Precalculus, Math, M-151, Fall 2009
This site updated Nov. 19, 2009
(Recent updates will usually be above the first horizontal line.
Looking for something? See the page index here.)
The will to win is grossly overrated.        
The will to prepare is far more important.
--  Bobby Knight, basketball coach


Here is the curve for Exam 3, Fall 2009:
88-100  A;   85-87  A- ;  82-84  B+ ;  78-81  B ;  75-77  B- ;  72-74  C+ ;  68-71  C ;  65-67  C- ;  62-64  D+ ;  58-61  D ;  55-57  D-; below 55  F.

How are you doing?  Add your three exam scores (Don't average them). If your quizzes are comparable and your homework has been handed in regularly, if the total is
at least 255 of 300, you are on track for at least an A-
at least 220, you are on track for at least a B-
at least 185, you are on track for at least a C-
at least 155, you are on track for at least a D-
  154 or below, you are on track for an F.

The last day to drop without a letter grade in the course is Friday, Nov. 20, the day after the exam. Make up your mind rapidly. Expect your course letter grade to be very similar to your exam letter grades, slightly modified by your homework and quiz performance if they are good. The final will be comprehensive and will cover some of everything. Because it worth twice a unit exam, a good final can help a lot and a bad final can hurt a lot.
    If you do not want a letter grade, fill out a "Drop form" and submit it to Montana Hall by the end of Friday, Nov. 20. (You may have a secretary sign it for your instructor if you can't find your instructor).

Check this website next week (Thanksgiving week) for important comments on how Chapter 7 is much different.

Nov. 9
Exam 3 is Thursday, Nov. 19 (not Tuesday). For most of us it is in a different room.
Rooms:
Sections 01 and 02 Esty and Knutson, Reid 108 (new)
03 Hunt, Reid 201 (new)
04 Forland, Reid 202 (new, but the same as the first exam)
05 and 10 Alsup and Kaluzny, Reid 105  (new)
06 and 07, Langley and Yates, Reid 104  (new)
08 and 09, Eichenberger, Reid 103 (same room)

    If you have an academic conflict, contact Dr. Esty, 994-5354 or 2-238 Wilson Hall, right away. Do not wait until the day of the exam.

What is on the exam?  Exam 3 emphasizes sections 4.5 through 6.4. It will be about half on trig and half on material before trig. Be careful when studying old exams. Some previous third exams did not cover 6.4. You are still responsible for all the older material, including formulas for the growth of money from the section on percents.
    The exam will give the Laws of Sines and Cosines. (I hope you have the Law of Cosines programmed into your calculator and know how to use it.) It will not give properties of logs or any of the models we used in Chapter 5.  Learn those models and what their letters mean so you can use them when appropriate.
    There is always either a Richter-scale problem or a decibel problem.
   Most exam questions address material newly learned in this course, not material you already know from previous courses. Expect questions at the level of the "B" problems in the text. We recommend you look at previous exams, which are available for purchase at Cards-n-Copies in the SUB and for viewing on-line at the library reserve site:  here. (If you are off campus you will need to use a username and password).  You can study by working "B" problems from the text which are solved in the solutions manual. 

    The last day to drop without a letter grade in the course is Friday, Nov. 20, the day after the exam. Make up your mind rapidly. Expect your course letter grade to be very similar to your exam letter grades, slightly modified by your homework and quiz performance if they are good. The final will be comprehensive and will cover some of everything. Because it worth twice a unit exam, a good final can help a lot and a bad final can hurt a lot.
    If you do not want a letter grade, fill out a "Drop form" and submit it to Montana Hall by the end of Friday, Nov. 20. (You may have a secretary sign it for your instructor if you can't find your instructor).

Nov. 2
Here is a summary of new research on multitaking. "Study: Multitasking hinders learning:  Distraction-free studying is more efficient and effective, new brain research suggests."
Oct. 29
 Most students really like trig and do very well in Chapter 6, triangle-trig. Take this chance to improve your grade and feel good about your math skills by devoting some time to this material.

