Course: MAT 145 Precalculus for
Business or Social
Sciences
Catalog Description: A second course in the mathematics sequence leading to business or social sciences calculus. Topics include polynomial, rational, and piecewise defined functions, equations and inequalities: exponential and logarithmic functions and their graphs; multivariable systems of equations and matrices; extensive use of modeling and graphing calculators.
Prerequisites: MAT141
with minimum C grade
Instructor: Richard Porter
|
Contact Info: E-mail:
porterr@mcc.ecu
Web Page: http://www.mcc.edu/~porterr Office: LA 114 Extension 3826 Office Hours: See Web Page |
Book: Precalculus, 6th edition by Larson and Hostetler Houghton Mifflin Publishers Graphing Calculator: TI-83 or 86 recommended TI 89 or
92 NOT permitted |
Course Info:
Grading: Grade Scale:
|
Quizzes (10
quizzes 1% each) 10% Regression
Project 10% EXAMS (2 exams, 10
% each) 20% Midterm 20% Final: 40%
100% |
90%-100%........A 80%-89.5%.......B 70%-79.5%.......C 60%-69.5%.......D <59.5%.............F |
Attendance: Perfect attendance is expected, and students are responsible for all material covered. Arriving late or leaving early will count as missing HALF a class. Any student missing the equivalent of 4 classes is not eligible to receive credit for the course. If a WI grade is appropriate it will be given, if not, the student will receive an F. No excuse will be considered if it is not presented in writing and produced in advance when possible.
Make-ups: No make-ups are given for any reason. When valid excuses are produced in writing, work may be replaced by equivalent work from the final exam. One quiz can be missed without excuse.
Quizzes: Students should expect to hand in homework every class. The quiz grade will be made of questions from the homework or lecture. For all quizzes, the homework may be used as reference for the quiz, so do your homework! Homework is not accepted late.
Regression Project: A modeling project will be assigned during the semester. It will require the choosing of a relevant topic, the collection of data, the creation of a function to model the data, a graph of the data, a useful prediction.
Exams: There will be two exams, a midterm, and a final. The timed midterm and final will be administered in class. The two exams will be given at the testing center with no time limit. Each exam is usually about 10 to 20 short answer questions. There are NO multiple choice questions, showing all work is required even for calculator problems, and partial credit is given for correct work shown on exam. No scrap paper, books, notes, formulas, or calculator programs may be used with the exam.
YOU MUST RECEIVE A 50% ON THE FINAL EXAM TO PASS THE COURSE
THE FINAL EXAM IS CUMULATIVE
Academic Integrity: Students are encouraged to work together on homework. Students are expected to do their own work. Students who are caught cheating on tests will fail the course.
Classroom: Do not smoke or eat in class. No visitors (especially children) may attend. Disruptive students are expected to leave. Cell phones, beepers, and pagers can be disruptive and must be silent.
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DATE |
TOPIC |
SEC. |
Homework |
|
|
1 |
T 1/20 |
Introduction to
Graphs and Equations |
1.1,1.2 |
1.1 1.2 |
|
|
2 |
R 1/22 |
Data and Functions |
1.3,1.4 |
1.3 1.4 |
|
|
3 |
T 1/27 |
Transformations of
Functions |
1.5,1.6 |
1.5 1.6 |
|
|
4 |
R 1/29 |
Combinations of
Functions |
1.7 |
|
|
|
5 |
T 2/3 |
Inverse Functions
and Solving Equations |
1.8 |
|
|
|
6 |
R 2/5 |
Models |
1.9 |
|
|
|
7 |
T 2/10 |
Review Exam 1 |
|
|
|
|
8 |
R 2/12 |
Intro to
Polynomial Functions |
2.1 |
|
|
|
9 |
T 2/17 |
Higher degree
Polynomial Functions |
2.2 |
|
|
|
10 |
R 2/19 |
Polynomial
Division and Complex Numbers |
2.3,2.4 |
