CHAPTER 2 SECTION 2-1 PATTERNS AND ITERATIONS SEQUENCE An arrangement of numbers in a particular...

CHAPTER 2

SECTION 2-1

PATTERNS AND ITERATIONS

SEQUENCE An arrangement of

numbers in a particular order. The numbers are

called terms and the pattern is formed by

applying a rule.

EXAMPLES OF SEQUENCES

0, 2, 4, 6, ___, ___, ___

1, 4, 9, 16, ___, ___,___

EXAMPLES OF SEQUENCES

2, 8, 14, 20, ___, ___, ___

1, -2, 4, -8, ___, ___,___

EXAMPLES OF SEQUENCES

4, 12, 20, 28, ___, ___, ___

2, 6, 18, 54, ___, ___,___

SECTION 2-2

THE COORDINATE THE COORDINATE PLANE, PLANE,

RELATIONS AND RELATIONS AND FUNCTIONSFUNCTIONS

COORDINATE PLANE Consists of two

perpendicular number lines, dividing the plane into four regions called

quadrants.

X-AXIS - the horizontal number line

Y -AXIS - the vertical number line

ORIGIN - the point where the

x-axis and y-axis cross

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)

RELATION – set of ordered pairs

DOMAIN – the set of all possible x-coordinates

RANGE – the set of all possible y-coordinates

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

FUNCTION – set of ordered pairs in which each element of the

domain is paired with exactly one element

in the range

SECTION 2-3

LINEAR FUNCTIONS

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

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

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, y=3, y= -3

SECTION 2-4

SOLVE ONE-STEP EQUATIONS

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

MULTIPLICATION PROPERTY OF

EQUALITY

For all real numbers a, b, and c, if a = b, then

ac = bc and ca = cb

22•18 = 18•22

Solve the equation

q + 18 = 32

-18 = -18

q = 14

SECTION 2-5

SOLVE MULTI-STEP EQUATIONS

Isolate the variable by:

a. Using the addition propertyb. Using the multiplication property

SOLVE: 4x + 3 = 15

SOLVE: 4(x – 2) = 3

SOLVE: -3(d – 5) = 18

SECTION 2-6

SOLVE LINEAR INEQUALITIES

ADDITION PROPERTY OF INEQUALITY

For all real numbers a, b, and c, if a < b, then

a + c < b + c

if a > b, then

a + c > c + b

MULTIPLICATION PROPERTY OF INEQUALITY

For real numbers a, b, and positive number c, if a > b then ac > bc and ca > cb

or if a <b, then

ac < bc and ca < cb

MULTIPLICATION PROPERTY OF INEQUALITY

For all real numbers a, b, and when c is negative,

if a > b, thenac < bc and ca < cb

or if a < b, thenac > bc and ca > cb

EXAMPLE

If a = 70, b = 50, and c = 10 then

a + c > b + c or

70 + 10 > 50 + 10

80 > 60

EXAMPLE

If a = 2, b = 5, and c = -10 then

2 < 5

2(-10) > 5(-10)

-20 > -50

REMEMBER

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

sign.

SOLVING INEQUALITIESExample

3x + 10 < 4

SOLVING INEQUALITIES

Example

23 ≥ 8 - 5y

Half-Plane – a graph of a solution of a linear inequality in two

variables

Boundary – the edge of the half-plane

Open Half-Plane – does not include the boundary

as part of the solution

Closed Half-Plane – does include the boundary as

part of the solution

GRAPHING INEQUALITIES

x + y ≥ 4

(0,4),(4,0)

SECTION 2-7

DATA AND MEASURES OF CENTRAL TENDENCY

POPULATION – entire group or collections

of things

SAMPLE a representative part

of the population

FREQUENCY TABLE – a common way to

organize data

MEASURES OF CENTRAL TENDENCY

MEAN – is the sum of the data divided by the number of dataMEDIAN – is the middle value of the data

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

SECTION 2-8

DISPLAY DATA

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.

18, 1920, 22,..30, 32,…40,42,…5666

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

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.

HISTOGRAM

0

10

20

30

40

50

60

70

80

90

1st Qtr 2nd Qtr 3rd Qtr 4th Qtr

East

West

North

BOX-and-WHISKERS PLOT

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

DEFINITIONS

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

DEFINITIONSWHISKERS – 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.

50 55 60 65 70

THE END