Information about Trig (for Chapters 6 and 7):  Do the on-line trig activities and program your calculator with two versions of the Law of Cosines.

Cool interactive, web-based, activities,
    for learning trigonometry (Chapters 6 and 7)
    Learn and have fun at the same time!   

I strongly recommend you enter two versions of the Law of Cosines as programs into your calculator. The programs are very short and given here:


Here is a TI-83 calculator program to do the Law of Cosines (SAS version to solve for the opposite side). Program 1:
Hit PRGM
            Follow each line here with ENTER. Comments you do not type are in black.
Go to NEW
Enter the name, letter by letter, say, LAWCOS   (the blinking "A" means Alphabetic mode which refers to the letters in green on your keyboard. Otherwise, to enter "D" hit "ALPHA (a green key) D")

Name:  LAWCOS
Prompt A,B,C
sqrt(A2 + B2 - 2*A*B*cos(C)) -> D
Disp D

[In the above, "sqrt" means the square root key, and "->" is the arrow or "STOre" key.]
In the above program A and B are adjacent sides and C is the included angle. D is the opposite side.

Keystroke details:
1)  Hit "PRGM"
2)  go to "NEW" and hit "ENTER"
3)  Type in a name, say, "LAWCOS" and ENTER
4)  Find the "Prompt" command by hitting "PRGM" [again], arrow over to "I/O" (input/output), arrow down to "Prompt" and hit ENTER.
5)  Type in "A,B,C"  [Use the alpha key to use the alphabet. There is a comma key]
6)  Type in the formula (above)
7)  "Display" the result (D) by typing PRGM, I/O and selecting "Disp" and alpha D
8)  Quit and run it on a problem where you know the answer, to check it. (Reproduce one of the calculations in the text.)
 

Program 2: To use the Law of Cosines to solve for an angle, use this program (short!):

COSANG
Prompt A,B,C
cos-1((C2-A2-B2)/(-2*A*B)) -> E
Disp E

In this program, A and B are adjacent sides and C is the opposite side, and E is the angle between the adjacent sides. "cos-1" is "2nd cos" on your calculator.

This site will be updated when we get closer to Chapter 7.
Be sure to do the trig activities.
Oct. 27
There is a false rumor circulating that "if our final exam grade is higher than our lowest test grade, then the final grade replaces the lowest test grade." This is false.
    The final is 200 points. So the final counts a lot and can make a big difference. If your final is strong it can easily raise your total and letter grade relative to other students who do not have a strong final. On the other hand, the final covers everthing and if you do not remember everything your final-exam percentage can be much lower, which can hurt your total and letter grade a lot. So there is hope for raising your grade with a good final, but not by replacing the lowest test grade with the final exam percentage.

Oct. 21
Here is the curve for Exam 2, Fall 2009:
88-100  A;   85-87  A- ;  82-84  B+ ;  78-81  B ;  75-77  B- ;  72-74  C+ ;  63-71  C ;  60-62  C- ;  57-59  D+ ;  53-56  D ;  50-52  D-; below 50  F.

How are you doing?  Add your two exam scores (Don't average them). If your quizzes are comparable and your homework has been handed in regularly, if the total is
at least 170 of 200, you are on track for at least an A-
at least 145, you are on track for at least a B-
at least 120, you are on track for at least a C-
at least 100, you are on track for at least a D-
  99 or below, you are on track for an F.

    If you are unhappy with your likely grade, you can submit (to Montana Hall) a signed drop form until November 20 (with two signatures, from your instructor and your advisor), or you can try to do much better on the next 100-point exam and the 200-point final exam. A strong final can help a lot. Also, a weak final can hurt a lot. You must prove you have retained what you learned by scoring well on the comprehensive final.
    If you want a better grade, study more, or study more effectively. You got a pink handout about how to study math. Also, here is advice from previous students.
    You are expected to learn by reading the text. If you skipped reading the text and your exam score was poor, it is time to take the hint. Make a big change and read the text seriously.

