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polynomials

square a number

first difference

second difference

an expression of more than 2 algebraic terms.

...to multiply a number by itself or to raise it to the power…

Values obtained by subtracting each term in a sequence from i…

Differences that are found by subtracting consecutive first d…

polynomials

an expression of more than 2 algebraic terms.

square a number

...to multiply a number by itself or to raise it to the power…

polynomials

square a number

first difference

second difference

an expression of more than 2 algebraic terms.

...to multiply a number by itself or to raise it to the power…

Values obtained by subtracting each term in a sequence from i…

Differences that are found by subtracting consecutive first d…

polynomials

an expression of more than 2 algebraic terms.

square a number

...to multiply a number by itself or to raise it to the power…

Absolute Value

Algebraic Expression

Boundary line

Domain

The distance a number is from zero on a number line

Consists of numerals, variables and other mathematical symbols

A line (dashed or solid) that indicates whether the points on…

The set of all possible input values for a relation or function

Absolute Value

The distance a number is from zero on a number line

Algebraic Expression

Consists of numerals, variables and other mathematical symbols

Standard Deviation

Logarithm Solution

Standard form

Vertex Form

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

Ax^2+Bx+C=0

Y=(x-h)^2+k (h,k)... (h, k) is the vertex

Standard Deviation

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

Logarithm Solution

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

linear equation

solving a linear equation

clearing fractions

linear absolute value equation

a variables have a degree of 1

To solve an equation, do whatever is necessary to both sides…

multiply each side by the LCM

|ax+b|=c

linear equation

a variables have a degree of 1

solving a linear equation

To solve an equation, do whatever is necessary to both sides…

Real Numbers

Rational Numbers

Integers

Whole Numbers

The numbers we use (non-imaginary)

Any number that can be expressed as a ration a/b, where a and…

The set of numbers we would use on a number line (negatives a…

The set of all positive integers including zero... -----> 0,1,2...

Real Numbers

The numbers we use (non-imaginary)

Rational Numbers

Any number that can be expressed as a ration a/b, where a and…

Natural

whole

integer

rational

positive integer (1, 2, 3...)

positive integers and 0 (0, 1, 2, 3,..)

positive whole numbers, negative whole numbers, and zero (-2,…

p/q where p and q are integers and q is not 0

Natural

positive integer (1, 2, 3...)

whole

positive integers and 0 (0, 1, 2, 3,..)

commutative property of addition

associative property of addition

identity property of addition

inverse property of addition

the order you add numbers together does not change the sum

the way you group numbers does not change the sum

the sum of a number and zero is the number

the sum of a a number and it's opposite is zero

commutative property of addition

the order you add numbers together does not change the sum

associative property of addition

the way you group numbers does not change the sum

function

Domain

Range

increasing interval

1. A relationship from one set (called the domain) to another…

The set of input values of a function. Also the independent v…

The set of output values of a function. Also the dependent va…

where the graph has a positive slope (x,y)

function

1. A relationship from one set (called the domain) to another…

Domain

The set of input values of a function. Also the independent v…

Equation of a circle

The Focus-Directrix form of the equati…

The Focus-Directrix form of the equati…

Standard Equations of Ellipses (Horizo…

(h.k)=center... radius=r

y = a(x - h)^2+k... Direction of opening: a>0: up a<0: down... Vert…

x= a(y-k)^2+h... Direction of opening: a>0: right a<0: let... Verte…

Center: (h,k)... Length of major axis: 2a... Length of minor axis: 2b

Equation of a circle

(h.k)=center... radius=r

The Focus-Directrix form of the equati…

y = a(x - h)^2+k... Direction of opening: a>0: up a<0: down... Vert…

Parent Function

Line of Best Fit

Scatterplot

Reflection

Simplest form of a set of functions that form a family

The trend line that finds the most accurate model of related…

Graph that relates two different sets of data by plotting the…

Flips the graph of a function across a line

Parent Function

Simplest form of a set of functions that form a family

Line of Best Fit

The trend line that finds the most accurate model of related…

Absolute value of a complex number

Axis of symmetry

Completing the square

Complex Number

Distance from the origin on the complex number plane

The line that divides a parabola into parts that are mirror i…

The process of finding the last term of the perfect square tr…

Imaginary numbers and real numbers together

Absolute value of a complex number

Distance from the origin on the complex number plane

Axis of symmetry

The line that divides a parabola into parts that are mirror i…

polynomials

square a number

first difference

second difference

an expression of more than 2 algebraic terms.

...to multiply a number by itself or to raise it to the power…

Values obtained by subtracting each term in a sequence from i…

Differences that are found by subtracting consecutive first d…

polynomials

an expression of more than 2 algebraic terms.

