Precalculus,
Math 160, Spring 2008
This site updated May 1, 2008
(Recent
updates will usually be
above the first horizontal line. For the beginning of the course, see here.)
The
will to win is grossly overrated.
The will to prepare is far more important.
-- Bobby Knight, basketball coach
Old exams are on line here.
The Final Exam is Tuesday
of Exam week, May 6,
at 6:00 pm. Be there.
All the the sections have their finals in
the
same
room as the third exam.
If you have an academic time conflict,
you must see Dr. Esty well in advance to fill out the
necessary
paperwork. You must clear the paperwork hurdles
and prove you actually have an academic
conflict.
About
Chapter 7:
Chapter 7 is different. In Chapter 7 you will learn
how to derive trig results
from simple
pictures. You must learn the connections between simple results you
know and other, less-familiar, results that can be derived from the
things you know. Chapter 7 emphasizes reasoning. You must learn why the results follow from one another.
Chapter 7 requires an attitude change. It requires less calculation and more understanding (of trig identities).
Long ago we posted links to on-line trig activities . If you did not do
them before, you will find them interesting and valuable for the
current material and we strongly recommend you do them now.
About the final.
I recommend you study old final exams which are on reserve in the
Library
and available from Cards n' Copies. But, be advised that no final can
cover
all possible types of questions and your final may have questions of
types
that have not been represented on previous finals.
The final has about half of the points on trig
(much of
which is from Chapter 7) and half of the points on Chapters
1-5,
rather evenly
spread.
The first part will resemble Exams 1 through
3.
The trig part will will have some triangle trig and trig of more-complicated figures such as in Section 6.4,
but it will mostly be unit-circle trig, including trig identities and their
derivations.
For the trig part you must know how to solve
triangles and more-complicated figures, but there is more emphasis deriving
trig facts. Learn how to derive the results in 7.1. Learn how to derive the identities in
7.2 and 7.3
1) From a unit-circle picture
2) From a right-triangle picture.
3) The entire sequence of reasoning in
7.3. You will be given the result of one stage and asked to derive the
next result. I strongly recommend you study and learn how Figure
7.3.3 yields the sum-of-angles identities and how all the rest of the
identities follow, step by step, from them.
Section 7.4 will not be on the exam.
Expect lots of questions asking you to derive
results from Chapter 7.
The "algebra" part will have questions from each of Chapters 1 through
5. It
will have several word problems, including problems with percents.
They are relatively easy ones of their types, but you must use basic
word-problem-solving skills.
The formulas at the top of the Fall 2007 Final exam will be given
again on the final, as will the trig formulas at the top of the trig
section.
Four closely-related typos (fix them now!) On pages 439 near the bottom and 440 in the middle, there is the term
"(sin α)(cos β)" and it should be "(sin α )(sin β)" each time. Page 439, lines 3 and 2 from the end; page 440, the last two offset lines.
In 7.1, B19 has the answer in the text [.93]. That is wrong. It is
correct in the solution manual. In the text it should say [1.6].
April 17
Here
is the curve for Exam 3, Spring 2008:
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
The last day to drop is
the day
after Exam 3, Friday, April 18. If you
need a drop signed, your instructor can sign it, or you can have it
signed in the Main Math Office, 2-214. It must be received at Montana
Hall by the end
of Friday. Make up your mind quickly.
How are you doing? Your
letter grade is likely to resemble your exam letter grades. If you have
done almost all the homework on time you will be adding in a number
above 90 to your exam numbers. If your quizzes are comparable to your
exams, that high homework number may well raise your letter grade a
notch.
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 250 of 300, you are on track for at least an A-
at least 215, you are on track for at least an B-
at least 185, you are on track for at least an C-
at least 155, you are on track for at least an D-
154 or below, you are on track for an F.
What does a drop mean? If
you "drop" a class by Friday, April 18, 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 do not 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 credits you took.
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.