What does a drop mean?  If you "drop" a class you get a "W" ("Withdrawn") on your transcript and you do not get credit for the course. A "W" is not a serious negative, but you don't get credit for all the work you have done so far. A "W" does not impact your GPA, but it does affect the number of credit hours. (If you have financial aid, you might need a certain number of credit hours.) 
    If you do not drop and you get a low grade, you may take the course again and the grade you get the second time will replace (erase) the first low grade.


I had a conversation with a person who had been writing job recommendations for graduating students. She said, "The world got competitive. And it happened fairly recently. I think that students from middle-class homes who cruised through high school are not aware of just how competitive the world has become. They do not realize that, unlike a few years ago, they cannot expect a good job just because they are Americans."

There are now many college graduates applying for each good job. Now you are in school, but soon you will be on the job market. What will you have done that will make a potential employer think you can make a contribution which is more valuable than the other applicants could make?

Maybe your performance in this math class will reflect a strong work ethic, precise thought, and ability to deal with problems with several steps. On the other hand, maybe it will show that you would rather spend your time being entertained (music, cell phones, videos, sports, facebook, youtube, wii, hulu, video games, hanging out, TV, ...) and are not a hard worker.
    If you were an employer would you hire someone who merely does "okay" in classes with the normal amount of work when there are many other hardworking people with better credentials applying for the same job?
    "The world got competitive. And, it happened fairly recently."

     Exam 2 Alert! Your exam room (at 6:00 pm Tuesday, Oct. 20), may not be the same room as last time.
Rooms:
Esty, Knutson, and Kaluzny, same room as last time, Linfield 125
Hunt and Forland, new room, Cheever 215  [Do you know where this room is?]
Alsup, new room, Reid 201
Langley and Yates, new room, Roberts 101
Eichenberger, same room as last time, Reid 103

This time Exam 2 emphasizes 2.3-4.4 instead of  2.2-4.3  There will be problems on percents (Section 4.4) this time. Of course, there will be word problems. Similar old exams are available at Cards-n-Copies in the SUB and on-line at the library reserve site.

Oct. 5
How am I doing?  
    Your course letter grade is likely to be the average of whatever letter grades you get on the exams, possibly a notch higher if your momework is regularly on time and your quizzes are comparable.  So far we have only had 100 points of exams and there will be 500, total. The remaining exams and the final exam (200 points!) count a lot. 
Oct. 2
In college your instructor does not have enough class time to cover all the material. You are responsible for leaning outside of class by reading the text. The homework and exam questions are all closely related to things discussed in the text. Read it! Then, if something is not clear, put in the time and effort to figure it out. 

"Eating fatty food appears to take an almost immediate toll on both short-term memory and exercise performance, according to new research on rats and people.  'We expected to see changes, but maybe not so dramatic and not in such a short space of time,' said Andrew Murray, the study’s lead author.’’ Continued here:
http://well.blogs.nytimes.com/2009/08/13/fatty-foods-affect-memory-and-exercise/?hp
Sept. 25
The typesetters introduced some typographical errors into the text. Look here for some recently found in Section 2.3. Fix them all in your text.

Sept. 23
Here is the curve for Exam 1, Fall 2009:
88-100  A;   85-87  A- ;  82-84  B+ ;  73-81  B ;  70-72  B- ;  67-69  C+ ;  63-66  C ;  60-62  C- ;  57-59  D+ ;  53-56  D ;  50-52  D-; below 50  F

   Your course letter grade is likely to resemble your exam letter grades, if your quizzes and homework are comparable. If your grade is good, congratulations! You know what it takes. If your letter grade is not good, consider adopting the suggestions from previous students here and from Dr. Esty here.
    Look at your exam to see what you got wrong. How much was difficulty with notation? You must learn how mathematical notation works. One way to do that is to read math a lot (Read your text!). Another way is to study the notation by inspecting how the theorems and identities fit the examples. For example, in Section 2.2 you can use your calculator to actually graph the examples, predict how they will look, and correct your thoughts if your prediction was not right.  Figure it out!
    Watching and following along is not the same as understanding and knowing how to do it. To do math well you must actively participate.  


