MATH 1090-006 Fall 2010 - Business Algebra - Bryan Wilson



Syllabus for MATH 1090


IMPORTANT FINAL EXAM INFORMATION

No graphing calculators or cell phones allowed.
You are allowed both sides of an 8 1/2 x 11 paper as a note sheet.
It is as important as ever to show your work. Some of the other graders may not be as lenient as I have been!

Review Assignment: This is optional review for the final. It is worth 3% Extra Credit added on to your final score in the class! The problems are directly from final exams of previous years. It is long, but if you do part of it you will get partial extra credit. Some of the problems you do not know how to do yet. The last day to turn in the review assignment is on the day of the final. You do not have to do problem 19, we did not go over this type of problem.
Review Assignment

Class Schedule and Homework
Day Sections Covered Homework (Due next Class) Extra announcements
Week 1
August 23 Intro, Section 1.1 1.1 #1-4, 9-12, 21-26
August 25 Section 1.1 1.1 #43-51, 65, 66, 68-71, Bonus
August 27 Section 1.2 1.2 #1-6, 21-27, Bonus Quiz #1 (Over 1.1)
Week 2
August 30 Section 1.2, 1.3 1.2 #55-57, 59, 60 and 1.3 #1-8
September 1 Section 1.3 1.3 #17, 18, 22, 26, 32, 40, 43, 46, 54, 60, 63, 66, 94
September 3 Section 1.4 1.4 #1-6, 9, 10, Bonus Quiz #2 (Over 1.2, 1.3)
Week 3
September 6 Labor Day! No class
September 8 Section 1.4 1.4 # 15, 17-23, 25-30, 61, 62, Bonus
September 10 Intro to Matrices
Week 4
September 13 Section 2.1, 2.2 2.1 # 12-14, 17, 34-38, Bonus Quiz #3 (Over 1.4)
September 15 Section 2.2, 2.3 2.2 # 9-18, Bonus = #35 (Show work)
September 17 Section 2.3 2.3 # 8-14, 28-34, 42, 43 Quiz #4 (Over 2.1, 2.2)
Week 5
September 20 Section 2.4 No Homework!
September 22 Section 2.4/2.5 2.4 # 7-12, 17, 18, 26-28
September 24 Section 2.5 2.5 # 7-9, 11, 23, 24, 27, Bonus = #2 Quiz #5 (Over 2.3, 2.4)
Week 6
September 27 Section 1.5 1.5 # 1-4, 11-13, 17, 18
September 29 Section 1.6 1.6 # 5-9, 16, 26-28, 35, 36, Bonus #40
October 1 Section 1.7 No Homework! Quiz #6 (Over 1.5, 1.6)
Week 7
October 4 Section 1.7 1.7 # 1, 4, 17, 20, 29, 31
October 6 Test Review Day No Homework ( Practice Test , Solutions , Study Guide )
October 8 Ch. 1 and 2 Test 1
Fall Break October 11-15, No Class
Week 8
October 18 Test Issues, Section 3.1 3.1 # 1, 3, 5, 7, 12, 35, 37-39, 52-55, Bonus
October 20 Section 3.1, 3.2 3.1 # 18-20, 22, 57, 63, 65 and 3.2 # 22, 23, 60-62
October 22 Section 3.3 3.3 # 1, 2, 9-12, 24, 27, 28, 51 Quiz #7(3.1, 3.2)
Week 9
October 25 Section 3.4, 3.5 3.4 # 5, 6, 9, 10, 11, 16
October 27 Section 3.5 3.5 # 11, 13, 15, 21, 26, Bonus
October 29 Section 3.6 No Homework! Quiz #8 (3.3, 3.4, 3.5)
Week 10
November 1 Section 3.6 3.6 # 11-15, 19, Bonus
November 3 Section 3.7 3.7 # 2, 4, 6, 15, 19, 25
November 5 Section 3.8 3.8 # 1, 5, 6, 9, 11, 13, (Optional 22-24, 25, 27), Bonus Quiz #9 (3.6, 3.7)
Week 11
November 8 Section 4.1 4.1 # 19, 20, 23, 28-35
November 10 Section 4.2 4.2 # 21-26, 32, 35, Optional (1-20)
November 12 Section 4.3 4.3 # 1-5, 15-17, 36, 39, 40 Quiz #10 (3.8, 4.1, 4.2)
Week 12
November 15 Section 4.4 No Homework!
November 17 Section 4.4, 4.5 4.4 # 2-4, 6-9, 13-17, 19, 20, Bonus
November 19 Section 4.5 4.5 # 4-7, 12-18, 29, 31, 38, Bonus Quiz #11 (4.3, 4.4)
Week 13
November 22 Test Review Day No Homework ( Practice Test , Solutions , Study Guide )
November 24 Ch. 3 and 4 Test 2
November 26 Thanksgiving Holiday, No Class!
Week 14
November 29 Section 4.6 4.6 # 2, 3, 12, 13, 17, 21, 22
December 1 Section 5.1 HW Listed Below
December 3 Chapter 5 HW Listed Below Quiz #12 (4.6, 5.1)
Week 14
December 6 Chapter 5 HW Listed Below
December 8 Chapter 5 HW Listed Below
December 10 Chapter 5 HW Listed Below No Quiz
Finals Week Final Exam Wednesday Dec. 15, 3:30-5:30 in JTB 310


Chapter 5 Problems (Due day of Final)
5.1 # 26-29, 35-38, 46, 47, 50, 54, 56, Bonus
5.2 # 1, 4, 8, 15-17, 24, 28, 29, 33
5.3 # 2, 3, 13, 19, 23, 26, 27
5.4 # 2, 3, 9, 17, 22, 24
5.5 # 1, 3, 7, 16-18, 32

Bonus Homework Problems


August 25 Bonus Problem (See Simple Interest from the Section 1.1 HW): You decide to invest P dollars in an account that gives 5% simple annual interest for 5 years. After this you find a better account that gives 8% simple annual interest and put the TOTAL from the first investment into this account for 3 years. After this your investment is worth $930. What is P? Show your work!

