Precalculus, Math, M-151,
Spring 2012
This site updated Feb. 9, 2012
(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
Your job in Chapter 3.
Is homework helping you as much as it should? Learn to view homework as self-assessment.
For more Frank and Ernest cartoons, see: http://frankandernest.com/comics/index.html
Feb. 2
Here is the curve for Exam 1:
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
If you did well, congratulations! If you want to do better next
time,
1) study two hours outside class for each class hour, on average,
2) use the Math Learning Center for free
tutoring,
3) study efficiently with this advice and
this advice from former students.
As in any college course, your instructor does not have time to
cover all the material during class. But the text covers it all. You
are expected to read the text and learn from it outside class.
The Math Department just had an American
instructor of high school math in China give a talk about high
school in China. Here is a
Chinese school week.
In Chapter 3, your job is
to:
3.1 Change how you think about
lines. Learn to use the "point-slope" form and the
"two-point" form of lines in preference to the famous "y = mx + b"
(slope-intercept) form. Do not
simplify to slope-intercept form (unless there is a good reason to).
Learn how to use point-slope form and two-point form when the points
are given functionally or with letters rather than numbers. Learn
how linear interpolation works using the "two-point" form.
3.2 Learn how to "complete the square" of quadratics. Learn
that when the square is complete the expression exhibits the
location of the graph and its axis of symmetry, which is also
visible in the Quadratic Formula. Learn how to apply the Quadratic
Formula to solve equations where the unknown is not "x" or the
coefficients are not the usual letters.
3.3 Learn how the formula for distance in the plane follows
from the Pythagorean Theorem. Similarly, equations of circles are
given by the distance formula.
3.4 Learn that quadratics which we used to write "ax 2
+ bx + c" often may instead be written in factored form "k(x - b)(x
- c)" (the "b" and the "c" are not the same in the two forms).
We can use graphs to factor and identify quadratics using the
"Factor Theorem." If the graph of a quadratic intersects the x-axis
at x = c, then "x - c" is a factor. The constant factor, k, is not
determined by where the graph crosses the x-axis, however it can be
found using one other point.
3.5 Indirect word problems require you to "Build your own
formula" which expresses the operations in the particular problem.
Learn how to write formulas that fit the operations expressed in
word problems. Cue words indicate operations you express in your
formula. Guess-and-check can help you see the operations you need to
put into the formula. Usually we build specialized formulas from
components that are well-known basic formulas, so write down
relevant basic formulas.
3.6. Learn how to approach problems you don't know how to do!
(In educational jargon this is called "problem solving.") The key is
to begin writing the stated information symbolically.
Jan. 25
Exam 1 has problems that require you to
use your calculator to calculate values
read a graph (like 1.5, B3ff and 2.1, A1ff, B7ff)
understand how the appearance of a graph changes when you change the
window
understand our terms, including "placeholder" and the terms for
functional notation
read and use new definitions like those in Section 1.4.
write methods symbolically (like 1.4, B37-60)
be able to identify which of the "four ways to solve an equation" is
most appropriate
find a window that produces a given picture (like 1.5, B17ff and 2.1
B10ff)
There will be a small number of other types of
problems, not listed above. You are responsible for everything in
Section 1.1-2.1, regardless of whether it was covered in class
(although almost all of it will have been).
Jan. 20
Exam 1 is Thursday, Feb. 2 at
6:00 pm. It is not in the usual room and not at the usual
time.
class time instructor Exam 1 room (The other exams will
be in different rooms!)
01 8:00 Paterson Linfield 125
02 9:00 Banfield EPS 103
03 10:00 Banfield EPS 103
04 11:00 Mosher Linfield 125
(Do you know where the building is?)
05 12:00 Watts Linfield 125
06 1:10 Luehrs Reid 105
07 2:10 Greener Reid 105
If you have an academic time conflict with our 6:00
pm exam (say, you have a class that meets at 6:00 Thursday
evenings), or a disability (with a "blue card" from Student
Services), please contact the course supervisor Prof. Esty
right away: 994-5354. Do not delay until the day of the
exam!
