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Commutative Property of Addition
 For all real numbers a and b:
 a+b=b+a

For all real numbers a and b:
a+b=b+a
Commutative Property of Addition

Commutative Property of Multiplication
for all real numbers a and b: a * b = b * a

for all real numbers a and b: a * b = b * a
Commutative Property of Multiplication

Associative Property of Addition
 For all real numbers a, b, and c:
 (a+b) + c = a + (b+c)

For all real numbers a, b, and c: (a+b) + c = a + (b+c)
Associative Property of Addition

Associative Property of Multiplication
For all real numbers a, b, and c: (a*b)c = a(b*c)

For all real numbers a, b, and c: (a*b)c = a(b*c)
Associative Property of Multiplication

Distributive Property of Multiplication over Addition and Subtraction
 For all real numbers a, b, c:
 a(b+c)=ab + bc and (b+c)a = ba+ca
 a(bc) = ab  ac and (bc)a = baca

For all real numbers a, b, c:
a(b+c)=ab + bc and (b+c)a = ba+ca
a(bc) = ab  ac and (bc)a = baca
Distributive Property of Multiplication over Addition and Subtraction

For all real numbers a, b, and c:
Reflexive Property
a = a (a number is equal to itself)

a = a (A number is equal to itself)
For all real numbers a, b, and c:Reflexive Property

If a = b, then b = a
 For all real numbers a, b, and c:
 Symmetric Property

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

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

If a = b and b = c, then a = c
For all real numbers a, b, and c: Transitive Property

For all real numbers a, b, and c:
Substitution Property
if a = b, then a can be replaced by b and b can be replaced by a

if a = b, then a can be replaced by b and b can be replaced by a
 For all real numbers a, b, and c:
 Substitution Property

Conversion Formula:
Fahrenheit to Celsius
C = 5/9(F  32)

C= 5/9(F  32)
Conversion Formula: Fahrenheit to Celsius

F = 9/5C + 32
Conversion Formula: Celsius to Fahrenheit

Conversion Formula: Celsius to Fahrenheit
F = 9/5C + 32

Formula for Density
D = m/v

D = m/v
Formula for Density

Formula for area of Trapezoid
A = 1/2h(b_{1} + b_{2})

A = 1/2h(b_{1} + b_{2})
Formula for area of Trapezoid

Formula: Circumference of a Circle

Formula: Circumference of a Circle

A = 2 ( lw + hw + lh )
Formula for total surface area of a box

Formula for total surface area of a box
A = 2 ( lw + hw + lh )

In these expressions a : b = c : d or a/b = c/d
which are the means and which are the extremes
 means: b and c
 extremes: a and d

Put the means (b, c) and the extremes (a, d) into 2 equation forms
 a : b = c : d

What is a percent?
a ratio that compares a number to 100

Describe this image:
a. What is it called?
b. For what method of finding percentage is this useful?
 a. Percent Bar
 b. The Proportion Method

Percentage, Base, Rate
a. What does the 20% represent?
a. the percent rate

Percentage, Base, Rate
a. What does the 30 represent?
a. the percentage of 75 that is 40%

Percentage, Base, Rate
a. What does the 75 represent?
a. the base

Viewing the sample Percent bar below, place these terms into the Proportion Method:
p = percentage (numbers 0 to 75)
b = base (represented by the 75)
r = percent rate (0% to 100%)

The Proportion Method for percent:
What do the terms stand for and how would they be represented on a percent bar?
 r = percent rate (0% to 100%)
 p = percentage (numbers 0 to 75 on bar below)
 b = base (represented by 75 on bar below)

Put these terms into The Equation Method for a percent problem:
r = percent rate
p = percentage
b = base
Use the above graph to also write an example equation substituting the unkowns
 example equation: .60 * 75 = 45

Formula: Experimental Probability
experimental probability of an event, P(E):
convert decimal answer to % answer

What is this formula?
Experimental Probability

Define: Mean
Of a data set: the quotient when the sum of all the elements is divided by the total number of elements.
 ex: {3, 0, 2, 5}
 the mean is 4

Of a data set: the quotient when the sum of all the elements is divided by the total number of elements.
ex: {3, 0, 2, 5} the quotient 4 is called what?
Mean

Of a data set: the middle number in the set when the elements are placed in numerical order. For an even number of elements, the median is the average of the two middle elements.
ex: {12, 4, 0, 1, 3, 4, 5} the number 1 is what?
ex: {3, 5, 6, 10} the number 5.5 is what?
Median

Define: Median
Of a data set: the middle number in the set when the elements are placed in numerical order. For an even number of elements, the median is the average of the two middle elements.
 ex: {12, 4, 0, 1, 3, 4, 5} the medain is 1
 ex: {3, 5, 6, 10} the median is 5.5

Define: Mode
of a set of data: the element, if any, that occurs most often. There can be none, one, or multiple modes.
 ex: {11, 4, 4, 2, 6, 8} the mode is 4
 ex: {5, 5, 0, 4, 7, 7, 10} the modes are 5 and 7
 ex: {2, 1.4, 6, 23} no mode

of a set of data: the element, if any, that occurs most often. There can be none, one, or multiple.
ex: {11, 4, 4, 2, 6, 8} one
ex: {5, 5, 0, 4, 7, 7, 10} multiple
ex: {2, 1.4, 6, 23} none
Mode

