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What are natural numbers?

What are whole numbers?

What are integers?

What are rational numbers?

A number from the set {1, 2, 3, ...}

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

The set of natural numbers, the negative natural numbers, and…

A number that can be expressed as a/b, the ratio of two inter…

What are natural numbers?

A number from the set {1, 2, 3, ...}

What are whole numbers?

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

Square Root Property

Completing the Square

Discriminant

Negative

take the square roots of both sides

1. coefficient = 1... 2. move number to the other side ... 3. compl…

b^2 - 4ac

two complex roots

Square Root Property

take the square roots of both sides

Completing the Square

1. coefficient = 1... 2. move number to the other side ... 3. compl…

Rational and irrational

Integer, fractions, and decimals

Positive and negative

Proper, improper, and mixed

What are the two categories under real numbers?

What are the three categories under rational numbers?

Two types of integers

Three types of fractions

Rational and irrational

What are the two categories under real numbers?

Integer, fractions, and decimals

What are the three categories under rational numbers?

Foil

Imaginary unit

Vertical line test

Coefficient

Method for multiplying 2 binomials (first,outer,inner,last)

The number i when i equals the square root of -1

Visual test to determine if a graph is a function

Number preceding variable

Foil

Method for multiplying 2 binomials (first,outer,inner,last)

Imaginary unit

The number i when i equals the square root of -1

Angle of rotation

Center of hyperbola

Center of a ellipse

Conic section

an acute angle formed by a set of axes rotated from the Carte…

the midpoint of both the transverse and conjugate axes of a h…

the midpoint of both the major and minor axes

any shape resulting from the intersection of a right circular…

Angle of rotation

an acute angle formed by a set of axes rotated from the Carte…

Center of hyperbola

the midpoint of both the transverse and conjugate axes of a h…

Annual percentage rate (APR)

Carrying capacity

Change-of-base formula

Common logarithm

the yearly interest rate earned by an investment account, als…

in a logistic model, the limiting value of the output

a formula for converting a logarithm with any base to a quoti…

the exponent to which 10 must be raised to get x; log10 (x) i…

Annual percentage rate (APR)

the yearly interest rate earned by an investment account, als…

Carrying capacity

in a logistic model, the limiting value of the output

Absolute maximum

Absolute minimum

Average rate of change

Composite function

the greatest value of a function over an interval

the lowest value of a function over an interval

the difference in the output values of a function found for t…

the new function formed by function composition, when the out…

Absolute maximum

the greatest value of a function over an interval

Absolute minimum

the lowest value of a function over an interval

Distributive Propety

Identity

Real

Imaginary

The Fact the 2(x+5)=2x+10

An equation that is satisfied for every value of the variable…

In the complex number , the number 2 is called the

In the complex number 2 + 3i the number 3 is called the

Distributive Propety

The Fact the 2(x+5)=2x+10

Identity

An equation that is satisfied for every value of the variable…

Addition method

Augmented matrix

Break-even point

Coefficient matrix

an algebraic technique used to solve systems of linear equati…

a coefficient matrix adjoined with the constant column separa…

the point at which a cost function intersects a revenue funct…

a matrix that contains only the coefficients from a system of…

Addition method

an algebraic technique used to solve systems of linear equati…

Augmented matrix

a coefficient matrix adjoined with the constant column separa…

Natural numbers

Whole numbers

Rational numbers

Irrational numbers

N(o zero) postivie ; 1,2,3 etc..

wh0le numbers. ... 0,1,2,3 etc..

Ratio 1:2 = 1/2... Next biggest group

Crazy, never stops, numbers that don't make sense.

Natural numbers

N(o zero) postivie ; 1,2,3 etc..

Whole numbers

wh0le numbers. ... 0,1,2,3 etc..

The equation of a circle.

Graphing a line

Domain

Range

(x-h)^2+(y-k)^2=r^2 ex: center (2,3), radius: 5/3 equels (x-2…

Find the x intercept (6,0) and the y intercept (0,-2) and the…

The width of a parabola from one number to another. EX (-infi…

The height of a graph from one number to another.

The equation of a circle.

(x-h)^2+(y-k)^2=r^2 ex: center (2,3), radius: 5/3 equels (x-2…

Graphing a line

Find the x intercept (6,0) and the y intercept (0,-2) and the…

V=1/3S(sq)H

PV=nRT

9, add, divide by

2, divide, h, subtract (the subtracted…

What is the formula for volume? (Use sq for squared)

Where: P is pressure V is volume n is the number of moles of…

To solve for "F" in formula: C=5/9(F-32), first multiply both…

To solve for B: A=1/2(B+b)h. First multiply both sides by __(…

V=1/3S(sq)H

What is the formula for volume? (Use sq for squared)

PV=nRT

Where: P is pressure V is volume n is the number of moles of…

Law of Closure for Addition

Not a Closed set

Statement or Proposition

Universal Statements (if true)

If a+b are natural #'s then a+b is natural #

Find counter example... (infinite amt of numbers cant prove -->…

A statement that is true or false (but not both)

