Download MTH 132 - MU BERT

MTH 132 (sec 103)
CRN 3474
Prerequisites:
Syllabus
Fall 2007
ACT Math score 21 or higher, or SAT Math score 500 or higher, or
MTH 120 or MTH123 ( preferably with a C or higher)
Meeting time : M – F 11– 11:50 am Room 511 Smith Hall
Instructor : Dr. Alan Horwitz
Office : Room 741 Smith Hall
Phone : (304)696-3046
Email : [email protected]
Text : Precalculus , 3rd edition, Bittinger , Beecher , Ellenbogen & Penna, Addison Wesley Longman
Grading : attendance
5% (34 points )
surprise quizzes
15% (100 points)
probably 4 major exams
60% (400 points)
Note:
If we have a 5th exam, then I will count the highest four exam scores
final( comprehensive ) exam 20% (133 points)
Final exam date: To be announced, possibly a common final on the algebra on Saturday December 8, 2007
at 2:00 pm or else on Thursday December 6, 2007 from10:15am to 12:15 pm
General Policies :
Attendance is required and you must bring your text and graphing calculator (especially on quizzes and exams ). You
are responsible for reading the text, working the exercises, coming to office hours for help when you’re stuck, and being
aware of the dates for the major exams as they are announced. The TI-83 will be used in classroom demonstrations and is
the recommended calculator, but you are free to use other brands (although I may not be able to help you with them in
class).
Exam dates will be announced at least one week in advance. Makeup exams will be given only if you have an
acceptable written excuse with evidence and/or you have obtained my prior permission.
I don’t like to give makeup exams, so don’t make a habit of requesting them. Makeups are likely to be
more difficult than the original exam and must be taken within one calendar week of the original exam date. You can’t
make up a makeup exam: if you miss your appointment for a makeup exam, then you’ll get a score of 0 on the exam.
If you anticipate being absent from an exam due to a prior commitment, let me know in advance so we can schedule
a makeup. If you cannot take an exam due to sudden circumstances, you must call my office and leave a message or
email me on or before the day of the exam!
Surprise quizzes will cover material from the lectures and the assigned homework exercises. These can be given at
any time during the class period. No makeup quizzes will be given, but the 2 lowest quiz grades will be dropped. The sum
of your quiz scores ( after dropping the two lowest) will be scaled to a 100 point possible maximum, that is, to 15% of the
667 total possible points in the course.
In borderline cases, your final grade can be influenced by factors such as your record of attendance, whether or not
your exam scores have been improving during the semester, and your class participation. For example, if your course point
total is at the very top of the C range or at the bottom of the B range , then a strong performance on the final exam can
result in getting a course grade of B, while a weak performance can result in getting a C.
Attendance Policy :
This is not a DISTANCE LEARNING class!
Attendance is 5% of your grade( 34 points total). If your grade is borderline, these points can be important
in determining the final result. Everyone starts out with 34 points, then loses 2 points for each class missed. Doing
boardwork problems (see below) is a way to win back those lost points. Your attendance score will be graded on a stricter
curve than your exam scores.
Having more than 3 weeks worth of unexcused absences (i.e., 15 of 70 lectures ) will automatically result in a
course grade of F! Being habitually late to class will count as an unexcused absence for each occurrence. Carrying on
conversations with your neighbor , as well as engaging in other forms of disruptive behavior, could be counted as an
unexcused absence. Walking out in the middle of lecture is rude and a distraction to the class ; each occurrence will count
as an unexcused absence. If you must leave class early for a doctor’s appointment , etc., let me know at the beginning and
I’ll usually be happy to give permission. Absences which can be excused include illness, emergencies, or official
participation in another university activity.
MTH 132 (sec 103)
Syllabus
Fall 2007
( continued )
Documentation from an outside source ( eg. coach, doctor, court clerk…) must be provided. If you lack documentation,
then I can choose whether or not to excuse your absence.
HEED THIS WARNING:
Previously excused absences without documentation can, later, instantly change into the unexcused type if you accumulate
an excessive number ( eg. more than 2 weeks worth ) of absences of any kind, both documented and undocumented :
You are responsible for keeping track of the number of times you’ve been absent. I won’t tell you when you’ve reached the
threshold. Attendance will be checked daily with a sign-in sheet. Signing for someone other than yourself will result in
severe penalties!! Signing in, then leaving early without permission will be regarded as an unexcused absence.
