MAT 1033
Intermediate
Algebra Handbook
Department of
Mathematics
University of
Central Florida
Course: Intermediate Algebra
Semester: Fall 2011
1
Table of Contents
Syllabus ......................................................................................................................................................... 3
Mathematics Assistance and Learning Lab (MALL) .................................................................................... 14
Policies and Procedures .............................................................................................................................. 14
Semester schedule ...................................................................................................................................... 17
Online Log-In Directions for MyLabsPlus .................................................................................................... 20
To change your password in MyLabsPlus ................................................................................................... 20
Technical Support ....................................................................................................................................... 20
Access Codes ............................................................................................................................................... 21
Temporary Access Code .............................................................................................................................. 21
Test Scheduling ........................................................................................................................................... 21
Test Taking .................................................................................................................................................. 22
Homework Assignments ............................................................................................................................. 23
Quiz Assignments ........................................................................................................................................ 24
Class Activity Assignments .......................................................................................................................... 25
MALL Assignments ...................................................................................................................................... 26
MyLabsPlus Help Documents...................................................................................................................... 27
Clearing Cookies and Cache/Files ............................................................................................................... 28
Browser Settings ......................................................................................................................................... 29
MAC Computer User Information: .............................................................................................................. 31
Key Concepts ............................................................................................................................................... 34
Calendars: ................................................................................................................................................... 53
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Syllabus
MAT1033 Intermediate Algebra, Fall 2011, 3 credit hours
Course
Description:
Course Goals:
Class Meetings:
Intermediate Algebra: PR: MAT 0024 OR SUITABLE
PLACEMENT SCORE or HIGH SCHOOL ALGEBRA OR
C.I.
MAT 1033, Intermediate Algebra, is a 3 semester hour college
credit course which may be applied towards a degree as
elective credit. Since it is considered a ―bridge‖ course, MAT
1033 cannot be applied towards the 6 hours of general
education or Gordon Rule requirements in mathematics.
MAT1033 is a prerequisite to MAC 1105, College Algebra.
The purpose of the course is reinforcement and development
of algebra skills needed for further study in mathematics.
Topics include operations with polynomials and rational
expressions, radicals, rational expressions, radicals, rational
exponents, linear and quadratic equations, linear inequalities,
and applications.
Upon successful completion of this course, the student will be
able to: 1. Factor positive integers into products of primes. 2.
Simplify algebraic expressions. 3. Recognize the order of
operations in algebraic expressions and equations. 4.
Manipulate rational expressions. 5. Convert between standard
and scientific notation. 6. Add, multiply, and divide
polynomials. 7. Factor monomials from polynomials, factor
trinomials, and use the special factoring formulas. 8. Simplify
expressions involving radicals, rational exponents, and
absolute value. 9. Set up and solve word problems. 10. Solve
linear, quadratic, and radical equations. 11. Solve linear
inequalities.
There is one lecture each week and a minimum of three hours
required in the Mathematics Assistance and Learning Lab
(MALL) located in MAP241.
Please see your specific class syllabus posted in MyLabsPlus
for time and location.
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Instructor Name,
Contact
Information, and
Office Hours:
Textbook and
Other Required
Materials:
Calculator:
Attendance/
Etiquette:
Academic
Honesty:
This information is also posted in your specific class Syllabus
and the Faculty Information section in MyLabsPlus.
Required: Intermediate Algebra, by Carson with MyLabsPlus
access code, TI-30XA calculator, 8.5‖X11‖ blue books for
each test and the final exam, and iClicker Transmitter.
You may use a Texas Instruments TI-30XA calculator on the
tests. You may not use any other type or model calculator in
this course. Cell phone calculators and sharing calculators of
any type will not be permitted. Use of an unauthorized
calculator will result in a grade of zero and possible
disciplinary action.
Please observe common rules of courtesy. Before entering the
classroom you should turn off all cell-phones and laptops as
they are not to be used during class. Past experience
indicates that the students who succeed in the class are those
who attend. You should plan on staying for the entire 50
minutes. Try to avoid leaving early or arriving late, as it is a
distraction to your classmates and your instructor.
Additionally, if you arrive late or leave early, you may lose
some or all of your class activity points for that day.
The work submitted in this class is expected to be your own.
Forms of cheating/academic dishonesty include (but are not
limited to): communicating with another student during a test
(this includes giving information to another student as well as
receiving that information), using an unauthorized calculator,
bringing in and/or using unauthorized material of any sort
during a test, submitting work that is not your own (both
parties are subject to disciplinary actions), and communicating
contents of a test to another student. UCF faculty members
have a responsibility for your education and the value of a
UCF degree, and so seek to prevent unethical behavior and
when necessary respond to infringements of academic
integrity. Penalties can include a failing grade in an
assignment or in the course, suspension or expulsion from the
university, and/or a "Z Designation" on a student's official
transcript indicating academic dishonesty, where the final
grade for this course will be preceded by the letter Z. For more
information about the Z Designation, please see
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http://www.z.ucf.edu/
In addition, further disciplinary action through the university
may be taken. Please be aware that disciplinary action through
the university could result in suspension or expulsion. For
more information on academic honesty, please see the Golden
Rule contents available at http://www.goldenrule.sdes.ucf.edu
Online Homework Online Homework: There will be graded online homework
and quizzes in MyLabsPlus, which utilize the MyMathLab
and Quizzes:
software packaged with your textbook. As these assignments
must be completed online, students will be expected to have
access to a computer. Students may use a computer in one of
the computer labs on the main campus.
All assignments will have posted due dates and these due
dates will not be extended, so please plan accordingly.
Personal computer issues, including login errors, will NOT
warrant an extension. If you are experiencing computer issues,
you are encouraged to contact the 24 hour a day technical
support at 1-888-883-1299.
The online homework questions are algorithmic iterations of
the textbook exercises. Homework assignments can be
repeated an infinite number of times within the time period
specified. The last submitted answer is the one used for
grading purposes. Your lowest homework grade will be
dropped when calculating your course average.
Online Quizzes: For each of the online homework
assignments, there is an associated online quiz that needs to be
completed. In order to begin the online quiz, you must score at
least 70% on the associated online homework assignment. (If
you do not score a 70% or higher on the homework by the due
date, you will not be able to take the associated quiz which
will result in you earning a 0% on that quiz.) Quizzes can be
taken up to seven times and the highest score of all the
attempts will be the recorded grade for that particular quiz. It
is highly recommended that you take a quiz more than once.
Your lowest quiz grade will be dropped when calculating your
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course average.
Cumulative/Comprehensive Assignments: There will be a
comprehensive online homework and quiz due on December
4, 2011. Both the cumulative online homework and the
cumulative online quiz will be due at 11:59pm on that day.
iClicker Policy &
Procedures:
We will be using the iClicker feedback system in every lecture
to provide an interactive classroom environment. Be prepared
to ―click-in‖ your answers to the questions posed. Class
activity grades will reflect iClicker responses.
Purchase: Be sure to purchase the correct iClicker for our
course as there several types of clickers available. If desired, it
may be possible to find an iClicker secondhand, and/or to sell
your used iClicker at the end of the semester.
Registration: Register at www.iclicker.com/registration. Be
sure to enter your NID in the Student ID field on the web site,
including the two leading letters. Students are required to
register their iClicker before the second class meeting. A
student who fails to register their iClicker by the second class
meeting will not receive class activity points until registered
and any zeros earned will not be changed.
Policy: The following policies will apply to the use of iClicker
in the course:
 Each student is responsible for registering their own
clicker ID under the correct student name.
 iClickers must be registered at the start of the semester
even if registered during a previous semester. Should a
student replace an iClicker during the semester, the
student is responsible for registering the new iClicker and
informing the instructor.
 Using two iClickers during class is PROHIBITED. If a
student ―clicks in‖ for another student who is not in the
classroom, both students will face disciplinary actions
which will include receiving a ZF for the course grade.
