Download Orange County Community College

SUNY ORANGE (ORANGE COUNTY COMMUNITY COLLEGE)
MIDDLETOWN, NEW YORK 12553
FALL 2011
COLLEGE ALGEBRA MAT 121 – MRS. N. GRIFFIN-PELLEW
(Course taken at S.S. Seward Institute)
COURSE DESCRIPTION: College Algebra is the first of the 2 course pre-calculus sequence. It is a
functional approach to algebra designed to provide (1) the necessary preparation for students who
intend to study calculus or other specialized college mathematics courses, and (2) opportunity for
students in general education to investigate and understand the pre-calculus level of mathematics.
Prerequisite: C- or better in MAT 102 or Math Placement Test (if taken at OCCC)
CCHS Seniors - Cumulative GPA of 85 or higher in all Regents Courses and a minimum of 85 on
the Algebra 2/Trigonometry Regents
CCHS Juniors- Cumulative GPA of 90 or higher in all Regents Courses and a minimum of 90 on
the Algebra 2/Trigonometry Regents
This course may be applicable to several programs. Consult your advisor and refer to the OCCC catalog which
contains authoritative information.
STUDENT LEARNING OUTCOMES: Upon successful completion of this course, students will be able to:
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Determine the domain and range of a function and perform elementary operations on functions
Analyze and graph linear and quadratic functions
Analyze and graph polynomial and rational functions
Analyze and graph exponential and logarithmic functions and apply these functions to application
problems
Analyze and graph conic sections
TEXT: College Algebra, Blitzer, 5th ed., Pearson
SUPPORT SERVICES:
I expect that each of you will need extra help outside of class at one time or another during the semester (if
you don’t, then you should probably have signed up for a more advanced course). When this happens, you
should immediately seek help from the following sources in the following order:

Me: Don’t hesitate to come in for extra help after school. If you are not free at that time, talk to me after
class and we will arrange a time that is convenient for both of us.
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Math Lab: The Math Lab is located in room 305 in the Harriman Building at SUNY Orange. It is
staffed by faculty and students all day, Monday through Saturday, including days most school districts
are off.
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Tutorial Center: Individual tutoring is available to all recommended students at the Tutorial Center on
the second floor of the library. You can reserve up to five hours of tutoring for thirty dollars per
semester.
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Instructor:
E-mail:
Mrs. N. GRIFFIN-PELLEW
[email protected]
Class Expectations:
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Assignments are to be done neatly. Take pride in your work. All assignments are to be handed in
on given assignment sheet with additional loose-leaf paper, and/or graph paper where
appropriate.
Bring your textbook and loose-leaf binder, graph paper and straight edge to each class.
Use index cards to help you study definitions, theorems and rules. You may also wish to rewrite
any questions that you get wrong on homework, quizzes or tests on an index card, with its correct,
detailed solution on the other side. These are great to hang on to for on-the-spot practice. By the
end of the semester you will have a stack of problems to review for the final exam.
Read each section assigned- there are a lot of helpful hints you may be able to use.
See, copy, and listen to the lecture.
Reread the section and your notes; see and do the examples in the text.
ALWAYS do the assigned daily exercises.
Make corrections to any problems where needed.
Calculator Use: For the majority of work done in this course, including most tests and quizzes, no
calculator of any type will be permitted.
For certain topics in this course a scientific calculator may be used. I will announce such topics. You must
have your own scientific calculator for any test or quiz that permits. Calculators may not be shared.
Graphing calculators are not permitted.
EVALUATION:
Homework: Completing your homework is crucial to your success in this class. There will be homework
assigned at the end of each class which should be completed by the beginning of the next
class. You will need to do your homework in a separate section of your notebook or have a
separate notebook just for your homework. Before attempting each assignment, it is
important that you spend time reading your textbook and class notes. The answers to each
of the odd numbered problems are located in the back of the text. You must verify each of
your answers. If you did not complete the problem correctly you must make note of any
missed questions, leave a space for those problems in your homework not completed
correctly, and ask about them at the beginning of the next class.
**The homework may be collected and counted as a quiz or a homework quiz may be
given during class without notice- be sure to bring your completed assignments with
you to class everyday. If you have any questions about the homework, they need to
be asked at the beginning of class the day they are due.
Quizzes: There will be a quiz given at the end of each week (or at crucial points during a topic). No extra
time will be given to take a quiz.
Exams: There will be 4-5 major exams. You must notify me before the exam or on the same day of the
exam if it becomes necessary for you to miss an exam. You can leave a message for me by calling
the school or sending me an e-mail. If I am not notified and you do not have a reasonable excuse
with proof, I will not schedule a make-up exam and a zero grade will be recorded. In general,
make-up exams may be of greater difficulty than regular exams because of the additional study
time you have had. (The exams are usually announced one week in advance.)
