph of th number and zero

Back

stretch

Front

What happens when a parent function is multiplied by a value less than one?

Back

Identity Function

Front

The function f(x)=x

Back

constant function

Front

Which parent function is f(x) = a?

Back

sample space

Front

the list of all possible outcomes

Back

Absolute Value function

Front

A function written as f(x)=lxl, where f(x)≥0 for all values of x

Back

corollary

Front

a theorem that c an be proved easily from another theorem

Back

Section 18

(53 cards)

Relation

Front

A set of ordered pairs

Back

One-to-One Function

Front

Each number is only paired once in the domain and range

Back

slope intercept form

Front

y=mx+b

Back

Factorial

Front

Factors in the coefficients of binomial expansions involve these special products.

Back

Linear Equation

Front

Only has addtion, subtraction, and multiplication of a variable by a constant

Back

Partial Sum

Front

Sn

Back

Function

Front

A special type of relation in which each element of the domain is paired with exactly one element from the range

Back

Standard Form

Front

Ax+By=C Integers, always reduce, and A cannot be negative

Back

Funtional Notation

Front

An equation of y in terms of x can be rewritten so that y=f(x)

Back

graphing

Front

the process of locating a point in the coordinate plane

Back

Geometric Means

Front

Missing terms between two nonsuccessive terms of a geometric sequence.

Back

Quadrants

Front

The four areas of the coordinate plane

Back

Vertical Line Test

Front

Determines if the graphed relation is a function

Back

Dependent Variable

Front

The variable, usually y, whose values make up the range

Back

Rate of Change

Front

What slope is often referred as. Measures how much a quantity changes, on average, relative to the change in another quantity, often time

Back

Perpendicular Lines

Front

Their slope is opposite reciprical

Back

Common Ratio

Front

R

Back

graph of the equation

Front

the line is called the ______________ in a graph

Back

linear equation in two variables

Front

is an equation that can be written in the form ax+by=c

Back

regression

Front

the process of using one variable to predict another

Back

Geometric Series

Front

indicated sum of the terms of a geometric sequence.

Back

Slope

Front

The ratio of the change in y-coordinates to the corresponding change in x-coordinates

Back

table of solutions

Front

constructed by choosing several values of x and finding the corresponding values of y

Back

slope triangle

Front

rise over run creates a ____________

Back

Fibonacci Sequence

Front

1,1,2,3,5,8,13

Back

Mapping

Front

Shows how each member of the domain is paired with each member of the range

Back

Mathematical induction

Front

A method of proof used to prove statements about positive integers.

Back

Parallel Lines

Front

Their slope is the same

Back

mapping diagram

Front

used to show how a function assigns to each member of the domain exactly one member of the range

Back

average rate of change

Front

to find this, we find the ratio of the change in the x and y

Back

straight line appreciation

Front

used when property or collectibles increase in value

Back

Independent Variable

Front

The variable, usually x, whose values make up the domain

Back

x-intercept

Front

The x-coordinate of the point at which a graph crosses the x-axis

Back

Recursive Formula

Front

Each term is formulated from one or more previous terms.

Back

y-intercept

Front

The y-coordinate of the point at which a graph crosses the y-axis

Back

Coordinate Plane

Front

Composed of the x-axis (horizontal) and the y-axis (vertical) which meet at the origin (0,0) and divide the plabe into four quadrants

Back

Pascal's Triangle

Front

a triangular array of numbers

Back

point-slop form

Front

y-y1=m(x-x1)

Back

Iteration

Front

process of composing a function with itself repeatedly.

Back

Infinite Geometric Series

Front

geometric series with an infinite amount of terms.

Back

Inductive Hypothesis

Front

The assumption that a statement is true for some positive integer, k

Back

subscript notation

Front

to distinguish between the coordinates of two general points on a line segment

Back

Index of Summation

Front

n in a sigma notation problem

Back

subscript notation

Front

to distinguish between the coordinates of the points we use ___________

Back

Domain

Front

The set of all first coordinates from the ordered pairs

Back

straight line depreciation

Front

used when aging equipment declines in value

Back

Geometric Sequence

Front

sequence in which each term after the first is found by multiplying the previous term by the constant r.

Back

Range

Front

The set of all second coordinates from the ordered pairs

Back

Linear Function

Front

A fuction whose ordered pairs satisfy a linear equation

Back

function

Front

a rule that assigns to each value one variable

Back

Section 19

(50 cards)

Parabola

Front

Graph of a Quadratic Function

Back

Addition method

Front

multipy to cancel out, add equations, cancel out variable, solve for a variable, substitute back into other equation, solve

Back

complex fraction

Front

rational expression whose numerator and or denominator contains a rational expression.