Exam 1 is Tuesday, Sept. 22, at 6:00 pm, as stated on the calendar. The exam room is not the usual room. The exam room is given here.

         Exam 1 covers sections 1.1-2.2. Last Spring it covered through 2.1. Be aware that this semester's exam covers more material.
        The exam has several problems about graphs and windows that you can do easily if you have practiced with your graphing calculator many hours, and which will be hard and time-consuming if you have not. Be sure to learn how your calculator works (sections 1.2, 1.5, and 2.1) and how mathematical notation and terminology works (sections 1.1, 1.3, 1.4, 1.6, 2.2). You will be tested on material newly learned in this course, not on material already known from Algebra II. 

    We have free tutoring! The Math Learning Center (1-110 Wilson) has free tutoring weekdays. Click here for more about its hours and when you can find a Math 151 instructor there.

    You should look at old versions of Exam 1. I recommend you get copies at Cards-n-Copies (in the SUB) or view them on-line here. (If you are on campus, it just works. If you are off campus may need to use a username and password).
    Be careful when you study the old exams. Not all old first exams cover the same sections. This semester the first exam covers Sections 1.1 through 2.2. Some old exams covered through through 2.1 (It says on the top of the exam which sections it covers.)  
    You are supposed to know a lot of algebra already. There are several levels of algebra, and most of the algebra you learned in school is at a lower level--a level that will not be emphasized on the exam. The exam tests you on higher-level skills. It tests you on material newly learned in this course.
    Be sure you can do the "B" problems. If there is something you don't know, or don't know how to do, be sure to study that. Don't be content with the algebra you knew before you signed up for this course.

    You are responsible for reading and writing mathematics. On the exam we will state a theorem or definition that you have not seen before and ask you to read it and use it. This is not a skill picked up in an hour or two. You learn to read by reading. We strongly recommend you learn to read math by reading your text.
    On the exam we may ask you to state methods symbolically (as in Section 1.4).

    Be sure to bring your graphing calculator with the Quadratic Formula programmed into it.

    There are many problems you will find hard if you have not put a lot of time in playing with your calculator and reading your text. You do not develop reading skills (required on the exam) by watching your instructor. You do not develop calculator skills without practicing a lot. 


This site has information about
    instructors, e-mails, rooms and exam rooms, times.  
    Previous exams you can use as study guides.
    Your likely grade.
    the calendar that lists all the homework due and exam dates.
    Math Learning Center hours (for free tutoring. Why not take advantage of it?)
    Typesetting errors in the text that you should correct in your copy of the book.
    Calculator programs (like the Quadratic Formula) we use.
    The course policies.
    Advice, designed for this course, about how to learn math.  
     Advice from previous students about how to do well in this course.
    If you have a time conflict on an exam, see here.
The course beginning

    The course policies. The policies give the rules, the required prerequisites, the grading policy, and more. You must read it. We are trying to reduce the number of pages of paper we hand you. In some ways this is good, but it does mean you must pay more attention to this on-line site. Be sure to read here about all the policies and help we offer, and check this site whenever you have administrative questions.

    Calculator programs we use in class
    The calendar that lists all the homework due. You got a hard-copy on paper in class. If not, ask for another one.
    Upcoming exams, and, after they are administered, exam curves
    Instructors, e-mails, rooms and exam rooms, times
    Occasional updates (at the top of this page) about upcoming exams, etc.

