AL 125 MATHEMATICS
Concordia University Wisconsin
STUDENT MODULE
revised by Carolyn L. Meitler, Ph.D.
Professor Emeritus
Department of Mathematics
School of Adult Education
May 2004
Revised January 2005
revised for the Second Edition of the textbook
and other minor editing
by Mike Weidner
September 2006
Kimberly Nelson
May 1, 2012
(Update to non-edition specific 6 wk module)
revised for minor editing by
Jim Akers
November 1, 2013
Concordia University is a Lutheran higher education community dedicated to helping students develop in
mind, body, and spirit for service to Christ in the Church and the world.
AL125 EL
MATHEMATICS
This course studies problem solving, applications of functions, growth, geometry,
patterns, financial mathematics, street networks, probability, descriptive statistics, and
linear regression. Skills of high school algebra and geometry is required. Prerequisite:
Prerequisite: AL 122, AL 096, or equivalent, or acceptable assessment score.3 credit
hours.
AL125 Mathematics meets the mathematics requirement in the standard core
curriculum of the School of Adult Education.
CUW Disability Policy
In accordance with the Americans and Disabilities Act (ADA) and Section 504 of the Vocational
Rehabilitation Act of 1973, individuals with disabilities are protected from discrimination and assured
services and accommodations that provide equal access to the activities and programs of the university.
Students with a documented disability who require accommodation in order to obtain equal access to this
course should inform the instructor, and must also contact Disability Support Services at (262) 243-2623
or https://www.cuw.edu/Departments/lrc/dss.html
CUW Academic Integrity Policy
CUW expects all students to display honest, ethical behavior at all times and under all circumstances.
Academic dishonesty is defined as follows:
a.
Cheating: includes, but is not limited to: a) the use of unauthorized assistance in taking any type
of test or completing any type of classroom assignment; b) assisting another student in cheating
on a test or class assignment, including impersonation of another student.
b. Plagiarism: includes, but is not limited to: a) failure to give full and clear acknowledgement of
the source of any idea that is not your own; b) handing in the same assignment for two different
courses without the consent of the instructors.
c.
Fabrication: the forgery, alteration, or misuse of any University academic document, record, or
instrument of identification.
d. Academic Misconduct: intentionally or recklessly interfering with teaching, research, and/or
other academic functions.
For more information on academic honesty, please see:
https://www.cuw.edu/Departments/residencelife/assets/studentconductcode.pdf
2
Adult Education Program Policies
Registration Deadline
Students must to be registered and ready to begin the course at a minimum seven calendar days before the
first face to face classroom session.
Course Format
The accelerated course format for all adult education courses is one four-hour face-to-face class meeting
one night per week for six weeks (24 hours total), usually from 6:00pm to 10:00pm, though courses may
also be scheduled during the day or on Saturday. Students also participate in online discussion for an
additional two hours per week prior to each of the six class meetings (12 hours total). These two
elements, face-to-face meetings and online discussions, comprise the 36 hours of instructor-student
contact for each course. In addition, students are also expected to spend an additional 16-18 hours prior
to each of the six class meetings (96-108 hours total) working independently on homework assignments.
The total number of hours of instructor-student contact and independent work hours totals 132- 144 hours
for this three-credit course, though some students may take more time to complete their independent
work.
Online Work
The course begins seven days prior to the first classroom session, and includes a minimum of two hours
of online work prior to each session. The online work related to each session is to be completed prior to
the face to face classroom session. Students should not delay in reading the discussion questions in the
learning management system, so they can formulate a post in response to the question several days prior
to the first face-to-face session. Each student will then develop a reply to two other students’ initial posts.
Learning Management System
All online work must be submitted through the Learning Management System (Angel).
Adult Education Written Assignment Format
All papers are to be prepared in a word processing program according to the Adult Education Written
Assignment Format.
3
Grading Scale
93-100= A
90-92= A88/89= B+
83-87= B
80-82= B78/79= C+
73-77= C
70-72= C68/69= D+
63-67= D
60-62= D59 and below= F
AL125 Mathematics
This course studies problem solving, applications of functions, growth, geometry, patterns,
financial mathematics, street networks, probability, descriptive statistics, and linear regression.
Prerequisite: AL122, AL096, or equivalent, or acceptable assessment score. 3 credit hours.
University-wide Student Learning Outcomes and Core Student Learning Outcomes
In support of Concordia’s mission, this course fulfills the University-Wide Student
Learning Outcomes related to Liberal Arts, Disciplinary Thinking, and Global Citizenship. In
addition, the following learning outcomes are addressed:
A. Concordia’s Statement of Purpose provides that programs of study are “designed to
develop the professional competencies and commitment required for responsible
participation and leadership in a complex society.”
