# Math Algebra I

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• For all real numbers a and b:
• a+b=b+a
2. For all real numbers a and b:
a+b=b+a
3. Commutative Property of Multiplication
for all real numbers a and b:  a * b = b * a
4. for all real numbers a and b:  a * b = b * a
Commutative Property of Multiplication
• For all real numbers a, b, and c:
• (a+b) + c = a + (b+c)
6. For all real numbers a, b, and c:  (a+b) + c = a + (b+c)
7. Associative Property of Multiplication
For all real numbers a, b, and c:  (a*b)c = a(b*c)
8. For all real numbers a, b, and c:  (a*b)c = a(b*c)
Associative Property of Multiplication
9. 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(b-c) = ab - ac and (b-c)a = ba-ca
10. For all real numbers a, b, c:
a(b+c)=ab + bc and (b+c)a = ba+ca
a(b-c) = ab - ac and (b-c)a = ba-ca
Distributive Property of Multiplication over Addition and Subtraction
11. For all real numbers a, b, and c:
Reflexive Property
a = a (a number is equal to itself)
12. a = a (A number is equal to itself)
For all real numbers a, b, and c:Reflexive Property
13. If a = b, then b = a
• For all real numbers a, b, and c:
• Symmetric Property
14. For all real numbers a, b, and c:
Symmetric Property
if a = b, then b = a
15. For all real numbers a, b, and c:
Transitive Property
if a = b and b = c, then a = c
16. If a = b and b = c, then a = c
For all real numbers a, b, and c:  Transitive Property
17. 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
18. 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
19. Conversion Formula:
Fahrenheit to Celsius
C = 5/9(F - 32)
20. C= 5/9(F - 32)
Conversion Formula:  Fahrenheit to Celsius
21. F = 9/5C + 32
Conversion Formula:  Celsius to Fahrenheit
22. Conversion Formula:  Celsius to Fahrenheit
F = 9/5C + 32
23. Formula for Density
D = m/v
24. D = m/v
Formula for Density
25. Formula for area of Trapezoid
A = 1/2h(b1 + b2)
26. A = 1/2h(b1 + b2)
Formula for area of Trapezoid
27. Formula: Circumference of a Circle
28. Formula: Circumference of a Circle
29. A = 2 ( lw + hw + lh )
Formula for total surface area of a box
30. Formula for total surface area of a box
A = 2 ( lw + hw + lh )
31. 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
32. Put the means (b, c) and the extremes (a, d) into 2 equation forms
• a : b = c : d
33. What is a percent?
a ratio that compares a number to 100
34. 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
35. Percentage, Base, Rate
a. What does the 20% represent?

a. the percent rate
36. Percentage, Base, Rate

a. What does the 30 represent?

a. the percentage of 75 that is 40%
37. Percentage, Base, Rate

a. What does the 75 represent?

a. the base
38. 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%)
39. 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)

40. 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
41. Formula:  Experimental Probability
experimental probability of an event, P(E):

42. What is this formula?
Experimental Probability
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. Define: Range
of a set of data: the difference between the greatest and least values

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

ex: {-3, 0, 5, 7}  10 is considered what?
Range
51. What is this type of arrangment of data called?
Stem and Leaf Plot
52. Visualize and label the parts of a Box-and-Whisker Plot

• example for this set of numbers:
• {18 27 34 52 54 59 61 68 78 82 85 87 91 93 100}
53. 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 stem-and-leaf plot)
54. 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
55. 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
56. Define: Relation
pairing between two sets of numbers
57. What is a pairing between two sets of numbers?
Relation
58. 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}
59. Define: Slope
ratio of vertical rise to horizontal run

60. what does this ratio describe?
Slope
61. Formula for: Slope
given two points with coordinates (x1,y1) and (x2,y2)

62. What is this the formula for?
Slope
63. a. The slope of a horizontal line is what?
b. The slope of a vertical line is what?
• a. 0
• b. undefined
64. 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
65. 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
66. Define Formula: Direct Variation
If y varies directly as x, then y = kx, or  where k is the constant of variation
67. What formula does this describe?
If
y varies directly as x, then y = kx, or  where k is the constant of variation
Direct Variation
68. 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)
69. 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).
70. 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).
71. Define: Kilogram
The SI unit of mass, equivalent to the international standard kept at Sèvres near Paris (approximately 2.205 lb).
72. The SI unit of mass, equivalent to the international standard kept at Sèvres near Paris (approximately 2.205 lb).
Kilogram
73. 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 cesium-133 atom
74. 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 cesium-133 atom
Second
75. What is Slope-Intercept Form?
for a line with a slope of m and a y-intercept of b is:

ymx b
76. y = mx   is what?
The slope-intercept form for a line with a slope of m and a y-intercept of b
77. Provide: Equations of Horizontal and Vertical Lines
• Horizontal: yb, where b is the y-intercept
• Vertival: xa, where a is the x-intercept
78. What are these equations of?
y = b, where b is the y-intercept
x = a, where a is the x-intercept
Horizontal and Vertical Lines
79. Provide: Standard Form of a Linear Equation

what are the conditions?
Ax + By = C

• A, B, C are real numbers
• A and B are not both zero
80. What does this describe?

A
x + By = C

A, B, C are real numbers
A and B are not both zero
Standard Form of a Linear Equation
81. Provide: Point-Slope Form
yy1m(x - x1)

The coordinates x1 and y1 are taken from a given point (x1, y1) and m is the slope
82. What does this describe?

y - y1 = m(x - x1)

The coordinates x1 and y1 are taken from a given point (x1, y1) and m is the slope
Point-Slope Form
83. What are the 3 forms for the equation of a line?
Slope-intercept:   y = mx b

Standard:  Ax + By = C

Point-slope:  y - y1 = m(x - x1)
84. Define: Perpendicular Lines
If the slopes of two lines are m and , the lines are perpendicular
85. If the slopes of two lines are m and , the lines are what?
Perpendicular
86. Define: Rational Number
Any number that can be expressed in the form  where and b are integers and
87. What is this?

Any number that can be expressed in the form  where and b are integers and
Rational Number
88. Define: Natural Numbers
N = 1, 2, 3, 4, ....
89. Define: Whole Numbers
W = 0, 1, 2, 3, 4, ...
90. Define: Integers
I = ..., -3, -2, -1, 0, 1, 2, 3, ...
91. Define: Irrational Number
• A non-terminating, non-repeating number
• Cannot be expressed in the form  where a and b are integers and
92. Visualize and describe a Venn diagram for the set of Real Numbers
 Author: Anonymous ID: 190225 Card Set: Math Algebra I Updated: 2012-12-20 00:34:19 Tags: algebra formula Folders: Description: Math Algebra formula Show Answers: