College Algebra

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  1. Real numbers
    Collection of all rational and irrational numbers, both positive and negative, including zero.
  2. Collection of all rational and irrational numbers, both positive and negative, including zero.
    Real numbers
  3. Integers
    Counting numbers 1,2,3....together with 0 and the negative numbers -1,-2,-3....
  4. Counting numbers 1,2,3....together with zero and the negative numbers -1,-2,-3....
    Integers
  5. Natural numbers
    • All positive integers.
    • Also called counting numbers.
  6. All positive integers.
    Natural numbers
  7. Counting numbers
    Natural numbers
  8. Two consecutive negative signs
    Double negative
  9. Double negative
    Two consecutive negative signs
  10. Distributive law of multiplication
    a(b + c) = ab + ac
  11. a(b + c) = ab + ac is the _.
    distributive law of multiplication.
  12. Rational numbers
    Can be expressed as a ratio of integers or as a fraction.
  13. Can be expressed as a ratio of integers or as a fraction
    Rational numbers
  14. Multiplying fractions
    Image Upload
  15. A fraction Image Upload is reduced if _.
    the numbers a and b have no common factors.
  16. A fraction Image Upload  is _ the numbers a and b have no common factors.
    reduced
  17. Another way to say the fraction Image Upload is reduced is to say _.
    that it is in lowest terms.
  18. Image Upload
    Image Upload
  19. Image Upload
    Image Upload
  20. Image Upload
    Image Upload
  21. Image Upload
    Image Upload
  22. Image Upload
    Image Upload
  23. Image Upload
    Image Upload
  24. General rule for adding fractions:
    Image Upload
  25. Image Upload
    Image Upload
  26. Image Upload
    Image Upload OR

    Image Upload
  27. General form for subtracting fractions
    Image Upload
  28. Subtract Image Upload from Image Upload
    Image Upload
  29. Reciprocal of a number x when multiplied by x yeilds _.
    1
  30. Reciprocal of any integer n (except 0) is _.
    Image Upload
  31. Reciprocal of Image Upload is _.
    n
  32. Find the reciprocal of Image Upload
    Image Upload
  33. Image Upload 
    Image Upload
  34. General rule for division
    Image Upload
  35. Irrational numbers
    • A number that is not rational.
    • Cannot be written as a fraction of integers.
  36. Cannot be written as a fraction of integers.
    Irrational
  37. Important class of irrational numbers
    Square roots of positive integers that are not perfect squares.
  38. Square roots of positive integers that are not perfect squares.
    Important class of irrational numbers.
  39. Integers from 2 and above are divided into two categories:
    • Prime
    • Composite
  40. Prime number
    • Not the product of two integers bigger than 1.
    • Divisible by itself and 1 only.
  41. Not the product of two integers bigger than 1.
    Prime number
  42. Divisible by itself and 1 only.
    Prime number
  43. Composite number
    Integer that is equal to or greater than 2 and is not prime.
  44. Integer that is equal to or greater than 2 and is not prime:
    Composite number
  45. Set of integers is closed under addition because _.
    whenever two integers are added, the result is another integer.
  46. Whenever two integers are added, the result is another integer, causing the set of integers to _.
    be closed.
  47. Set of integers is not closed under division, because _.
    it is not always true that an integer divided by another integer yields an integer.
  48. Set of negative integers is (close/not closed) under multiplication.
    not closed
  49. Absolute value of a number x is denoted _.
    |x|
  50. |x| denotes _.
    absolute value of a number
  51. Absolute value
    Distance from the number to 0.
  52. Distance from a number to 0.
    Absolute value
  53. |Image Upload|
    Image Upload
  54. Is every integer a rational number? Why?
    Yes. Each integer can be written as a fraction with 1 in the denominator, like 4 = Image Upload.
  55. Is Image Upload a rational number? Is  Image Upload rational? How about Image Upload?
    Image Upload is irrational. Image Upload is rational because it is the integer of 3. Image Upload is not even real, so it is certainly not rational.
  56. List the prime numbers between 50 and 60.
    53 and 59 are the only primes between 50 and 60.
  57. Is Image Upload rational?
    No. Image Upload is close to both Image Upload and 3.14, but it is not equal to either.
  58. Are the negative integers closed with respect to the operation of addition?
    Yes. Whenever you add two negative integers, the result is another negative integer.
  59. Is the product of two irrational numbers always irrational?
    No. Consider Image Upload times Image Upload = 2. Image Upload is irrational, but 2 is not.
  60. Is it true that for any real numbers a, b, and c, a(b - c) = ab - ac?
    Yes. Subtracting a number is equivalent to adding its negative, so the distributive law applies here: a X (b + (-c) = a X b + a X (-c).
  61. Write Image Upload as a single fraction.
    Image Upload
  62. Write Image Upload as a single fraction.
    Image Upload
  63. Place these numbers on the number line. Which is largest? Which is smallest?