Back

Arithmetic Series

Front

indicated sum of the terms of an arithmetic sequence

Back

Term

Front

each number in a sequence

Back

substitution method

Front

solve on equation, substitute first variable, substitute that variable into the next equation, solve

Back

Sequence

Front

a list of numbers in a particular order.

Back

Vertex Form

Front

Quadratic Equation written as y=a(x-h)+k

Back

Intercept Form

Front

Quadratic equation written as y=a(x-q)(x-p)

Back

Binomial

Front

A polynomial with two terms that can be added or subtracted.

Back

Standard Form

Front

Quadratic equation written as y=ax²+bx+c

Back

Axis of Symmetry

Front

Line that goes through the parabola that splits it into two mirror images.

Back

asymptote

Front

line that the graph of the function approaches but never crosses.

Back

direct variation

Front

y=kx

Back

positive number

Front

a number greater than zero

Back

dashed line

Front

< or >

Back

Maximum Value

Front

The highest point on the parabola. Parabola opens down if the leading constant is negative.

Back

rational equation

Front

any equation the contains one or more rational equations.

Back

point discontinuity

Front

hole in a graph

Back

rational inequality

Front

inequalities containing one or more rational expressions.

Back

Quadratic Function

Front

An equation where the maximum exponent is 2.

Back

transformation

Front

an operation that maps an original geometric figure onto a new figure called an image

Back

z axis

Front

a vertical line through the origin of the graph

Back

octants

Front

the three axis determine three coordanate planes that divide space into octants

Back

Common difference

Front

D

Back

solution

Front

an ordered pair that satisfies a system of equations

Back

reflection

Front

when you flip a figure over a line

Back

Monomial

Front

A polynomial with one term that can be multiplied.

Back

Series

Front

indicated sum of the terms of a sequence

Back

translation

Front

when you slide a figure from one position to another without turning it

Back

3D coordinate system

Front

a graph with three systems

Back

Minimum Value

Front

The lowest point on the parabola. Parabola opens up if the leading constant is positive.

Back

opposites

Front

two numbers with the same absolute value but different signs (-4 and 4)

Back

graph of a system

Front

the graph of all solutios of the system

Back

quadrant

Front

the x-axis and the y-axis seperate the coordinate plane into four regions. (I , II, III, IV)

Back

inverse variation

Front

As one quanity increases, the other one decreases. xy=k

Back

constant of variation

Front

The constant K is used with direct or inverse variation.

Back

Quadratic Equation

Front

Same as a Quadratic Formula. An equation where the maximum exponent is 2.

Back

a linear equation with thee variables

Front

ax + by + cz = d

Back

Trinomial

Front

A polynomial with three terms that can be added or subtracted.

Back

continuity

Front

a graph of a function that can be traced with a pencil that never leaves the paper.

Back

joint variation

Front

occurs when one quanity varies directly as the product of two or more other quanities. y=kxz

Back

Arithmetic Means

Front

terms between any two nonsuccessive terms of an arithmetic sequence

Back

ordered triple

Front

(x,y,z)

Back

Arithmetic Sequence

Front

sequence in which each term after the first is rounded by adding a constant.

Back

rational function

Front

f(x)=x/x+3

Back

rational expression

Front

a ratio of two polynomial expressions.

Back

solid line

Front

≤ or ≥

Back

negative number

Front

a number less than zero

Back

Vertex

Front

The point where the parabola turns, or crosses the axis of symmetry. Minimum or maximum.

Back

Section 20

(50 cards)

focus (horizontal parabola)

Front

(h + (1/4a), k)

Back

cot

Front

cosθ/sinθ

Back

tan

Front

1/cotθ

Back

horizontal hyperbola

Front

(x-h)²/a² - (y-k)²/b² = 1

Back

axis of symmetry (horizontal parabola)

Front

y = k

Back

vertical parabola

Front

y = a(x-h)² + k

Back

Geometric Sum

Front

Sn = (a₁-a₁rⁿ) / (1-r)

Back

vertical hyperbola

Front

(y-k)²/a² - (x-h)² /b²= 1

Back

Arithmetic Series

Front

an = a₁ + (n-1)d

Back

1

Front

sin²θ + cos²θ =

Back

hyperbola asymptotes (horizontal axis)

Front

y = ± (b/a)x

Back

ellipse with horizontal major axis

Front

((x-h)²/a²) + ((y-k)²/b²) = 1

Back

horizontal hyperbola with origin as center

Front

x²/a² - y²/b² = 1

Back

sec

Front

1/cosθ

Back

coordinate

Front

the number that corresponds to the point on a number line

Back

horizontal parabola

Front

x = a(y-k)² + h

Back

focus (vertical parabola)

Front

(h, k + (1/4a))

Back

horizontal ellipse (with origin as center)

