How can we help?

You can also find more resources in our Help Center.

Monomial

Polynomial

Degree of a Monomial

Degree of a Polynomial

A number, a variable, or a product of numbers and/or variables

A monomial or a sum difference of monomials

The sum of the powers of the VARIABLES

The largest degree of its monomials

Monomial

A number, a variable, or a product of numbers and/or variables

Polynomial

A monomial or a sum difference of monomials

Additive Inverse

Graph

Number Line

Integers

the number in the set of real numbers that when added to a gi…

to draw, or plot, the points name by a certain numbers or ord…

a line on which numbers are marked at intervals, used to illu…

The set of numbers that include {... -2, -1, 0, 1, 2, ...}

Additive Inverse

the number in the set of real numbers that when added to a gi…

Graph

to draw, or plot, the points name by a certain numbers or ord…

Absolute Value

Additive Inverse

Integers

Irrational Number

The absolute value of a number "n" is its distance from zero…

A number and its opposite are additive inverses of each other…

The set {..., -2, -1, 0, 1, 2, ...}

Numbers that cannot be expressed as terminating or repeating…

Absolute Value

The absolute value of a number "n" is its distance from zero…

Additive Inverse

A number and its opposite are additive inverses of each other…

Congruence Definition

Theorem 2.1

Theorem 2.2

Congruence Class Definition

Let a,b,n be positive integers with n > 0. Then a is congruen…

Let n be a positive integer. For all a,b,c ε ℤ,... (1) a ≡ a (mo…

If a ≡ b (mod n) and c ≡ d (mod n), then ... (1) a + c ≡ b + d (…

Let a and n be integers with n > 0. The congruence class of a…

Congruence Definition

Let a,b,n be positive integers with n > 0. Then a is congruen…

Theorem 2.1

Let n be a positive integer. For all a,b,c ε ℤ,... (1) a ≡ a (mo…

i^ (i - hat)

j^ (j - hat)

Basis vectors

Basic of vector space

The vector pointing to x direction

The vector pointing to y direction

A set of elements (vectors) in a vector space V is called a b…

Set of **linearly independent** vectors that span the full space.

i^ (i - hat)

The vector pointing to x direction

j^ (j - hat)

The vector pointing to y direction

expression

variable

constant

coefficient

when we combine numbers and/or variables using operations suc…

the x or other letter in an expression

a number like 6 or 0.5 or 2.3 that can only ever have one spe…

when a constant is multiplied by a variable

expression

when we combine numbers and/or variables using operations suc…

variable

the x or other letter in an expression

Compound Statement... (sentencia compuesta)

Compound Inequality... (desigualdad compu…

Intersection vs. Union... (intersección f…

Truth Table... (tabla de verdad)

Formed by combining two or more simple statements; can be tru…

Formed by combining two or more simple inequalities.

Intersection = AND; the overlapping region of simple inequali…

A truth table is a table whose columns are statements, and wh…

Compound Statement... (sentencia compuesta)

Formed by combining two or more simple statements; can be tru…

Compound Inequality... (desigualdad compu…

Formed by combining two or more simple inequalities.

Absolute Value

Additive Inverse

Coordinate

Inequality

The distance a number is from zero on the number line.

An integer and its opposite.

A number that corresponds with a point on a number line.

A mathematical sentence that contains <,>,≤,≥, or ≠ sign.

Absolute Value

The distance a number is from zero on the number line.

Additive Inverse

An integer and its opposite.

Rational Number

Natural number

Whole number

Integers

Any number that can be written as a fraction

Any number 1 and above

Any number 0 and above

Any negative or positive number

Rational Number

Any number that can be written as a fraction

Natural number

Any number 1 and above

consecutive integers

equivalent equations

identity

inverse operations

Integers differ by one.

Equations that had the same solution(or solutions).

An equation that is true for every value of the variable.

Operations that undo one another.

consecutive integers

Integers differ by one.

equivalent equations

Equations that had the same solution(or solutions).

Formula

Solve an Equation

Equivalent Equations

Multi-step equations

A rule for the relationship between certain quantities.

The process to find the value of the variable that makes the…

Equations that have the same solution.

More than on step to solve the problem.

Formula

A rule for the relationship between certain quantities.

Solve an Equation

The process to find the value of the variable that makes the…

Domain

Linear inequlity

Negative slope

parallel

Set of input values, x values= input,

Ax + By > C, y < 2x = 5

the slope that falls when you follow the graph from left to r…

lines that do not intersect, Their slopes are identical/same

Domain

Set of input values, x values= input,

Linear inequlity

Ax + By > C, y < 2x = 5

Absolute Value Function

Boundary

Cartesian Coordinate Plane

Constant Function

A function written as f(x) = IxI, where f(x) is greater than…

A line or curve that seperates the coordinate plane into two…

A plane divided into four quadrants by the intersection of th…

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

Absolute Value Function

A function written as f(x) = IxI, where f(x) is greater than…

Boundary

A line or curve that seperates the coordinate plane into two…

complement

compound inequality

disjoint sets

empty or null set

all elements in the universal set that are not in the set.

