Algebra

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Author:
atcannon
ID:
133165
Filename:
Algebra
Updated:
2012-02-08 07:11:17
Tags:
Intermediate Algebra
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Description:
Test Chapters 1-3
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  1. Natural numbers
    • Includes numbers we use for counting:
    • 1,2,3,4,5,6,7,8,9,...
  2. Whole numbers
    • Includes natural numbers together with 0:
    • 0,1,2,3,4,5,6,7,8,9,...
  3. Integers
    • includes natural numbers, 0, and the negatives of the natural numbers:
    • -5,-4,-3,-2,-1,0,1,2,3,4,5,...
  4. Prime numbers
    • Are natural number greater than 1 that are divisible by 1 and themselves:
    • 2,3,5,7,11,13,17,19,23
  5. Composite numbers
    • Are natural numbers greater than 1 that are not prime:
    • 4,6,8,9,10,12,14,15,16,18,20,21
  6. Even integers
    • Are integers that are exactly divisible by 2:
    • -8,-6,-4,-2,0,2,4,6,8,...
  7. Odd integers
    • Are integers that are not exactly divisible by 2:
    • -9,-7,-5-3-1,1,3,5,7,9,...
  8. Rational numbers
    • a a is an integer and b is a nonzero integer
    • b
  9. Irrational numbers
    x x is a nonterminating, nonrepeating decimal
  10. Real numbers
    x x is a terminating decimal, a repeating decimal, or a nontermination nonrepeating decimal
  11. Interval notation
    • (-5,8]
    • parenthesis indicates that endpoints are not included, brackets indicates that the endpoints are included
  12. Compound Inequalities
    Expressions that involve more than one inequality and involves the word (or,and) so it can be written in interval notation with the union symbol (U, upside down for and)
  13. Absolute value
    is the distance on a number line between 0 and the point with the coordinate.
  14. Sum
    Result when two numbers are added
  15. Difference
    Result when one number is subtracted from another number
  16. Product
    Result when two numbers are multiplied
  17. Quotient
    • Result when two numbers are divided
    • Division by 0 is undefined
  18. Mean
    The Sum of the values divided by the number of values
  19. Median
    • The middle value
    • if odd, choose the middle
    • if even, find the mean of the middle two values
  20. Mode
    Value that occurs mors often
  21. Perimeter
    • Distance around a figure
    • Square P=4s
    • Rectangle P=2l+2w
    • Triangle P= a+b+c
    • Trapezoid P=a+b+c+d
  22. Circumfrence
    • Distance around a circle
    • C=pie * D
    • C=2*pie*radius
    • (pie is approximately)
  23. Communitive Property
    Multiplication and Addition
    • a+b = b+a
    • ab = ba
  24. Associative Property
    Multiplication and Addition
    (a+b) + c= a + (b+c)
  25. Distributive Property
    Multiplication over addition
    a(b+c) = ab + ac
  26. The product Rule of exponents
    xm xn = xm+n
  27. Power Rules of Exponents
    • (xm)n = xm*n
    • (xy)n = xn*yn
    • (x/y)n= xn/yn
  28. Zero exponents
    x0=1
  29. Negative Exponents
    • x-n = 1/xn
    • and
    • 1/x-n = xn
  30. Quotient Rule
    xm/xn = xm-n
  31. Fractions to Negative Powers
    (x/y)-n = (y/x)n = yn/xn
  32. Equation
    A statement indicating that two quantities are equal
  33. Conditonal equations
    Equations have exactly one solution
  34. Identiy
    Equation that is satisfied by every number for which both sides of the the equation are defined. All real numbers
  35. Contradiction
    Equation that has no solution
  36. Right angle
    angle whose measure is 90 degree
  37. Straight angle
    Angle whose measure is 180 degree
  38. Acute anle
    Angle whose measure is greater than 0 degree but less than 90
  39. Complementary angles
    the sum of two angles equals 90 degrees
  40. Supplementary anles
    the sum of two angles equals 180 degrees
  41. Coordinate System
    • x-axis-horizontal line
    • y-axis-vertical line
    • origin-point where axis cross
    • coordinate plane-two axis form this
    • quadrants-coordinate plane divide into four regions
    • x-coordinate-point on x axis
    • y-coordinate-point on y axis
    • ordered pair-when the order of the coordinate is important
  42. Linear equation
    general form
    • When the graph of an equation is a line
    • Ax + By = C
    • A,B,C are constants
    • x,y are variables
  43. Y-intercept
    Point of a line where the line intersects the y-axis
  44. X-intercept
    Point of a line where the line intersects the x-axis
  45. Horizonatal and Vertical lines
    • the graph of x=a is a vertical line with x-intercept at (a,0)
    • the graph of y=b is a horizoneal line with y intercept at (0,b)
  46. Midpoint
    the middle point of a line with ends at P(x1,y1) and Q(x2,y2) calculated:

    (x1+x2/2 , y1=y2/2)
  47. Slope of the line
    Constant rate of change of line passing through points (x1,y1) and (x2,y2) calculated:

    • m= Change in y/Change in x
    • m= y2-y1/ x2-x1
    • m+ rise/run
  48. Slopes of Horizontal and Vertical lines
    • all horizontal lines (lines with equations of the form y=b) have a slope of O
    • all vertical lines (lines with equations of the form x=a) have no defined slope
  49. Slope of parallel lines
    • Nonvertical parallel lines have the same slope, and lines having the same slope are parallel
    • Since vertical lines are parallel, lines with no defined slop are parallel
  50. Negative reciprocals
    Two real numbers a and b if ab=-1
  51. Slopes of perpendicular lines
    If two nonvertical lines are perpendicular, their slopes are negative reciprocals.
  52. Point slope form
    • the point slope equation of a line passing through P(x1,y1) and with the slope M is:
    • y-y1=m(x-x1)
  53. Slope-Intercept Form
    • The slope-intercept equation of a line with slope m and y-intercept (0,b) is:
    • y=mx+b
  54. Slope and Y-intercept from the general form
    • Ax+By=C
    • slope = - a/b
    • y-inetercept = (0, c/b)
  55. Relations
    Sets of ordered pairs
  56. Domain of the relation
    the set of all the first components in the relation
  57. Range of the relation
    The set of all the second components in the relation
  58. Function
    Is any set of ordered pairs (a relation) in which each first component determines exactly one second component
  59. Vertical line test
    Determines whether the graph of an equation represents a function. If every vertical line that intersects a graph does so exactly once, the graph represents a function.
  60. Function Notation
    The notation y= f(x) denotes that the variable is a function of x.
  61. y is a Function of x
    An equation, table, or graph in x and y in which each value of x (the input) determines exactly one value of y (the output) is a function of x.
  62. Graph of a function
    the graph of the ordered pairs (x,f(x)) that define the function
  63. Linear function
    • a function defined by an equation that can be written in the form:
    • f(x)=mx+b
    • or
    • y=mx+b
  64. Squaring function
    • f(x)=x^2 (or y=x^2)
    • parabola
  65. Cubing function
    f(x)=x^3 (or y=x^3)
  66. Absolute value function
    • f(x)=lxl (or y=lxl)
    • V shaped graph
  67. Horizontal Translations
    • If f is a fuction and k is a positive number, then:
    • the graphe of f(x-k) is identical to the graph of f(x), except that it is translated k units to the right
    • The graph of f(x+k) is identical to the graph of f(x), except that it is translated k units to the left.
  68. Vertical translations
    • If f is a function f and k is a positive number, then:
    • The graph of f(x)+k is identical to the graph of f(x), except that it is translated k units upward
    • The graph of f(x)-k is identical to the graph f(x), except that it is translated k units downward
  69. Reflection of a Graph
    The graph of y=-f(x) is the graph of f(x) reflected about the x-axis
  70. Solving the system
    The process of finding the ordered pair that satisfies both equations in the system
  71. Consistent system
    When the system has a solution
  72. Inconsistent system
    When the system has no solution, the solution set is 0 (put line thru the zero)
  73. Dependent system
    When the system has infinately many solutions, 2 equations give the same line.
  74. Substitution method
    • 1. solve one equation for one of its variables
    • 2. substitute the result from Step 1 into the other equation and solve
    • 3. find the value of the other variable by substittuting the value from step 2 into one of the original equations.
    • 4. State the solution
  75. Addition Medthod
    • 1. write both equations in general form
    • 2. if necessary, multiply the terms of one or both equations to cake the coefficients on one of the variables differ only in sign
    • 3. Add the equation and solve.
    • 4. substitute the value in step 3 into either of the original equations and solve
    • 5. state the solution
  76. Solving a system of three linear equations in three variables
    • 1. pick any two equations and elimate a variable
    • 2. pick a different pair and elinate the same variable
    • 3. solve the resulting pair of two equations in two variables
    • 4. find the value of the third variable, substitute the values from step three into one of the original equations with three variables and solve the equation

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