Front

(x²/a²) + (y²/b²) = 1

Back

csc

Front

1/sinθ

Back

length of latus rectum

Front

|(1/a)|

Back

additive inverse

Front

an integer and its opposite

Back

tan

Front

sinθ/cosθ

Back

vertical ellipse (with origin as center)

Front

(x²/b²) + (y²/a²) = 1

Back

distance formula

Front

d = √((x₂-x₁)² + (y₂-y₁)²)

Back

Geometric Sum

Front

Sn = a₁(1-rⁿ) / 1-r

Back

Geometric Series

Front

an = a₁rⁿ⁻¹

Back

Law of Sines

Front

(Sin A)/a = (Sin B)/b = (Sin C)/ c

Back

integer

Front

any number from the set {..., -3, -2, -1, 0, 1, 2, 3, ...}

Back

cos

Front

1/secθ

Back

Arithmetic Sum

Front

Sn = (n/2)(a₁ + an)

Back

ellipse with vertical major axis

Front

((x-h)²/b²) + ((y-k)²/a²) = 1

Back

directrix (horizontal parabola)

Front

x = h- (1/4a)

Back

Law of Cosines

Front

c²=a²+b²-2ab(cosC)

Back

Definition of Sine

Front

sinθ = y

Back

absolute value

Front

the distance the number is from zero on a number line. (-6 and 6 have the same absolute value)

Back

inequality

Front

compares numbers or quantities (any mathematical sentence containing < or >)

Back

vertex of a parabola

Front

(h,k)

Back

cot

Front

1/tanθ

Back

hyperbola asymptotes (vertical axis)

Front

y = ± (a/b)x

Back

circle

Front

(x-h)² + (y-k)² = r²

Back

sin

Front

1/cscθ

Back

equation of a conic section

Front

Ax² + Bxy + Cy² + Dx + Ey + F = 0 (A,B, & C cannot all be zero)

Back

vertical hyperbola with origin as center

Front

y²/a² - x²/b² = 1

Back

Definition of Cosine

Front

cosθ = x

Back

Infinite Series Sum

Front

S = a₁ / (1-r)

Back

axis of symmetry (vertical parabola)

Front

x = h

Back

Geometric Series

Front

an = a(n-1) - 1^r

Back

mean

Front

find the sum of the numbers and then divide by the number of items in a set

Back

directrix (vertical parabola)

Front

y = k- (1/4a)

Back

midpoint of a line coordinates

Front

(x₁+x₂)/2, (y₁+y₂)/2

Back

Section 21

(50 cards)

Inconsistent

Front

a system of equations that has no solutions

Back

sin(x-y)

Front

sinx cosy-cosx siny

Back

sin (x/2)

Front

±√(1-cosx)/2

Back

Area of a Triangle

Front

1/2 ab sinC

Back

10

Front

³√1,000

Back

Intercept form

Front

x/a + y/b=1

Back

Line of fit

Front

a line that closely approximates a set of data

Back

identity matrix

Front

[1/0 0/1]

Back

inverse matrix

Front

the products of 2 matrices is the identity matrix

Back

equal

Front

2 matrices that are exactly the same

Back

Dependent

Front

a system of equations that has infinite solutions

Back

Regression line

Front

a line of best fit

Back

4

Front

Back

parallel lines

Front

a system with no solution

Back

cos2x

Front

cos²x-sin²x

Back

sin2x

Front

2(sinx)(cosx) =

Back

cos2x

Front

2cos²x-1

Back

System of inequalities

Front

a set of inequalities with the same variables

Back

1

Front

√1

Back

8

Front

³√512

Back

single lines

Front

a system with infinite solutions

Back

scalar

Front

number used to multiply

Back

dimension

Front

the size of the matrix

Back

cos(x+y)

Front

cosx cosy-sinxsiny

Back

cos (x/2)

Front

±√(1+cosx)/2

Back

sin(x+y)

Front

sinx cosy+cosx siny

Back

343

Front

Back

System of equations

Front

two or more equations with the same variables

Back

sec²θ

Front

1 + tan²θ =

Back

Prediction equation

Front

an equation suggested by the points of a scatter plot that is used to predict other points

Back

Substitution method

Front

a method of solving a system of equations in which one equation is solved for one variable in terms of the other

Back

Scatter plot

Front

a set of data graphed as ordered pairs in a coordinate plane

Back

Linear correlation coefficient

Front

the number r

Back

Median-fit line

Front

a particular type of line of fit

Back

Line of best fit

Front

a line that best fits a set of data

Back

cos2x

Front

1-2sin²x

Back

Consistent

Front

a system of equations that has a least one solution

Back

matrix

Front

a rectangular arrangement of numbers

Back

8

Front

√64

Back

determinant

Front

a real number associated with a square matrix

Back

7

Front

√49

Back

0

Front

Back

Boundary

Front

line or curve that separates the coordinate plane into two regions

Back

csc²θ

Front

1 + cot²θ =

Back

system of equations

Front

a collection of linear equations invoking the same set of variables

Back

5

Front

√25

Back

1

Front

Back

cos(x-y)