Sleeping in Class :
Habitual sleeping during lectures can be considered as an unexcused absence for each occurrence. If you are that
tired, go home and take a real nap! You might want to change your sleeping schedule, so that you can be awake for class.
Policy on Cap Visors :
During quizzes and exams, all cap visors will be worn backward so that I can verify that your eyes aren’t roaming to
your neighbor’s paper.
Cell Phone and Pager
Policy :
Unless you are a secret service agent, fireman, or paramedic on call, all electronic communication devices such as
pagers and cell phones should be shut off during class. Violation of this policy can result in confiscation of your device and
the forced participation in a study of the deleterious health effects of frequent cell phone use.
Policy on Cheating :
Don't. Don't even help your neighbor cheat. If I suspect you are, then you'll get a 0 on that quiz or exam, and worse.
Addendum to MTH 132 Syllabus :
I would like to motivate greater participation in class. Frequently, I will be selecting a few homework
problems so that volunteers can post their solutions immediately before the start of the next lecture. For each
solution that you post on the board ( and make a reasonable attempt on ) , I will ADD 2 points to your total score
in the course. Boardwork points can help determine your final grade in borderline cases and can help you to recover
points lost from your attendance score. ( They will not cancel your accumulation of unexcused absences, which can
result in failing the course if you have too many ) Rules for doing boardwork follow:
RULES FOR DOING BOARDWORK :
1.
I’ll assign a selection of homework exercises to be posted for the next lecture.
2.
Arrive early!! Have your solutions written on the board by the beginning of the class period.
Be sure to write the page number of the problem. Read the question carefully and be
reasonably sure that your solution is correct and that you have showed the details in your
solution.
3.
Don’t post a problem that someone else is doing. On choosing which problem you do,
remember : The early bird gets the worm !
4.
Write small enough so that your neighbors also have space to write their problems.
I don’t want territorial disputes. Also write large enough for people in the back rows to see.
5.
Work it out, peaceably among yourselves, about who gets to post a problem.
Don’t be greedy: if you frequently post problems, give someone else an opportunity
if they haven’t posted one recently. On the other hand, don’t be so considerate that
nobody posts any problems.
6.
Circle your name on the attendance sheet if you’ve posted a problem that day.
Use the honor system: don’t circle for someone else. The number of problems on the board
should match the number of circled names on the attendance sheet. Make sure you also keep
a record in your notes, just in case I lose the attendance sheet.
MTH 132( sec 103)
Fall 2007
Keeping Records of Your Grades and Computing Your Score
Quiz#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
score
Raw Quiz Score= sum of all, but the two lowest quiz scores
Adjusted Quiz Score =
Exam #
score
100
 Raw Quiz Score
10  ( # of quizzes  2)
1
2
3
4
Exam Total = sum of all exam scores(not including the final exam)
grade range for
Exam 1
Exam 2
Exam 3
average of range values
for all four exams
Exam 4
A
B
C
D
Absence #
Date absent
Excused? Y or N?
Attendance Score
1
2
3
4
5
6
7
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10
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15
16
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32
30
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12
10
8
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4
2
0
Attendance Score = 34 – 2  (# of days you were absent or extremely late)
Boardwork #
Date done
Boardwork Score
1
2
3
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5
6
7
8
9
10
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2
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36
Boardwork Score = 2  ( # of boardworks you did , not counting the ones you really did badly )
Total % of Points = (Attendance Score
+Boardwork Score
+Adjusted Quiz Score
+Exam Total
+Final Exam Score)/667
MTH 132(sec 103)
Corrected Topics List (for 3rd edition of Precalculus )
Fall 2007
8/20/07
The following brisk schedule optimistically assumes we will cover a multitude of topics at a rapid pace:
approximately 4 sections per week! Realistically speaking, we may surge ahead or fall somewhat behind,
but we can’t afford to fall too far off the pace. The major exams will be roughly on the 3rd, 6th, 9th, and
13th weeks, plus or minus one week. Their precise dates will be announced at least one week in advance
and the topics will be specified ( and may possibly differ from what is indicated below).
Come to class regularly and you won’t be lost.
Week
1
Dates
Fall
2007
8/208/24
2
8/278/31
3
9/49/7
Labor
Day
day on
9/3/07
Approximate schedule : Sections covered and topics
R1. - R7. Review of exponents, radical notation, factoring, simplifying
1.1
distance formula for points in the plane
midpoint formula
equation of circle in standard form
1.2 definition of function, domain and range of function
vertical line test
finding domains of functions
1.3 equations of horizontal and vertical lines
slope formula
graphing a line through a point with a known slope
average rate of change
1.4 slope intercept form
point slope form
using graphing calculator to fit data to a linear function
correlation coefficient
1.5 finding relative maximum and relative minimum values of a function
graphing piecewise functions
algebra with functions, finding the domain of sums, products and quotients
1.6 algebra of functions
finding the composition of functions
finding the domain of a composite function
writing a function as a composition
1.7 testing a graph for x-axis symmetry, y-axis symmetry and
symmetry about the origin
testing if a function is even or odd or neither
transformations:
vertical and horizontal translations of graphs
vertical stretching and shrinking of graphs
horizontal stretching and shrinking of graphs
reflections across the x-axis and across the y-axis
2.1
algebraically solving for a zero of a linear function
solving equations on calculator by finding the zero of a function, by finding
where graphs intersect
EXAM 1
Week
4
Dates
Fall
2007
9/109/14
5
9/179/21
6
9/249/28
Approximate schedule : Sections covered and topics
2.2
real and imaginary parts of complex numbers
addition, subtraction , multiplication of complex numbers
complex conjugation
dividing one complex number by another
2.3
using the technique of completing the square to solve quadratic equations
using the quadratic formula : discriminant determines the type of answer
solving equations which are quadratic in form
2.4 graphing quadratic functions in vertex form, in standard form :
finding the vertex, shape and axis of symmetry
max-min word problems which involve quadratic functions
2.5 solving rational equations: check solutions in original equation
solving radical equations: first isolate a radical on one side,
remember to check your solution in the original equation
solving equations with absolute value
2.6 multiplication principle for inequalities
solving linear inequalities
solving inequality statements joined by conjunction(and) & disjunction(or):
graphing the solution on a number line and using interval notation to
express the answer
solving absolute value inequalities
3.1 degree and leading coefficient of a polynomial function
the leading term test for general shape of the graph
maximum number of intercepts and turning points for a
polynomial of degree n
using Intermediate Value Theorem to estimate the location of a zero
3.3 doing long division: identifying dividend, divisor, quotient and
remainder and interpreting the result
the remainder theorem and factor theorem
3.4 multiplicity of zeros
finding real and complex zeros of polynomial functions by factoring
complex zeros of polynomials with real coefficients occur in conjugate pairs
rational zeros theorem for polynomials with integer coefficients
Descarte’s Rule of Signs
3.5 finding the domain of a rational function
finding equations of vertical asymptotes and the horizontal asymptote
oblique asymptote occurs when degree of numerator is 1 more
than degree of denominator
3.6 using sign charts and test points to solve polynomial and rational inequalities
using the graphing calculator to solve inequalities
3.7 direct variation, inverse variation and finding constant of proportionality
combination of direct and inverse variation
EXAM 2
Week
7
Dates
Fall
2007
10/110/5
Approximate schedule : Sections covered and topics
4.1
4.2
4.3
4.4
8
10/810/12
4.5
4.6
5.1
5.2
5.3
interchanging x and y coordinates to graph the inverse relation
one to one functions have inverses
using the horizontal line test to decide if a function is one to one
reflecting across line y = x to graph the inverse function
restricting the domain when the function is not one to one
to define an inverse function
graphs of exponential functions
definition of “log base a of x” log a x as the inverse of a x
converting a logarithmic to an exponential equation and vice versa
domain of logarithmic functions
natural logarithms, common logarithms
using the change of base formula to compute logarithms
using rules for logarithm of a product, quotient and power
to simplify expressions
other properties of logarithms
solving simple exponential equations
solving exponential equations by taking a logarithm on both sides
solving logarithmic equations: you must check your answer
