PATTERNS AND ITERATIONS

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CHAPTER 2
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SECTION 2-1
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• PATTERNS AND ITERATIONS

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• SEQUENCE
• An arrangement of numbers in a particular order.
  The numbers are called terms and the pattern is
  formed by applying a rule.

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EXAMPLES OF SEQUENCES

• 0, 2, 4, 6, ___, ___, ___
• 1, 4, 9, 16, ___, ___,___

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EXAMPLES OF SEQUENCES

• 2, 8, 14, 20, ___, ___, ___
• 1, -2, 4, -8, ___, ___,___

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EXAMPLES OF SEQUENCES

• 4, 12, 20, 28, ___, ___, ___
• 2, 6, 18, 54, ___, ___,___

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SECTION 2-2
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• THE COORDINATE PLANE, RELATIONS AND FUNCTIONS

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• COORDINATE PLANE Consists of two perpendicular
  number lines, dividing the plane into four
  regions called quadrants.

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• X-AXIS - the horizontal number line
• Y -AXIS - the vertical number line
• ORIGIN - the point where the
• x-axis and y-axis cross

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• ORDERED PAIR - an unique assignment of real
  numbers to a point in the coordinate plane
  consisting of one x-coordinate and one
  y-coordinate
• (-3, 5), (2,4), (6,0), (0,-3)

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• RELATION set of ordered pairs
• DOMAIN the set of all possible x-coordinates
• RANGE the set of all possible y-coordinates

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• MAPPING the relationship between the elements
  of the domain and range

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• FUNCTION set of ordered pairs in which each
  element of the domain is paired with exactly one
  element in the range

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SECTION 2-3
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LINEAR FUNCTIONS
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• ABSOLUTE VALUE the distance of any real number,
  x, from zero on the number line.
• Absolute value is represented by x
• 6 6, -6 6

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• LINEAR FUNCTIONS equations in two variables that
  can be written in the form y ax b. The graph
  of such equations are straight lines.

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• CONSTANT FUNCTION special linear function where
  the domain consists of all real numbers and where
  the range consists of only one value
• y 2, y -1, y3, y -3

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SECTION 2-4
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SOLVE ONE-STEP EQUATIONS
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• ADDITION PROPERTY OF EQUALITY
• For all real numbers a, b, and c, if a b,
  then
• a c b c and
• c a c b
• 22 18 18 22

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• MULTIPLICATION PROPERTY OF EQUALITY
• For all real numbers a, b, and c, if a b,
  then
• ac bc and ca cb
• 2218 1822

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• Solve the equation
• q 18 32
• -18 -18
• q 14

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SECTION 2-5
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SOLVE MULTI-STEP EQUATIONS
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Isolate the variable bya. Using the addition
propertyb. Using the
multiplication property
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• SOLVE 4x 3 15

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• SOLVE 4(x 2) 3

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• SOLVE -3(d 5) 18

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SECTION 2-6
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SOLVE LINEAR INEQUALITIES
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• ADDITION PROPERTY OF INEQUALITY
• For all real numbers a, b, and c, if a lt b,
  then
• a c lt b c
• if a gt b, then
• a c gt c b

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• MULTIPLICATION PROPERTY OF INEQUALITY
• For real numbers a, b, and positive number c,
  if a gt b then ac gt bc and ca gt cb or if a ltb,
  then
• ac lt bc and ca lt cb

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• MULTIPLICATION PROPERTY OF INEQUALITY
• For all real numbers a, b, and when c is
  negative,
• if a gt b, then
• ac lt bc and ca lt cb
• or if a lt b, then
• ac gt bc and ca gt cb

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EXAMPLE

• If a 70, b 50, and c 10 then
• a c gt b c or
• 70 10 gt 50 10
• 80 gt 60

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EXAMPLE

• If a 2, b 5, and c -10 then
• 2 lt 5
• 2(-10) gt 5(-10)
• -20 gt -50

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REMEMBER

• When you multiply or divide both sides of an
  inequality by a negative number REVERSE the sign.

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SOLVING INEQUALITIES

• Example
• 3x 10 lt 4

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SOLVING INEQUALITIES

• Example
• 23 8 - 5y

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• Half-Plane a graph of a solution of a linear
  inequality in two variables

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• Boundary the edge of the half-plane

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• Open Half-Plane does not include the boundary
  as part of the solution

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• Closed Half-Plane does include the boundary as
  part of the solution

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GRAPHING INEQUALITIES
x y 4 (0,4),(4,0)
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SECTION 2-7
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DATA AND MEASURES OF CENTRAL TENDENCY
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• POPULATION entire group or collections of things

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• SAMPLE
• a representative part of the population

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• FREQUENCY TABLE a common way to organize data

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MEASURES OF CENTRAL TENDENCY

• MEAN is the sum of the data divided by the
  number of data
• MEDIAN is the middle value of the data

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• MODE is the number that occurs most in the set
  of data
• RANGE is the difference between the highest and
  lowest values of the data

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SECTION 2-8
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DISPLAY DATA
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• STEM-AND-LEAF PLOT is another way to organize
  data where the leaf is the rightmost digit of the
  number and the stem is the remaining digits.

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18, 19
20, 22,..
30, 32,
40,42,
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• OUTLIERS numbers that are much smaller or
  larger than the rest of the data
• CLUSTER a large grouping of data about
  particular values
• GAP spaces between clusters and outliers data

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• HISTOGRAM is a type of bar graph used to display
  data. The height of the bars of the graph are
  used to measure frequency. Histograms are used to
  display data that have been grouped into
  intervals.

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HISTOGRAM
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BOX-and-WHISKERS PLOT

• Another way to organize data by grouping the data
  into quartiles.

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DEFINITIONS

• QUARTILE is another way to organize data by
  grouping the data into four equal parts
• INTERQUARTILE RANGE is the difference between
  the first and third quartiles.

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DEFINITIONS

• WHISKERS lines drawn from the ends of the boxes
  to the least and greatest values.
• OUTLIERS data that are at least 1.5 times the
  interquartile range below the first quartile.

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50 55 60 65 70
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THE END