Front

cosx cosy+sinx siny

Back

Independent

Front

a system of equations that has exactly one solution

Back

Elimination method

Front

eliminate on of the variables in a system of equations by adding or subtracting the equations

Back

Section 22

(50 cards)

Slope

Front

the ratio of the change in y-coordinates to the corresponding change in x-coordinates

Back

Translation matrix

Front

a matrix that represents a translated figure

Back

Quadrants

Front

the four areas of a Cartesian coordinate plane

Back

Solution

Front

each replacement that results in a true sentence

Back

Example set-builder notation

Front

{x I x>9}

Back

Augmented matrix

Front

a coefficient matrix with an extra column containing the constant terms

Back

Arithmetic mean

Front

the terms between any two nonconsecutive terms of an arithmetic sequence

Back

Relation

Front

a set of ordered pairs

Back

Ordered Pairs

Front

representation of data

Back

Functional notation

Front

an equation of y in terms of x can be rewritten so that y=f(x)

Back

x-intercept

Front

the x-coordinate of the point at which a graph crosses the x-axis

Back

Arccosine

Front

the inverse of y = cos x, written as x = arccos y

Back

Determinant

Front

a square array of numbers or variables enclosed between two parallel lines

Back

Example interval notation

Front

(-infinity, 2) or [-2, +infinity)

Back

Axis of symmetry

Front

a line about which a figure is symmetric

Back

Multiplication Property of Inequality 2

Front

For any real numbers a, b, and c, where c is negative: If a>b, then ac<bc. If a<b, then ac>bc

Back

Third-order determinant

Front

determinants of a (3)(3) matrix

Back

Zero matrix

Front

a matrix in which every element is zero

Back

Equation

Front

a mathematical sentence stating that two mathematical expressions are equal

Back

Mapping

Front

shows how each member of the domain is paired with each member of the range

Back

Division Property of Inequality 2

Front

For any real numbers a, b, c, where c is negative: If a>b, then a/c<b/c. If a<b, then a/c>b/c.

Back

Asymptote

Front

a line that a graph approaches but never crosses

Back

Intersection

Front

the graph of a compound inequality containing "and"

Back

Vertices

Front

the maximum of minimum value that a linear function has for the points in a feasible region

Back

Union

Front

the graph of a compound inequality containing "or"

Back

Arctangent

Front

the inverse of y = tan x, written as x = arctan y

Back

Angle of elevation

Front

the angle between a horizontal line and the line of sight from the observer to an object at a higher level

Back

Cartesian coordinate plane

Front

a plane divided into four quadrants by the intersection of the x-axis and the y-axis at the origin

Back

Family of graphs

Front

group of graphs that displays one or more similar characteristics

Back

Division Property of Inequality

Front

For any real numbers, a, b, c, where c is positive: If a>b, then a/c>b/c. If a<b, then a/c<b/c

Back

Transitive Property of Equality

Front

For all real numbers a, b, and c, if a=b and b=c, then a=c

Back

Arithmetic sequence

Front

a sequence in which each term after the first is found by adding a constant, the common difference d, to the previous term

Back

Addition Property of Inequality

Front

For any real numbers a, b, c: If a>b, then a+c>b+c. If a<b, then a+c<b+c

Back

Multiplication Property of Inequality

Front

For any real numbers a, b, and c, where c is positive: If a>b, then ac>bc. If a<b, then ac<bc

Back

Translation

Front

a figure is moved from one location to another on the coordinate plane without changing its size, shape, or orientation

Back

Parent graph

Front

simplest of the graphs in a family

Back

y-intercept

Front

the y-coordinate of the point at which a graph crosses the y-axis

Back

Vertical line test

Front

if no vertical line intersects a graph in more than one point, then the graph represents a function

Back

Reflexive Property of Equality

Front

For any real number a, a=a

Back

Transformation

Front

functions that map points of a pre-image onto its image

Back

Dependent variable

Front

the other variable in a function, usually y, whose values depend on x

Back

Properties of Equalities

Front

Reflexive, Symmetric, Transitive, Substitution

Back

Angle of depression

Front

the angle between a horizontal line and the line of sight from the observer to an object at a lower level

Back

Arithmetic series

Front

the indicated sum of the terms of an arithmetic sequence

Back

Arcsine

Front

the inverse of y = sin x, written as x = arcsin y

Back

Symmetric Property of Equality

Front

For all real numbers a and b, if a=b then b=a

Back

Substitution Property of Equality

Front

If a=b, then a may be replaced by b and b may be replaced by a

Back

Independent variable

Front

in a function, the variable, usually x, whose values make up the domain

Back

One-to-one function

Front

a function where each element of the range is paired with exactly one element of the domain

Back

Subtraction Property of Inequality

Front

For any real numbers a, b, c: If a>b, then a-c>b-c. If a<b, then a-c<b-c.