is two distinct inequalities joined by the word "and" or the…

have no elements in common

contains no elements. It is a subset of every set. Use Ø or {…

complement

all elements in the universal set that are not in the set.

compound inequality

is two distinct inequalities joined by the word "and" or the…

real numbers

integers

absolute value

counterexample

the set of all rational and irrational numbers

whole numbers and their opposites

The distance a number is from zero on a number line

an example that proves a statement false

real numbers

the set of all rational and irrational numbers

integers

whole numbers and their opposites

Consumer Math

Tax

Tip

Mark up

math used in everyday life which includes, tax, tips, and mar…

Additional money paid to the government on sold goods

Additional money paid for a service provided

The amount of money a store will "mark up" the praice of a good

Consumer Math

math used in everyday life which includes, tax, tips, and mar…

Tax

Additional money paid to the government on sold goods

Closure Property

Commutative Property

Associative Property

Terms

For all real numbers a and b:... a + b is a unique real number... a…

For all real numbers a and b:... a + b = b + a... ab = ba... The order…

For all real numbers a, b, and c:... (a+b) + c = a + (b+c)... (ab)c…

Numbers being added

Closure Property

For all real numbers a and b:... a + b is a unique real number... a…

Commutative Property

For all real numbers a and b:... a + b = b + a... ab = ba... The order…

closure property of addition

commutative property of addition

identity property of addition

inverse

adding any pair of numbers from the set and the sum is also i…

allows the order of the addends to change without affecting t…

the sum of any integer and zero equals the original integer

the sum of any integer and its additive inverse equals zero,…

closure property of addition

adding any pair of numbers from the set and the sum is also i…

commutative property of addition

allows the order of the addends to change without affecting t…

compound inequality

inequality

intersection

solution of an inequality

two simple inequalities that are combined into one statement…

a statement that compares two expressions using one of the fo…

the set of all elements that are common to both sets, denoted…

any value that makes the inequality true

compound inequality

two simple inequalities that are combined into one statement…

inequality

a statement that compares two expressions using one of the fo…

parent function

transformation

translation

reflection

The simplest form in a set of functions that form a family.

The moving of a figure by a translation (slide), rotation (tu…

Shifts the graph of the parent function horizontally, vertica…

Flips the graph of a function over a line such as the x-axis…

parent function

The simplest form in a set of functions that form a family.

transformation

The moving of a figure by a translation (slide), rotation (tu…

In y=a|x+b|+c what does b do

In y=a|x+b|+c what does c do

In y=a|x+b|+c what does a do

Constant function

Shifts left if negative and right if positive

Shifts graph down if negative and up if positive

Determines slope and direction it opens if negative down

Y=4

In y=a|x+b|+c what does b do

Shifts left if negative and right if positive

In y=a|x+b|+c what does c do

Shifts graph down if negative and up if positive

Identity prop. of mult.

Identity prop. of add.

Inverse prop. of add.

Inverse prop. of mult.

multiply anything by 1 and get the same number

add 0 to any number and get the same number

13 +9=9+13

3x7=7x3

Identity prop. of mult.

multiply anything by 1 and get the same number

Identity prop. of add.

add 0 to any number and get the same number

solve an equation

equivalent equation

formula

identity

to find all values of the variable that make the equation a t…

equations that have the same solution, but just look different

an equation that states a rule for the relationship between c…

an equation that is true for all real values of the variable…

solve an equation

to find all values of the variable that make the equation a t…

equivalent equation

equations that have the same solution, but just look different

Dimensional Analysis

Equivalent Equations

Formula

Identity

The process of carrying units throughout a computation

Equations that have the same solution

An equation that states a rule for the relationship between c…

An equation that is true for every value of the variable

Dimensional Analysis

The process of carrying units throughout a computation

Equivalent Equations

Equations that have the same solution

discrete

continuous

vertical line test

domain

a relation in which the domain is a set of individual points

the domain of a relation has an infinite number of elements a…

if a vertical line does not intersect a graph in more than on…

all X values (can't be repeated)

discrete

a relation in which the domain is a set of individual points

continuous

the domain of a relation has an infinite number of elements a…

Consecutive integers

Dimensional analysis

Equivalent equations

Extremes

Integers in counting order

The process of carrying units throughout a computation

Equations that have the same value

In the ratio a/b=c/d, a and d are extremes

Consecutive integers

Integers in counting order

Dimensional analysis

The process of carrying units throughout a computation

Equivalent Equations

addition (subtraction) property of equ…

isolate

inverse operations

Equations that have the same solution

adding/ subtraction the same number to each side of an equati…

to get a variable with a coefficient of 1 alone on one side o…

operations that undo eachother

Equivalent Equations

Equations that have the same solution

addition (subtraction) property of equ…

adding/ subtraction the same number to each side of an equati…

Equivalent Equations

Isolate

Inverse Operation

Literal Equation

Equations with the same solutions.

