Math Algebra I

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Math Algebra I
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2012-12-19 19:34:19
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algebra formula
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Math Algebra formula
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  1. Commutative Property of Addition
    • For all real numbers a and b:
    • a+b=b+a
  2. For all real numbers a and b:
    a+b=b+a
    Commutative Property of Addition
  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
  5. Associative Property of Addition
    • 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)
    Associative Property of Addition
  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):



    convert decimal answer to % answer
  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

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