MATH 1030-005 Spring 2011 - Introduction to Quantitative Reasoning - Bryan Wilson

ANNOUNCEMENTS (Updated Monday, April 25)

April 25
Basically a recap of the email that I sent out, but with a little extra information:

To study for the final exam I recommend going over the two tests we have taken so far, and also include Quiz A in your studying. Everything in the class is fair game for the final EXCEPT for the following, which I am guaranteeing you are NOT on the final:

Memorizing metric to english ratios (dont have to remember 1 inch = 2.54 cm, etc.)
Section 2C (Problem Solving)
Estimation (from 3B)
Accuracy vs. Precision, using sig. digits when combining measured numbers (You still have to know about sig. digits in general, and scientific notation)
Income Tax (4E)
Logistic Growth

You will NOT get to write a reference "cheat sheet" for the final! The only formulas that will be provided for you on the final are the "Savings Plan" and "Loan Payment". Everything else is up to you to memorize.

About calculators: You will NOT get to use cell phone calculators or programmable calculators. I have let this slide a bit for the first two tests, but if I see you using one of these on the final, I WILL take it away! Please do not make me do this. Almost everyone has been using approved calculators so far.

From Section 10.1 (which we are covering Monday), you need to know about areas, perimeters, volumes, and surface areas of basic objects, and also about scaling (like the problem from Quiz A). We will not cover angles. I will probably say something briefly about what a point, a line, and a plane are. I would suggest skimming the entire chapter but focusing on what I wrote above.

IMPORTANT PROJECT INFO

Every person in the group must turn in a group effort evaluation form by Wednesday. These are turned in separately from your actual project. You can either give me a hard copy (preferred) or email a completed copy to me. You do not collaborate on these - each person works separately to complete one. If you do not turn one in, you will lose some points on the project!

You can find the form either on WebCT under Course Materials, or here: Group Effort Evaluation Form
I will also hand out hard copies in class on Monday if you'd like.

March 18
Everyone has now been assigned groups for the class project. Those of you who were not placed in groups yet as of the week before Spring break were randomly assigned groups (trying the best possible to assign you projects you wanted to work on).

List of Projects:
1. Investigating Water Usage
2. Planning for Retirement
3. Home Mortage
4. Buying a Car
5. College Funds for your Children
6. Population Projections
7. Periodic Drug Doses
8. A Growing Income Gap

List of Groups:

Patrick, Maria, Lilian - 6 or 7
Amy, Jacob, Marissa, Allison - 3
Bennett, Alex C, Sinoor - 7
Blaire, Kaleb, Preston, Jessica B - 4
Ben, Tyson, Kalani - 1
Brooke Gardner, Garrett Hertel - 3
Jessica R, Scott, Alex Brittain - 4
Lavinia, Ian, Caitlan - 5 or 6 or 7

If you have not already done so, get the Project handout from me. It will be available online soon but you should have a hard copy anyways. The list above is a brief description of each project, but the handout is more detailed about what needs to be done. You will need this handout to see what you need to do for the project.

Class Schedule and Homework
Day	Sections Covered	Homework	Extra announcements
Week 1
January 10	Review
January 12	Review/ 1A, 1B	Skim 1A, 1B	Quiz A
Week 2
January 17	MLK Day		No Class!
January 19	Section 1C	1C #29, 35, 36, 37-42, 45-49, 57, 60, 66, 67
Week 3
January 24	Section 1D	1D #15-20, 23, 24, 29-32, 45, 46, 51, 52	Quiz 1 (1C)
January 26	Section 2A/2B	2A #19-22, 27-35 odd, 38a, 39, 42, 47-50, 54-58, 79
Week 4
January 31	Section 2A/2B	2B #33-36, 37-42, 47, 55-57, 69	Quiz 2 (1D, 2A)
February 2	Section 2C	2C #7, 9, 10, 16, 20, 22, 26, 31, 37
Week 5
February 7	Section 3A	3A #33-36, 38, 39, 50, 53, 58, 65, 72, 73, 81, 82, 97-100	Quiz 3 (2B, 2C)
February 9	Section 3B/3C	3B #9-14, 17, 23-25, 30, 41-43, 57, 59, 64
Week 6
February 14	Estimation/Common Sense	Fun Lecture! 3B #31-34, 35-40	Quiz 4 (3A, 3B)
February 16	Section 3C/3E	3C # 21-26, 32, 55, 57, 59-61, 3E # 11, 18, 19
Week 7
February 21	Presidents Day		No Class
February 23	Test Review	( Sample Test ) ( Solutions ) ( Study Guide )	Quiz 5 (3C, 3E)
Week 8
February 28	Chapters 1-3		Test 1
March 2	Section 4A/4B	4A # 21-23, 25-28, 30, 41, 43, 53, Decide projects	Project Announcement
Week 9
March 7	Section 4B	4B #43, 45, 49, 51, 52, 55-60, 63, 64, 67-69, 80,	Split into Project Groups
March 9	Section 4C	4C #23-25, 27-29, 32-34, 36, 37, 39, 41, 69
Week 10
March 14	Section 4D	4D # 15-19, 29, 30, 37, 38, 41, 43, 51	Quiz 6 (4A, 4B, 4C)
March 16	Section 4E	4E # 19, 22, 23, 25-28, 29-32, 37, 39, 41, 47
Spring Break
Week 11
March 28	Section 8A	8A # 9-16, 29, (30 optional)
March 30	Project Work Day		Quiz 7 (4D, 4E)
Week 12
April 4	Section 8B	8B # 13, 14, 23, 25, 27, 29, 37, 49, 54
April 6	Section 8C/9A	8C # 14, 15, 21, 29, 30, 9A # 9, 11, 16, 17, 21, 24, (27 optional)	Quiz 8 (8A, 8B)
Week 13
April 11	Section 9A/9B	9B # 17-22, 25, 26, 27, 29, 32, 35, 37
April 13	Section 9C	9C # 11-14, 23-29, 37, 42, 43	Quiz 9 (9A, 9B)
Week 14
April 18	Ch. 4, 8, 9	( Practice Test ) ( Solutions ) ( Study Guide )	Test Review
April 20	Ch. 4, 8, 9		Test 2
Week 15
April 25	Section 10.1	10.1 # 31, 37, 38, 45, 48, 50, 53, 56, 60, 62-64, 68-71
April 27	Section 10.1 / Final Review		Project is Due!
Final Exam - Mon. May 2