2.3 2.4 |
|
|
11 |
T 2/24 |
Zeros of
Polynomials and Graphing |
2.5 |
|
|
|
12 |
R 2/26 |
Rational Functions
|
2.6 |
|
|
|
13 |
T 3/2 |
Exponential
Functions |
3.1 |
|
|
|
14 |
R 3/4 |
Logarithmic
Functions |
3.2 |
|
|
|
15 |
T 3/9 |
Review Midterm |
|
|
|
|
16 |
R 3/11 |
In Class Midterm |
|
|
|
|
17 |
T 3/23 |
Review of Logs and
Exponents |
3.3 |
|
|
|
18 |
R 3/25 |
Solving Log
Equations |
3.4 |
|
|
|
19 |
T 3/30 |
Applications of
Logs and Exponents |
3.5 |
|
|
|
20 |
R 4/1 |
Discussions of
Projects |
|
|
|
|
21 |
T 4/6 |
Systems of
Equations |
7.1,7.2 |
7.1 7.2 |
|
|
22 |
R 4/8 |
Multivariable
Systems |
7.3,8.1 |
7.3 8.1 |
|
|
23 |
T 4/13 |
Review Exam 2 |
|
|
|
|
24 |
R 4/15 |
Systems of
Inequalities |
7.4 |
|
|
|
25 |
T 4/20 |
Linear Programming |
7.5 |
|
|
|
26 |
R 4/22 |
Matrices and
Equations |
8.1 |
|
|
|
27 |
T 4/27 |
Matrix Operations |
8.2-8.4 |
8.2 8.3 8.4 |
|
|
28 |
R 4/29 |
Applications of
Matrices |
8.5 |
|
|
|
29 |
T 5/4 |
Other Applications
of Precalculus |
TBA |
|
|
|
30 |
R 5/6 |
Review for Final
Exam |
|
|
|
|
|
T 5/11 |
Final Exam |
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Course Objectives
Answer the
questions:
- Why are you taking this course? Because
it is required.
- Why is the course required for your major?
Because the field uses functions.
- What are functions? Representations of
how one variable affects another.
- How are the ways that functions can be
represented? Points, equations, graphs.
- How can data be turned into equations?
Modeling or Regressions
- How can equations be turned into graphs?
Plotting, technology, graphing techniques
- How can equations and graphs be used to
make predictions? Evaluating, solving, interpreting, technology, and
techniques.
- How good are the predictions? What do
you think of others’ predictions?
- What is calculus? The study of change.
- How are you prepared for calculus and
everyday living?
|
|
Define,
state, or identify: |
You should be able to: |
|
1 |
1.
graph of an
equation 2.
intercepts 3.
symmetry 4.
linear equations
in 2 variables 5.
slope 6.
slope intercept
form of a linear equation 7.
point slope form
of a linear equation 8.
general form of
a linear equation 9.
parallel lines 10.
perpendicular
lines 11.
relation 12.
function 13.
domain 14.
range 15.
independent
variable 16.
dependent
variable 17.
function
notation 18.
implied domain 19.
vertical line
test 20.
zeros, roots and
solutions of a function 21.
relative minimum 22.
relative maximum
23.
symmetry in even
functions 24.
symmetry in odd
functions 25.
vertical and
horizontal shifts of a graph 26.
stretches and
compressions of a graph 27.
reflections of a
graph about the x or y axes 28.
inverse
functions, notation and symmetry 29.
horizontal line
test 30.
one to one
function 31.
direct
proportion or variation 32.
inverse
variation 33.
joint variation |
1.
sketch the graph
of an equation and confirm the sketch by choosing an appropriate
viewing window on the graphing calculator 2.
find the
intercepts, symmetry, domain, and range, identify types of symmetry and
confirm each on the graphing calculator 3.
make a table of
values on the graphing calculator for a given equation 4.
write the equation
of a circle in standard form given its center and a point on the circle and
sketch the graph 5.
find the slope
of a line and use it to graph the line 6.
use slope to
identify parallel or perpendicular lines 7.
write the
equation of a line when given a point on the line and its slope or two points
on the line 8.
write a linear
equation in slope intercept or standard form 9.
determine
whether a relation is a function when given a set of ordered pairs, an
equation, or a graph 10.
use function
notation to evaluate functions 11.
determine the
domain and range of a function and the implied domain, if applicable 12.