  Other important information that you will want to know. For example, copies of previous exams are available on reserve in the Library and at Cards n' Copies. They are also on-line here.  (However, it is cheaper to buy them at CnC than use your expensive printer ink.) (If you are on campus, it just works. If you are off campus you might need to use a username and password).
   Advice, designed for this course, about how to learn math. (Read this!  It has some helpful, and perhaps surprising, ideas. Here is a copy in Word.) 
    Advice from previous students about how to do well in this course.  Believe it!

    We have free tutoring! The Math Learning Center (1-110 Wilson) has free tutoring 9:00-2:00 weekdays. Click here for more about its hours.

 ****************************************************************************************************
Math, M-151, Precalculus, Syllabus.

Course supervisor for M-151 (formerly Math 160):  Prof. Warren Esty, Department of Mathematical Sciences, Wilson Hall 2-238. (406) 994-5354.
    Warren Esty, at    westy  AT  math.montana.edu      (If you want to arrange something, I prefer phone calls. My office hours are here.)

You must satisfy our special prerequisite to stay in M-151. Have you satisfied it?

"I took precalculus (or calculus) in High School, so I have satisfied the prerequisite, right?"  No!  You must test into the course. What you took in high school is does not count. What you know counts. Here are the rules about prerequisites.

Course Policies  (which includes sections about these and other topics):
    Prerequisite (you must satisfy the prerequisite!), Work, Calculators, Exams and Grading, Course Goals

Calendar   A daily schedule, including homework assignments. You will get a hard copy in class.
Exams are common-hour exams given in the evening in rooms to be announced on this site. 
Exam 1 is Tuesday, Sept. 22. Exam 2 is Tuesday, Oct. 20. Exam 3 is Thursday, Nov. 19. The Final Exam is at 6:00-7:50 pm Wednesday Dec. 16, during exam week.  Mark your personal calendar with these dates and times.
Be there!  If you have an unavoidable academic conflict, see the policies.  If you are taking other common-hour exam courses, you may have a conflict. Look up their exam times now and see. If you have an academic conflict, you may be able to resolve it by signing up (with Dr. Esty in 2-238 Wilson Hall) for our alternative exam time (probably at 4:45 the same day for common-hour exams). However, you must sign up well in advance. Signing up the last day is not an option.

Read each section. Do not skip the harder parts. In fact, when the going gets rough you need to slow down and read it several times until it makes sense. If it remains unclear, ask!  

Reading is hard!  But, you will be learning an extremely valuable skill.
Don't skim.
Don't expect that only high points are important (Don't read only the bold parts).
Don't skip the rest of the paragraph because you want to move along to the next high point. 
Really do read the next paragraph in the text..

"Is Google is making us stupid?"  Read about it here:
 http://www.npr.org/templates/story/story.php?storyId=91543814
    (Really, it is short, so read it!)  
 The original article in The Atlantic magazine is not short (I don't expect you to read it):   http://www.theatlantic.com/doc/200807/google
It has provoked quite a buzz, so search on the title will get many hits.

CNN Money has an article on the "Most lucrative college degrees":
 http://finance.yahoo.com/college-education/article/107402/most-lucrative-college-degrees.html?mod=edu-collegeprep
"The top 15 highest-earning college degrees all have one thing in common -- math skills."

Do you multitask well?  Here is some surprising information about the effectiveness of multitasking.

The typesetters introduced a few typos in the text.
Here is a page of typos already discovered.
Go to that page and correct your text now. (Don't be confused about details later when you can fix the concern in a few minutes now.)
If you find one that is not already listed, please let us know. (Tell your instructor, or me at westy at math dot montana dot edu.) If you are the first to report a typo to Dr. Esty, (westy at math dot montana dot edu) you will receive our thanks and a minor reward.

We use calculators a great deal. Instructors will use the TI-83 or TI-84, but you may use other models. Learn to use and program your calculator. One program you will need many times is given next.