BONUS PROBLEMS:

Be sure to show all your work or you will get no credit for these problems! Explain your answers!

Wednesday, Jan 19 (Due Monday, Jan 24)
In a certain high school, 75% of the students are in a school club and 60% are taking a math class this year. Using just this information,
a) Is it possible to tell for sure what percent of the students are both in a club and taking a math class?
b) If so, how many? If not, what is the highest possible percent of students who could be doing both? What is the lowest possible percent?
Hint: Use a Venn Diagram! If the percents seem difficult to work with, pretend the high school has 1000 students and try to solve the problem. Then take the percents when you get your final answer there.

Wednesday, Jan 26 (Due Monday, Jan 31)
(From the adventures of Singood the pirate!) While on the enchanted island, Singood, the first mate, and the second mate were chased up a tree by a giant serpent. One of them, however, fell off and was attacked! A second one of them came to the rescue, and the third just stayed in the tree like a coward. Given the following premises (all of which are true), who did what?

1) If Singood was attacked by the serpent, the first mate stayed in the tree.
2) If the first mate stayed in the tree, the second mate did not go to the rescue.
3) If the second mate did not stay in the tree, the first mate was attacked by the serpent.
4) If Singood stayed in the tree, the first mate went to the rescue.

Hint: Just like the one from class, it is helpful to take one premise, affirm the hypothesis, and see if it eventually leads to anything wrong. If it leads to something false, then Deny the Conclusion! The conclusion is false, so the premise must be false.
I'll get you started: Suppose Singood was attacked by the serpent. Then the first mate stayed in the tree by (1). Then by (2) The second mate did not go to the rescue. But this is wrong, since going to the rescue is the only thing left for the second mate to do after (1)! Thus we must deny the conclusion, which tells us the premise, "Singood was attacked", is also false...

Wednesday, Feb 2 (Due Monday, Feb 7)
The "Chicken McNuggets" or "Coin" Problem
One famous wording of this problem is in terms of the original Mcdonalds Chicken McNuggets boxes. They came in sizes of 6, 9, or 20 pieces. The question is, what is the biggest number of exact pieces you cannot get by ordering boxes of size 6, 9, or 20? For example, you cannot get exactly 10 pieces. You can find more about this on Wikipedia if you are interested, although you may not recognize some of the notation they use: McNuggets

This is quite a complicated problem, so the one I give you is a little easier. Suppose we restrict scoring in football to 7-point Touchdowns and 3-point Fieldgoals. What is the largest score that is impossible to have by just scoring Touchdowns and Fieldgoals?

Hint: There are 2 parts to this problem. One part is demonstrating that the score you find is, in fact, impossible to reach just with Touchdowns and Fieldgoals. For example, 5 is impossible. But there are higher numbers. The other part is showing somehow that ALL scores above that score ARE possible to reach with Touchdowns and Fieldgoals only. Think: what would happen if 3 scores in a row were all possible?