Get variable with coefficient of 1 .

An operation the undo another

An equation with two or more variables

Equivalent Equations

Equations with the same solutions.

Isolate

Get variable with coefficient of 1 .

real numbers

Rational numbers

integers

whole numbers

all numbers are real numbers

any number that can be turned into a decimal

all numbers except decimals or fractions

all positive numbers and zero

real numbers

all numbers are real numbers

Rational numbers

any number that can be turned into a decimal

quadratic function

parabola

vertex

vertex form

a function that can be written in the form f(x)=ax2+bx+c, whe…

the shape of the graph of a quadratic function. also, the set…

the highest or lowest point on the parabola

a quadratic function written in the form f(x)=a(x-h)2+k, wher…

quadratic function

a function that can be written in the form f(x)=ax2+bx+c, whe…

parabola

the shape of the graph of a quadratic function. also, the set…

Formula

Solve an equation

equivalent equations

multistep equation

A rule for the relationship between quantities

Finding a value for a variable that makes the equation true

Equations that have the same answer or solution

an equation that has more than one step

Formula

A rule for the relationship between quantities

Solve an equation

Finding a value for a variable that makes the equation true

Discrete

Continuous

Vertical line test

Independent variable

Points that are not connected

Points that are connected with a line or curve

Test to see if the relation is a function

X value / domain

Discrete

Points that are not connected

Continuous

Points that are connected with a line or curve

Real Numbers

Real Number Line

Origin

Negative Numbers

Numbers that can be pictured as points on a horizontal line.

A horizontal line that displays real numbers.

The point labeled as zero.

The points to the left of zero.

Real Numbers

Numbers that can be pictured as points on a horizontal line.

Real Number Line

A horizontal line that displays real numbers.

real numbers

origin

negative numbers

positive numbers

The set of numbers consisting of the positive numbers, the ne…

The point labeled zero on the number line

Any of the numbers less than zero

Any of the numbers greater than zero

real numbers

The set of numbers consisting of the positive numbers, the ne…

origin

The point labeled zero on the number line

Relation

Domain

Range

Function

A set of pairs of input and output values.

A relation is the set of inputs, also called x-coordinates, o…

The set of outputs, also called y-coordinates, of the ordered…

A relation in which each element of the domain corresponds wi…

Relation

A set of pairs of input and output values.

Domain

A relation is the set of inputs, also called x-coordinates, o…

Absolute value

Absolute value function

Additive property of inequality

Additive identity

The distance a number is from zero on the number line (always…

A function whose equation contains absolute value symbols- it…

If a<b, then a+c<b+c

The number "zero" -properly states that adding zero does not…

Absolute value

The distance a number is from zero on the number line (always…

Absolute value function

A function whose equation contains absolute value symbols- it…

Correlation

Positive Correlation

Negative Correlation

Explanatory Variable

Similarity/association between two variables

If the value of one variable increases while the other one in…

If the value of one variable decreases while the other variab…

The variable in that causes the other variables to change

Correlation

Similarity/association between two variables

Positive Correlation

If the value of one variable increases while the other one in…

Equivalent Equation

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Equations that have the solution

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

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

If a = b, then a**c = b**c

Equivalent Equation

Equations that have the solution

Addition Property of Equality

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

The property which says that grouping…

The property which states that it does…

Integers in counting order

a(x+y)=ax+ay

The distance a number is from zero on the number line (always…

A function whose equation contains absolute value Symbols-it'…

If a<b then a+c<b+c

The number zero-property states that adding zero does not cha…

The property which says that grouping…

The distance a number is from zero on the number line (always…

The property which states that it does…

A function whose equation contains absolute value Symbols-it'…

Distributive Property

Division Property of Equality

Inverse Operations

Like Terms

Shows how multiplication affects an addition or subtraction:…

States that if both sides of an equation are divided by the s…

Inverse operations are operations that undo each other. For e…

Terms that have the same variable or no variable.

Distributive Property

Shows how multiplication affects an addition or subtraction:…

Division Property of Equality

States that if both sides of an equation are divided by the s…

equations that have the same solution…

to get the variable with a coefficient…

it undoes another operation. for examp…

compares two numbers by division

equivalent equations

isolate

inverse operation

ratio

equations that have the same solution…

equivalent equations

to get the variable with a coefficient…

isolate

parent function

transformation

slope

scatter plot

simplest form in a set of functions that forms a family.

each function in the family is a transformation of the parent…

of a non vertical line is the ratio of vertical change to the…

a graph that relates two sets of by plotting the data as orde…

parent function

simplest form in a set of functions that forms a family.

transformation

each function in the family is a transformation of the parent…

percent of change

proportion

rate

ratio

the ratio of the change in an amount to the original amount e…

an equation stating the two ratios are equal

the ratio of two measurements having different units of measure

a comparison of two numbers by division

percent of change

the ratio of the change in an amount to the original amount e…

proportion

an equation stating the two ratios are equal