Sample Final Exam Solutions

The solutions to the sample final can be found at the link below.  Please alert me immediately if you believe there to be an error in the solutions.

Sample Final Solutions

Just a reminder. . .

If you are in MAT110:01 (9:00am), your final exam is on Friday, December 18 at 8:30 am.

If you are in MAT110:02 (10:00am), your final exam is on Monday, December 14 at 8:30 am.

You may bring 1 side (handwritten-by you) of a 3x5 notecard to be used on the final.

Final Blog Post - Due Wednesday, December 16

For your final blog post, write about what, if anything, from this class you believe you will remember 10 years from now.  Explain why you think that's what you will remember or why you won't remember anything.

Also, reflecting on this semester, explain how you plan to study for the final.  What has worked for previous exams and what will you do differently?

Finally, you may include any comments you have on how this class went this semester.

Have a great Christmas break!

Financial Math Review

Below is the review sheet we will be using in class for the Financial Math Review.  Please print it out and bring it with you to class on Wednesday, December 9.

Financial Math Final Exam Review

Probability and Statistics Review

Below are the links to the Probability and Statistics Review worksheets we will be using in class.


Probability Review

Statistics Review

Graph Theory Final Exam Review

The link below is the graph theory review worksheet we will be working on in class.  Please print the worksheet and bring it with you to class on Wednesday, December 2.

Final Exam Review - Graph Theory

Sample Final Exam

You can find a sample final exam at the link below.

Sample Final Exam

Financial Math Review Solutions

The solutions to the financial math review are posted below.

Financial Math Review Solutions

November 16 - 20: Financial Mathematics

This week we will be finishing up our unit on Financial Mathematics.  We will discuss paying ahead on your amortized loan payments on Monday.  Our exam over this unit will be on Friday and we will review on Wednesday.  Please make sure that you print off the review and work on it before class on Wednesday so that we can maximize our time together in class to make sure that all of your questions are answered before the exam.

For this week's blog, instead of doing the five fill-in-the-blanks, please choose one of the prompts below to write 5-6 paragraphs responding to the prompt.  The blog will be due by Sunday, November 29.

1. Research Adjustable Rate Mortgages (ARMS).  What is an ARM?  How can they vary?  Explain what is meant by a) the index; b) the margin; c) No-Doc/Low-Doc loans; d) interest rate caps; e) periodic adjustment caps; f) lifetime caps; g) payment caps; and h) types of ARMS.  Discuss several cautions related to ARMS.  How did ARMS contribute to the housing crisis?  The following site is a good resource: http://files.consumerfinance.gov/f/201204_CFPB_ARMs-brochure.pdf

2. Determine the average salary for someone in the career you hope to have after graduation.  Based on this salary, how expensive a house could you afford to purchase?  Locate 2 house listings in an area that you would like to live in using Zillow.com, trulia.com, or realtor.com.  For each of these houses, describe the listing and sale price, assume that you will make a 20% down payment, and locate a current loan rate for a 30 year mortgage.  How much would your monthly payment be for each house?  Create an amortization schedule for the first four months of payments for each house.  Using the mortgage calculator at bankrate.com, investigate ways that you could shorten the length of your mortgage by making additional monthly payments, yearly payments or one-time payments.  Report on your findings.

Financial Math Review

Remember our exam over the financial math section will be on Friday, November 20.  Please work the review below before class on Wednesday and be prepared to ask any questions that you have over the material.

Financial Math Review

Mid-Semester Survey

The evaluations below are anonymous.  You will be asked to log in to ensure that each user only fills out the survey once, but your log in information will not be recorded.  Please take a moment to follow the link and fill the evaluation out.


Mid-Semester Survey

Nov 2 - 6: Financial Mathematics

This week we will be continuing with financial mathematics.  We will start the week with consumer loans and finish off the week with annuities.  There are a lot of formulas to keep track of in this unit; I would recommend that you create a formula sheet for yourself to remind you of each one.

For your blog posts this week, in addition to answering the five fill-in-the-blanks, use the credit card calculator available at bankrate.com (full link below) to answer the following questions:
(1) Suppose you have a credit card balance of $5500 with a rate of 18% and a minimum payment of 4%.  If you make only the minimum payment, how long will it take for you to pay off the balance?  How much will you end up paying in interest?
(2) Suppose you use your credit card to purchase bedroom furniture at a total cost of $4395.  If your card has an annual rate of 16.9% and a minimum payment of 3%, determine how long it will take to pay off the balance for the bedroom furniture.  How much will you pay in interest?

Bankrate Credit Card Minimum Payment Calculator

Also, this week, please fill out the mid-semester evaluation, linked in the next blog post.  