4
B. Students gain respect for the complexity of mathematical problems and demonstrate a
working knowledge of the factors to consider in math to apply in future careers.
C. AL125 Mathematics meets the mathematics requirement in the standard core
curriculum of the School of Adult Education.
D. This course addresses the core curriculum goals of problem solving and numeracy
through the classroom assignments and discussions, and the final examination.
5
INTRODUCTION
This course studies problem solving, applications of functions, growth, geometry, patterns,
financial mathematics, street networks, probability, descriptive statistics, and linear regression.
Prerequisite: AL 122, AL 096, or equivalent, or acceptable assessment score. 3 credit hours.
UNIT I
PROBLEM SOLVING
One big idea in mathematics is using mathematics to solve problems. There are many ways of
approaching and making sense of a problem, developing a strategy for solving the problem,
carrying out the solution process, and checking or reflecting on the answer. Units of measure are
very important in expressing the answer to a problem.
UNIT II
MATHEMATICS OF FUNCTIONS
A second big idea is function. A function can be represented as a table, an algebraic expression,
or a graph. Students will consider several particular examples of functions in various disciplines.
UNIT III
GEOMETRY
Geometry is not restricted to the postulate that two parallel lines never meet. Non-Euclidean
geometry includes geometry on a sphere where there are no parallel lines. Fractals, iterative
process, self-similarity and similarity dimension are all part of our daily life, as are the more
familiar areas of geometry.
UNIT IV
THE MATHEMATICS OF GRAPHS
Students may be familiar with the graph of a line or a bar graph. There are other types of graphs
that can be used to determine how to construct efficient computer networks, design routes to
remove snow from city streets, and deliver mail in an optimal way.
6
UNIT V
THE MATHEMATICS OF FINANCE
Financial calculations are part of an almost daily experience. Discounts on merchandise, sales
tax added to a purchase, interest charged on a credit card, car payments, and mortgages are just
some of the instances where a knowledge of how these calculations are performed provide us
with the ability to be informed consumers.
UNIT VI
PROBABILITY AND STATISTICS
Probability and statistics permeates everyday life in ways we may not realize. The concepts are
used daily in all media venues. Understanding these concepts is vital to making informed
decisions, whether in career, spending, voting, or time management.
Module Objectives:
A. Concepts, principles, and understandings.
As a result of this course, students;
1.
Recall basic ideas of problem solving.
2.
Recall and expand ideas of functions and graphing.
3.
Develop concepts of circuits and paths.
4.
Examine concepts of non-Euclidean geometry, fractals, iterative process and selfsimilarity.
5.
Develop knowledge and appreciation of investing and borrowing money.
6.
Examine basic concepts of probability and counting principles.
7.
Appreciate measures of central tendency, dispersion, relative position for sets of
data, regression and correlation.
8.
Assess the Normal Probability Distribution.
7
B. Attitudes, interests and appreciations.
The students also:
1. identify the use of data in making decisions.
2. examine the use of mathematics in solving linear and quadratic functions.
3. appreciate the use of non-Euclidean geometry in real-life situations.
4. develop a critical attitude in statistics and probability.
5. develop an appreciation for financial knowledge and computation.
C. Habits, conduct, and skills.
Furthermore, students:
1. develop an ability to collect, organize, present, summarize and interpret data.
2. develop skills in operating the graphing calculator to perform linear and quadratic
functions and their graphs.
3. develop skills in operating the graphing calculator to solve interest, loans, and
financial planning problems.
4. develop skills in finding circuits and paths.
5. develop skills in operating the graphing calculator to perform statistical tests.
6. develop skills in finding patterns and expressing them using recursive functions.
Resources
A. Textbook(s)
Aufmann, Richard, Joanne Lockwood, Richard Nation, Dan Clegg. Mathematical
Excursions, Second Edition. Boston: Houghton Mifflin, 2007.
A TI-83 Plus calculator equivalent is recommended for this course.
8
B. Websites
http://college.hmco.com/mathematics/aufmann/excursions/2e/student_home.html
The student homepage to accompany the text. Find current news stories with
underlying mathematical concepts and links to other useful resources.
http://college.hmco.com/mathematics/aufmann/excursions/2e/resources.html
Algebra review
http://college.hmco.com/mathematics/aufmann/excursions/2e/assets/keyguide.pdf
Graphing Calculator guide. Includes keystrokes for the TI-83 Plus graphing
calculator.
http://www.barna.org/
The Barna Group publishes articles on faith in America based on statistical survey
research. This site may be helpful in selecting an article for review during the last
session.
http://www.freemathhelp.com/
Lessons, tutoring, and a message board.
C. Books
Jones, Morgan D. The Thinker's Toolkit: 14 Powerful Techniques for Problem
Solving . New York: Three Rivers Press, 1998.