 If a student fails to bring their iClicker to class, they will
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not receive class activity points for that day.
 Students are expected to come to class prepared with
fresh batteries for their iClicker. Dead batteries will not
excuse missed iClicker responses.
 Students experiencing difficulties with their iClicker
should notify a classroom assistant right away and plan
on meeting with their instructor immediately after class.
Your instructor will make any determination regarding
credit for that day‘s class activities grade.
 Discussing iClicker questions in class is NOT cheating; it
is part of the iClicker learning exercise.
Class Activity:
Course activities are 10% of your overall course grade.
Your course activities in the course will be evaluated at the
end of the semester as follows:
1) The average of your Class Activity grades (including
iClicker grades) will be 5% of your total grade.
2) The average of your MALL Activity grades (including
MALL hour and practice test assignment scores) will be
5% of your total grade.
Class Activity Grades: Students will earn a grade for their inclass activities. Points will be earned for attending class in a
timely manner, being actively engaged during class time,
answering questions in-class through the use of the iClicker,
submitting assigned work, and working in groups when
required.
MALL Activities Grades: Each specified time period
students are required to spend at least 3 hours in the
Mathematics Assistance and Learning Lab (MALL), located in
MAP 240, 241 and 242. When entering or exiting the MALL,
students must present their UCF ID which will be swiped to
record arrival and departure times.
While in the MALL, students are expected to be actively
working on Intermediate Algebra and nothing else.
Acceptable activities include working on homework,
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quizzes, practice tests, test scheduling, and watching
course related multimedia content. Sleeping, accessing
material from other courses, or accessing electronic
devices such as cell phones, iPods, and/or any other
portable media players for any reason while in the MALL
is prohibited. Violating any of these rules can result in a zero
for your MALL participation grade for the time period, even if
all required hours have been completed. Chronic violators may
face disciplinary actions. Additionally, all cell phones and
any electronic device that beeps, rings, vibrates, or makes
a sound of any sort must be turned off while in the MALL.
No food or drinks are allowed in the MALL, with the
exception of bottled water in a see-through container.
Please note:
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You are responsible for tracking your own MALL
hours.
There will be no partial credit for earning less than the
minimum required MALL hours in a time period.
Hours earned in one time period over the minimum
required hours do not ―roll over‖ to the next time
period.
Any time spent in the MALL less than 15 minutes will
not accrue to your total MALL time. For example, if
you spend 14 minutes and 59 seconds in the MALL, you
will have 0 minutes added to your total MALL time. If
you spend 15 minutes in the MALL, you will have 15
minutes added to your total MALL time.
When a time period contains a holiday, the minimum
number of required hours will still be required.
Note that certain days and times are busier than others, so you
may occasionally have to wait for an open computer. If your
schedule permits, plan to use the MALL at one of the less busy
time periods. Additionally, it is strongly recommended that
you bring your math notebook with you to the MALL, do all
of your work in it in an orderly manner, and refer back to this
work whenever necessary.
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Tests and Final
Exam:
There will be three tests throughout the semester and a
comprehensive final exam. They will be administered in a
dedicated testing lab and it will be your responsibility to
register for them through a dedicated website; see the section
on test scheduling. We will announce a time period in which
you must schedule your test. All tests must be scheduled
during the allotted time period for that particular test. Once the
scheduling time period has ended, there will not be any
changes or additions to the test schedules.
Please make sure that you have scheduled your test prior to the
schedule closing date as you will receive a grade of 0% if you
do not schedule your test. This policy applies to the three
semester tests. For the final exam, see the make-up policies.
If you do not show up for your scheduled appointment, a grade
of 0% will be given for the test. This includes showing up at a
time other than the one your test is scheduled for. Students
electing to take their tests with the Student Disability Services
must schedule their tests with SDS during the usual scheduling
period, follow all SDS requirements for test scheduling, and
take their test in one of the testing days scheduled for their
course section.
It is your responsibility to make sure your registration was
successful. You are not registered for an exam unless,
when you log in into the scheduling website, you see your
reservation listed under “Check reservation”. You should
also receive a confirmation message on the computer
screen upon successfully completing your exam
registration, and/or a confirmation email within a few
hours; however, the only actual indication that you are
indeed scheduled for the exam is the reservation listed
under “Check Reservation / Need Support?” link.
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Students should attend each test with the following items:
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Valid UCF Student Identification Card
Knowledge of your MyLabsPlus login and password
Bluebook 8.5‖ x 11‖
Pen or pencil
TI30-XA Calculator
Should a student come to the MALL without his/her UCF
ID and a Bluebook, he/she will not be admitted to the
testing session until they are able to present both their
UCF ID and Bluebook.
Test Dates:
A grade of zero on a test will be assigned in one of the
following situations:
 the student fails to schedule his/her exam during the
allotted scheduling period (including the case in which
the student does not complete the exam scheduling
process);
 the student misses his/her scheduled appointment to take
the exam;
 the student violates the UCF Golden Rule during the
exam or in any circumstance relating to the exam;
 any of the student‘s electronic devices, including cell
phone, iPod, and/or portable media player, rings,
vibrates, or is accessed for any reason while in the
testing lab
Test 1: Scheduling opens 9/12/11 at 10:00am and closes
9/19/11 at 1:00pm
Test 1: September 20 – 23, 2011
Test 2: Scheduling opens 10/10/11 at 10:00am and closes
10/17/11 at 1:00pm
Test 2: October 18 – 21, 2011
Test 3: Scheduling opens 11/7/11 at 10:00am and closes
11/14/11 at 1:00pm
Test 3: November 15 – 18, 2011
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Final Exam: Scheduling opens 10/31/11 at 10:00am and closes
12/4/11 at 1:00pm
Final Exam: December 5 - 10, 2011
Make-up Policy:
All tests are scheduled through the online scheduling system.
Dates and times of tests will vary based on course enrollment.
Personal travel plans, medical reasons, and personal or family
emergencies will not be valid reasons for taking tests at a time
different than scheduled. Test, homework, and quiz make-ups
are not given. Option B will be used if a student misses a test.
University related absences that require special scheduling
must be arranged one week prior to the assessment date.
THE FOLLOWING POLICY APPLIES TO THE FINAL
EXAM ONLY. In the event you are not able to arrive
during your appointment time for the final exam for any
reason at all or you fail to schedule a final exam test
appointment, you will be permitted to take your final exam
at the following times with a 20 percentage point penalty:
Tuesday, December 6, 2011 at 7:00pm
Thursday, December 8, 2011 at 7:00pm
Saturday, December 10, 2011 at 10:00am
This policy is applicable for the FINAL EXAM ONLY!!!
Grading Policy:
The 20 percentage point penalty is not negotiable!
Example: A student who uses this option and scores a 94%
on the final exam would have a 74% recorded in the grade
book.
Your grade will be calculated based on the following options:
Option A:
Test 1 – 15% of total grade
Test 2 – 15% of total grade
Test 3 – 15% of total grade
MyMathLab Online homework average – 7% of total grade
MyMathLab Online quiz average – 8% of total grade
Course Activities – 10% of total grade
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Final exam score–30% of total grade
Option B:
Average of the highest two test scores – 30% of total grade
MyMathLab Online homework average – 7% of total grade
MyMathLab Online quiz average – 8% of total grade
Course Activities – 10% of total grade
Final exam score– 45% of total grade
Option B will be used if a student misses a test. If all three
tests are taken, the option resulting in the highest grade will be
used.
Email:
Please note: The penalty for an academic integrity violation
will range from a grade of zero on an exam to a grade of F for
the course. If a grade of 0% is given on any test due to a
Golden Rule violation, Option A will be used to calculate the
course grade. A "Z Designation" on the student's official
transcript indicating academic dishonesty may also be used for
any integrity violation.