in the original logarithmic equation
exponential growth and doubling time
exponential decay and half life
measuring angles in degrees, minutes and seconds
right triangle definitions of sine, cosine, tangent: SOH CAH TOA
reciprocal trig functions: cosecant, secant, cotangent
values of trig functions for special acute angles
using co-function identities to find trig functions of complementary angles
word problems involving solving right triangles
positive and negative angle, complementary and supplementary angles,
co-terminal angles
definitions of trig functions for angles on a circle of radius r
using reference angles to find trig functions for non-acute angles
using the value of one basic trig function and knowing the quadrant to find
the value of the other five basic trig functions
Week
9
10
11
Dates
Fall
2007
10/1510/19
Approximate schedule : Sections covered and topics
5.4
radian measure of angles on the unit circle
converting radians to degrees and vice versa
arc length formula for arc subtended by an angle( measured in radians )
relationship between linear speed and angular speed
5.5 unit circle definitions of the basic trig functions
using reflections and reference angles to find trig functions of any angle
on unit circle
cosine and sine of the negative of an angle
properties of graphs of cosine and sine:domain and range,
period and amplitude
basic shapes of graphs for tangent, cotangent, secant and cosecant
5.6 hand sketching graphs of transformed sine and cosine functions:
phase shift and starting point, period and ending point of one cycle,
axis of periodicity, basic shape of graph, amplitude
given a picture of a transformed sine or cosine graph, figure out what
the equation is
EXAM 3
10/226.1 the three Pythagorean Identities
10/26
cosine and sine of a sum/difference of angles
finding the cosine and sine of angles which are sums/differences
(Last day
of familiar angles
to drop
using trig identities to simplify expressions
on
6.2
co-function identities
10/26)
using double angle identities
using half angle identities to evaluate trig functions at half the value of a
familiar angle
using identities to simplify expressions
6.3 proving trig identities: using trig identities and substitution to make one side
look like another
10/296.4 using concept of restricting the domain to define
11/2
inverse functions for sine, cosine, tangent
definition of arcsine, arccosine, arctangent : know their domains
and ranges
simplifying compositions of trig functions with inverse trig functions:
sometimes a picture of a right triangle helps
6.5 solving trigonometric equations
7.1 Law of Sines
solving AAS and ASA triangles
solving SSA triangles: one solution, two solutions or no solution
finding area of an oblique triangle
Week
12
13
Dates
Fall
2007
11/511/9
11/1211/16
Thanksgiving
Break
next
week
14
11/2611/30
Week
of
the
Dead
(11/2812/4)
15
12/312/4
Approximate schedule : Sections covered and topics
7.2
7.3
using the Law of Cosines to solve SSS triangles
absolute value of a complex number
plotting a complex number in the coordinate plane
converting a complex number from standard form
to polar form and vice versa
using polar form to multiply, divide complex numbers
using DeMoivre’s Theorem to raise complex numbers to powers
finding roots of complex numbers in polar form
7.4 converting rectangular to polar coordinates and vice versa
hand graphing polar equations
EXAM 4
7.5 equivalent vectors have same direction and length
parallelogram law for addition and subtraction of vectors
7.6 standard position of a vector
writing a vector in component form
computing magnitude of a vector
addition, subtraction and scalar multiplication
finding a unit vector in the direction of a given vector
finding the direction angle of a vector
using dot products to find the angle between two vectors
8.1 solving system of two equations and two unknowns:
substitution and elimination methods
8.2 solving systems of three equations by Gaussian elimination
8.3 augmented matrix for a system of linear equations
elementary row operations
recognizing row reduced echelon form
Gauss-Jordan method of solving systems of equations
8.4 addition, subtraction, and scalar multiplication of matrices
additive inverse of a matrix, the zero matrix
knowing when you can multiply matrices together
matrix multiplication
8.5
the identity matrix
definition of the multiplicative inverse of a square matrix
Gauss-Jordan method of finding an inverse, if it exists
using inverses to solve matrix equations
8.6 determinants of square matrices
Cramer’s Rule
Review if we have time, or we may schedule it outside class hours
5.7
5.8
using geometric linear programming techniques to
solve systems of linear inequalities
decomposing rational expressions into partial fractions