Kahane, Adam. Solving Tough Problems: An Open Way of Talking, Listening, and
Creating New Realities . San Francisco: Berrett-Koehler Publishers, Inc., 2004.
White, Jonathon S. Basic Math and Pre-Algebra. New York: Wiley, c2003
9
RECOMMENDED EVALUATION PROCEDURES
All written work must be handwritten including the Unit, page number, name and problems in the top
right corner.
Review and Application Questions: The student will prepare written answers to selected review and
application questions from the chapters as discussed in each section. The student’s work, ideas, and
questions are important and should be included.
Quizzes will focus on material covered in each session.
Student Classroom Contribution occurs during each session. This grade is based on the quality of
contributions gleaned from the readings, problems, and participation in in-class activities and exercises.
Students should come to class prepared to contribute to classroom discussion with insights and
understandings from the assigned problems, and be prepared to participate in interactive classroom
experiences.
Online Discussions are an integral aspect of this course. Grading is based on whether students complete
the required number of posts as well as the contributions made to others posts in a thoughtful and timely
manner.
10
UNIT I
PROBLEM SOLVING
One big idea in mathematics is using mathematics to solve problems. There are many ways of
approaching and making sense of a problem, developing a strategy for solving the problem, carrying
out the solution process, and checking or reflecting on the answer. Units of measure are very important
in expressing the answer to a problem.
Learning Objectives for Session I:
As a result of this session, the student will:
1. Define Inductive and Deductive Reasoning.
2. Use Inductive and Deductive Reasoning to solve an application.
3. Determine whether a statement is an example of inductive or deductive reasoning.
4. Define the terms of a sequence.
5. Construct a difference table given a sequence.
6. Define and discuss the Fibonacci Sequence.
7. Explain Polya’s Problem-Solving Strategy.
8. Apply Polya’s Strategy in a mathematical application.
9. Use the rectangular coordinate system to plot points.
10. Solve and graph an equation in two variables.
11. Define a function.
12. Apply the definition of a function to evaluate and graph a linear function.
13. Define the x- and y-intercepts of a graph.
14. Determine the slope of a line between two points.
15. Apply the slope and intercepts of a function to solve real life problems.
11
Assignments To Be Completed Prior to Session I:
1. Read the following sections in the text: 1.1, 1.2, 1.3, 6.1, and 6.2.
2. Login to the online course management system and respond to the discussion questions 1.1 and 1.2.
Discussion questions will be reflective of the assigned readings and learning objectives for this unit.
Be prepared to spend two hours on this portion of the units work.
3. Review and Application Questions: Prepare neatly handwritten answers to the questions below and
be prepared to discuss your answers in class as well as submit them for review and evaluation by
your instructor.
1. Use inductive reasoning to predict the most probable next number in each list:
a. 4, 8, 12, 16, 20, 24, ?
b. 3, 5, 9, 15, 23, 33, ?
c. 1, 4, 9, 16, 25, 36, 49, ?
2. Use inductive reasoning to decide whether the conclusion for each argument is
correct.
a. The product of an odd integer and an even integer is always an even number.
b. Pick any counting number. Multiply the number by 6. Add 8 to the product.
Divide the sum by 2. Subtract 4 from the quotient. The resulting number is twice
the original number.
3. Determine whether the argument is an example of inductive reasoning or deductive
reasoning.
a. Andrea enjoyed reading the Dark Tower series by Stephen King, so I know
she will like his next novel.
b. Every English setter likes to hunt. Duke is and English Setter, so Duke likes
to hunt.
12
4. Find a counterexample to show that the statement is FALSE.
a. x 
1
x
b. x + x > x
c. –x < x
5. Construct a difference table to predict the next term of each sequence.
a. 1, 7, 17, 31, 49, 71, …
b. -1, 4, 21, 56, 115, 204, …
6. Use the given nth term formula to compute the first five terms of the sequence.
a. an 
n(2n  1)
2
b. an  5n 2  3n
7. Pieces vs. Cuts. One cut of a stick of licorice produces two pieces. Two cuts
produce three pieces. Three cuts produce four pieces.
a. How many pieces are produced by five cuts and by six cuts?
b. Predict the nth term formula for the number of pieces of licorice that are
produced by n cuts.
8. Fibonacci Properties. The Fibonacci sequence has many unusual properties.
Experiment to decide which of the following properties are valid.
a. 3Fn  Fn2  Fn 2
for n  3
b. 5Fn  2Fn2  Fn3 for n  3
13
9.
Number of Girls. There are 364 first-grade students in Park Elementary School.
If there are 26 more girls than boys, how many girls are there?
10.
What is the 44th decimal digit in the decimal representation of
11.