square a number

...to multiply a number by itself or to raise it to the power…

Bounded

Break-Even Point

Coefficient Matrix

Cramer's Rule

Graph of a system of constraints is a polygonal region

Point at which the income and cost is equal

Matrix that only contains coefficients of a system of equations

Method that uses determinants to solve to solve a system of l…

Bounded

Graph of a system of constraints is a polygonal region

Break-Even Point

Point at which the income and cost is equal

commutative addition/multiplication

associative addition/multiplication

identity addition/multiplication

inverse addition/multiplication

a+b=b+a... ab=ba

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

a+0=a, 0+a=a... 1xa=a, ax1=a

a+(-a)=0... ax1/a=1

commutative addition/multiplication

a+b=b+a... ab=ba

associative addition/multiplication

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

Complex Conjugate Theorem

Irrational Root Theorem

Fundamental Theorem of Algebra

Intermediate Value Theorem

if the imaginary number a+bi is a root of a polynomial equati…

let a and b be rational numbers and let the square root of b…

If P(x) is a polynomial of degree n(greater than or equal to)…

let f be a polynomial function with real coefficients, if f(a…

Complex Conjugate Theorem

if the imaginary number a+bi is a root of a polynomial equati…

Irrational Root Theorem

let a and b be rational numbers and let the square root of b…

Real Numbers

Imaginary Numbers

Rational Numbers

Irrational Numbers

Have points on the number line

Do NOT have points on the number line

Can be expressed in a ratio or two integers

Can't be expressed in a ratio or two integers

Real Numbers

Have points on the number line

Imaginary Numbers

Do NOT have points on the number line

radian

amplitude

frequency

period

a unit used to measure angles

The amplitude is the distance from the midline to the minimum…

the number of complete cycles in a basic period

the distance of a single cycle

radian

a unit used to measure angles

amplitude

The amplitude is the distance from the midline to the minimum…

set

element/member

subset

real numbers

a collection of objects ; sometimes named with capital letters

each object in a set ; typically use braces {} to enclose them

a set that's a part of a larger set

consists of several subsets of numbers ; set of rational numb…

set

a collection of objects ; sometimes named with capital letters

element/member

each object in a set ; typically use braces {} to enclose them

Relation

Domain

Range

Function

A mapping or pairing of input values with output values.

The set of input values.

The set of output values.

A relation for which each input has exactly one output.

Relation

A mapping or pairing of input values with output values.

Domain

The set of input values.

vertical stretch

vertical shrink

if a is negative

if a>1 or a<-1

number greater than 1 and stretches away from x-axis

number less than 1 and shrinks towards x-axis

graph is reflected

vertical stretch

vertical stretch

number greater than 1 and stretches away from x-axis

vertical shrink

number less than 1 and shrinks towards x-axis

Leading coefficient

Polynomial

Monomial

Degree of a polynomial

The coefficient of the first term of a polynomial in standard…

A monomial or a sum or difference of monomials

A number or product of numbers and variables with whole numbe…

The degree of the term of the polynomial with the greatest va…

Leading coefficient

The coefficient of the first term of a polynomial in standard…

Polynomial

A monomial or a sum or difference of monomials

√(b^2-4ac) > 0... a perfect square

√(b^2-4ac) > 0... but not a perfect square

√(b^2-4ac) < 0... (negative)

√(b^2-4ac) = 0

2 real rational roots

2 real but irrational roots

2 imaginary/complex roots

1 real rational double root

√(b^2-4ac) > 0... a perfect square

2 real rational roots

√(b^2-4ac) > 0... but not a perfect square

2 real but irrational roots

Standard Deviation

Logarithm Solution

Standard form

Vertex Form

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

Ax^2+Bx+C=0

Y=(x-h)^2+k (h,k)... (h, k) is the vertex

Standard Deviation

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

Logarithm Solution

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

What are the 6 trigonometric functions?

Find the 6 trigonometric functions for…

Find the 6 trigonometric functions for…

Find the 6 trigonometric functions for…

Sin... Cosine... Tangent... Cosecant... Secant ... Cotangent

(1/2), (√(3)/2), (1/√(3)), 2, (2/√(3)), √(3)

(1/√(2)), (1/√(2)), 1, √(2), √(2), 1

(√(3)/2), (1/2), √(3), (2/√(3)), 2, (1/√(3))

What are the 6 trigonometric functions?

Sin... Cosine... Tangent... Cosecant... Secant ... Cotangent

Find the 6 trigonometric functions for…

(1/2), (√(3)/2), (1/√(3)), 2, (2/√(3)), √(3)

Natural

whole

integer

rational

positive integer (1, 2, 3...)

positive integers and 0 (0, 1, 2, 3,..)

positive whole numbers, negative whole numbers, and zero (-2,…

p/q where p and q are integers and q is not 0

Natural

positive integer (1, 2, 3...)

whole

positive integers and 0 (0, 1, 2, 3,..)

Standard Deviation

Logarithm Solution

Standard form

Vertex Form

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

Ax^2+Bx+C=0

Y=(x-h)^2+k (h,k)... (h, k) is the vertex

Standard Deviation

o= √(1st #-mean)^2+....(Last #-mean)^2/n... n= number of terms…

Logarithm Solution

15^3x=6000... log15^3x=log285 (log 10 of each side)... 3xlog15=log2…

Function

Piecewise function

Compound inequalities

Linear equation

One X gets you one and only one y

2or more equations that have different domains

2 or more in equalities joined by and or or.

Equation where the highest power is one

Function

One X gets you one and only one y

Piecewise function

2or more equations that have different domains

algebra

counting numbers

whole numbers

integers

a systematic study of numbers and their relationship. It uses…

numbers that are positive. There are no zeros, no fractions,…

counting numbers including zero

numbers that are positive, negative, or zero. It does not inc…

algebra

a systematic study of numbers and their relationship. It uses…

counting numbers

numbers that are positive. There are no zeros, no fractions,…

Horizontal Translation

Vertical Translation

Reflection

Vertical Stretch

a. (x-h or x+h)... b. IN parenthesis... c. GO the opposite directio…

a. x+k or x-k... b. NO parenthesis... c. Go direction shown... d. Up/d…

a) Y-axis: x-value changes... a. f(-x)... b) X-axis: y-value chang…

a) Multiply x by: coefficient > 1

Horizontal Translation

a. (x-h or x+h)... b. IN parenthesis... c. GO the opposite directio…

Vertical Translation

a. x+k or x-k... b. NO parenthesis... c. Go direction shown... d. Up/d…