evaluate a
difference quotient given in function notation when given the function 13.
find the zeros, roots and solutions of a
function 14.
determine the
intervals where the function is increasing, decreasing, or constant 15.
identify even or
odd functions 16.
find relative
extrema for a given function and confirm by using the maximum or minimum
functions on the graphing calculator 17.
recognize the
equations and graphs of basic types of functions such as linear, constant,
identity, square or quadratic, cubic, square root, reciprocal, absolute value and greatest integer function 18.
sketch the graph
of a piecewise defined function and confirm on the graphing calculator 19.
analyze the effect
of and determine vertical and horizontal shifts, stretches and shrinks, and
reflections about the axes of a basic graph 20.
find the
equation for the sum, difference, product, or quotient of two given functions and determine the domain of
each 21.
find the
composite of two given functions and determine the domain of the composite 22.
find two
functions, f and g, such that 23. find the inverse and its domain and range of a given
one to one function and verify that two functions f(x) and g(x) are inverses
of each other by showing f(g(x)) = x
and g(f(x)) = x 24.
determine
whether a given set of ordered pairs, given graph, or given equation is a one
to one function 25.
graph a function
and its inverse on the same axes and graph the line of symmetry y = x 26.
use mathematical
models to analyze sets of data 27.
write
mathematical models for direct variation, inverse variation, and joint
variation 28.
use the
regression function of a graphing calculator to find the equation of a least
squares regression line 29.
solve
applications/word problems which assess all of the above topics |
|
2 |
1.
polynomial
function and its degree 2.
parabola 3.
vertex (h,k) of
a parabola 4.
standard form of
a quadratic function 5.
continuity of a
polynomial function 6.
zeros, roots or solutions
of a polynomial and their multiplicity k 7.
Intermediate
Value Theorem 8.
Remainder
Theorem 9.
Factor Theorem 10.
complex numbers 11.
Fundamental
Theorem of Algebra 12.
Linear
Factorization Theorem 13.
Rational Zeros
Test 14.
Descartes Rule
of Signs 15.
upper and lower
bounds on real zeros 16.
rational
functions 17.
discontinuity of
a rational function 18.
vertical
asymptotes 19.
horizontal
asymptotes 20.
slant or oblique
asymptotes 21.
synthetic
division |
1.
sketch the graph
of a polynomial or rational function and confirm the sketch by choosing an appropriate
viewing window on the graphing calculator 2.
put a quadratic
function in standard form to identify the vertex, and intercepts to aid in graphing it 3.
identify the
vertex of a parabola from its graph and write its equation in standard form 4.
use transformations
to assist in sketching the graph of a given polynomial function 5.
determine the
left and right end behavior of a polynomial using the degree and leading
coefficient 6.
find all real
zeros of a polynomial or rational function and their multiplicity and confirm
the zeros by using the “root” or “zero” function on the graphing calculator 7.
describe the
behavior of the graph of a polynomial at a zero with an odd or even
multiplicity 8.
write an
equation of a polynomial having given zeros and a given degree 9.
perform
algebraic long division and synthetic division of polynomials 10. evaluate a polynomial by using the remainder theorem
and synthetic division 11. find, if possible, all the zeros and their
multiplicity of a polynomial function with real coefficients and write the
polynomial as a product of linear and irreducible quadratic factors over the
real numbers using the Rational Zeros Theorem and upper and lower bounds on
the zeros 12. determine if two complex numbers are equal 13. add, subtract, and multiply complex numbers 14. use complex conjugates to write the quotient of two
complex numbers in standard form 15. find complex solutions of quadratic equations 16. use Descartes Rule of Signs to determine the possible
number of positive and negative zeros a polynomial has 17. find the upper and lower bounds on the real zeros for
a given polynomial 18. find the domain, range, vertical, horizontal, and/or
oblique asymptotes, if any, for a given rational function 19. solve applications that result in equations which are
polynomial or rational functions |
|
3 |
1.
algebraic
functions 2.
transcendental
functions 3.
exponential
function with base b or e 4.
continuously
compounded interest and interest compounded n times annually 5.
logarithmic
functions with base a, base 10, or
base e 6.
