Management Precalculus
The strategies will consist of applications to the mathematical concepts as they
are developed
through graphical, numeric and analytic procedures. The primary objectives are:
• Mastery of algebra prerequisites: - A review of manipulation with exponents,
development and manipulation of algebraic fractions, and solution of systems of
equations . Technology will be used to help define and solve systems of linear
equations.
• Function definition and linear functions: - Mathematical concepts will be
developed for
functional notation and examples presented for linear functions. Data will be
presented
and linear models developed with the aid of graphing calculator technology .
• Exponential and log functions : - Growth/decay functions, and both common and
natural
log functions will be graphed, trends discussed and applications developed.
• Polynomials and rational functions : - The discussion of functions beyond the
linear
function will be presented mathematically and graphically. Trends in the
behavior of
these functions and applications will be discussed.
Grading policy: There will be a total of 500 possible points during the
semester. A combination
of quizzes and/or technology lab assignments will be given following material
coverage and
review. Quizzes will be based on assigned homework. These quizzes, projects and
classroom
participation will be worth 100 points and account for 1/5 of the grade. There
will also be three
fifty-minute examinations. Each of these examinations will be worth 100 points
and account for
1/5 of the grade. The common cumulative final examination will be worth 100
points and the
remaining 1/5 of the grade. One half of an 8.5 by 11 sheet of paper with notes
on both sides will
be allowed for the common final. It is the responsibility of each student to be
present for each
quiz and examination. Only validated exceptions will be allowed. Graphing
calculators can be
used on all quizzes and exams.
A guideline for course grade assignment will be:
FINAL AVERAGE
94-100 | 90-93 | 87-89 | 84-86 | 80-83 | 77-79 | 74-76 | 70-73 | 67-69 | 58-66 | 0-57 |
A | A- | B+ | B | B- | C+ | C | C- | D+ | D | F |
Arrangements are possible in individual sections for adjusted weights to be
assigned in order to
enhance individual overall performances.
Attendance policy: Students are expected to attend all classes and are
responsible for all
material covered. Quizzes will be given during class time. A missed quiz, late
lab assignment or
missed examination will result in a zero grade unless prior arrangements or
acceptable written
documentation is provided. Details of the attendance policy follow:
1. Attendance is required;
2. Students are allowed ONE unexcused absence;
3. Additional absences are excused only if the request is accompanied by a
Doctor's note or a
note from the Dean of Students on appropriate letterhead. This encompasses all
situations and
unforeseen hardships (accidents, illness, death of a relative, etc.);
4. TWO points will be deducted from the student's final course average per
unexcused absence
(minus the one allowed);
5. To monitor attendance, at the instructor’s discretion, each student will sign
his or her name to
a daily attendance sheet. No signature will be accepted for any student entering
class after the
first 15 minutes of scheduled class time and no sign-in for a particular class
will be allowed other
than the day of that class.
Technology: The TI-84 Plus Silver Edition or equivalent will be used throughout
the course as a
visual aid for learning. While technology will be used, students are responsible
for mastery of
analytic procedures presented.