Homework Quizzes and Weekly Quizzes will count for 40% of your final semester grade. The 5
major in class exams will count for 40% of your final semester grade. The comprehensive final
exam will count 20% of your final semester grade.
A minimum grade of C- (70%) is required in order to register for College Trigonometry – MAT122.
**Cell phones, their calculator mode, or other electronic devices are not to be utilized in class. Please turn
off all cell phones and pagers including those set to vibrate mode before entering the classroom so as
not to distract the instructor or your classmates during lectures, quizzes and tests.
**Any necessary changes to the above policies will be announced. **
INSTRUCTOR NOTE TO STUDENTS:
It is next to impossible to learn and retain information by giving a halfhearted amount of time to this
course. The students who succeed are able to keep current on the homework and more importantly,
do all the homework assigned. Please also be advised that the rigor and pace of this course is not
like that of a normal high school math class. Please reserve enough time to dedicate to working
through the assignments for this course.
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Section
P.1
P.2
P.3
P.4
P.5
P.6
1.1
1.7
Topic
Sets and Set Notation, Number Systems, Absolute Value,
Order of Operations
Exponent Rules
Radical Expressions and Rational Exponents
Polynomial Vocabulary, Add, Subtract, Multiply, Divide
Polynomials
Factoring Polynomials
Simplifying/Adding/Subtracting/Multiplying/Dividing
Rational Expressions, Complex Rational Expressions
Graphing 2-Variable Equations
Interval Notation
Chapter P and Other Prerequisites Review
Pg.
2
Exercises to Practice
21 – 41 odd, 51 – 95 odd
19
33
49
1 – 63 odd
1 – 107 odd
1 – 13 odd, 15 – 79 every other
odd, 81 – 85 odd
1– 61 odd, 65, 67, 69, 79, 81, 83
7 – 55 odd
62
73
89
172
86
Exam #1
2.1
197
Functions, Domain, Range, Notations
2.2
2.5
2.6
2.7
Difference Quotient, Increasing, Decreasing, Piecewise
Functions, Relative Max and Min, Symmetry
Transformations of Functions
The Algebra of Functions, Composite Functions
Inverse Functions, One to One Functions
Chapter 2 Review
4.1
4.2
4.3
4.4
4.5
Exam #2
Exponential Functions
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations
Exponential Growth and Decay, Modeling Data
Chapter 4 Review
Exam #3
215
254
270
282
302
411
424
437
447
460
474
13 – 27 odd and additional
handouts
1 – 25 odd
4-8, 25-31 odd, 41-117 every
other odd
Date to be announced
1, 3, 5, 15, 17, 19, 21, 23, 25, 27,
29, 31, 33, 35, 37, 39, 41,
43,51,57,59,61,63,65,67,75,
77-89 odd, 103, 108-116 all
1 – 41 odd, 45 – 65 odd,
95 – 105 all
17 – 29 odd, 53 – 59 odd,
67 – 73 odd, 81 – 87 odd, 95,
97, 99, 107, 109, 129 – 134 all
1 – 11 odd, 17, 19, 21,
31 – 35 odd, 49 – 79 odd, 103,
105,110
1 – 51 odd, 70 -73 all
1–25 odd,55,59,65,67,69–93
odd
Date to be announced
1 – 55 odd, 65, 66, 77, 78, 80
1 – 99 every other odd, 120,
122, 125, 139-145 all
1 – 77 every other odd, 89-101
every other odd 105, 106, 107,
109
1-89 every other odd, 101, 102,
117 – 122 all, 139-143 odd
1 – 19 odd, 31,33,37,42, 43,
45,56,58,59,62
1 – 87 every other odd
Date to be announced
3.1
3.2
3.3
3.4
3.5
Quadratic Functions
Polynomial Functions – Endpoint Behavior
Zeros, Intermediate Value Theorem
Polynomial and Synthetic Division; Remainder and
Factor Theorems
Rational Zero Theorem, Fundamental Theorem of
Algebra, Linear Factorization Theorem
Rational Functions
Domain, Intercepts, Vertical, Horizontal and Slant
Asymptotes and Sketches
Chapter 3 Review
2.8
7.1
7.2
7.3
Exam #4
Circles
Ellipse
Hyperbola
Parabola
Chapter 7 Review (along with 2.8)
Cumulative Review
Cumulative Final
311
328
1 – 37 odd, 74 – 79 all
1 – 63 odd, 75,77 – 88 all
342
1 – 45 odd, 58, 59, 61, 62, 63, 64,
70-73
1 – 31 odd, 65,69, 93-97
352
366
1 – 35 odd, 37, 39,
49 – 77 every other odd, 9397,98, 101, 102, 103, 104,105
404
1 – 35 odd, 41 – 45 odd (exclude
part b for each),
47 – 63 odd
Date to be announced
293
623
636
651
308
663
666
31 – 59 odd, 90-93
1 – 55 odd, 69-73
1 - 49 odd, 65-73
1 – 47 odd, 69-73
101 – 105
1 – 11 odd, 15 – 25 odd,
27 – 35 odd
1 – 7 all, 11, 12, 14a, l5, 16, 17
Date to be announced
Mrs. A. Rickard and Mrs. N. Griffin-Pellew
College Algebra
Pre-Requisites and Refreshers
The following information is what the SUNY Orange Math Department expects you to already be familiar with.