Back

Section 23

(50 cards)

Feasible Region

Front

intersection of the inequalities (shaded region)

Back

Types of Word Problems

Front

Integer Problems, Angle Problems, Geometry Problems, Motion Problems

Back

function

Front

all x's must be different, x's are used one time only,use vertical line test on the graph

Back

relation

Front

set of ordered pairs

Back

Linear Equation

Front

an equation that contains no operations other than addition, subtraction, and multiplication of a variable by a constant

Back

Rational Numbers

Front

numbers that can be written as a fraction, m/n, where m and n are integers and n does not equal 0; if written as a decimal, it will either terminate or it will repeat

Back

Associative Property of Multiplication

Front

(ab)c=a(bc)

Back

A relation can be represented by

Front

an equation, a list of ordered pairs, a mapping or a graph

Back

(a^2)( a^6)

Front

a^8

Back

Trichotomy Property

Front

for any two real numbers, a and b, exactly one of the following is true: a<b, a>b, or a=b

Back

Irrational Numbers

Front

a real number that is not rational; if written as a decimal, it does not terminate nor repeat

Back

Slope Intercept Form

Front

y=mx+b

Back

Inverse Property of Addition

Front

a+(-a)=0=(-a)+a

Back

Counterexample

Front

specific case that shows that a statement is false

Back

Standard Form

Front

Ax+By=C

Back

Formula

Front

mathematical sentence that expresses the relationship between certain quantities

Back

Commutative Property of Multiplication

Front

(a)(b)=(b)(a)

Back

Identity Property of Multiplication

Front

(a)(1)=a=(1)(a)

Back

Constraints

Front

integers

Back

Commutative Property of Addition

Front

a+b=b+a

Back

Trace

Front

The line in which a plane intersects a coordinate plane

Back

Supplement

Front

180-x

Back

Linear Programming

Front

the process of finding the maximum or minimum value of a function for a region defined by inequalities

Back

Open Sentence

Front

a mathematical sentence containing one or more variables

Back

Grouping Symbols

Front

parenthesis, brackets, braces

Back

Function

Front

special type of relation in which each element of the domain is paired with exactly one element of the range

Back

Relation

Front

set of ordered pairs

Back

Distributive Property

Front

a(b+c)=ab+ac and (b+c)a=ba+ca

Back

Point Slope Form

Front

y-y1 =m(x-x1 )

Back

Compound Inequalities

Front

two inequalities joined by the word "and" or the word "or"

Back

range

Front

y-coordinates, output

Back

Order of Operations

Front

1. grouping symbols; 2. exponents; 3. multiplication and division; 4. addition and subtraction

Back

Algebraic Expression

Front

an expression that contains at least one variable

Back

Absolute Value

Front

the distance an object is from zero on the number line

Back

Absolute Value Inequalities

Front

Get the absolute value by itself on the left side. Then check to see if it is a "greater" or "less than" statement

Back

Five Special Functions

Front

Identity Function, Absolute Value Function, Greatest Integer Function, Piecewise Function

Back

Unbounded Feasible Region

Front

when the feasible region is not closed

Back

Domain

Front

set of all first coordinates from the ordered pairs

Back

Real Numbers

Front

All of the numbers that you use in everyday life

Back

Identity Property of Addition

Front

a+0=a=0+a

Back

Variable

Front

symbol, usually letters, used to represent unknown quantities

Back

Closure Property

Front

The product of any two whole numbers is always a whole number. So, the set of whole numbers is said to be closed under multiplication

Back

Range

Front

set of all second coordinates from the ordered pairs

Back

Scatter Plot

Front

Data graphed in ordered pairs

Back

domain

Front

x-coordinates, input

Back

Associative Property of Addition

Front

(a+b)+c=a+(b+c)

Back

Bounded Feasible Region

Front

when the feasible region is a polygon

Back

Inverse Property of Multiplication

Front

If a does not equal 0, then (a)(1/a)=1=(1/a)(a)

Back

Complement

Front

90-x

Back

To solve compound inequalities

Front

If it is an "and" statement, graph the intersection. If it is an "or" statement, graph the union

Back

Section 24

(50 cards)

What does the rational exponent mean?

Front

power/root = "power over root"

Back

Area of a triangle given coordinates for the three vertices?

Front

Enter three vertices, (x, y) in a 3 X 3 matrix, in rows 1, 2, and 3, with 1's in the last column. Take plus or minus 1/2 of the determinant.