    4.2   Image Upload   Image Upload   Image Upload   Image Upload   Image Upload
    • Image Upload is approximately -3.14159 (is the smallest),
    •  Image Upload and is approximately .571429
    • Image Upload is approximately 1.7320508,
    • Image Upload = 3, and
    • Image Upload = 10 (is the largest)
  64. Are |3 - 1| and |1 - 3| equal?
    Yes. |3 - 1| = |2| = 2. |1 - 3| = |-2| = 2.
  65. Is it true that for real numbers a and b, |a + b| = |a| + |b|? Provide an example where this is false.
    No. When the numbers have opposite signs, it is false. Consider a = 6 and b = -4. |6 + (-4)| = |6 - 4| = |2| = 2, while |6| + |-4| = 6 + 4 = 10. 2 Image Upload 10, so the statement is not true for all a and b.
  66. Exponents
    Multiplying a number by itself several times
  67. Multiplying a number by itself several times
    exponent
  68. First law of exponents
    anam = an+m

    Adding the powers of exponents
  69. The law of adding powers of exponents
    First law of exponents
  70. Second law of exponents
    (ab)c = abc

    Multiplying the powers of exponents
  71. Law of multiplying the powers of exponents
    Second law of exponents
  72. Third law of exponents
    acbc = (ab)c

    Exponent roots are paired off
  73. Law of pairing of the exponent roots
    Third law of exponents
  74. Last rule of exponents
    • Involves fractions
    • Image Upload = an-m
  75. Law that involves fractions
    Last law of exponents
  76. Variable
    Letter that represents some unknown or undetermined number.
  77. Letter that represents some unknown or undetermined number.
    Variable
  78. (4ab)33a2b =
    43a3b33a2b = 433a3a2b3b = 64 X 3a5b4 = 192a5b4
  79. Image Upload =
    Image Upload = 25-332-3 = 223-1Image Upload
  80. Image Upload =
    Image Upload = Image Upload = Image Upload
  81. Image Upload =
    32x2(3x-3)-1 = 32x23-1x3 = 31x5 = 3x5

    OR

    Image Upload =  Image Upload = 3x5
  82. 4-6 =
    Image Upload
  83. Image Upload =
    32
  84. x0 =
    1
  85. xnxm =
    xn+m
  86. (xn)m =
    xnm
  87. (xy)n =
    xnyn
  88. Image Upload =
    xm-n
  89.   m
    Image Upload  =
    Image Upload
  90.   -n
    Image Upload  =
    •   n
    • Image Upload
  91. x-m =
    Image Upload
  92. 25 =
    32
  93. 52 =
    25
  94. 1100 =
    1
  95. 2-1 =
    Image Upload
  96. 2527 =
    212 = 4096
  97. (32)3 =
    36 = 729
  98. Image Upload =
    42 = 16
  99. Image Upload =
    (2-1)-3 = 23 = 8
  100. 19170 =
    1
  101. 6-2 =
    Image Upload
  102. Is there a difference between 2x-4 and (2x)4?
    Yes. In 2x-4, only the x is being raised to the 4th power. (2x)4, on the other hand, is 24x4= 16x4.
  103. Image Upload =
    35-1x5-2y2-1 = 34x3y= 81x3y
  104. (2xy)2(2x2y)2 =
    22x2y222x4y2 = 24x6y4 = 16x6y4
  105. Image Upload =
    Only x's cancel. Image Upload
  106. Image Upload =
    (r2s)4(s2r2) = r8s4s-2r2 = r10s2
  107. Image Upload =
    Image Upload
  108. Image Upload
    Image Upload
Author:
MarlieHopkins
ID:
167544
Card Set:
College Algebra
Updated:
2012-08-29 22:59:46
Tags:
Algebra
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Description:
Algebra
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