Cost of a Shirt. A shirt and a tie together cost $50. The shirt costs $30 more than
the tie. What is the cost of the shirt?
12.
True-False Test. In how many ways can you answer a 12-question true-false test
if you answer each question with either a “true” or a “false”?
13.
Change for a quarter. How many ways can you make change for 25cents using
dimes, nickels, and/or pennies?
14.
Determine the units digit of 47022 .
15.
Graph the ordered pairs on graph paper: (0,-1), (2,0),(3,2), and (-1,4)
16.
Draw a line through all points with a y-coordinate of -3.
17.
Graph the ordered-pair solutions of y  x  1 when x = -5, -3, 0, 3, and 5.
18.
Graph the ordered-pair solutions of y  x3  2 when x = -1, 0, 1.
19.
Graph each equation:
a. y 
14
2
x 1
3
1
?
11
b. y  2 x 2  1
20.
Evaluate the function for each given value:
b. v(s)= s3  3s 2  4s; s  2
a. f(x)=2x + 7; x = -2
21.
Graph the function:
a. f(x) = 2x -5
b. g(x) =
2
x2
3
c. f(x)= x 2  1
22. Find the x- and y-intercepts of the graph of the equation.
23.
a. f(x) = 3x – 6
b. y =  x – 4
c. 2x - 3y = 9
d. x 
y
1
2
Find the slope of the line containing the two points.
a. (-1, 4), (2, 5)
b. (0, 3), (4, 0)
c. ( 2, 5), (-3, -2)
d. (0, 4), (-2, 5)
4. Complete the Unit Quiz. Quiz will cover material 1.1, 1.2, 1.3, 6.1, and 6.2
15
UNIT II
MATHEMATICS OF FUNCTIONS
A second big idea is function. A function can be represented as a table, an algebraic expression, or a
graph. Students will consider several particular examples of functions in various disciplines.
Learning Objectives for Session II:
1. List the properties of a quadratic function.
2. Define the vertex of a parabola.
3. Identify the x-intercepts of a parabola.
4. Describe the minimum of a Quadratic Function.
5. Describe the maximum of a Quadratic Function.
6. Solve applications of Quadratic Function.
7. Define Exponential Functions and their properties.
8. Evaluate Exponential Functions.
9. Graph Exponential Functions.
10. Define the Natural Exponential Function.
11. Graph the Natural Exponential Function.
Assignments to Be Completed Prior to Session II:
1. Read the following sections in the text: 6.4, 6.5.
2. Login to the online course management system and respond to the discussion questions 2.1 and 2.2.
Discussion questions will be reflective of the assigned readings and learning objectives for this unit.
Be prepared to spend two hours on this portion of the units work.
3. Review and Application Questions: Prepare neatly handwritten answers to the questions below and
be prepared to discuss your answers in class as well as submit them for review and evaluation by
your instructor.
16
1. Find the vertex of the graph of the equation:
a. y  x 2  2
b. y  
1 2
x 2
2
c. y  x 2  x  2
2. Find the x-intercepts of the parabola given by the equation:
a. y  2 x 2  4 x
b. y  x 2  2 x  1
3. Find the minimum or maximum value of the quadratic function. State whether the value is a
minimum or a maximum.
a. f ( x)  x 2  2 x  3
b. f ( x)  x 2  5 x  3
c. f ( x)   x 2  x  2
4. The graph of which of the following equations is a parabola with the larger minimum value?
y  x2  2x  3
y  x 2  10 x  20
y  3x 2  1
5. Manufacturing. A manufacturer of camera lenses estimates that the average monthly cost C of
producing camera lenses is given by the function:
C ( x)  0.1x 2  20 x  2000
where x is the number of lenses produced each month. Find the number of lenses the company
should produce to minimize the average cost.
17
6. Fuel Efficiency. The fuel efficiency of an average car is given by the equation:
E v   0.018v 2  1.476  3.4,
E0
Where E is the fuel efficiency in miles per gallon and v is the speed of the car in miles per hour.
a. What speed will yield the maximum fuel efficiency?
b. What is the maximum fuel efficiency?
7. Given f ( x)  3x , evaluate:
a. f(2)
b. f(0)
c. f(-2)
1
2
8. Given G ( r )  ( ) 2 r , evaluate:
3
2
b. G ( )
a. G(0)
c. G(-2)
9. Given H ( x)  e x 3 , evaluate the following.
Round to the nearest ten-thousandths.
a. H(-1)
b. H(3)
10. Given f ( x )  e
a. f(-2)
 x2
2
c. H(5)
, evaluate the following. Round to the nearest ten-thousandths.
b. f(2)
c. f(-3)
11. Graph each function:
x
a. g ( x)  32
b. f ( x)  2 x 3
18
r
n
Investments. In the following exercises use the compound interest formula A  P (1  ) nt , where P
is the amount deposited. A is the value of the money after t years, r is the annual interest rate as a
decimal, and n is the number of compounding periods per year.