Wednesday, Feb 9 (Due Monday, Feb 14)
The "Bridge Crossing" Problem.
Four people are trying to cross a bridge at night. The bridge can only support the weight of two people at a time. Also, the group only has 1 flashlight, and it is too dangerous to travel without it. Each person individually would take 1, 5, 10, or 20 minutes to get across the bridge, but if two people go at once, they must both go at the rate of the slower person. The question is, what is the shortest amount of time that all 4 people could get across in?

Hint: The most intuitive way to cross the bridge is to have the fastest person, the 1-minute person, just escort everyone else across one at a time. The whole thing would be:
1 and 5 cross (5 min). Then 1 goes back (1 min).
1 and 10 cross (10 min). Then 1 goes back (1 min).
1 and 20 cross (20 min).
Now everyone is across in 37 minutes. But there is a faster way! Find it!

Wednesday, Feb 16 (Due Wednesday, Feb 23)
Today's problem comes from the estimation book we worked out of on Monday. The question is: Which is worth more, the president's salary or the number of pennies that would fit in his office (The Oval Office)?
Hint: Some values you may want to find in the course of doing this problem (you can look online for some of them, or do estimates): The volume of the Oval Office, the volume of a penny, the president's salary. You will get full credit as long as your process makes sense, your estimates are reasonable, and you reach an answer. Don't be afraid to round some things to make the calculations easier!

Monday, March 7 (Due Monday, March 14)
In class I discussed an episode of Futurama, in which the character Fry is frozen in stasis for 1000 years. During this time, he has 93 cents invested in a bank account with annually compounded interest. After 1000 years, his account is worth about 4.3 billion dollars. The question is, what was the APR on Fry's bank account in order to earn this much money over the 1000 years?
Hint: Use the compounding interest formula. Either one will work since the compounding is annually. Which one of the variables do you not know? How do you get it by itself? Your answer should be somewhere between 1% and 10%.

Wednesday, April 6 (Due Wednesday, April 13)
Two companies, company A and company B, currently have the same total revenue. However, they are going in opposite directions. Company A's revenue is increasing by 3% per year, while Company B's revenue is decreasing by 3% per year.
a) Using approximate doubling times / half lifes, write the expressions for the revenue of A and B compared to what they are now.
b) Write a formula to answer the question: At time "t", Company B's revenue is _____ % of Company A's revenue.
c) The formula in part (b) can be written in the form of an exponential decay with half-life formula. Do so, and then tell me about how long it is before Company B has half the revenue of Company A.
Hints: You will need to know the following two things to answer Part c:
(a^x)/(b^x) = (a/b)^x
(a^2)^x = a^(2x)
Notice that I'm basically asking you to find the "half life" of Company B's revenue vs. Company A. Work backwards from the half-life formula you get to find what the half-life is.

Wednesday, April 6 (Due Wednesday, April 13)
Computer processor speeds are measured in Hertz (Hz). The unit Hz is "per second", 1/second. Basically in reference to computers it means number of instructions it can handle per second. Good computers today have 3 Gigahertz (GHz) processors.
a) Write 3 GHz in scientific notation (in terms of Hertz). You will need to find what the prefix Giga- means.
b) Briefly study the history of processor speeds over time by searching online. They of course increased as technology improved, but how? Would you describe the increase in processor speed over time as linear? Exponential? Logistic? Overshoot + Collapse? Explain your answer.

Wednesday, April 13 (Due Wednesday, April 20)
One obvious application of slopes is, well, slopes! You can determine how steep a mountain is based on how far you've walked vs. how much elevation you've gained. The following table gives values from my own hiking experiences in the Wasatch. For each hike I give the length of the hike, the elevation gain, the amount of time I spent going up, amount of time spent going down, and time of year.
a) Find the slope of each hike in the list.
b) One of the most important applications of mathematics is the ability to search for patterns in data. This is called Data Mining. My question is, can you find any patterns in the table? Do I make slower progress on steeper hikes? Does it slow me down to hike during the winter? Do steeper hikes change the relative difference between time going up and time going down? Write down any other observations you can find or factors that may affect the data.

Hike	Length (1 Way)	Elevation Gain	Time Up	Time Down	Time of Year
Mt. Timpanogos	6.8 miles	4860 ft.	3 hr 30 min.	3 hr 15 min.	August 2009
Grandeur Peak	2.7 miles	2387 ft.	1 hr 30 min.	45 min.	January 2010
Red Butte Peak	1.4 miles	1340 ft.	1 hr.	45 min.	February 2010
Bell's Canyon	2.8 miles	2361 ft.	2 hr 35 min.	1 hr 20 min.	February 2010
Deseret Peak	5.3 miles	4013 ft.	3 hr.	2 hr. 40 min.	May 2010
Twin Peaks	4.9 miles	5090 ft.	4 hr 30 min.	3 hr 25 min.	August 2010