Challenge Problem: Find a credit card application online.  Provide the link to your card.  Describe the application.  Your description you should include the answers to the following questions.  What interest rate(s) are they offering? Does the card offer any initial benefits, such as an introductory APR?  Does the card offer any rewards? If so, what are they?  What is the minimum payment required each month? Are there any fees associated with the card? Do you think the card is worth getting?
After finding all of this information, find a "big ticket" item that you would like to purchase.  (For example, a new TV.)  If you put this item on your credit card, use the minimum payment calculator t determine how long it would take to pay off the item if you made only the minimum payments.  How much would you end up paying in interest?

October 26 - 30: Financial Mathematics

This week we've started the unit on Financial Mathematics.  You will need your calculator every day for this unit, so be sure to bring it with you to class.  We will begin with simple interest and compound interest this week.  Next week we will talk about credit card loans, annuities, and other types of loans.

Midterm grades were posted this week.  Please be sure to check your midterm grade.  You can see the break down of your grade on Moodle.  If you have any questions about your grade, please see me in office hours.

Challenge Problem: Suppose you invest $1000 in an account earning a simple interest rate of 20%.  If you invest another $1000 into an account earning an interest rate of 5%, compounded quarterly, when will the two accounts reach the same balance?

October 19 - 23: Statistics

This week, we have finished our unit on Probability and Statistics.  Your exam will be on Friday, October 23.  This unit is generally the most difficult one for students; please make sure you allow adequate time to study for this exam!  Take advantage of the extra problems provided in the exam review and the Probability and Statistics Worksheets on the right hand of the blog.

For your blogs this week, please visit the site below.  This website provides many applets to model probability experiments.  Of particular interest to you may be the examples under "Finite Sampling Models", "Dice", and "Games of Chance".  Play with 2 or 3 of the applets and in your blog, describe the applets you chose.  How do they model the probability experiment? How could you actually find the probabilities being modeled?

Probability Applets

Challenge Problem: Research the Monty Hall problem and write a 2-3 paragraph summary of the problem, explaining how to determine whether you should switch doors or not.  Were you surprised by the probability in this problem? Be sure to give your references.

Probability and Statistics Review

Our probability and statistics exam will be in class on Friday, October, 23.  The link below is to the probability and statistics review worksheet.  Please try all of these problems and be prepared on Wednesday to ask any questions you have over them.

Probability and Statistics Review Worksheet

October 12 - October 16: Statistics

This week we will be focusing our attention on statistics.  At this point, you should be able to do WebWork assignments 3 and 4.  Hopefully, by reading the slate article last week, you have a better appreciation for why statistics is an important topic to study.  Regardless of your major, you will encounter statistics in many forms throughout your life.  I hope that what we discuss in this section will help you to make sense of the statistics you see outside of this class.

We will be using the table linked below to calculate areas under a normal curve with z-scores.  Please make sure to print a copy for yourself.

z-score table

Challenge Problem: In 2007, when she was a high school senior, Eleanor scored 680 on the mathematics part of the SAT. The distribution of 2007 SAT math scores was a normal distribution with mean 515 and standard deviation 14.. Gerald took the ACT math test and scored 27 in 2007. ACT math scores were normally distributed with mean 21 and standard deviation 5.1 in 2007. Assuming that both tests measure the same kind of ability, who had the higher score? Explain your reasoning and show all work.

October 5 - October 9

This week we will continue to discuss probability.  These problems can be very tricky for students, so you'll want to spend some time practicing outside of class.  Be sure to ask lots of questions during class!

For this week's blog, in addition to the fill in the blanks, you should read the article linked below and give a brief (2-3 sentence) response to it.

Take a Statistics Class

Challenge Problem:  According to the U.S. Census Bureau, the
probability that a randomly selected worker primarily drives a
car to work is 0.867. The probability that a randomly selected
worker primarily takes public transportation to work is 0.048.
(a)  What is the probability that a randomly selected worker primarily
drives a car or takes public transportation to work?
(b)  What is the probability that a randomly selected worker
neither drives a car nor takes public transportation to
work?
(c)  What is the probability that a randomly selected worker does
not drive a car to work?
(d)  Can the probability that a randomly selected worker walks to
work equal 0.15? Why or why not?

Probability Out of Class Assignment for 10/02/15

You should read the notes on Probability and watch the video above.  Then answer the questions on the worksheet below.  I will collect your solutions in class on Monday, October 5.

Out of Class Assignment 10/02/2015

September 28 - October 2

This week we will be starting the Probability and Statistics portion of the course.  Make sure you get the notes printed out so that you can focus on adding to them in class. We will discuss counting methods this week and introduce probability at the end of the week. It is really important that you keep on task with the homework on WebWork as we complete each week.  The best way to learn this material is to practice doing problems.  Remember, there are also additional problem worksheets on Moodle to go along with each homework assignment.  The solutions to those worksheets are available in the CAS.