12. A computer network specialist deposits $2500 into a retirement account that earns 7.5% annual
interest, compounded daily. What is the value of the investment after 20 years?
13. A $10,000 certificate of deposit (CD) earns 5% annual interest, compounded daily. What is the
value of the investment after 20 years?
14. Isotopes. Iodine-131 is an isotope that is used to study the functioning of the thyroid gland. This
isotope has a half-life(time required for half the material to erode) of approximately 8 days. If a patient
is given an injection that contains 8 micrograms of iodine-131, what will be the iodine level in the
1
2
t
patient after 5 days? Use the function A(t )  8( ) 8 , where A is the amount of the isotope, in
micrograms, in the patient after t days. Round to the nearest tenth.
4. Complete the Unit Quiz. Quiz will cover material 6.4, 6.5.
19
UNIT III
GEOMETRY
Geometry is not restricted to the postulate that two parallel lines never meet. Non-Euclidean geometry
includes geometry on a sphere where there are no parallel lines. Fractals, iterative process, selfsimilarity and similarity dimension are all part of our daily life, as are the more familiar areas of
geometry.
Learning Objectives for Session III:
1. Define Euclidean Geometry.
2. Define Non-Euclidean Geometry.
3. Apply Euclid’s Postulates.
4. Discuss the meaning of The Parallel Postulate.
5. Describe Gauss’s and Riemann’s Alternative to the Parallel Postulate.
6. Define a Geodesic.
7. Define a Great Circle.
8. Apply the Spherical Triangle Area Formula.
9. Solve Applications with the City distance Formula.
10. Solve Applications with the Euclidean Distance Formula.
11. Define a Fractal.
12. Construct a Fractal given the initiator and generator of the Fractal.
13. Draw the stages of a Fractal.
14. Interpret the Replacement Ratio and Scaling Ratio of a Fractal.
15. Define Self-Similarity.
20
Assignments to Be Completed Prior to Session III:
1. Read the following sections in the text: 8.6, 8.7.
2. Login to the online course management system and respond to the discussion questions 3.1 and 3.2.
Discussion questions will be reflective of the assigned readings and learning objectives for this unit.
Be prepared to spend two hours on this portion of the units work.
3. Review and Application Questions: Prepare neatly handwritten answers to the questions below and
be prepared to discuss your answers in class as well as submit them for review and evaluation by
your instructor.
1. State the parallel postulate for each of the following:
a. Eulidean Geometry.
b. Lobachevskian geometry.
c. Riemannian geometry.
2. Name the mathematician who was the first to consider a geometry in which Euclid’s Parallel
Postulate was replaced with “Through a given point not on a given line, there are at least two lines
parallel to the given line.”
3. What can be stated about the sum of the measures of the angles of a triangle in:
a. Euclidean Geometry?
b. Lobachevskian geometry?
c. Riemannian geometry?
4. What name did Lobachevsky give to the geometry he created?
5. What is a geodesic?
21
6. What model was used in this text to illustrate hyperbolic geometry?
7. Find the exact area of a spherical triangle with angles of 150o ,120o , and 90o on a sphere with a
radius of 1.
City Geometry. Find the Euclidean distance between the points and the city distance between the
points. Assume that both d E ( P, Q) and dC ( P, Q) are measured in blocks. Round approximate
results to the nearest tenth of a block.
8. P(-3,1), Q(4,1)
9. P(2,-3), Q(-3,5)
10. P(-1,4), Q(5,-2)
11. Use an iterative process to draw Stage 2 and Stage 3 of the fractal with the given initiator(stage 0)
and the given generator(stage 1).
________________________________________
Stage 0
_______________
_________________
Stage 1
12..Research using your text or a computer the iterative process to draw Stage 0, Stage 1, and Stage 2 of
the given fractal. Then compute, if possible, the similarity dimension of the fractal.
a. The Sierpinski carpet.
b. The river tree of Peano Cearo
4. Complete the Unit Quiz. Quiz will cover material 8.6, 8.7.
22
c. The square fractal
UNIT IV
THE MATHEMATICS OF GRAPHS
Students may be familiar with the graph of a line or a bar graph. There are other types of graphs that
can be used to determine how to construct efficient computer networks, design routes to remove snow
from city streets, and deliver mail in an optimal way.