Most students in line for an unacceptably low grade
decide to drop. There are 200 points on the final, and they can make a
big difference, but it is not common for students to do much better on
the final than on the first three exams. However, it does happen
and some students "get it together" and do much better on the final, in
which case they are rewarded with a better grade.
The final exam is comprehensive. Students who have
forgotten most of their math and do very poorly on the final will have
the final exam score fully counted. The final can make a big
difference, positive or negative. Make yours positive!
April 10
On Exam 3
There will be a Richter scale or decibel scale problem.
There will be a problem with the "bearing" notation (such as "S 30 degrees W") from Section 6.4.
There will be a "plan" problem like those in the complicated
textbook examples and exercises from Section 6.4. Learn to plan well
and be carefull enough to get several steps in a row right.
April 8
Exam 3 is Thursday April 17 at 6:00 pm, as noted on the syllabus. You must take it with your own instructor.
Liz McGoff has Exam 3 and the final in Reid 103 (where the first exam was).
Joe Manlove has Exam 3 and the final in Reid 101.
Len Lutz has Exam 3 and the final in Reid 104 (where the first exam was).
Darron Fry has Exam 3 and the final in Reid 104.
Kevin Joyce has Exam 3 and the final in Reid 102.
If you have an academic conflict, contact Dr. Esty,
994-5354, right away. Do not wait until the day of the exam.
Exam 3
emphasizes sections
4.4 (percents) through 6.4. Be careful when studying old
exams. Previous third exams did not cover 4.4. For problems on percents, see old second exams. Last semester, the third exam did not cover 6.4, but only went through 6.3, so Section 6.4 was on the final.
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 (main floor, north end, just west of the bank) and for viewing on-line at
the library reserve site: http://www.lib.montana.edu/reserves/math160/.
(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, the day after the exam. Come to class Friday to get your exam. Expect your course letter grade to be very similar to your exam letter grades,
slightly modifed 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. (You
may have a secretary sign it for your instuctor if you can't find your
instructor).
March 25
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, QUAD
(the blinking "A" means Alphabetic
mode which refers to the letters in green on your keyboard)
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 is the end of the trig material. Be sure to do the trig activities.
March 7
Exam 2 was Thursday, March 6. Here is the curve: 83-100
A; 80-82 A-; 77-79 B+; 68-76 B; 65-67 B-;
62-64 C+; 58-61 C; 55-57 C-; 52-54 D+;
48-51 D; 45-47 D-; below 45 F
How are you doing? Your course letter grade is likely to
resemble your exam letter grades, assuming your HW and quizzes are
comparable. Doing the HW every day can raise your letter grade a notch.
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 165 of 200, you are on track for at least an A-
at least 140, you are on track for at least an B-
at least 120, you are on track for at least an C-
at least 100, you are on track for at least an 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 by April 18 (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.
March 4
Some students have an academic
conflict because they are taking Mysteries of the Sky. If you are
taking Mysteries of the Sky, confirm it to Dr. Esty (994-5354). He will
tell you where the makeup exam will be administered. It will be at 4:45
pm Thursday. It will finish at 5:45 and you will have time to make it
to the physics exam. You must bring to the makeup some proof you
are taking that course and your photo ID.
Students should report conflicts as soon
as they are discovered. Please do not wait until the last week and make
faculty scramble to create makeup exams and confirm room arrangements.
The second exam is Thursday before Spring Break, at 6:00 pm. It is in a room listed here. Some will be in the same room as the first exam, but Liz McGoff and Len Lutz have the second exam, March 6, in a different room.
Exam 2 does not cover the exact same sections as
last semester. This one emphasizes 2.2-4.3 instead of 2.3-4.4
So expect questions on 2.2 (composition) and do not expect
questions on percents (4.4). Of course, there will be word
problems. Similar old exams are avaible at Cards-n-Copies inthe
SUB and on-line at the library reserve site.
Feb. 8
Here is the curve for Exam I, Spring 2008: 88-100 A; 85-87 A-;
82-84 B+; 78-81 B; 75-77 B-; 72-74 C+;
63-71 C; 65-67 C-; 62-64 D+; 58-61
D; 55-57 D-; 0-54 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
grade is not good, consider adopting the suggestions from previous
students here and from Dr. Esty here (This advice from Dr. Esty was a pink handout you got the first day.)