Define: Range
of a set of data: the difference between the greatest and least values
ex: {3, 0, 5, 7} = 10

of a set of data: the difference between the greatest and least values
ex: {3, 0, 5, 7} 10 is considered what?
Range

What is this type of arrangment of data called?
Stem and Leaf Plot

Visualize and label the parts of a BoxandWhisker Plot
 example for this set of numbers:
 {18 27 34 52 54 59 61 68 78 82 85 87 91 93 100}

Visualize and describe a histogram
 Histogram is a bargraph with no space between the bars and that shows frequency of data. (easily constructed from the data in a stemandleaf plot)

Define: Function
pairing between two sets of numbers in which each element of the first set is paired with exactly one element of the second set
 ex: (1, 2) (3, 4) (3, 5) True
 ex: (1, 3) (1, 5) (1, 7) False

What is a pairing between two sets of numbers in which each element of the first set is paired with exactly one element of the second set?
ex: (1, 2) (3, 4) (3, 5) True
ex: (1, 3) (1, 5) (1, 7) False
Function

Define: Relation
pairing between two sets of numbers

What is a pairing between two sets of numbers?
Relation

Define the domain and range of this set of ordered pairs:
{(14, 68), (11, 64), (13, 65)}
 Domain: 1st coordinates of the ordered pairs {11, 13, 14}
 Range: 2nd coordinates of the ordered pairs {64, 665, 68}

Define: Slope
ratio of vertical rise to horizontal run

what does this ratio describe?
Slope

Formula for: Slope
given two points with coordinates (x _{1},y _{1}) and (x _{2},y _{2})

What is this the formula for?
Slope

a. The slope of a horizontal line is what?
b. The slope of a vertical line is what?

Looking at this set of ordered pairs, what is apparent about the slope of the line?
{(3,4), (2,5), (2,6), (3,5)}
The slope is undefined because the domain repeats itself with different range elements and therefore is not a function

Looking at this set of ordered pairs, what is apparent about the slope of the line?
{(3,6), (1,6), (2,6), (3,6)}
The slope of the line is horizontal or = 0

Define Formula: Direct Variation
If y varies directly as x, then y = kx, or where k is the constant of variation

What formula does this describe?
If y varies directly as x, then y = kx, or where k is the constant of variation
Direct Variation

Define: Hooke's Law
provide equation
 Relation of the distance a spring stretches to the amount of force applied to the spring.
 F=kd
 F = force in Newtons
 k = constant determined by experiment
 d = distance stretch in meters
(One Newton is about the weight of one medium apple)

What is this a picture of?
 The seven SI base units and the interdependency of their definitions.
 Clockwise from top: kelvin (temperature), second(time), metre (length), kilogram (mass), candela (luminous intensity), mole (amount of substance) and ampere (electric current).

Make a map:
The seven SI base units and the interdependency of their definitions.
Clockwise from top: kelvin (temperature), second(time), metre (length), kilogram (mass), candela (luminous intensity), mole (amount of substance) and ampere (electric current).

Define: Kilogram
The SI unit of mass, equivalent to the international standard kept at Sèvres near Paris (approximately 2.205 lb).

The SI unit of mass, equivalent to the international standard kept at Sèvres near Paris (approximately 2.205 lb).
Kilogram

Define: Second
A sixtieth of a minute of time, which as the SI unit of time is defined in terms of the natural periodicity of the radiation of a cesium133 atom

A sixtieth of a minute of time, which as the SI unit of time is defined in terms of the natural periodicity of the radiation of a cesium133 atom
Second

What is SlopeIntercept Form?
for a line with a slope of m and a yintercept of b is:
y = mx + b

y = mx + b is what?
The slopeintercept form for a line with a slope of m and a yintercept of b

Provide: Equations of Horizontal and Vertical Lines
 Horizontal: y = b, where b is the yintercept
 Vertival: x = a, where a is the xintercept

What are these equations of?
y = b, where b is the yintercept
x = a, where a is the xintercept
Horizontal and Vertical Lines

Provide: Standard Form of a Linear Equation
what are the conditions?
A x + B y = C
 A, B, C are real numbers
 A and B are not both zero

What does this describe?
Ax + By = C
A, B, C are real numbers A and B are not both zero
Standard Form of a Linear Equation

Provide: PointSlope Form
y  y_{1} = m(x  x_{1})
The coordinates x_{1} and y_{1} are taken from a given point (x_{1}, y_{1}) and m is the slope

What does this describe?
y  y_{1} = m(x  x_{1})
The coordinates x_{1} and y_{1} are taken from a given point (x_{1}, y_{1}) and m is the slope
PointSlope Form

What are the 3 forms for the equation of a line?
Slopeintercept: y = mx + b
Standard: Ax + By = C
Pointslope: y  y_{1} = m(x  x_{1})

Define: Perpendicular Lines
If the slopes of two lines are m and , the lines are perpendicular

If the slopes of two lines are m and , the lines are what?
Perpendicular

Define: Rational Number
Any number that can be expressed in the form where a and b are integers and

What is this?
Any number that can be expressed in the form where a and b are integers and
Rational Number

Define: Natural Numbers
N = 1, 2, 3, 4, ....

Define: Whole Numbers
W = 0, 1, 2, 3, 4, ...

Define: Integers
I = ..., 3, 2, 1, 0, 1, 2, 3, ...

Define: Irrational Number
 A nonterminating, nonrepeating number
 Cannot be expressed in the form where a and b are integers and

Visualize and describe a Venn diagram for the set of Real Numbers