You will receive several important messages from your
instructor during the semester, all of which will be sent to your
Knights email account. It is therefore your responsibility to
check your account on a regular basis.
Writing to Faculty: Although email is typically used as an
informal method of communication, this is not the case when
writing to a faculty member. In order therefore to ensure a
response to your message, you should follow the template
below:
Include a subject to indicate the course you are taking,
section number, time that the lectures meet, your first and
last name, and a meaningful topic.
 Address your instructor respectfully.
 Write a short formal message that outlines your concern.
 Include your name at the conclusion of the message.
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Grading Scale:
The +/- system will not be used in this class. Letter grades will
be awarded according to the following grading scale:
Average
90 – 100%
80 – 89%
70-79%
60-69%
0-59%
Disability Related
Accommodations:
Grade
A
B
C
D
F
The Z Designation will be used in cases of academic
dishonesty. For more information about the Z Designation,
please see the academic honesty section of the syllabus and
http://www.z.ucf.edu/
The University of Central Florida is committed to providing
reasonable accommodations for all persons with disabilities.
This syllabus is available in alternate formats upon request.
Students who need accommodations must be registered with
Student Disability Services, Student Resource Center Room
132, phone (407) 823-2371, TTY/TDD only phone (407) 8232116, before requesting accommodations from the professor.
No accommodations will be provided until the Student
Disability Services office has notified the professor concerning
appropriate accommodations.
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Mathematics Assistance and Learning Lab (MALL)
Policies and Procedures
The following describes the policies and operating procedures for the Mathematics
Assistance and Learning Lab (MALL) located in MAP 240, 241, and 242. It is
intended to provide important information and instructions for all users of the lab.
Students should review the following information and procedures.
1. Reporting problems. If you encounter difficulty with any equipment or software
in the MALL, you must report the problem to a proctor or staff member for
assistance before proceeding/attempting to fix the problem on your own. Report as
much information about the problem and your location as you can. Because many
exams are timed, reporting a technical problem as quickly as possible will
minimize the time required to get back online and complete the exam. If you have
a concern about an exam question, you may complete a Test Question Form to
report the concern to your instructor.
2. Electronic Monitoring. The MALL environment and its computers are
electronically monitored/recorded to include real-time video. Any and all
perceived incidents of student misconduct will be reported to the Student Conduct
Board for appropriate action.
3. Acceptable use. Students in the MALL are expected to use the resources
responsibly and in accordance with the Campus Use of Information Technology
and Resources Policy, which may be found at http://www.ucf.edu/rule/rule2.html.
Computer workstations must not be logged off, turned off, moved, or unplugged.
When departing the testing area, each student should return his or her keyboard,
mouse, and chair to their normal positions, and remove all trash from the area.
4. No unauthorized materials. It is preferred that NO cell phones, iPods, PDAs, or
books and notebooks for other classes be brought to the MALL. However, if a
student must bring one or more of the aforementioned items, they will be stored in
a backpack out of sight at the student‘s feet under the desk. If skateboards are
brought to the lab, they must be left in a designated skateboard bin. Should the
skateboard bin fill up, skateboards will be left outside the MALL in the hallway.
The MALL is not responsible for lost, damaged, or stolen items. Cell phones are to
be turned off, not set on vibrate or to an audible ringer, and at no time is a student
to access an electronic device, including a cell phone, while in the MALL. A
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student caught using a cell phones PDAs, ipods, etc., will receive a 0% for that
MALL period.
5. Unauthorized Individuals. No unauthorized individuals are permitted in the
MALL.
6. Entry to the MALL. A student must have their UCF ID to gain entry to the
MALL. Other forms of identification will not be accepted.
7. Food and Drink. No food or drinks may be brought into the MALL with the
exception of bottled water. Bottled water must be in a see-through container.
In addition to the above policies, the following policies are specific to testing.
8. Scheduling a Test. There will be an announced time period for which the test
will open and close for scheduling. Students will schedule their tests by clicking on
the ―Schedule a Test‖ menu button in MyMathLab. Once the scheduling time
period has ended, there will not be any changes or additions to the test schedules.
Please make sure that you have scheduled your test prior to the schedule closing
date as you will receive a grade of 0% if you do not schedule your test. Please
note: upon completion of a test scheduling process, a confirmation message
containing the test date and time will appear on the screen, and a confirmation
email will be sent to the email account you have indicated. You should confirm
that the reservation is complete by clicking on the “Check Reservation / Need
Support?” link in the system. You have not scheduled a test until you see this
confirmation message!
9. Items needed for an exam. Items required for entry into the testing lab are a test
reservation appointment, your UCF ID, and an 8.5‖ x 11‖ bluebook. You may also
bring a pen or pencil and a TI-30XA calculator. Please do not bring backpacks ,
skateboards, or any other personal items into the testing lab.
10. Check-in and out for an exam. Please arrive at the MALL 15 minutes before
your scheduled testing appointment. A valid UCF Student ID Card and a full sized
(8.5‖x11‖) Bluebook are required to gain entrance to the lab. Your UCF ID will be
electronically scanned to authenticate your access to the exam by the lab manager,
other lab staff, or one of the proctors. You will be assigned to sit at a particular
computer workstation.
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11. No unauthorized materials. If a student is caught using any unauthorized
materials in the testing lab (see policy #4 above) such as a cell phone or other
electronic device, or if that device rings or vibrates while in the testing lab, that
student will receive a grade of 0% on the test and possible disciplinary actions.
12. Leaving the testing area. Once a student is seated for an exam, he or she is not
permitted to move from that location for the duration of the exam. The exam must
be submitted prior to leaving the MALL.
13. Policy for General Power Failures. In extreme situations, such as a general
power failure, a server failure, forced evacuation of the building, etc. should a
testing session be interrupted student test work will automatically be saved, so that
when power or connection is re-established the student may again log into their test
and resume work for the remainder of their time. If a testing session is interrupted
for some other reason, it is likely that the student will be advised by a test proctor
to X out of their test (by clicking on the upper right corner X of their browser); the
student in this case should not click the Submit button for their test because then
the student will not be permitted to re-start and finish their test. For whatever
reason the testing session is interrupted, the test may resume soon thereafter or at a
later time. Students will be advised by the test proctor whether they should wait in
their seats until the test can be re-started, or whether they should submit their
names and then leave the MALL to return at a later time. If the latter is the case,
the return time will typically be within 24 hours.
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Semester schedule
Please Note: The following schedule may be modified at the discretion of the
instructor. Any change notification will be made via email or the announcement
page of MyLabsPlus.