(start w/ all of every)... if and only if when we substitute in…

Law of Closure for Addition

If a+b are natural #'s then a+b is natural #

Not a Closed set

Find counter example... (infinite amt of numbers cant prove -->…

If the domain of the function f is not…

In calculus, one of the basic definiti…

It is used to determine whether the gr…

The values for which f(x)=0

Implied Domain

Difference Quotient

Vertical Line Test

zeros

If the domain of the function f is not…

Implied Domain

In calculus, one of the basic definiti…

Difference Quotient

Expression

Linear Expression

Equation

Linear Equation

Any combo of numbers, variables, and mathematical operations

An expression in which the only operations involving variable…

A mathematical statementtbat two expressions are equal

An equation containing only linear expressions

Expression

Any combo of numbers, variables, and mathematical operations

Linear Expression

An expression in which the only operations involving variable…

A set

Elements or members

∈

set braces

A collection of objects

The objects that belong to a set; In algebra they are usually…

Means a number is an element of a set (4∈{1,2,3,4})

{a,b,c} set braces are used to show a set

A set

A collection of objects

Elements or members

The objects that belong to a set; In algebra they are usually…

the sum/product of 2 real numbers=real…

we may group addition or multiplicatio…

we may multiply or add numbers in any…

you can add 0 to any number

Closure

Associative

Commutative

Additive identity

the sum/product of 2 real numbers=real…

Closure

we may group addition or multiplicatio…

Associative

Variable

Expression

Equation

Algebraic

A letter which represents or stands for a value

A combination of variables, numbers and operators

Two expressions joined by an equal sign

An expression that does not contain words

Variable

A letter which represents or stands for a value

Expression

A combination of variables, numbers and operators

Distance Formula

Midpoint Formula

X-intercepts

Y-intercepts

d(P,Q)=√[(x₂−x₁)²+(y₂−y₁)²]... P (x₁,y₁) Q (x₂,y₂)

M(x,y)=[(x₁+x₂)/2, (y₁+y₂)/2]... P(x₁,y₁) Q(x₂,y₂)

where graph touches x-axis or crosses... set y=0 and solve for x

where graph touches y-axis or crosses... set x=0 and solve for y

Distance Formula

d(P,Q)=√[(x₂−x₁)²+(y₂−y₁)²]... P (x₁,y₁) Q (x₂,y₂)

Midpoint Formula

M(x,y)=[(x₁+x₂)/2, (y₁+y₂)/2]... P(x₁,y₁) Q(x₂,y₂)

All Exponent Rules

All Radical Rules

Difference of squares

Rational Expressions

add if around paranthesis

Power from the top, Root from the bottom

a^3+b^3=(a+b)(a^2-ab+b^2)... a^3-b^3+(a-b)(a^2+ab+b^2)

Factor first, then cancel

All Exponent Rules

add if around paranthesis

All Radical Rules

Power from the top, Root from the bottom

Information age

Induction

Mentoring

No Child Left Behind Act

The current age in which information and its management are c…

Years one to three of full time teaching.

An experienced professional helping a less experienced collea…

A federal law passed in 2001 that sets goals for achievement…

Information age

The current age in which information and its management are c…

Induction

Years one to three of full time teaching.

Correlation coefficient

Decreasing linear function

Extrapolation

Horizontal line

a value, r, between -1 and 1 that indicates the degree of lin…

a function with a negative slope: If f (x) = mx + b, then m <…

predicting a value outside the domain and range of the data

a line defined by f (x) = b, where b is a real number. The sl…

Correlation coefficient

a value, r, between -1 and 1 that indicates the degree of lin…

Decreasing linear function

a function with a negative slope: If f (x) = mx + b, then m <…

Absolute value equation

Area

Cartesian coordinate system

Completing the square

an equation in which the variable appears in absolute value b…

in square units, the area formula used in this section is use…

a grid system designed with perpendicular axes invented by Re…

a process for solving quadratic equations in which terms are…

Absolute value equation

an equation in which the variable appears in absolute value b…

Area

in square units, the area formula used in this section is use…

An equation is a function if...

Definition of a function

Vertical Line Test

Even Function

each x-value has only one y-value

a correspondence from a first set, called the domain, to a se…

if any vertical line intersects a graph in more than one poin…

f(-x) = f(x), reflected over y-axis

An equation is a function if...

each x-value has only one y-value

Definition of a function

a correspondence from a first set, called the domain, to a se…

Set Notation

N={1,2,3,4,5,6,...}

W={1,2,3,4,5,6,...}

Z+={1,2,3,4,5,6,...}

Set is a well-defined as collection of numbers in objects

set of NATURAL numbers

set if WHOLE numbers

set of positive integers

Set Notation

Set is a well-defined as collection of numbers in objects

N={1,2,3,4,5,6,...}

set of NATURAL numbers

Rashau made a rectangular frame for he…

It has been shown that the force of gr…

The first angle of a triangle is 10 de…

Kate has a summer job as a swim instru…

Width = 11 cm... Length = 37 cm... If L = 28 cm then ... W = 10 cm,…

The object would weigh 550 lb on Jupiter

x-10 = the first angle... x = the second angle... 2x = the third an…

To earn at least $72 per week, Kate will need 4 hours of over…

Rashau made a rectangular frame for he…

Width = 11 cm... Length = 37 cm... If L = 28 cm then ... W = 10 cm,…

It has been shown that the force of gr…

The object would weigh 550 lb on Jupiter