Learning Objectives for Session IV:
1. Define Graph Theory.
2. Explain Equivalent Graphs.
3. Define the properties of a Euler Graph.
4. Describe the Eulerian Graph Theorem.
5. Apply the Euler Walk Theorem to solve problems.
6. Define the properties of Hamiltonian Circuits.
7. Discuss Dirac’s Theorem.
8. Find Hamiltonian Circuits in a Weighted Graph.
9. Apply The Greedy Algorithm.
10. Apply The Edge-Picking Algorithm.
11. Define Planarity in graph theory.
12. Define Nonplanar Graph Theorem.
13. Describe “faces” and “vertices” in Euler’s Formula.
14. Analyze Graph Theory to color a map.
15. Represent a Map as a Graph.
16. Determine the Chromatic Number of a Graph.
23
Assignments To Be Completed Prior To Session IV:
1. Read the following sections in the text: 9.1, 9.2, 9.3, 9.4.
2. Log into the online course management system and respond to the discussion questions 4.1 and 4.2.
Discussion questions will be reflective of the assigned readings and learning objectives for this unit.
Be prepared to spend two hours on this portion of the units work.
3. Review and Application Questions: Prepare neatly handwritten answers to the questions below and
be prepared to discuss your answers in class as well as submit them for review and evaluation by
your instructor.
Exercise set 9.1
Pg. 583-587 # 3, 5, 9, 13, 21, 27, 33, 35
Exercise set 9.2
Pg. 601-604 # 1, 3, 5, 7, 9, 11, 21, 23
Exercise set 9.3
Pg. 615-617 # 1, 3, 5, 7, 17, 23
Exercise set 9.4
Pg. 628-630 # 1, 5, 11, 15, 17, 23
4. Complete the Unit Quiz. Quiz will cover material 9.1, 9.2, 9.3, 9.4.
24
UNIT V
THE MATHEMATICS OF FINANCE
Financial calculations are part of an almost daily experience. Discounts on merchandise, sales tax
added to a purchase, interest charged on a credit card, car payments, and mortgages are just some of the
instances where a knowledge of how these calculations are performed provide us with the ability to be
informed consumers.
Learning Objectives for Session V:
1. Define Simple Interest.
2. Compute problems with the Simple Interest Formula.
3. Define Future Value and Maturity Value.
4. Calculate a Maturity Value.
5. Calculate the Future Value.
6. Define Compound Interest.
7. Solve applications using the Compound Amount Formula.
8. Calculate the Compound Amount using a scientific calculator.
9. Define Present Value.
10. Solve applications using the Present Value Formula.
11. Calculate Present Value using a scientific calculator.
12. Define Inflation.
13. Calculate the Effect of Inflation on Salary.
14. Calculate the Effect of Inflation on Future Purchasing Power.
15. Define Effective Interest Rate.
16. Calculate the Effective Interest Rate.
17. Calculate Interest on a Credit Card.
18. Calculate a Finance Charge and an APR.
19. Calculate a Monthly Payment on a Consumer Loan.
20. Calculate Loan Payoffs on a Consumer Loan.
21. Define a Mutual Fund.
22. Calculate the Net Asset Value of, and the Number of, Shares Purchased in a Mutual Fund.
25
Assignments To Be Completed Prior To Session V:
1.
Read the following sections in the text: 10.1, 10.2, 10.3, 10.4.
2.
Login to the online course management system and respond to the discussion questions 5.1 and
5.2. Discussion questions will be reflective of the assigned readings and learning objectives for this
unit. Be prepared to spend two hours on this portion of the units work.
3.
Review and Application Questions: Prepare neatly handwritten answers to the questions below
and be prepared to discuss your answers in class as well as submit them for review and evaluation
by your instructor.
1. Simple Interest. You deposit $1500 in an account earning 10.4% interest.
interest earned in 6 months.
Calculate the simple
2. Maturity Value. Calculate the maturity value of a simple interest, eight-month loan of $7000 if the
interest rate is 8.7%.
3. Future Value. You deposit $750 in an account paying 7.3% simple interest. Find the future value
of the investment after 1 year.
4. Calculate the compound amount. Use the compound amount formula and a calculator:
a. P = $1200, r = 7% compounded semiannually, t = 12 years.
b. P = $8500, r = 9% compounded monthly, t = 10 years.
5. Calculate the compound amount. Use a calculator with a finance mode.
a. P = $1600, r = 8% compounded quarterly, t = 10 years.
b. P = $1700, r = 9% compounded semiannually, t = 3 years.
26
6. Calculate the future value.
a. P = $4600, r = 9.5% compounded semiannually, t = 12 years.
7. Calculate the present value.
a. P = $25,000, r = 10% compounded quarterly, t = 12 years.
b. P = $15,000, r = 8% compounded quarterly, t = 5 years.
8. Compound Amount. If you leave $2500 in an account earning 9% interest,
compounded daily, how much money will be in the account after 4 years?
9. Compound Interest. How much interest is earned in 5 years on $8500 deposited in an account
paying 9% interest, compounded semiannually?