Section
Week of 08/22/11-08/28/11
Week 1 Assignments
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Syllabus, Intermediate Algebra Handbook, MLP
MALL 1 (Orientation)
2.1
Linear Equations and Formulas
HW 1, QZ 1
2.2
Solving Problems
Class Activity 1
2.3
Solving Linear Inequalities
Section
Week of 08/29/11-09/04/11
Week 2 Assignments
2.4
Compound Inequalities
MALL 2
2.5
Equations involving Absolute Value
HW 2, Quiz 2
2.6
Inequalities Involving Absolute Value
Class Activity 2
Section
Week of 09/05/11-09/11/11
Week 3 Assignments
3.1
Graphing Linear Equations
MALL 3
3.2
The Slope of a Line
HW 3, Quiz 3
3.3
The Equation of a Line
Class Activity 3
Holiday: 09/05/2011 Campus closed for Labor day
Practice Test 1: Parts 1 and 2
Section
Week of 09/12/11-09/18/11
Week 4 Due Dates
3.4
Graphing Linear Inequalities
MALL 4
3.5
Introduction to Functions and Function notation
HW 4, Quiz 4
5.1
Exponents and Scientific Notation
Class Activity 4
Schedule Test 1
Practice Test 1: All Parts
Section
Week of 09/19/11-09/25/11
Week 5
5.2
Polynomials and Polynomial Functions
MALL 4 (cont’d)
5.3
Multiplying Polynomials
HW 5, Quiz 5
6.1
Greatest Common Factor and Factor by Grouping
Class Activity 5
Test 1: 2.1 – 2.6, 3.1 – 3.5, 5.1
Section
Week of 09/26/11-10/02/11
Week 6
6.2
Factoring Trinomials
MALL 5
6.3
Factoring Special Products and Factoring Strategies
HW 6, Quiz 6
Class Activity 6
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Section
Week of 10/03/11-10/09/11
Week 7
6.4
Solving Equations by Factoring
MALL 6
HW 7, Quiz 7
Class Activity 7
Practice Test 2: Parts 1 and 2
Section
Week of 10/10/11-10/16/11
Week 8
7.1
Simplifying, Multiplying, and Dividing Rational Equations
MALL 7
7.2
Adding and Subtracting Rational Expressions
HW 8, Quiz 8
Schedule Test 2
Class Activity 8
Practice Test 2: All Parts
Section
Week of 10/17/11-10/23/11
Week 9
7.3
Simplifying Complex Rational Expressions
MALL 7 (cont’d)
7.4
Solving Equations Containing Rational Expressions
HW 9, Quiz 9
Test 2: 5.2 – 5.3, 6.1 – 6.4, 7.1 – 7.2
Class Activity 9
Section
Week of 10/24/11-10/30/11
Week 10
8.1
Radical Expressions and Functions
MALL 8
8.2
Rational Exponents
HW 10, Quiz 10
8.3
Multiplying, Dividing, and Simplifying Radicals
Class Activity 10
Withdrawal Deadline: Thursday, October 27, 2011
Section
Week of 10/31/11-11/06/11
Week 11
8.4
Adding, Subtracting, and Multiplying Radicals
MALL 9
8.5
Rational Numerators and Denominators of Radical
Expressions
Football:
11/03/2011 Campus closed at 12:30pm
HW 11, Quiz 11
Schedule Final Exam
Practice Test 3: Parts 1 and 2
Section
Week of 11/07/11-11/13/11
Week 12
8.6
Radical Equations and Problem Solving
MALL 10
8.7
Complex Numbers
HW 12, Quiz 12
Holiday: 11/11/2011 Campus closed for Veterans day
Class Activity 12
Schedule Test 3
Practice Test 3: All Parts
Section
Week of 11/14/11-11/20/11
Week 13
9.1
The Square Root Principle and Completing the Square
MALL 10 (cont’d)
9.2
Solving Quadric Equations Using the Quadric Formula
HW 13, Quiz 13
9.3
Solving Equations that are Quadric in Form
Class Activity 13
Test 3: 7.3 – 7.4, 8.1 – 8.7
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Class Activity 11
Section
Week of 11/21/11-11/27/11
Week 14
4.1
Solving Systems of Linear Equations in Two Variables
MALL 11
4.6
Solving Systems of Linear Inequalities
HW 14, Quiz 14
11/23/11: MALL Closes at 7:30pm
Cumulative HW and QZ
Holiday: 11/24-25/11 Campus closed for Thanksgiving
Class Activity 14
Section
Week of 11/28/11-12/04/11
Week 15
Ch 2 - 9
Review for Final
MALL 11 (cont’d)
HW 15, Quiz 15
Cumulative HW and QZ (cont’d)
Class Activity 15
Section
Week of 12/05/11-12/10/11
Week 16
Final Exam Week!
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 It is in your Junk folder.
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Technical Support
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Access Codes
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Temporary Access Code
Please note that in an effort to get students started on their homework and quizzes
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Test Scheduling
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To make a reservation for a testing session:
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 Click on your course.
 Click the ―Test Scheduling‖ link on the left-hand menu bar.
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 Enter your NID and last name (first letter capitalized).
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Test Taking
To be admitted to the testing session, you must have three things:
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It is also highly recommended that you bring the following as well
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 Knowledge of your MyLabsPlus login and password
If it is necessary to retrieve login credentials subsequent to the student‘s
admittance to the testing room, the test will begin first, and that student will lose
some testing time.
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Homework Assignments
Online HW assignments
Due Dates
HW 1: 2.1 – 2.3
8/30/2011 at 11:59pm
HW 2: 2.4 – 2.6
9/6/2011 at 11:59pm
HW 3: 3.1 – 3.3
9/13/2011 at 11:59pm
HW 4: 3.4 – 3.5, 5.1
9/20/2011 at 11:59pm
HW 5: 5.2 – 5.3, 6.1
9/27/2011 at 11:59pm
HW 6: 6.2 – 6.3
10/4/2011 at 11:59pm
HW 7: 6.4
10/11/2011 at 11:59pm
HW 8: 7.1 – 7.2
10/18/2011 at 11:59pm
HW 9: 7.3 – 7.4
10/25/2011 at 11:59pm
HW 10: 8.1 – 8.3
11/1/2011 at 11:59pm
HW 11: 8.4 – 8.5
11/8/2011 at 11:59pm
HW 12: 8.6 – 8.7
11/15/2011 at 11:59pm
HW 13: 9.1 – 9.3
11/22/2011 at 11:59pm
HW 14: 4.1, 4.6
11/29/2011 at 11:59pm
HW 15: Past Exams
12/4/2011 at 11:59pm*
Cumulative HW**
12/4/2011 at 11:59pm*
My Score
My HW Average
* designates a different due date than normal
**designates an assignment that is mandatory for all students and can‘t be dropped
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Quiz Assignments
Online QZ assignments
Due Dates
QZ 1: 2.1 – 2.3
8/31/2011 at 11:59pm
QZ 2: 2.4 – 2.6
9/7/2011 at 11:59pm
QZ 3: 3.1 – 3.3
9/14/2011 at 11:59pm
QZ 4: 3.4 – 3.5, 5.1
9/21/2011 at 11:59pm
QZ 5: 5.2 – 5.3, 6.1
9/28/2011 at 11:59pm
QZ 6: 6.2 – 6.3
10/5/2011 at 11:59pm
QZ 7: 6.4
10/12/2011 at 11:59pm
QZ 8: 7.1 – 7.2
10/19/2011 at 11:59pm
QZ 9: 7.3 – 7.4
10/26/2011 at 11:59pm
QZ 10: 8.1 – 8.3
11/2/2011 at 11:59pm
QZ 11: 8.4 – 8.5
11/9/2011 at 11:59pm
QZ 12: 8.6 – 8.7
11/16/2011 at 11:59pm
QZ 13: 9.1 – 9.3
11/23/2011 at 11:59pm
QZ 14: 4.1, 4.6
11/30/2011 at 11:59pm
QZ 15: Past Exams
12/4/2011 at 11:59pm*
Cumulative QZ**
12/4/2011 at 11:59pm*
My Score
My Quiz Average
* designates a different due date than normal
**designates an assignment that is mandatory for all students and can‘t be dropped
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Class Activity Assignments
Class Activity
Day
Type
Class Activity 1
8/24/2011
In-class
Class Activity 2
8/31/2011
In-class
Class Activity 3
9/7/2011
In-class
Class Activity 4
9/14/2011
In-class
Class Activity 5
9/21/2011
In-class
Class Activity 6
9/28/2011
In-class
Class Activity 7
10/5/2011
In-class
Class Activity 8
10/12/2011
In-class
Class Activity 9
10/19/2011
In-class
Class Activity 10
10/26/2011
In-class
Class Activity 11
11/2/2011
In-class
Class Activity 12
11/9/2011
In-class
Class Activity 13
11/16/2011
In-class
Class Activity 14
11/23/2011
In-class
Class Activity 15
11/30/2011
In-class
My Class Activity
Average
25
My Score
MALL Assignments
Students are generally required to spend at least 3 hours twice a week in the
designated Mathematics Assistance and Learning Lab located in MAP 240, 241,
and MAP 242.