We have pre-exam review
sessions:
Tuesday Jan. 31 and Wednesday Feb. 1, 6 - 8
pm in Wilson 1-121.
You must come
prepared to show you have seriously tried the problems you
ask about. Do not kid yourself that asking questions on Wednesday is
good preparation for a Thursday exam. Most of your preparation
should have been done long before Wednesday!
We have free tutoring all day long in the "Math
Learning
Center". Hours with a Precalculus instructor are noted.
Exam 1, like previous
exams, comes with instructions. It says, "Show clear
supporting work on problems with several steps. Algebraic problems that
display little or no supporting work will get little or no
credit. You do not need to show work on one-step
calculator problems. To solve numerical problems
guess-and-check is legal unless you are requested to solve
them 'algebraically.'”
You
should look at old versions of Exam 1. I recommend you get copies
at CopyCats (in the SUB) or view them on-line here
or on the Library Reserve page.
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 2.1.
Fall semester old exams covered through 2.2 (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 theorems or definitions that you have not
seen before and ask you to read them and use them. This is a
skill that cannot be 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.
Jan. 18
The Math Learning Center hours with a Precalculus instructor as a tutor are given here. (Free tutoring! Why not use it?)
Jan 17.
Prior to each exam there will be two two-hour review sessions in
Wilson 1-121, 6:00 - 8:00 pm.
Prior to Exam 1 which is on Thursday, Feb. 2: Tuesday Jan. 31
and Wednesday Feb. 1.
Prior to Exam 2 which is Monday, March 5: Thursday March 1 and
Sunday March 4.
Prior to Exam 3 which is Tuesday, April 10: Sunday, April 8
and Monday, April 9.
Prior to the Final Exam: To be announced.
Jan. 12
In class the first day we gave this non-credit
prerequisite quiz. We will give extremely similar quizzes
twice more, and these two times will be for credit. (All right = 10,
one error = 8, two errors = 6, more than two errors = 0). We need
you to get them all right! Please memorize how to do those problems.
Jan. 4
At the beginning of the course check out these links.
How can I add the class?
Have I satisfied the
prerequisite?
The course policies.
Thoughts about the workload in this course.
When is homework due and when are the
exams?
Do you have advice about how to do well?
How can I get tutoring?
A calculator program you will want to use.
Do I need a calculator? Yes.
Who is my instructor?
Who is the course supervisor?
Section
summaries: Your job is to
1.1. Learn what it means for a problem to be indirect and to
become comfortable with working indirectly, that is, writing about
operations you don't actually do.
1.2. Learn how order is expressed in written mathematics and on your
personal calculator so well that you can rapidly evaluate
complicated expressions correctly. This requires learning how to
insert parentheses that are not in the usual written mathematics.
1.3. Learn how functional notation is used to express
sequences of operations. Learn to distinguish the function from the
notation used to express it, and how to apply that function to
expressions other than "x".
1.4. Learn how to read definitions and theorems (They express
mathematical methods). Learn how to write mathematical methods in
symbolic notation. (This is a course-long project, begun in Section
1.1 and treated as the focus of Section 1.4.)
1.5. Learn to read graphs (that is, extract information they
contain). Learn how to graph with your graphing calculator and
obtain a "representative" graph. Learn to select and modify windows,
and use the calculator's capabilities to determine key points on
graphs.
1.6. Recall the usual algebraic ways to solve equations. Learn
to rapidly classify equations according to which way to solve them,
chosen from the "four ways to solve an equation."
2.1 Learn how to choose windows that make graphs
"representative" or have a particular look. Learn how changes in the
window will change the appearance of graphs.
2.2. Learn how notation expresses functional composition.
Learn how given graphs are affected by composition with addition,
subtraction, multiplication, division, and attaching a negative
sign.
2.3 Learn that solutions to "f(x) = c" may not be unique if
the function is not "one-to-one." So, there may be more than one
solution even though your calculator has an inverse function which
gives you only one. Learn how find the other solutions. Learn how to
recognize when a function is not one-to-one and how to deal with the
complications that occur when your calculator has an inverse
function but the original function is not one-to-one.