10. Future Value. $15,000 is deposited for 4 years in an account earning 8% interest.
a. Calculate the future value of the investment if interest is compounded semiannually.
b. Calculate the future value if interest is compounded quarterly.
c. How much greater is the future value of the investment when the interest is compounded
quarterly?
11. Loans. To help pay your college expenses, you borrow $7000 and agree to repay the loan at the
end of 5 years at 8% interest, compounded quarterly.
a. What is the maturity value of the loan?
b. How much interest are you paying on the loan?
27
12. Present Value. You want to retire in 30 years with $1,000,000 in investments.
a. How much money would you have to invest today at 9% interest, compounded daily, in
order to have $1,000,000 in 30 years?
b. How much will the $1,000,000 generate in interest each year if it is invested at 9% interest,
compounded daily?
13. Inflation. The average monthly rent for three bedroom apartment in San Luis Obispo, California,
is $1686. Using an annual inflation rate of 7%, find the average monthly rent in 15 years.
14. Calculate the effective annual rate for an investment that earns the given rate of return. Round to
the nearest hundredth of a percent.
a. 7.2% interest compounded quarterly.
b. 8.1% interest compounded daily.
15. You are given the 2004 price of an item. Use an inflation rate of 6% to calculate its price in 2009,
2014, 2024. Round to the nearest tenth.
a. Gasoline: $2.00 per gallon
b. Ticket to a movie: $9
16. Calculate the purchasing power using an annual inflation rate of 7%. Round to the nearest cent.
a. $50,000 in 10 years.
b. $75,000 in 5 years.
17. Effective Interest Rate. Blake Hamilton has money in a savings account that earns an annual
interest rate on 3%, compounded monthly. What is the effective rate of interest on Blake’s
savings? Round to the nearest hundredth of a percent.
18. Annual Yield. One bank advertises an interest rate of 5.8%, compounded quarterly, on a certificate
of deposit. Another bank advertises an interest rate of 5.6%, compounded monthly. Which
investment has a higher annual yield?
28
19. Calculate the finance charge for a credit card that has the given average daily balance of $118.72
and interest rate of 1.25%.
20. Finance Charges. On August 10th, a credit card account had a balance of $345. A purchase of $56
was made on August 15, and $157 was charged on August 27. A payment of $75 was made on
August 15. The interest on the average daily balance is 1.25% per month. Find the finance charge
on the September 10th bill.
21. Monthly Payments. Optics Mart offers a Meade ETX Astro Telescope for $1249, including taxes.
If you finance the purchase of this telescope for 2 years at an annual percentage rate of 7.2%, what
is the monthly payment?
22. Buying on Credit. Waterworld marina offers a motorboat with a mercury engine for $38,250. The
sales tax is 6.5% of the purchase price.
a. What is the total cost, including sales tax?
b. If you make a down payment of 20% of the total cost, find the down payment.
c. Assuming you finance the remaining cost at an annual interest rate of 5.7% for three years, find the
monthly payment.
23. Car Payments. Luis Mahla purchases a Porsche Boxster for $42,600 and finances the entire
amount at an annual interest rate of 5.7% for 5 years. Find the monthly payment. Assume the sales
tax is 6% of the purchase price and the license fee is 1% of the purchase price.
24. Loan Payoffs. Suppose you have a four-year car loan at an annual interest rate of 8.9% and a
monthly payment of $303.52. After 3 years, you decide to purchase a new car. What is the payoff
on your loan?
25. Mutual Funds. A mutual fund has $500 million worth of stock, $500,000 in cash, and $1 million
in other assets. The fund’s total liabilities amount to $2 million. There are 10 million shares
outstanding. You invest $12,000 in this fund. How many shares will you purchase?
4. Complete the Unit Quiz. Quiz will cover material 10.1, 10.2, 10.3, 10.4.
29
UNIT VI
PROBABILITY AND STATISTICS
Probability and statistics permeates everyday life in ways we may not realize. The concepts are
used daily in all media venues. Understanding these concepts is vital to making informed decisions,
whether in career, spending, voting, or time management.
Learning Objectives for Session VI:
1. Define Probability.
2. Discuss the Probability of an Event.
3. Define Empirical Probability.
4. Discuss the Empirical Probability of an Event.
5. Calculate the Odds of an Event.
6. Define the relationship between Odds and Probability.
7. Determine Probability from Odds.
8. Define Mean, Median, Mode, and the Weighted Mean.
9. Find the Mean of Data Displayed in a Frequency Distribution.
10. Define Range and Standard Deviation.
11. Compute Range and Standard Deviation.
12. Use a Scientific Calculator to find the Mean and Standard Deviation.
13. Discuss Properties of a Normal Distribution.
14. Use the Empirical Rule to Solve an Application.
Assignments to Be Completed Prior to Session VI:
1. Read the following sections in the text: 11.3, 12.1, 12.2, 12.3, 12.4.
2. Login to the online course management system and respond to the discussion questions 6.1
and 6.2. Discussion questions will be reflective of the assigned readings and learning
objectives for this unit. Be prepared to spend two hours on this portion of the units work.