Activities.  Chapter 1

Program your calculator with the Quadratic Formula. Here is a simple four-line program for the TI-83 or 84.
Hit PRGM
            Follow each line here with ENTER. Comments you do not type are in green.
Arrow right to NEW       ENTER
Enter the name, letter by letter, say, QUAD    (the blinking "A" means Alphabetic mode which refers to the letters in green on your keyboard)
ENTER
 Prompt A, B, C
        To find the Prompt command, while writing the program, hit PRGM (again) which brings up a menu.
        Arrow right to I/O  (for Input/Output) and down to Prompt. There is a comma key above the 7 key.
        For "A", type ALPHA A,  (then ALPHA B, ALPHA C, then ENTER)
(-B+√(B2-4*A*C))/(2*A) -> P      [again "B" is ALPHA B]      
        The "->" command is for STOre (it appears as an arrow), on a key near the bottom left.
        It stores numbers in memory We use "P" for "plus" and "M" for "minus".
(-B-√(B2-4*A*C))/(2*A) -> M        ENTER
Disp P, M
         The Disp command is for Display, which is also under I/O (hit PRGM, arrow over to I/O, and down to Disp  ENTER).
At this line, you can QUIT  (2nd QUIT)

If something goes wrong, don't worry. Just QUIT (= 2nd QUIT in yellow) and resume from where you were by hitting PRGM and, this time, EDIT (instead of NEW). 

    [Now "quit" and try it out on an example where you know the answer. For example, to run it, hit
PRGM
arrow to QUAD and hit ENTER and ENTER again.
Try to solve x2 - 8x + 15 = 0. Did you get  5, 3? If not, check your keystrokes.]  If you want to do a second example, you need not begin over, just hit ENTER and it will ask you for the next value of "A".] 

    Free tutoring!  Math students can get help at the Math Learning Center (Wilson Hall, west wing, south end, first floor) from 9:00 to 3:00 each weekday. Not all hours have a Precalculus tutor. Check here for the Precalculus tutoring hours.

    You are supposed to know a lot of algebra already. There are several levels of algebra, and most of the algebra you learned in school is at a lower level--a level that will not be emphasized on the exams. The exams test you on higher-level skills. They test you on material newly learned in this course.
    Be sure you can do the "B" problems. If there is something you don't know, or don't know how to do, be sure to study that. Don't be content with the algebra you knew before you signed up for this course.

    You are responsible for reading and writing mathematics. On Exam 1 we will state a theorem or definition that you have not seen before and ask you to read it and use it. This is not a skill picked up in an hour or two. You learn to read by reading. We strongly recommend you learn to read math by reading your text.
    On Exam 1 we will ask you to state methods symbolically (as in Section 1.4).
    We recommend you look at previous exams, which are available at Cards-n-Copies in the SUB, on reserve at the library, and on-line at the library reserve site:  http://www.lib.montana.edu/reserves/ (If you are off campus you may need to use a username and password).



************************************************************************************************
Advice about how to learn math.

Advice from previous students about how to do well in this course.  Believe it!

How do you study? Here is research on multitasking.

This is the end of the required Precalculus material at this time. Check back for updates on calculator programs and exam preparation.

You can quit here.  The rest gives some interesting links, not directly relevant to Math 151.


The following links are interesting, but not required and not directly relevant to Math 151.

Why economists care about math:
 http://gregmankiw.blogspot.com/2006/09/why-aspiring-economists-need-math.html

The Top Ten Best Jobs in America:  http://www.cnbc.com/id/28527404/
(Math and stat come out pretty well!)

"Amusing Ourselves to Death" is a prophetic book that was written in 1985. Here is a cartoon that illustrates its preface.  http://www.recombinantrecords.net/docs/2009-05-Amusing-Ourselves-to-Death.html
The book itself is extremely interesting. It is amazing the something written then could still be so relevant (even more relevant) now.

Montana State has students who work on experiments in space.  Check out the MSU Space Grant web site.

More about learning:

Here is a link to a fascinating commercial site on learning (believe it!), and a link to its page on the role of sleep in learning.

This webpage is maintained by Warren Esty:    westy  at  math dot montana dot edu     994-5354
Please report broken links, etc.