August 27 Bonus Problem: Solve and graph the inequality (2x+5)/(x-1) > 3. Show your work! (Hint - You will have to multiply by (x-1) in order to get rid of the fraction. But (x-1) might be negative! Split it into two cases.)

September 3 Bonus Problem: It takes Amanda 5 days to build a tree house and it takes Bob 20 days to build the same tree house (he plays a lot of World of Warcraft). How long would it take them to build the tree house together?

September 8 Bonus Problem: Solve this system of 5 equations:
2v + w + x + y + z = -5
v + 2w + x + y + z = -6
v + w + 2x + y + z = -1
v + w + x + 2y + z = 3
v + w + x + y + 2z = -16
Hint: Try adding all of the equations together, dividing to find what v + w + x + y + z is, and then using elimination.

September 13 Bonus Problem: A 2 x 2 matrix B is such that B added to its transpose is the 2 x 2 zero matrix. Find out as much as you can about what B must be! Show your work, as always.

September 15 Bonus Problem: Problem #35 in Section 2.2. Show all of your steps, of course, since the answer is in the back! (Hint - Label the entries of X as a, b, c, d. You will end up solving four different systems of linear equations.)

September 24 Bonus Problem: Problem #2 in Section 2.5. Read the first part of the section to find out how to encode and decrypt messages before attempting this problem.

September 29 Bonus Problem: Problem #40 in Section 1.6. Show all of your work! (Hint - try to turn the information you know about the "assembly" into an inequality involving the number of small and large tables and the amount of time available for assembly. Do the same for "finish work".)

October 18 Bonus Problem: Solve this equation:
2x4 + 3x2 - 1 = 0
Hint: x4 = (x2)2

October 28 Bonus Problem: Find a polynomial that has the following points: (-2, -14), (1, -8), (3, 6)
Hint: It will have the form f(x) = ax2 + bx + c. Plugging in the 3 points gives 3 equations with the variables a, b, and c. Find them by solving the system of equations.
Note: This method can be used as an alternate way to find a line through any two points. Write the line as y = ax + b and plug the two points in. This gives a system of 2 equations with 2 variables, a and b.
Note: In general, to determine a polynomial of degree n, we need to know n + 1 points that are on it.

November 1 Bonus Problem: A Slant Asymptote is a slanted line that the graph nears as x gets large. A rational function has a slant asymptote if the degree of the top is exactly 1 bigger than the degree of the bottom. To find a slant asymptote, if f(x) = r(x)/d(x), we want to rewrite it like this:

f(x) = px + q + m/d(x), where p, q, and m are real numbers.
If we succeed in doing so, then "px + q" is the slant asymptote.

The Problem: Find the slant asymptote of f(x) = (x2 - 2x + 3) / (x - 1) and use it to graph the function.
Hint: Example 3 in Section 3.6 in the book has a slant asymptote of y = x + 4. The first step to getting this answer would be breaking up (x2 + x - 6) / (x - 3) into (x2 - 3x) / (x - 3) + (4x - 12) / (x - 3) + 6 / (x - 3).

November 5 Bonus Problem: Determine the value of the infinitely continuing fraction 1 + 1/(1 + 1/(1 + 1/(1 + 1/ .... )))).
Hint: Set X = the whole expression, and observe that the continued fraction has copies of itself inside, kind of like a fractal.
Interesting Note: Set f(x) = 1 + 1/x. The repeating fraction can be represented by the infinite function composition f(f(f(f(f(.... )))), and remarkably, this "infinite composition" can be seen as a function that has a range with only 2 numbers in it! These numbers are found by solving the above problem.
Bonus, part 2: What is the domain of the infinite function composition above? For example, 0 is obviously not in the domain. But neither is -1, because f(f(-1)) = f(0), which does not exist. Continue...

November 17 Bonus Problem: What is the domain of the expression in 4.4 # 7? No hints for this one!

November 19 Bonus Problem: Describe the set of numbers b such that logb(x) = x has at least one solution for x.
Hint: Think of f(x) = logb(x) and g(x) = x as two separate functions. If the above equation is true, then f(x) and g(x) are equal at that x-value. Thus the graphs must cross... it might also help writing the equation in exponential form and solving for b.
The exact answer to this problem is difficult and (I think) requires calculus, but it is within your knowledge to come pretty close to the correct answer, and I will give full points for the right idea.

December 1 Bonus Problem: We learn in Section 5.1 how to add up the first n terms of a geometric sequence. But sometimes it is also possible to find the sum of a sequence with an infinite number of terms! Starting from the formula for the sum of the first n terms of a geometric sequence, take a guess for how the formula should be modified for infinitely many terms.
Hint: You may want to consider different cases for whether c < 1 or c > 1. What if c = 1? What if c is negative? You basically want to think about what should happen if n = infinity.
Hint: The sum of 1/2, 1/4, 1/8, ... should be 1 using the formula you create. The sum of 1/3, 1/9, 1/27, .... should be 1/2. The sum of 2, 4, 8, 16, .... should be infinity.