common
logarithms 7.
natural logarithms 8.
change of base
formula 9.
properties of
logarithms |
1.
graph a given
exponential function or logarithmic function, indicate its domain and range,
x or y intercept, describe it as increasing or decreasing and identify any
asymptotes the graph has 2.
perform vertical
and horizontal shifts, stretches and shrinks and reflections when given an
exponential or logarithmic function together with its graph 3.
convert a given
equation from exponential to equivalent log form or from log to equivalent
exponential form 4.
simplify and
evaluate log expressions 5.
write a given
expression as a single log using the properties of logarithms 6.
use the change
of base formula to find the log of any number in any base > 0 using base
10 or base e 7.
Solve
applications that result in exponential or log equations such as radioactive
decay, bacterial growth, compound interest, decibel level, earthquake
intensity, etc. 8.
solve
exponential equations by converting to log form or by converting to the same
base and equating exponents 9.
solve log equations
by converting to exponential form or by using the properties of logs 10. use a graphing calculator to solve exponential and
log equations 11. recognize exponential growth, exponential decay,
Gaussian, logistic growth, and logarithmic models and use these models to
solve given
problems |
|
7 |
1.
system of 2
linear equations in 2 variables 2.
solution of a
system of equations 3.
points of
intersection and graphing method of solution 4.
substitution
method of solution 5.
break-even point 6.
elimination by
addition or subtraction method 7.
equivalent
systems 8.
consistent
systems 9.
inconsistent
systems 10.
independent
systems 11.
dependent
systems 12.
row-echelon form 13.
ordered triple 14.
Gaussian elimination
method 15.
nonsquare
systems of equations 16.
linear
inequalities 17.
solution of an
inequality 18.
graph of an
inequality 19.
solution of a
system of inequalities 20.
linear
programming 21.
optimization 22.
objective
function 23.
constraints 24.
feasible
solutions 25.
optimal feasible
solution |
1.
Solve a system
of 2 equations in 2 variables by graphing and finding the points of
intersection, if any. If a special case results (same line or parallel
lines or no intersection) you should be able to identify the system as
dependent or inconsistent or having no solution respectively. 2.
solve a system
by substitution which works best if at least one equation has one variable
with a coefficient of + 1 3.
solve a system
by addition or subtraction to eliminate one of the variables 4.
use back substitution
to solve linear systems in row-echelon form 5.
use Gaussian
elimination to solve systems of linear equations 6.
solve nonsquare
systems of linear equations and write the solution as an ordered triple in
terms of an independent variable 7.
sketch the graphs
of inequalities in 2 variables and shade the solution region 8.
solve systems of
inequalities and shade the solution region for the system and describe the
solution as bounded or unbounded 9.
solve a linear
programming problem by identifying the objective function or the quantity to
be optimized, setting up a system of linear constraints or inequalities,
graphing their intersection to determine the vertices of the set of feasible
solutions and substituting these vertex points in the objective function to see
which gives the optimal value 10.
solve
applications that result in systems of equations or inequalities or linear
programming problems and use a graphing calculator where possible to
aid in each of these topics |
|
8 |
1.
matrix 2.
order of a
matrix (m x n) 3.
square matrix 4.
column matrix 5.
row matrix 6.
entry of a
matrix notation (aij) 7.
augmented matrix 8.
coefficient
matrix 9.
row equivalent
matrices 10. principal or main diagonal of a matrix 11. elementary row operations 12. row-echelon form 13. reduced row echelon form 14. Gauss-Jordan elimination method 15. determinant of a square matrix 16. minors 17. cofactors 18.
Cramer’s Rule |
1.
write a matrix
and identify its order 2.
perform
elementary row operations on matrices 3.
use the
augmented matrix for a system and the Gaussian elimination or the Gauss Jordan
elimination method to solve a system of linear equations 4.
describe an
entry in a matrix using aij notation 5.
find the
determinant of a 2x2 matrix 6.
find minors and
cofactors of square matrices 7.
find
determinants of an n x n square
matrix 8.
use Cramer’s
Rule to solve a system of linear equations 9.
solve
applications that result in systems of equations |