PRACTICE TEST NOTE: Practice test grades will be computed by averaging the different parts
of the practice test. For example, if a student scores 97, 75, 84, and 0 on the four parts of a
practice test, then the student‘s practice test grade will be 64. If the student completes a specific
part of the practice test more than once, the highest score for that part will be used in the average.
This score in turn will be averaged with the student‘s semester MALL grades.
MALL Assignments
Date Range
MALL Hour 1 (orientation)
Mon 8/22/11 – Tues 8/30/11*
MALL Hour 2
Wed 8/31/11 – Tues 9/06/11
MALL Hour 3
Wed 9/7/11 – Tues 9/13/11
Practice Test 1
Due: Mon 9/19/11 at 11:59pm
MALL Hour 4
Wed 9/14/11 – Tues 9/27/11
MALL Hour 5
Wed 9/28/11 – Tues 10/4/11
MALL Hour 6
Wed 10/5/11 – Tues 10/11/11
Practice Test 2
Due: Mon 10/17/11 at 11:59pm
MALL Hour 7
Wed 10/12/11 – Tues 10/25/11
MALL Hour 8
Wed 10/26/11 – Tues 11/1/11
MALL Hour 9
Wed 11/2/11 – Tues 11/8/11
Practice Test 3
Due: Mon 11/14/11 at 11:59pm
MALL Hour 10
Wed 11/9/11 – Tues 11/22/11
MALL Hour 11
Wed 11/23/11 – Sun 12/4/11*
My MALL Participation Average
* designates a different due date than normal
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My Score
MyLabsPlus Help Documents
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29
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30
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Key Concepts
Sets and the Structure of Algebra
Operations with Real Numbers;
Properties of Real Numbers
Carson, 1.1
Carson, 1.2
Definitions
Properties of Addition
Inequality: Two expressions separated by  ,  ,  , <, >
Set: A collection of objects
Subset: If every element of a set B is an element of a set A,
then B is a subset of A.
Rational Number: Any real number that can be expressed in
a
the form , where a and b are integers
b
and b  0 .
Irrational Number: Any real number that is not rational
Prime Number: A natural number with exactly two different
factors, 1 and the number itself.
The set of natural numbers: {1, 2, 3,…}
The set of whole numbers: {0, 1, 2, 3…}
The set of integers: {…, −3, −2, −1, 0, 1, 2, 3,…}
Absolute Value: A number‘s distance from zero on a number
line.
Identity of Addition: a  0  a
Commutative Property of Addition: a  b  b  a
Associative Property of Addition: a  (b  c)  (a  b)  c
Properties of Multiplication
Multiplicative Property of 0: a  0  0
Identity Property: a 1  a
Commutative Property of Multiplication: ab  bc
Associative Property of Multiplication: a(bc)  (ab)c
Distributive Prop of Mult. over Add.: a(b  c)  ab  ac
Exponents, Roots, and Order of Operations
Carson, 1.3
Exponential form is used to represent repeated multiplication.
nth power of b: b n  b  b  b  ...  b (b is used as a factor n
times)
Inequality Symbols and Their Translations
Symbolic Form Translation
Eight is not equal to three
83
5<7
Five is less than seven
7>5
Seven is greater than five
x is less than or equal to three
x3
y2
y is greater than or equal to two
b = base
n = exponent
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Square Root: one of two equal factors
Order of Operations Agreement
Perform operation in the following order:
1. Within Grouping symbols. (Work from the inside out.)
Examples: parentheses (), brackets [], braces {},
absolute value | |, above and/or below fraction bars, and
radicals √
2. Exponents/Roots
(from left to right)
3. Multiplication/Division
(from left to right)
4. Addition/Subtraction
(from left to right)
General Rules of Square Roots:
1.
Every positive number has two sq. roots. (+, )
2.
The radical denotes the positive (principal) root.
3.
The sq. root of a negative number is not a real
number.
Cube Root: one of three equal factors
In general,
n
a = nth root of a
Use your favorite acronym:
Please, Excuse, My Dear Aunt Sally (PEMDAS)
OR
Golly! Excuse My Dear Aunt Sally (GEMDAS)
called the radical
a
n
called the radicand
called the index
Evaluating and Rewriting Expressions
Division and Square Roots:
a
a
, where a  0 and b  0 .

b
b
35
Addition
the sum of x and three
h plus k
t added to seven
three more than a number
y increased by two
Translation
x+3
h+k
7+t
n+3
y+2
Subtraction
the difference of three and x
h minus k
seven subtracted from t
three less than a number
two decreased by y
Translation
3−x
h–k
t −7
n–3
2−y
Carson, 1.4
Multiplication
the product of x and three
h times k
twice a number
triple the number
two-thirds of a number
Translation
3x
hk
2n
3n
2
n
3
Division
the quotient of x and three
Translation
x
x  3 or
3
h
h  k or
k
k
k  h or
h
a
a  b or
b
h divided by k
h divided into k
the ratio of a and b
Exponents
c squared or the square of c
k cubed or the cube of k
n to the fourth power
y raised to the fifth power
Translation
c2
k3
n4
y3
Roots
the square root of x
Translation
x
the cube root of y
the fifth root of n
Combining Like Terms: To combine like terms, add or
subtract the coefficients and keep the variables and their
exponents the same.
To evaluate an algebraic expression:
1. Replace each variable with its corresponding given
value
2. Simplify the resulting numerical expression
Linear Equations and Formulas
Carson, 2.1
Solution: A number that makes an equation true when it
replaces the variable in the equation.
Solution Set: A set containing all of the solutions for a given
equation.
Linear Equation in one Variable: An equation that can be
written in the form ax + b = c, where a, b, and c are real
numbers and a ≠ 0.
3
y
To solve:
1.
Simplify each side. (collect like terms, distribute, etc.)
2.
Use adding or subtracting (while maintaining the
equation‘s balance) to collect all variable terms on one
side and all constants on the other.
3.
Multiply or divide on both sides to clear any remaining
coefficient.
5
n
Goal = Isolate the variable.
36
Addition Principle of Equality: If a = b, then a + c = b + c is
true for all real numbers a, b, and c.
Solving Linear Inequalities
Linear Inequality in one variable:
An inequality that can be
written in the form ax + b > c (OR <, >, < ), where a ≠ 0.
Multiplication Principle of Equality: If a = b, then ac = bc is
true for all real numbers a, b, and c, where c ≠ 0.
To solve an inequality:
1. Solve just like an equation.
2. When multiplying or dividing by a negative number,
reverse the inequality.
3. Solution is a set of numbers: all the possible values of x
making the inequality true.
Three Types of Equations:
Conditional:
A specific solution.
Identity:
Solution is every real number.
Contradiction: No solution.
Solving Problems
Carson, 2.3
Carson, 2.2
Graphing Inequalities
To graph an inequality in one variable of the form x  a ,
x  a , x  a , or x  a on a number line,
1. If the symbol is  or  , draw a bracket (or solid circle)
on the number line. If the symbol is < or >, draw a
parenthesis (or open circle) on the number line
2. If the variable is greater than the indicated number,
shade to the right. If the variable is less than the
indicated number, shade to the left.
Problem Solving by Polya
Understand, Plan, Execute, Answer, Check
Word Problems:
1. Represent one unknown with a variable.
2. Represent other unknowns using a relationship in
problem.
3. Write an equation.
4. Solve the equation.
5. Check.
words that
means 
at least
minimum of
no less than
37
words that
mean >
is greater than
more than
words that
mean 
at most
maximum of
no more than
words that
mean <
is less than
smaller than
Compound Inequalities
Carson, 2.4
Equations Involving Absolute Value
Compound inequalities:
In a compound inequality the symbols will point in the same
direction. Two inequalities joined by either and or or.