Syllabus
92.121 Management Precalculus
Section | Topic | Exercises |
Chapter P | Prerequisites | |
P.1 | Real Numbers and Properties | p.9/19-37 odd,39,45,61,63,67,71,75,79,81, 83,97,99,101 |
P.2 | Exponents and radicals | p.21/1-35 odd,37,39,65,67,69,73,79,81,95, 97,99,107,110 |
P.3 | Polynomials and Special Products | p.29/25-53 odd,93,99,103 |
P.4 | Factoring | p.38/11,19-43 odd,47-59 odd,65,67,79,81, 87,89 |
P.5 | Rational Expressions | p.48/9-25 odd,31,32,35-49 odd,55,57,69,70, 73 |
P.6 | Errors and the Algebra of Calculus | p.56/1-7 odd,8-15 all,17,19,21,43,45 |
P.7 | Rectangular Coord. System/Graphs | p.64/1-15 odd,23-35 odd,47,49,50,55,56,57 |
Chapter 1 | Equations and Inequalities | |
1.1 | Graphs of Equations | p.86/1-11 odd,13,14,15,63,64 |
1.2 | Linear Equations in One Variable | p.94/23,25,29-37 odd,49,51,53,93,95,99 |
1.4 | Quadratic Equations/Applications | p.120/7-15 odd,21-27 odd,35-43 odd,51,53, 55,67,69,71,79,81,123,125,127 |
Chapter 2 | Functions and Their Graphs | |
2.1 | Linear Eqs in Two Variables | p.183/5-17 odd,21,23,29,31,39,45,47,51,53, 65,67,69,73,79,81,87,101,103,105,107,113 |
2.2 | Functions | p.197/11,12,13,15,17,25,27,29,57,59,61,97 |
2.5 | Transformations of Functions | p.228/9,11,13,15,43,45,47,51 |
2.6 | Combinations of Functions | p.238/5,7,13,15,19,21,35,37,63 |
2.7 | Inverse Functions | p.248/13-19 odd,33,39,42,43,55,82 |
Chapter 3 | Polynomial Functions | |
3.1 | Quadratic Functions | p.270/9,13,14,53,55,57,59,61,79,81,83 |
3.3 | Polynomial Division | p.295/5,7,11,13,69,70 |
3.5 | Least Squares Regression (p.314) | p.320/9,10 |
Chapter 4 | Rational Functions | |
4.1 | Rational Functions and Asymptotes | p.341/1-7 odd,43,44,45 |
4.2 | Graphs of Rational Functions | p.350/1-7 odd,13,22,23,82,83 |
Chapter 5 | Exponential and Log Functions | |
5.1 | Exponential Functions and Their Graphs | p.392/7,9,11,13,33,37,43,59,61,63 |
5.2 | Logarithmic Functions and Their Graphs |
p.402/1,3,9,17,19-23 all,25,45,53,59-67 odd, 87,89 |
5.3 | Properties of Logarithms | p.409/39-57 odd,61,63,65,69,73 |
5.4 | Exponential and Logarithmic Eqs | p.419/9-17 odd, 31,37,39,47,75,77,83,91, 107,109 |
Chapter 6 | Systems of Equations | |
6.1 | Solving Systems of Equations | p.455/5,7,15,23,49,63,64,67 |
6.2 | Two- Variable Linear Systems (elimination, and application to linear least squares regression) |
p.467/1-7 odd,11,13,45,47,53,55,57,63 |
Graphing Calculator Implementation
Systems of Equations
The following approach can be used for n by n systems of equations.
• | ax +by= c |
dx +ey= f | |
• | y_{1} = y_{2} : 2nd CALC intersect |
• | AX = B |
X = A^{-1}B | |
ex: | 3x +2y= 7 |
5x- y=3 |
a) MATRX, -> to EDIT, 1 to edit matrix A
b) 2 enter (row), 2 enter (column)
3 enter 2 enter
5 enter -1 enter to define matrix A then 2nd QUIT
c) MATRX, -> to EDIT, 2 to edit matrix B
d) 2 enter (row), 1 enter (column)
7 enter
3 enter to define matrix B then 2nd QUIT
e) to compute X = A^{-1}B , MATRX 1 (i.e. matrix A), x^{-1} (inverse of
A),
• (multiplication symbol is optional) MATRX 2 (i.e. matrix B), enter
output is
f) MATRX, 1, x^{-1} enter, yields A^{-1}
ex: show thatMATRX, NAMES, 1 (i.e. matrix A)
then * (optional), MATRX, NAMES, 1 (i.e. matrix A), x (inverse of A), enter
Linear Regression
ex: Model the Dow Jones (D.J.) weekly data with a linear regression model y=
ax+b.
a) STAT, EDIT to create data
b) 2nd QUIT, 2nd CATALOG, DiagnosticOn, enter (twice)
c) STAT, CALC, LinReg(ax+b)
d) LinReg(ax+b) L_{1},L_{2} ,y_{1} enter
e) 2nd STAT PLOT , option 1 , on
f) ZOOM, option 9
g) turn off plot 1 at y=screen or at STAT PLOT
Additional notes:
1. Collaborative techniques will be used as appropriate to supplement the
suggested list of
homework assignments and to help get the material across.
2. Use the TI repeatedly to encourage learning by visual, numeric and analytic
approaches. The
TI-84 Plus Silver Edition is recommended for new purchases.
3. The attendance policy WILL BE followed. To set the tone that students need to
conscientiously do the homework, at least two evaluations (quizzes or exams)
WILL BE given
by the end of the third week of class.
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