Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
Math 123
PracticeExam
Name_
Youmustshowworkforcredit.
Converttheunits.
1) 966 mm =
cm
1)
A) 96,600cm
2) 12yd=
B) 9.7cm
C) 96.6 cm
D) 9660cm
ft
2)
A) 36
B) 432
C) 108
D) 144
Choosethemostreasonableunitofmeasure.
3) Hammerlength: 36
(mm,cm,m,km)
A) km
3)
B)
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
Math 123
Practice Exam II
Name_
The actual exam will be 21  26 questions.
Find the measure of the dihedral angle indicated.
1) The figure shown is a right prism whose bases are regular octagons. Find the measure of the
dihedral angle between adjacent lat
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
Math 123
Practice Exam I
Name:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine the number of outcomes as requested.
1) Two 6 sided dice are thrown. Determine the number of ways that a score
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
91
How Probabilities are Determined
Determining Probabilities
Mutually Exclusive Events
Complementary Events
NonMutually Exclusive Events
Experiment:
an activity whose results can be observed and recorded.
Outcome:
each of the possible results of an exp
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
101 Displaying Data: Part I
Statistics is a branch of mathematics that deals with the collection and
summarization of data. Visual illustrations are an important part of
statistics.
Illustrations or graphs can take the following forms:
Pictographs
Circle
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
102: Displaying Data Part II
Line Graphs
A line graph typically shows trends in a variable over time. Usually the
horizontal axis represents time; whereas, the vertical axis represents the
variable being considered. The following graph shows the weight o
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
95 Using Permutations and Combinations in Probability
Permutations of Unlike Objects
Permutation:
an arrangement of things in a definite order with no repetitions
Fundamental Counting Principle: If an event M can occur in m ways and, after
M has occurred
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
94 Odds, Conditional Probability, and Expected Value
Computing Odds
Let P(A) be the probability that A occurs and P ( A) be the probability that A does
not occur. Then the odds in favor of an event A are
P ( A)
P( A)
, or
P ( A)
1 P ( A)
and the odds ag
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
92 Multistage Experiments with Tree Diagrams and Geometric
Probabilities
Tree diagrams
Suppose the spinner is spun twice. The tree diagram shows the
possible outcomes.
Multiplication Rule for Probabilities for Tree Diagrams
For all multistage experiments
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
93 Using Simulations in Probability
Random Digits Table
Example 1
A baseball player has a batting average of 0.400; that is, his probability of getting
a hit on any particular time at bat is 0.400. Estimate the probability that he will get
at least one h
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
103 Measures of Central Tendency and Variation
So far, we have discussed some graphical methods of data description. Now, we
will investigate how statements of central tendency and variation can be used.
Statements of central tendency are nothing more th
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
104 Abuses of Statistics
Then there was a man who drowned crossing a stream with an average
depth of six inches.
W. I. E. Gates
There are three kinds of lies: lies, damned lies, and statistics.
Benjamin Disraeli
We are constantly bombarded in our everyda
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
115 Networks
Knigsberg Bridge Problem
Is it possible to walk across all the bridges so the each bridge is crossed exactly
once on the same walk?
The solution is represented as a network.
Vertices the points in a network
Arcs the curves in a network
Trave
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
121 Congruence Through Constructions
Congruence vs. Similarity
Definition
Congruent Segments and Angles
Geometric Constructions
Constructing a circle given its radius
Circles
An arc of a circle is any part of the circle that can be drawn without lifting
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
114 Geometry in Three Dimensions
Simple Closed Surfaces: surfaces with exactly one interior, no holes, and hollow
These two figures are not simple, closed surfaces.
Sphere the set of all points at a given distance from a given point (the center)
Solid th
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
Section 11.3 More About Angles
Vertical Angles
Vertical angles created by intersecting lines
area pair of angles whose sides are two pairs
of opposite rays.
Angles 1 and 3 are vertical angles.
Angles 2 and 4 are vertical angles.
Vertical angles are congru
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
111 Basic Notions
Undefined terms: points, lines, and planes
Lines
A line has no thickness and it extends forever in two directions.
Given two points, there is one and only one line that connects these points.
If P and Q are any two points, we can cre
Statistical & Geometrical Concepts For Elementary School Teachers
MATH 123

Fall 2010
112 Polygons
Curves and Polygons
Simple curve a curve that does not cross itself; starting and stopping points may
be the same.
Closed curve a curve that starts and stops at the same point.
Polygon a simple, closed curve with sides that are line segments