Carson, 2.5
Absolute Value Property:
If |x| = a, where x is a variable or
an expression and a > 0, then x = a or x = −a.
Absolute Value: A number‘s distance from zero on a number
line. (Always equal to a positive number; represents distance.)
Option 1: Approach as intersection/overlap of 2 separate
inequalities:
Option 2: Approach as a ―3-sided equation‖ performing
operations on all 3 sides.
To solve an equation containing a single absolute value:
1. Isolate the absolute value so it is in the form ax  b  c
2. Separate into 2 cases: ax  b  c and ax  b  c
3. Solve both equations.
Intersection: For two sets A and B, the intersection of A and B,
symbolized by A  B , is a set containing only elements that
are in both A and B.
To solve an equation in the form ax  b  cx  d :
To solve a compound inequality involving and:
1. Solve each inequality in the compound inequality.
2. The solution set will be the intersection of the
individual solution sets.
1. Separate into 2 cases: ax  b  cx  d and
ax  b  (cx  d )
2. Solve both equations
Union: For two sets A and B, the union of A and B, symbolized
by A  B , is a set containing every element in A or in B
To solve a compound inequality involving or:
1. Solve each inequality in the compound inequality
2. The solution set will be the union of the individual
solution sets.
38
Inequalities Involving Absolute Value
Carson, 2.6
Graphing Linear Equations
x  a means x  a and x  a (or more compactly as
–a < x < a)
Cartesian OR rectangular coordinate system
Ordered Pair: (x, y), which translates to (horizontal coordinate,
vertical coordinate), where the coordinates represent distances
from the origin (+ means right or up, – means left or down)
Origin:
Set-builder notation:
x  a  x  a
Interval notation:
(a, a)
x x  a, or, x  a
Interval notation:
(,a)  (a, )
(0, 0)
Quadrants:
I, II, III, IV
start in upper-right
corner; count counterclockwise
x  a means x  a or x  a
Set-builder notation:
Carson, 3.1
x-intercept: A point where the graph intersects the x-axis.
To find (x, 0): Replace y with zero in the given equation.
Solve for x.
To solve an inequality of the form x  a , where a > 0:
1. Rewrite the inequality as a compound inequality
involving and: x > −a and x < a (or use –a < x < a)
2. Solve the compound inequality
y-intercept: A point where the graph intersects the y-axis.
To find (0, y): Replace x with zero in the given equation.
Solve for y.
To solve an inequality of the form x  a , where a > 0:
1. Rewrite the inequality as a compound inequality
involving and: x < −a and x > a
2. Solve the compound inequality
To graph a linear equation:
1. Find at least two solutions to the equation
2. Plot the solutions
3. Draw a line through the points
39
The y-intercept of y  mx  b :
Given an equation in the form y  mx  b , the coordinates
of the y-intercept are (0, b)
Positive Slope (m > 0):
Negative Slope (m < 0):
Undefined Slope (m = undef):
Slope is 0 (m = 0):
Horizontal Lines
The graph of y = c, is a horizontal line parallel to the x-axis
with a y-intercept at (0, c).
Vertical Lines
The graph of x = c, is a vertical line parallel to the y-axis
with an x-intercept at (c, 0)
The Slope of a Line
The Equation of a Line
Carson, 3.2
Point-Slope Form:
Given the slope, m, and any point (x1, y1)
on the line, write the equation of the line using point-slope
form:
y − y1 = m (x − x1)
Slope-Intercept Form: A linear equation in the form y = mx + b.
The coordinates of the y-intercept are (0, b).
The coefficient m affects the incline of the line.
(pg. 126)
(pg. 135)
Parallel Lines: Non-vertical parallel lines have equal slopes and
different y-intercepts. Vertical lines are parallel.
Slope : steepness or slant of a line
Point #1 on the line: ( x1, y1 )
Point #2 on the line: ( x2, y2 )
m = slope =
Carson, 3.3
Perpendicular Lines: The slope of a line perpendicular to a
a
b
line with a slope of
is  . Horizontal and vertical lines are
b
a
perpendicular.
y2  y1 rise y


x2  x1 run x
40
Standard Form: The equation of a line in standard form is
Ax  By  C , where A, B, and C are integers and A > 0.
Introduction to Functions and
Function Notation
Relation:
Graphing Linear Inequalities
A set of ordered pairs.
Carson, 3.4
Domain:
A set containing initial values of a
relation; its input values; the first
coordinates in ordered pairs.
Range:
A set containing all values that are
paired to domain values in a relation; its
output values; the second coordinates in
ordered pairs.
Function:
A relation in which each value in the
domain is assigned to exactly one value
in the range.
Linear Inequality in 2 Variables:
An inequality that can be
written in the form Ax + By > C
(or <, <, >)
where A, B, C are real numbers and A, B are not both zero.
Solution set: A set of points described by a shaded region in the
xy-plane.
Solutions to the corresponding equation for the boundary line
for this shaded region. This boundary line may or may not be
included.
To graph a linear inequality in two variables:
1.
→
→
2.
→
→
Carson, 3.5
Input, x

Domain
Independent variable
Graph the related equation (boundary line).
If the inequality symbol is < or >, then use a solid line.
If the inequality symbol is < or >, then use a dotted line.
function

Output, y
Range
dependent variable
Representing a Function using a Formula:
Name of function = f
Input = x
Output = f (x) or y
f (x) represents output received when function f is applied to x.
Choose a test point NOT on the boundary line.
If this point satisfies the inequality, then shade the
region that contains it.
If this point does not satisfy the inequality, then shade
the region on the other side of the boundary line.
41
Finding the Value of a Function:
Given a function f (x), to find f(a), where a is a real number in
the domain of f, replace x in the function with a and then
evaluate or simplify.
4c)
n
5)
6)
7)
Vertical Line Test:
 If each vertical line intersects the graph at only one
point, the relation is a function.
 If any vertical line intersects the graph more than once,
the relation is not a function.
Exponents and Scientific Notation
Negative Exponent Rule (Part 3 – applied to a quotient:
n
a
b
   
b
a
Power-raised to a-Power Rule: (a m ) n  a mn
Product-raised to a-Power Rule: (ab) n  a n b n
n
Quotient-raised to a-Power Rule:
an
a
   n
b
b
Scientific Notation:
 is used to write very large or very small numbers.
 a number in the form a 10n
 where a is a decimal number with 1  a  10
Carson, 5.1
Exponential form is used to represent repeated multiplication.
nth power of b:
(n times)
b n  b  b  b  ...  b
b = base
n = exponent
 and n is an integer
n > 1: pos exponent on 10.
n <1: neg exponent on 10
Properties of Exponents:
1)
2)
3)
4a)
4b)
Polynomials and Polynomial Functions
Product Rule: a m  a n  a m n
Zero Exponent Rule: a 0  1
am
Quotient Rule: n  a m  n , (a  0)
a
Negative Exponent Rule (Part 1 – the definition):
1
a n  n
a
Negative Exponent Rule (Part 2 – in the denominator):
1
 an
n
a
Carson, 5.2
Term: A number or the product of a number and one or more
variables raised to powers.
Polynomial: A term or a finite sum of terms where each
coefficient is a real number and variables are raised to only
whole number powers.
 Monomial: Polynomial with one term. (see above)
 Binomial: Polynomial with two terms. (x3 + 4)
 Trinomial: Polynomial with three terms. (r4 – 3r2 + 8r)
42
Coefficient:
The numerical factor in a monomial.
Degree of a Monomial:
variables in the monomial.
The sum of the exponents of all
Degree of a Polynomial:
terms in the polynomial.
The greatest degree of any of the
Special Products:
(a  b) 2  a 2  2ab  b 2
(a  b) 2  a 2  2ab  b 2
(a  b)(a  b)  a 2  b 2
Conjugates: Binomials that are the sum and difference of the
same two terms.