Back

joint variation

Front

y=kxz, y varies jointly with x and z

Back

Column Matrix

Front

Consists of one column

Back

Standard Form for a Line

Front

Ax + By = C

Back

Intercept Form for a Quadratic

Front

y = a(x - p)(x - q)

Back

What do you know about slopes of perpendicular lines?

Front

Perpendicular lines have slopes that are opposite reciprocals of each other!

Back

How do you factor a sum or difference of cubes?

Front

first one, second one, first one squared, product of the two and the last one squared, first sign's the same, second one's not, last one's always plus and here's what you've got!

Back

log base a of x + log base a of y =

Front

log base a of (x times y) This is the product property of logarithms.

Back

What must be true to multiply two matrices?

Front

The columns of the first must match the rows of the second matrix.

Back

Write log base a of b = c in exponential form .

Front

a ^ c = b

Back

Completing the Square

Front

Remember to have a coefficient of 1 for the squared term. Take 1/2 of b and square it. Add to both sides. Solve through square roots.

Back

What must be true to add two matrices?

Front

The dimensions must be the same. (Rows and Columns)

Back

Compound Interest Formula

Front

A = P(1 + r/n)^(n x t), r is the rate, n is the number of times compounded, t is time

Back

What ways can you solve a system?

Front

1. graph, 2. substitution, 3. linear combination or elimination, 4. use a matrix equation, if the system is linear

Back

a^12

Front

(a^2)^6

Back

What type of matrix must you have to take a determinant?

Front

A square matrix

Back

Methods to Solve a Quadratic

Front

1. Graphing, 2. Factoring, if factorable, 3. Completing the Square, 4. Quadratic Formula

Back

Quadratic Formula

Front

x = (-b plus or minus) the square root of b^2 -4ac) / 2a from y = ax^2 + bx + c

Back

Range for a Logarithmic Function?

Front

All real numbers

Back

What does the value of the discriminant tell about a quadratic?

Front

If the discriminant = 0, there is one real solution & graph "sits or bumps" x-axis. If the discriminant > than 0, there are two real solutions & graph crosses x-axis twice. If the discriminant < 0, there are no real solutions, two imaginary solutions & graph does not cross x-axis.

Back

Standard Form for a Quadratic

Front

f(x) = ax^2 + bx + c

Back

Domain for an Exponential Function?

Front

All real numbers

Back

Standard Form Equation for a Circle with center (h, k)

Front

(x - h)^2 + (y - k)^2 = r^2, circle with center at (h, k) and radius of r

Back

Matrix

Front

Rectangular array of numbers in rows and columns

Back

Row Matrix

Front

Consists of one row

Back

x-intercepts for rational expressions

Front

set numerator equal to zero and factor, remember to divide out any common factors from denominator!

Back

Continuous Compounding

Front

A = Pe^(rt)

Back

What's i^2?

Front

-1

Back

Point-Slope Formula

Front

y - y(sub1) = m(x - x(sub 1))

Back

What do you know about slopes of parallel lines?

Front

Parallel lines have the same slope!

Back

x log base n of y =

Front

log base n of y ^ x This is the power property of logarithms.

Back

What is the discriminant?

Front

b^2 minus 4ac

Back

vertical asymptoptes for rational expressions

Front

set denominator equal to zero and factor; remember to divide out any common factors from numerator!

Back

horizontal asymptotes for rational expressions

Front

(BOSTON)-if degree of Bottom is bigger, y=0; if degrees are same for numerator and denominator, use coefficients a/c; if Top has a larger degree, NO horizontal asymptote

Back

How do you find the inverse of a function?

Front

1. "y = " form, 2. switch x and y, 3. solve for y

Back

Solving Absolute Value Inequalities

Front

GOLA; Greater than - OR, Less than - AND

Back

inverse variation

Front

y=k/x

Back

When solving a matrix equation, use...?

Front

"A inverse times B" meaning A^-1 times B

Back

What's the square root of -1?

Front

i

Back

Vertex Form for a Quadratic

Front

y = a(x - h)^2 + k

Back

Does every matrix have an inverse?

Front

No. If the determinant equals 0, there will not be an inverse.

Back

Slope Formula

Front

m = (y (sub 2) - y (sub 1))/(x (sub 2) - x(sub 1)), difference of the y's over the difference of the x's

Back

direct variation

Front

y=kx

Back

What is the slope for a horizontal line?

Front

0

Back

log base a of x - log base a of y =

Front

log base a of (x divided by y) This is the quotient property of logarithms.

Back

Standard Form Equation for a Circle with center at the origin

Front

x^2 + y^2 = r^2

Back

How do you set up a matrix equation to solve a linear system of equations?