Some of you may need to brush up on these definitions, skills and techniques. Please see me for extra help
immediately. If this information is completely foreign to you, we may need to discuss your placement in this
course. Again, see me immediately if this concerns you.
Number Systems
Natural Numbers: {1, 2, 3, 4, …}
Whole Numbers: {0, 1, 2, 3, 4, …}
Integers: {…-3, -2, -1, 0, 1, 2, 3,…}
a
Rational Numbers: take the form , where a and b are integers, and b  0 . ( In laymen’s terms,
b
any fraction, terminating or repeating decimal)
Irrational Numbers: a number that cannot be written as the ration of two integers. This includes the
transcendental numbers such as  and e , and radicals which are not perfect roots ex:
3
25 . (In laymen’s terms, non-repeating, non-terminating decimals).
Real Numbers: All of the above, and the part of a complex number that is not imaginary.
Complex Numbers: All of the above when written in the form a  bi. Where a is the real part, and
bi is the imaginary part if b  0 and b is real.
Definition of i: i   1
Interval Notation and Set Notation
See page 4 of text for more details.
Given the real numbers a and b:
English Translation
Interval Notation
( a, b)
The set of reals between, but not including, a and b
( a, b]
The set of reals greater than a ending at b.
[ a, b)
The set of reals beginning at a up to but not
including b.
[ a, b]
The set of reals beginning at a and ending at b.
Set Notation
{x | a  x  b}
{x | a  x  b}
{x | a  x  b}
{x | a  x  b}
Order of Operations
Parentheses, exponents, multiplication or division (whichever comes first from left to right), addition or
subtraction (whichever comes first from left to right).
Rules of Exponents
a m  a n  a m n
Product Rule
am
 a m  n , a  0 Quotient Rule
n
a
(a m ) n  a mn Power Rule
(ab) m  a m b m Product to a power
m
am
a
   m Quotient to a power
b
b
a 0  1, a  0 Zero as a power
b0
Working with Fractions and Rational Expressions
Addition and subtraction: Must find a common denominator, then add or subtract numerators, keep common
denominator, final answer if possible.
Multiplication: Look to reduce either diagonally, or vertically, then multiply across: numerator times
numerator, denominator times denominator. Check to reduce again.
Division: Keep, change, flip. Meaning keep the first fraction (dividend) as it is, change division to
multiplication, and write the reciprocal of the second fraction (divisor). Then proceed to multiply as above.
Factoring Polynomials
1. Always look to factor out a Greatest Common Factor.
2. If given a binomial, look for special cases:
difference of two squares which factors into conjugate pairs. Ex: a 2  b 2  (a  b)(a  b)
difference of cubes: a 3  b 3  (a  b)(a 2  ab  b 2 )
sum of cubes: a 3  b 3  (a  b)(a 2  ab  b 2 )
3. If given a trinomial, look for special cases:
perfect square trinomial which factors to the square of a binomial.
Ex: a 2  2ab  b 2  (a  b) 2 and a 2  2ab  b 2  (a  b) 2
4. If no special cases exist, use guess and check (reverse FOIL) or factor by grouping.
5. If given a four termed polynomial, try factor by grouping.
Graphing Linear Equations
1. Use a straight edge to draw and label the x-axis and y-axis.
2. Get equation into slope-intercept form. ( y  mx  b)
3. Plot the ordered pair of the y-intercept.
Note: x and y intercepts are points. A point is written as an ordered pair. Ex: In the given equation
 2 
y=3x+2, the y-intercept is the point (0,2) and the x-intercept is the point   ,0  .
 3 
4. From the y-intercept, rise and run the given slope, and plot the next point.
5. Connect the points with a straight edge, and label the line with its equation.
More on Linear Equations
y 2  y1
Slope formula: m 
Point-Slope form: y  y1  m( x  x1 )
x 2  x1
Parallel lines have the same slope, but different y-intercepts.
Perpendicular lines have slopes which are negative reciprocals of o