Like Terms: Variable terms that have the same variable(s)
raised to the same exponents, or constant terms.
To Add Polynomials: Combine like terms.
Greatest Common Factor and
Factor by Grouping
To Subtract Polynomials:
Use the additive inverse.
Distribute the negative to each term of the second polynomial.
Factored Form: A number or expression written as a product
of factors.
Multiplying Polynomials
Greatest Common Factor (GCF):
A monomial with the
greatest coefficient and degree that evenly divides all of the
given terms.
Carson, 5.3
Multiplying by a Monomial:
 use distributive property
 use exponent property – product rule
Carson, 6.1
Factoring using the GCF:
 Find the GCF of the terms of the polynomial.
 Rewrite the polynomial as a product of the GCF and
the quotient of the polynomial and the GCF.
Multiplying Polynomials:
 Multiply each term in the second polynomial by each
term in the first polynomial.
 Combine like terms.
 make use of the distributive property
 polynomial 
Factored Form = GCF 

 GCF

NOTE: For 2 binomials, use FOIL(First, Outside, Inside, Last)
43
Factoring by Grouping: ( Try when there are 4 terms. )
 Factor any GCF that is common to all 4 terms.
 Group 4 terms into pairs. Factor out the GCF in each pair.
 Factor out a common binomial factor (the parentheses).
 NOTE: Rearranging the terms may be necessary.
Trinomial:
Factoring by Trial-and-Error: ax2 + bx + c, where a ≠ 1
 Factor any GCF that is common to all terms.
 Write in a pair of first terms whose product is ax2.
 Write in a pair of last terms whose product is c.
 Verify that the sum of the inner and outer products is
bx.
Zero-Factor Theorem: If a and b are real numbers and ab = 0,
then a = 0 or b = 0.
Factoring Trinomials
Trinomial:
Understanding the process:
Factoring by Grouping: ax2 + bx + c, where a ≠ 1
 Factor any GCF that is common to all terms.
 Find two factors of the product ac whose sum is b.
 Rewrite the polynomial by splitting the middle term.
 Factor by grouping.
Carson, 6.2
A polynomial with 3 terms.
A polynomial with 3 terms. (pg. 281)
(pg. 281)
(Trial and Error)
reversing FOIL (x + ___ )(x + ____ )
Factoring by Substitution:
Make a substitution so that an equation may be written in the
format: ax2 + bx + c.
Factoring Special Products and
Factoring Strategies
Procedure: To factor x2 + bx + c:
 Find two numbers: multiplying to equal c adding to
equal b
 The factored trinomial will have the form: (x + #)(x + #)
Carson, 6.3
Perfect Square Trinomials:
(special patterns)
2
2
 a  2ab  b  (a  b)(a  b)  (a  b) 2
 a 2  2ab  b 2  (a  b)(a  b)  (a  b) 2
NOTE about SIGNS:
If the last term of the trinomial is positive,
 then both factors will have the same sign (as the middle
term).
If the last term of the trinomial is negative,
 then the factors will have opposite signs.
Factoring a Difference of Squares:
 a 2  b 2  (a  b)(a  b)
44
(use the conjugate)
Factoring Perfect Cubes:
Difference of Cubes:
a  b  (a  b)(a  ab  b )
Sum of Cubes:
a 3  b3  (a  b)(a 2  ab  b 2 )
Memory Aid: S-O-A-P
S-same
O-opposite
A-always
P-positive
refers to the signs
Solving Equations by Factoring
3
3
2
Polynomial Equation in Standard Form: P = 0,
where P is a polynomial in terms of one variable written in
descending order of degree.
Quadratic Equation: Written in the form: ax2 + bx + c = 0,
where a, b, c are real numbers and a ≠ 0.
Cubic Equation: Written in the form: ax3 + bx2 + cx + d = 0,
where a, b, c, d are real numbers and a ≠ 0.
Note: A sum of squares, a 2  b 2 , is prime
Zero-Factor Theorem:
If a and b are real numbers and ab = 0, then a = 0 or b = 0.
Factoring Tips:
(listed in detail on page 353)
 Factor any GCF that is common to all terms first.
 Consider the number of terms involved and choose a
factoring strategy.
o Four Terms: Factor by grouping.
o Three Terms: Factor the trinomial using
 Trial and Error / Reversing FOIL
 Split the middle term / Use
grouping
 Use substitution

Carson, 6.4
2
Recall from section 3.1…
x-intercept: A point where the graph intersects the x-axis.
To find (x, 0): Replace y with zero in the given equation.
Solve for x.
NOTE: Quadratic Functions (whose graph is a parabola)
may have at most 2 x-intercepts.
Cubic Functions (whose graph is an S-shape)
may have at most 3 x-intercepts.
If the trinomial factors into 2 equal factor, write
your answer as a perfect square.
o Two Terms: Factor the binomial using
 Difference of Two Squares
 Difference of Two Cubes
 Sum of Two Cubes
Always factor completely.
Read the detailed description on pages 364-365.
Pythagorean Theorem: Given a right triangle where a and b
represent the lengths of the legs and c represents the length of
the hypotenuse, a 2  b 2  c 2 .
45
Simplifying, Multiplying, and Dividing
Rational Expressions
Rational Function:
expressions.
Carson, 7.1
Rational Expression: A fraction dividing 2 polynomials.
An expression that can be written in the form
Domain of a Rational Function: (before simplifying)
 Recall: In a rational expression, the denominator ≠ 0.
 Write an equation that sets the denominator equal to 0.
 Solve the equation.
 Exclude the value(s) found from the function‘s domain.
P
, where
Q
P and Q are polynomials and Q ≠ 0.
To Simplify a Rational Expression:
 Factor the numerator and denominator completely.
 Divide out all common factors.
 Multiply the remaining factors in both the numerator
and denominator.
Sign Placement Rule: 
P P
P


Q
Q
Q
A function described in terms of rational
Adding and Subtracting
Rational Expressions
Carson, 7.2
To Add & Subtract with the Same Denominator:
 Add or subtract numerators. Keep denominator the
same.
 Simplify the fraction.
(pg. 387)
Least-Common-Denominator:
 The smallest number divisible by all of the
denominators.
 The polynomial of least degree that has all of the
denominators as factors.
To Multiplying a Rational Expression:
 Factor each numerator and denominator.
 Divide out factors common to both numerator and
denominator.
 Multiply numerator by numerator and denominator by
denominator.
 Simplify.
Finding the LCD:
 Find the prime factorization of each denominator.
 Write a product that contains each unique prime factor
the greatest number of times that factor occurs in any
factorization.
 Simplify.
To Divide a Rational Expression:
 Write an equivalent multiplication statement using
P R P S
where Q, R, S ≠ 0.
  
Q S Q R
46
To Add & Subtract with Different Denominators:
 Find the LCD.
 Rewrite each fraction with the LCD.
 Add or subtract numerators. Keep denominator the
same.
 Simplify.
Simplifying Complex
Rational Expressions
Solving Equations Containing
Rational Expressions
To solve a rational equation:
1. Factor the denominator.
Multiply both sides by the LCD of all the rational
expressions in the equation.
2. Solve the resulting equation.
3. Check your solution in the original equation.
Results may be extraneous solutions.
Carson, 7.3
Restrictions: Solutions cannot make the denominator zero.
Complex Rational Expression:
A rational expression that
contains rational expressions in the numerator and/or
denominator.
To simplify a complex fraction:
Carson, 7.4
a c

b d
Cross multiplication can be used ONLY when an equation fits
the format of a proportion.
Proportion:
(2 methods)
Method #1:
1. If necessary, rewrite the numerator and/or denominator as
a single rational expression.
2. Rewrite as a horizontal division problem and simplify.
If
Method #2:
1. Multiply the numerator and denominator of the complex
rational expression by the LCD of all the fractions in both
the numerator and denominator.