Front

There are three matrices in the equation. A coefficient matrix, where coefficients come from standard form equations, a variable matrix, and a constant matrix.

Back

How do you solve an absolute value equation?

Front

Set the expression from inside the absolute value equal to the positive constant and to the negative constant.

Back

Slope-Intercept Form for a Line

Front

y = mx + b

Back

Section 25

(50 cards)

Rate

Front

a ratio that involves two different units

Back

FOIL

Front

A method for multiplying binomials

Back

How to determine if its a function?

Front

Must pass the vertical line test. (Y only lands on 1 point)

Back

Sn=n(a1+an/2)

Front

Arithmatic Sum

Back

Slope intercept form

Front

y=mx+b

Back

Yes, and the answer will be negative. A negative number raised to an odd power equals a negative.

Front

Can you take a cube root of a negative number?

Back

Vertical line has what type of slope?

Front

Undefined slope

Back

Composition of Functions

Front

f ( g(x)) means that function g is the input to function f

Back

Absolute value function

Front

V shape Y = IxI (make y and x chart)

Back

Constant functions

Front

Consistent horizontal, slope = 0 (Horizontal line)

Back

Polynomial

Front

An algebraic expression with "many" terms

Back

Monomial

Front

A polynomial with one term

Back

Discrete function

Front

a relation in which the domain is a set of individual points that are not connected

Back

linear equation in one variable

Front

can be written in the form of ax=b

Back

Quadratic

Front

Second degree polynomials are called...

Back

Slope-intercept form

Front

y=mx+b

Back

f ( g(x)) = g (f(x)) = x

Front

How do you know that two functions are inverses of each other?

Back

Slope Formula

Front

y1-y2 / x1-x2

Back

Sn=a1(1-r^n/1-r)

Front

Geometric Sum

Back

Trinomial

Front

A polynomial with 3 unlike terms

Back

An=a1+(n-1)d

Front

Arithmatic series

Back

y = x

Front

What is the line of reflection for inverses?

Back

Continuous function

Front

When the domain of a relation has an infinite number of elements and the relation can be graphed with a line or smooth curve.

Back

Identity function

Front

Y= 1 x X + 0 Always: y=x (Diagonal line)

Back

equation

Front

mathematical statement that two expressions are equivalent

Back

Horizontal line has what type of slope?

Front

Zero slope

Back

Point slope form

Front

y-y1 = m(x-x1)

Back

Ratio

Front

a comparison of two numbers by division

Back

Linear

Front

First degree polynomials are called...

Back

What is a determinant?

Front

A real number associated with a square matrix.

Back

To solve for x and y intercept

Front

plug in zero

Back

y = a(x - h)^2 + k

Front

Absolute Value Equation with vertex (h, k)

Back

Binomial

Front

A polynomial with 2 unlike terms

Back

similar

Front

their corresponding angle are congruent and corresponding sides are proportional

Back

Inequality

Front

a statement that compares two expressions by using symbols <,>

Back

Parallel lines

Front

Same slope

Back

What's the horizontal line test?

Front

Used on an original function to determine if the inverse would be a function. Yes, you may still use the vertical line test on an inverse.

Back

Identity

Front

an equation that is true for all values of the variable

Back

What is a circle?

Front

The set of all points (x, y) that are equidistant from a fixed point called the center.

Back

Standard form

Front

Ax + By = C

Back

Cubic

Front

Third degree polynomials are called...

Back

Vertical line test

Front

Used to determine whether the reaction is a function

Back

proportion

Front

an equation stating that two ratios are equal

Back

Quadratic function

Front

Parabola, U shape, y = x2 (make y and x chart)

Back

An=a1R^n-1

Front

Geometric series

Back

S=a1/1-r

Front

Geometric infinite sum

Back

Quartic

Front

Fourth degree polynomials are called...

Back

Two, positive and negative roots

Front

How many roots does a square root have?

Back

Perpendicular lines

Front

Negative reciprocal

Back

solution set of an equation

Front

value or values of the variable that make an equation true

Back

Section 26

(50 cards)

Principal

Front

an amount of money borrowed or invested

Back

Similar

Front

two figures that have the same shape, but not necessarily the same size

Back

correlation coefficient

Front

measure of how well the data set is fit by a model

Back

discount

Front

an amount by which an original price is reduced

Back

boundary line

Front

divides the coordinate plane into two regions

Back

x-intercept

Front

the x-coordinate of a point where the line crosses the x-axis

Back

Percent Change

Front

an increase or decrease given as a percent of the original amount

Back

absolute value

Front

the distance from zero to x on a number line

Back

regression

Front

the statistical study of the relationship between two variables

Back

disjunction

Front

a compound statement that uses the word or

Back

Formula

Front

a literal equation that states a rule for a relationship among quantities

Back

Line of best fit

Front

a line used to make predictions that best fits the data

Back

Scale Factor

Front

a factor used to produce a similar object

Back

y-intercept

Front

the y-corrdinate of a point where the line crosses the y-axis

Back

Unit Rate

Front

a rate in which the second quantity in the comparison is one unit

Back

Indirect measurement

Front

uses known lengths, similar figures and proportions to measure objects that cannot be easily measured