30
3. Review and Application Questions: Prepare neatly handwritten answers to the questions
below and be prepared to discuss your answers in class as well as submit them for review and
evaluation by your instructor.
1. List the elements of the sample space defined by each experiment:
a. Select at random an even single-digit whole number between 1 and 11.
b. Select on day from the days of the week.
c. Toss a coin twice.
d. Roll a single die and then toss a coin.
e. Choose a complete dinner from a dinner menu that allows a customer to choose
from two salads, three entrees, and two desserts.
f.
Three letters addressed to A, B, and C are randomly placed in three envelopes
addressed to A, B, and C.
2. Use the counting principle to determine the number of elements in the sample
space:
a. Two digits are selected without replacement from the digits 1, 2, 3, and 4.
b. The possible ways to complete a multiple-choice test consisting of 20 questions,
with each question having four possible answers (a, b, c, or d).
c. The possible four-digit telephone number extensions that can be formed if 0, 8, and
9 are excluded as the first digit.
3. Find the mean, the median, and the mode(s), if any, for the given data.
Round noninteger means to the nearest tenth.
a. 2, 7, 5, 7, 14
b. 2.1, 4.6, 8.2, 3.4, 5.6, 8.0, 9.4, 12.2, 56.1, 78.2
c. -12, -8, -5, -5, -3, 0, 4, 9, 21
31
4. Course Grades. A professor grades students on three tests, four quizzes,
and a final examination. Each test counts as two quizzes and the final
examination cunts as two tests. Sara has test scores of 85, 75, and 90. Sara’s
quiz scores are 96, 88, 60, and 76. Her final examination score is 85. Use the
weighted mean formula to find Sara’s average for the course.
5. Meteorology. During a 24-hour period on January 23-24, 1916, the temperature in
Browning, Montana decreased from a high of 44 degrees Fahrenheit to a low of -56
degrees Fahrenheit. Find the midrange of the temperatures during this 24-hour
period.
6. The average rate for a trip is given by AverageRate 
totaldis tan ce
totaltime
If a person travels to a destination at an average rate of r1 miles per hour and returns
over the same route to the original starting point at an average rate of r2 miles per hour,
when show that the average rate for the round trip is r 
2r1r2
.
r1  r2
7. Find the range, the standard deviation, and the variance for the given samples.
Round noninteger results to the nearest tenth.
a. 2.1, 3.0, 1.9, 1.5, 4.8
b. 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4
c. -8, -5, -12, -1, 4, 7, 11
8. Heights of Students. Which would you expect to be the larger standard deviation:
the standard deviation of the weights of 25 students in a first-grade class, or the
standard deviation of the weights of 25 students in a college statistics course?
9. A data set has a mean of X  75 and a standard deviation of 11.5. Find the zscore for each of the following.
a. x = 85
b. x = 95
c. x = 50
d. x = 75
32
10. Blood Pressure. A blood pressure test was given to 450 women ages 20 to 36. It
showed that their mean systolic blood pressure was 119.4 mm Hg, with a standard
deviation of 13.2 mmHg.
a. Determine the z-score to the nearest hundredth, for a woman who had a systolic
blood pressure reading of 110.5 mmHg.
b. The z-score for one woman was 2.15. What was her systolic blood pressure
reading?
11. Reading Test. On a reading test, Shaylen’s score of 455 was higher than the
scores of 4256 of the 7210 students who took the test. Find the percentile, rounded
to the nearest percent, r Shaylen’s score.
12. Test Scores. Kevin scored at the 65th percentile on a test given to 9840 students.
How many students scored lower than Kevin?
Use the Empirical Rule to answer each question.
13. Shipping. During 1 week an overnight delivery company found that the weights of
its parcels were normally distributed, with a mean of 24 ounces and a standard
deviation of 6 ounces.
a. What percent of the parcels weighed between 12 ounces and 30 ounces?
b. What percent of the parcels weighed more than 42 ounces?
14. Traffic. A highway study of 8000 vehicles that passed by a checkpoint found that
their speeds were normally distributed, with a mean of 61 miles per hour and a
standard deviation of 7 miles per hour.
a. How many of the vehicles had a speed of more that 68 miles per hour?
b. How many of the vehicles had a speed of less than 40 miles per hour?
4. Prepare for the final exam. The final exam will cover all class material.
33