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 2.1. Some old exams only
covered through 1.6 and others through 2.2 (It says on the top of the exam what
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 will ask you to state
methods symbolically (as in Section 1.4).
We have
free tutoring! The Math
Learning Center
(1-112 Wilson) has free tutoring weekdays. Here is a list of the hours with a current or former Math 160 instructor.
Be sure to program your calculator with the quadratic formula. Here is how.
This
site has
information about
the course syllabus.
You will get a hard-copy
in class. The syllabus gives the rules, the required prerequisites, the
grading policy, and more. You must read it.
calculator programs
we use in class
the calendar
that lists all the homework
due. You got a hard-copy on blue
paper in class. If not, ask for
another one.
upcoming
exams, and, after they are
administered, exam curves
instructors,
e-mails, 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, did you know 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 will need to use a username and
password).
We have
free tutoring! The Math
Learning Center
(1-110 Wilson) has free tutoring weekdays. Click here for more about
its hours.
****************************************************************************************************
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 phone
calls. My office hours are here.)
You must
satisfy our
special
prerequisite
to stay in Math 160. 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
Syllabus
(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 at 6:00 pm.
Exam 1 is Thursday, Feb. 7.
Exam 2 is Thursday, March 6. Exam 3 is Thursday, April 17.
The Final
Exam is at 6:00 pm Tuesday, May 6, during exam week.
Mark your personal calendar with
these dates and times.
Be there! If you have an unavoidable
academic conflict, see the syllabus. If
you
are taking other common-hour exam courses, you may have a conflict.
Look
up their exams 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 at 4:45 pm the same day. However, you must sign
up well in advance.
Signing up the last day is not an option.
Instructors,
e-mails, class times, rooms,
and exam rooms.
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.
Go to NEW
Enter the name, letter by letter,
say, QUAD
(the blinking "A" means Alphabetic
mode which refers to the letters in green on your keyboard)
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.
(-B+√(B2-4*A*C))/(2*A) -> P
The
-> command is for STOre (it appears as an
arrow), on a key
near
the bottom left.
It
stores numbers in memory.
(-B-√(B2-4*A*C))/(2*A) -> M
Disp P, M
The
Disp command is for Display, which is also under
I/O (hit PRGM,
arrow over to I/O).
[Now "quit" and try it out on
an example where
you
know the answer. For example, try
to solve x2 - 8x
+ 15 = 0. Did you
get
5, 3? If not, check your keystrokes.]
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.
Most
exam questions address material newly
learned in this course, not material you already know from
previous algebra courses. 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/math160/.
(If you are off
campus you will 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!
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 160.
The following
links are
interesting,
but not required and not directly relevant to Math 160.
An interesting optical illusion where you see pink as green:
Here is a neat site (not having anything to do with Precalculus). "Live Science,"
( http://www.livescience.com/ ) that discusses new research in
everything from hurricanes to sexual attitudes of
teens.
Cool
sites:
About powers of 10: Zooming
in from space to a microscopic scale.
(It takes a while for the java to load.)
Powers of 10 in
words.
The earliest known uses of various math
terms: http://members.aol.com/jeff570/mathword.html
Math
quotes,
indexed by author or subject, or simply for browsing.
A math
dictionary.
Obscure math
humor.
An astronomical
picture
of the day.
A MSU
physics faculty member is participating in a project about
gravitational waves (Waves are in chapter 7).
http://sciencebulletins.amnh.org/astro/f/gravity.20041101/essays/47_1.php
This site mentions that sites in the universe from which these waves
emanate could be located by using several detectors and measuring the
time delay associated with the different times that different detectors
note the waves. Precalculus gives you the tools to follow the math
(which is not on that link). The same sort of math is used to
locate cell-phone users.
More about
learning:
A link to a Canadian page about "Preparing
for University Calculus."
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