Your blogs this week just need to be the five fill in the blanks.

Challenge Problem: How many five-card hands chosen from a standard deck contain two aces and three kings?

Graph Theory Review Worksheets

Please print both of these worksheets out and be prepared to discuss them in class on Monday and Wednesday this week.

In Class Worksheet

Graph Theory Exam Review

New Blog Post Prompt - Due by Sunday, September 27

For this additional blog post, I would like you to read one of the articles below and write a 2-3 paragraph response to the article.  Tell me which article you chose and give a brief summary of the article, explaining how graph theory was applied.  Finally, tell me what you thought of the way they applied graph theory in the article.  Were you surprised that graph theory applied in this situation?

“Is Graph Theory Key to Understanding Big Data?”

“Network Theory sheds new light on origins of consciousness”  

Explained: Graphs from MIT News

"New approach to vertex connectivity could maximize networks’ bandwidth” 

“Sudoku and Graph Theory”

“Rebooting the Human Genome” 

September 14-19: Hamiltonian Paths and Trees

This week we will be finishing up most of the graph theory material.  We will start by discussing Hamiltonian paths and circuits and weighted graphs.  A weighted graph is just a graph with numbers (weights) on the edges.  Our goal will be to use weighted graphs and Hamiltonian circuits to solve the Traveling Salesman Problem that we discussed last week.  We will see three algorithms for solving this: The Nearest Neighbor Algorithm, The Side-Sorted (or Best Edge) Algorithm, and the Repetitive Nearest Neighbor Algorithm.  We will also discuss how to solve this using Brute Force.  You will need to memorize each of these algorithms.  We will end the week with a discussion of trees and spanning trees.

Don't forget to keep up with the homework on WebWork.  The first two assignments are due this week.


Challenge Problem: Suppose your favorite presidential candidate is planning a tour of campaign talks in Missouri.  He (or she) will visit Kansas City, St. Louis, St. Joseph, Columbia, Springfield, and Jefferson City.  Using maps.google.com, find the distance between each of these cities.  Using your favorite method from this week, find an optimal route for the candidate to travel, visiting each city once and returning to where he starts.  Describe the method you used and provide all details.  Your solution should also include a picture of an appropriate weighted graph.

September 7-11: Graph Theory

This week we will be discussing Euler circuits and paths.  Last week, we talked about tracing a graph.  An Euler path or circuit is what you get when you can trace a graph.  An Euler path is a path that uses every edge of the graph exactly once.  (Think "E" for Euler and edge.)  An Euler circuit is just an Euler path that begins and ends at the same vertex (so is a circuit).  Euler's Theorem will be an important theorem for us.  It will give us a quick way to determine if a graph has an Euler path or Euler circuit.  You will need to memorize this theorem.

Challenge Problem: The picture below is the floor plan for a section of prison rooms.  If all the doors are open, is it possible for a guard to enter this section at the entrance, pass through each door locking it behind him, and then exit without ever having to open a door that has been previously locked?  Answer by turning this into a graph theory question.  You may describe your graph by giving the vertices and edges or post a picture of your graph in your blog.  Your solution should include a path in the graph you create.

Out of Class Assignment for 9/4

Math 110 Graph Theory Out of Class Assignment

You should complete each of the problems below on a separate sheet of paper. These problems will be collected in class for a grade on Wednesday, September 9, 2015.

1. For each of the following conditions, draw a graph that satisfies the conditions. If you believe it is impossible, explain your reasoning.
   (a) A simple graph with 4 vertices, two of which have degree 2. (b) A simple graph with 3 odd vertices.
   (c) a connected graph with a bridge. Identify the bridge.
   
2. Sketch a graph with vertices A, B, C, D, E and edges {AB, AE, BD, BC, BE, CE, DE}.
   
3. The following questions deal with the graph below.
   
   
   
   
   
   
   
   1. (a)  Give the degree of vertex F .
      
   2. (b)  What is the length of the path FBCGEF?
      
   3. (c)  Can the graph be colored with four colors? Three? If so, give a coloring (label the vertices with the assigned color).
      
4. The following questions deal with the graph below.
   
   
   
   
   
   1. (a)  Give the degree of vertex C.
      
   2. (b)  Is ABGE a path in the graph?
      
   3. (c)  Give a path of length 4 in the graph, starting at A.
      
   4. (d)  Can you start at one vertex, and trace every edge in the graph exactly once (so no repeating edges), and return to the starting vertex? (ie, Does the graph have an Euler circuit?) Why or why not?
      