Do you wish you were
able to add a section of Precalculus,
but it is full? Keep trying on
line. Numerous students are switching classes and slots
are continually opening. We hope you can add on line.
If you can't get what you want by Tuesday Jan 17, it
may not be possible, but it might be. Come see me in my office,
2-238 Wilson Hall (upstairs, close to the catwalk) Thursday
(not before) and we will see if something can be
arranged.
Math Learning Center
hours with a Precalculus instructor have been posted here.
This site has
information about
the calendar that lists the homework
due every class day and exam dates.
The course policies (prerequisites, work, the grading policy, calculators, and more)
instructors,
e-mails, rooms and exam rooms,
times.
Math Learning
Center hours (We offer free
tutoring. Why not take advantage of it?)
Previous
exams you can use as study guides.
Typesetting
errors in the text that you should correct (actually do it!)
in your copy of the book.
Calculator programs (like
the Quadratic Formula) we use.
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.
Links for Chapters 6
and 7 of trigonometry.
Math, M-151, Precalculus. The course beginning
Course supervisor: 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 visits or phone calls. My office hours are here.)
Homework is due every day. Here is the calendar that lists all the homework
due. You got a hard-copy in class. If not, ask for another
one.
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.
The course policies. The policies give the
rules, the required prerequisites,
work, the grading policy, calculators, 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 (e.g. homework and
exam policies).
We use calculator programs
starting the second day of class.
Don't fall behind! We have free tutoring! The Math
Learning Center (1-110 Wilson) has free tutoring all day weekdays. Click here for more about its hours.
Exams
are common-hour exams given in the evening at 6:00 pm in rooms
to be announced on this site.
Exam 1 is Thursday, February 02, 2012
6:00-7:00 pm. Exam 2 is Monday, March 05. Exam 3 is Tuesday, April 10. The Final Exam is during exam week on
Monday, April 30, at 6:00 - 7:50 pm. 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 in the
Registration Handbook (page 24) 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, 994-5354) 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.
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 a typo 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 an
unlisted typo to Dr. Esty, (westy at math dot montana dot edu) you
will receive our thanks and a minor reward.
About this course:
This course is a lot of work.
We expect to teach
you so much that you need to study, on average, two hours
outside of class for every hour of class, minimum.
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.
The text has homework classified as "A" and "B"
problems. "A" problems are easy and short and you probably
already know how to do them. Be sure you can do the "B"
problems. Exams will emphasize B-level 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).
On Exam 1 we will ask you to exhibit
graphing-calculator skills that are only developed by practicing
with your calculator a lot.
We recommend you look at previous
exams, which are available at Cards-n-Copies and here.
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. It all adds up. You
get good at reading by reading. So read!
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".]
************************************************************************************************
Pages and links directly relevant
to Precalculus:
Advice about how to learn math.
Advice from previous students
about how to do well in this course.
Believe it!
You should look at old versions of Exam 1. I recommend you get
copies at CopyCats (in the SUB) or view them on-line here.
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.
Spring semester old exams only covered 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 theorems or definitions that you have not
seen before and ask you to read them and use them. This is a
skill that cannot be 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
is
the
end
of
the required Precalculus material at this time. Check back for
updates on calculator programs and exam preparation.
Pages and links relevant to all learning:
"Is the internet
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, "Is Google making us stupid?" in The Atlantic magazine is not
short (I don't expect you to read it):
http://www.theatlantic.com/magazine/archive/2008/07/is-google-making-us-stupid/6868/
It has provoked quite a buzz, so search on the title will get many
hits.
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."
How do you study? Here is research on multitasking.
"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
"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.
Comments and links about jobs:
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, twitter,
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."
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."
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!)
A TED
talk about the math we teach (or should teach) by Conrad
Wolfram (brother of Stephen, of Wolfram alpha, etc.)
This webpage is maintained by Warren
Esty: westy at math dot montana dot
edu 994-5354
Please report broken links, etc.