Back

Tip

Front

an amount of money added to a bill for service

Back

Scale Model

Front

a three-dimensional model that uses a scale to represent an object as smaller or larger than the actual object

Back

Scale Drawing

Front

a drawing that uses a scale to represent an object as smaller or larger than the original object

Back

Indirect Masurement

Front

a method of measuring an object by that is difficult to measure

Back

Scale

Front

the ratio of any length in a drawing to the corresponding actual length

Back

Linear function

Front

functions with a constant rate of change: f(x)=mx+b

Back

Correlation

Front

the strength and direction of the linear relationship between two variables

Back

Constant Ratio

Front

A Ratio that a has constant value

Back

Corresponding Angles

Front

angles in the same relative position in two different polygons that have the same number of angles

Back

Ratio

Front

a comparison of two numbers by division

Back

Direct Variation

Front

The Relationship between two quantities x and y have a constant Ratio;One qantity varies directly with the other

Back

Equation

Front

A statement that is formed by placing an equal sign between the two expressions

Back

slope intercept form

Front

y=mx+b

Back

slope

Front

the constant rate of change for a linear function

Back

Percent Decrease

Front

a decrease given as a percent of the original amount

Back

Commission

Front

money paid to a person or company for making a sale

Back

Solution

Front

a value or values that make the equation or inequality true

Back

absolute value function

Front

a function whose rule contains an absolute value expression

Back

Equation

Front

a mathematical sentence that shows that two expressions are equivalent

Back

Interest

Front

the amount of money charged for borrowing money or the amount of money earned when saving or investing money

Back

Percent

Front

a ratio that compares a number to 100

Back

point-slope form

Front

y-y1=m(x-x1)

Back

Corresponding Sides

Front

sides in the same relative position in two different polygons that have the same number of sides

Back

Rate

Front

a ratio that compares two quantities measured in different units

Back

Proportion

Front

an equation that states that two ratios are equal

Back

Sales Tax

Front

a percent of the cost of an item that is charged by governments to raise money

Back

Percent Increase

Front

an increase given as a percent of the original amount

Back

Cross Products

Front

the product bc and the product ad in the statement a = b

Back

Literal Equation

Front

a decrease given as a percent of the original amount

Back

Linear inequality

Front

relates two variables using an inequality symbol y>2x-4

Back

conjunction

Front

a compound statement that uses the word and

Back

Identity

Front

an equation that is true for all values of the variables

Back

Markup

Front

the amount by which a wholesale cost is increased

Back

Conversion Factor

Front

the ratio of two equal quantities, each measured in different units

Back

Section 27

(51 cards)

Sample Standard Deviation

Front

Sx

Back

Range

Front

set of dependent variables (y values) assumed by a function or relation over all permitted values of the independent variable(s)

Back

Decreasing function

Front

a function with a graph that goes down as it is followed from left to right

Back

Amplitude of y = a sin bx

Front

|a|

Back

1. Y-intercept: x=0 is not a root of the denominator, so evaluate function at x=0. y=-6 2. Horizontal Asymptote(s): oblique asymptote, divide the equation to find it. x+18 3. End behavior of graph: x3/x2 which would be a line increasing as x increasing that crosses the graph at x=2 and x=6 4. Degree of numerator/denominator: 3/2

Front

x^3+10x^2+12x-72 ----------------------- x^2-8x+12 1. Y-intercept: 2. Horizontal Asymptote(s): 3. End behavior of graph: 4. Degree of numerator/denominator:

Back

log a + log b

Front

log (ab)

Back

f(x) notation

Front

same as y=

Back

Period of y = a sin bx

Front

(2π)/b or (360°)/b

Back

unit rate

Front

Rate per given unit

Back

Increasing function

Front

a function with a graph that goes up as it is followed from left to right

Back

Continuous

Front

a connected set of numbers such as the set of real numbers

Back

Tax rate

Front

The Percent used to calculate the amount of money taken out of your gross pay

Back

Conjugate of a binomial (a+b)

Front

Switch the sign in the middle (a-b)

Back

Horizontal asymptote at y=a/b

Front

Asymptote of a^n ------- b^n

Back

Percent

Front

A ratio whose Denominator is 100.

Back

Gross Pay

Front

The total amount an employee earns before any taxes or deductions are made

Back

randomly chosen

Front

This means that no particular rule was used to choose a person

Back

Quadratic Function

Front