1 

Intro to Graph Theory

Welcome back to classes!  We will be kicking off the semester this week with an introduction to graph theory.  A graph is a collection of vertices (think dots) and edges (think lines) between the vertices.  We can use graphs to study many things in the world around us.  For example, a graph can represent streets and intersections from a map (see The Traveling Salesperson Problem), computer networks, social networks, or even be used to study DNA (see A Graph Theoretical Approach to DNA Fragment Assembly).  By the end of this week, you should know what a graph is and be able to describe several properties of a graph.

Challenge Problem: Sketch several examples of graphs.  Determine the degree of the vertices in each graph.  When you add the degrees of all the vertices, you will always get an even number.  Why is that?

Blog Guidelines

Starting your blog:

1. Log in to www.blogger.com with your Missouri Western email. 

2. Click “New Blog” on the left hand side of the screen.  You may name your blog however you like. 

3. After creating your first blog entry (see below), send me an email with the subject line “’YOUR NAME’ BLOG”.  (For example, I would type “MCCUNE BLOG”) In the body of the email give me the URL for your blog. (For example, my blog is at www.mat110mccune.blogspot.com.)

Privacy Settings:

You may decide whether you want your blog to be private or public.  The blog will default to public.  You can change the privacy settings by clicking on the settings icon to the left of the screen when you are in your blog.  Under “Basic”, choose click the “Edit” button next to Privacy to remove your blog from Blogger listings and to make it invisible to search engines.   You can scroll down to “Permissions” to limit your blog readers.  If you don’t want your blog to remain public, you must add me (lmccune@missouriwestern.edu) as a reader.  To do this, click on “Edit” next to “Blog Reader” and choose the option “Private – Only these readers”.  You may add my email to the list of readers.  You may also choose to limit your readers to only your classmates.

Following Blogs:

Go to www.blogger.com/home.  Scroll down to “Reading List” and click “add” on the left-hand side of the screen.  You should add my blog for this class: www.mat110mccune.blogspot.com.

Your first Blog entry:

After creating your blog, you can create a new post in one of two ways:

1.     From www.blogger.com/home, click on the orange button with the pencil to write a new post for your blog.

2.     From your blog overview, click on the orange button labeled “New post” to create a new post. 

In your first blog post, tell me a little about yourself.  You should answer the following questions:  What was the last math class you had?  Why are you taking MAT110?  Our semester will be broken up into three topics: Graph Theory, Financial Mathematics, and Probability and Statistics.  What do you think each of these topics is about? What do you hope to learn in each of these topics?

General Blog post Guidelines:

You will be asked to make a post each week to your blog.  Blog posts should be posted after class on Wednesday and before Sunday at 11:59pm CST for the previous week.   Each week you should fill in the following sentences in your post. 

1.     I thought ________________________ was the most interesting thing discussed this week because __________________________.

2.     I thought _____________________ was the most challenging topic discussed this week because ________________________.

3.     I’d like to learn more about/spend more time on _________________________ in class because __________________________.

4.     I’d like to spend less time on ________________________ in class because _________________.

5.     What is something we discussed this week that you can see yourself using (either directly or indirectly) after this semester?  How and why?

You may complete your post with a free discussion on anything related to our class.  Some ideas of things to discuss are how you feel the class is progressing, things I can do to better facilitate your learning, specific questions you have about problems discussed in class, applications of the material we are learning to your life outside of MAT110, links to articles/websites related to our discussions in class, etc. 

In addition, you will occasionally be asked to write more detailed blog posts.  Such posts may include solving a problem, researching a topic discussed in class more in depth and reporting on your findings, or responding to an article related to the mathematics discussed in class.  For these posts, you will be provided a prompt at www.mat110mccune.blogspot.com.

You are encouraged to read one another’s blogs and leave your comments.  Please remember to be respectful in your posts and comments.  You should follow the guidelines set out in the MWSU Student Code of Conduct available at https://www.missouriwestern.edu/studentaffairs/student-code-of-conduct/.

Welcome to MAT110!

Welcome to MAT110 Fall 2015!  Our semester will be broken into three units: Graph Theory, Financial Math, and Probability and Statistics.  I hope that you will enjoy learning a little bit about each of these topics and how they are used in your everyday life and the world around you. I'm looking forward to a great semester!

A little bit about me: I am in my fourth year as an Assistant Professor of mathematics here at Missouri Western State University.  Before coming to MWSU, I spent a year as a visiting assistant professor at Ashland University.  I received my PhD from the University of Nebraska-Lincoln. (Go Big Red!)  My husband is also a mathematician at William Jewell College.  We have a 15-month old daughter who is a bundle of energy and absorbs all our free time. This summer we took her hiking in the Great Smoky Mountains where she hiked a mile on her own and got to see a black bear.

Please ask for help as soon as you are having trouble with this class.  You can visit me in my office (Agenstein 135K).  Peer tutoring is also available (for free) through the Center for Academic Support.