2. Simplify.
An equation of the form
a c
 , where b  0 and d  0 , then ad  bc .
b d
Radical Expressions and Functions
Carson, 8.1
General Rules of for Even Roots:
1. Every positive number has two even roots. (+, )
2. The radical denotes the positive (principal) root.
3. The even root of a negative number is not a real
number.
Complex Fractions with Negative Exponents:
 Rewrite with positive exponents
 Simplify
Radical Function:
A function containing a radical
expression whose radicand includes a variable.
47
To find the Domain of a Radical Function:
 If the index is odd, Domain = (−∞, ∞)
 If the index is even, the radicand must be nonnegative.
Find the domain by solving the inequality:
―radicand > 0‖
Rational Exponents
Multiplying, Dividing, and
Simplifying Radicals
Product Rule for Radicals:
If both n a and n b are real numbers, then
n
An exponent that is a rational number.
Quotient Rule for Radicals:
n
If both
1
Rule #1:
a n n a
A rational exponent with numerator 1 represents an nth root.
Rule #2:
a
An exponent of m
Rule #3:
a
n
m
n
m
n
 n am 
applies both:
a
m
a and
n
b are real numbers, then
m
For any nonnegative real number a,
nth root & mth power.
n
a n a
, b ≠ 0.

b
b
 a  a .
n
n
Simplifying nth Roots:
1. Write the radicand as a product of the greatest perfect
nth power and an expression that has no perfect nth
power factors.
2. Use the product rule to apply the root to each factor.
3. Find the nth root of the perfect nth power radicand.
1

n
Raising an nth Root to the nth Power:
 a
n
a  n b  n ab .
NOTE: Radicals must have the same index in order to
apply this property.
Carson, 8.2
Rational Exponent:
Carson, 8.3
n
Multiplying and Dividing Radicals:
1. Change from radical to exponential form
2. Multiply or divide using the appropriate rule(s) of
exponents
3. Write the result from Step 2 in radical form
A radical in simplest form has:
 All possible factors removed from the radical.
 No fractions under the radical.
 No radicals in the denominator.
 All sums, differences, products, and quotients have
been found.
48
Adding, Subtracting, and Multiplying
Radical Expressions
Rationalize the Denominator: (pg. 487)
 Goal: Rewrite the fraction without a radical in the
denominator.
 Multiply the fraction by a ‗well chosen 1‘.
 Find a factor that multiplies the nth root in the
denominator so that its radicand is a perfect nth power.
Carson, 8.4
Add or Subtract ―LIKE‖ Radicals.
Like Radicals: Radical expression with identical radicands and
identical indices.
 Same root type
 Same expression under the radical
Square Root Denominators: Multiply by a square root factor
that will create a perfect square in the denominator.
Add or Subtract the coefficients leaving radical parts the same.
Radical Equations and
Problem Solving
Conjugate Relationships:
Radical expressions can be conjugates.
Radical Equation: An equation containing at least one radical
expression whose radicand has a variable.
Conjugates differ only in the sign (+ or ) separating the terms.
Product of two conjugates gives a rational number.
a  b is the conjugate of a  b
Rationalizing Numerators and
Denominators of Radical Expressions
Carson, 8.6
Power Rule for Solving a = b:
 Raise both sides of the equation to the same integer
exponent, say n.
 Solution set of an = bn will contain the solutions of
a = b.
 Solution set of an = bn may contain solutions that DO
NOT solve the original equation.
 Check your answers: Extraneous solutions may
appear!
Carson, 8.5
A radical in simplest form has: (pg. 486)
 All possible factors removed from the radical.
 No fractions under the radical.
 No radicals in the denominator.
 All sums, differences, products, and quotients have
been found.
49
To Solve a Radical Equation:
1. Isolate a radical in the equation.
2. Apply the power rule.
3. Repeat steps 1 & 2 if necessary.
4. Check each solution.
Complex Numbers
Imaginary Unit:
Standard form:
a + bi
a:
real part
b:
imaginary part
Two complex numbers are equal when BOTH real and imaginary
parts are equal.
Carson, 8.7
Adding and Subtracting:
 operate as though i were a variable
 combine ‗like‘ terms
The number represented by i,
where i   1 and i 2  1 .
Multiplying:
 operate as though i were a variable
 use FOIL when needed
 remember:
i 2  1
Imaginary Number:
A number that can be expressed in the form bi,
where b is a real number and i is the imaginary unit.
Square root of a negative:
n
1. Separate the radical into two factors:
2. Replace
 1 with i.
3. Simplify
n
Conjugate Relationships:
Complex numbers can be complex conjugates.
1  n
Conjugates differ only in the sign (+ or ) separating the terms.
Product of two conjugates gives a real number.
Complex Number:
A number that can be expressed in the
form a + bi, where a and b are real numbers and i is the
imaginary unit.
a + bi is the conjugate of
a – bi.
Dividing:
 multiply by a ‗well chosen 1‘
 multiply numerator and denominator by the conjugate
of the denominator
The set of complex numbers contains BOTH real and
imaginary numbers.
50
Solving Quadratic Equations
Using the Quadratic Formula
Solve using a radical:
1.
Isolate the base and exponent.
2.
Take a root of both sides.
3.
Solve remaining equation.
Carson, 9.2
Quadratic Equation
→
standard form: ax2 + bx + c = 0
a,b, c real numbers (a ≠ 0)
→
the highest degree term is 2 (x2)
Square Root Principle, Completing the Square\Carson, 9.1
Ways to solve:
Square Root Principle—solving equations of the forms:
 x2  a
 ax 2  b  c
 (ax  b) 2  c
Quadratic Formula:
Completing the Square—solving equations of the forms
 x 2  bx  c  0
 ax 2  bx  c  0 , a  1
Create a perfect square on one side of equation; then
solve using the Square Root Principle.
1)
2)
3)
4)
Factoring
Square Root Method
Completing the Square
Quadratic Formula
 b  b 2  4ac
x
2a
Using the Discriminant: b 2  4ac
To determine the number and type of solutions, evaluate the
discriminant.
 b 2  4ac > 0,  two real-number solutions.
- Rational if b 2  4ac is a perfect square
- Irrational otherwise.
 b 2  4ac = 0  one rational solution
 b 2  4ac < 0  two nonreal complex solutions
To Solve by Completing the Square: ax 2  bx  c  0
1. Divide each term by a if a  1 .
2. Move the constant term to the right-hand side.
2
b
3. Find   . Add this to both sides.
2
4. Factor the left hand side.
5. Use the square root principle to find the solution(s).
51
Solving Equations That
Are Quadratic in Form
Using the graphing method to solve:
Three solution possibilities:
 One solution - two distinct lines intersecting at exactly
one point.
 Infinitely many solutions - two lines overlap as the
same line.
 No solutions - two parallel lines.
These three solution possibilities exist no matter how the linear
system of equations is solved.
Carson, 9.3
Equations quadratic in form:
An equation is quadratic in form if it can be rewritten as a
quadratic equation au 2  bu  c  0 , where a  0 and u is a
variable or an expression.
To solve equations that are quadratic in form using
substitution:
1. Rewrite the equation so that it is in the form
au 2  bu  c  0 .
2. Solve the quadratic equation for u.
3. Substitute for u and solve.
4. Check the solution
Solving Systems of Linear Equations
Substitution Method:
→
Isolate 1 variable in 1 equation.
→
Substitute into 2nd equation.
Elimination Method:
→
the coefficients of the eliminated variable in two
equations must be additive inverses
→
multiply one or both equations by a number if needed
→
add equations to eliminate one variable
Carson, 4.1
To verify or check a solution to a system of equations:
1. Replace each variable in each equation with its
corresponding value.
2. Verify that each equation is true.
Solving Systems of Linear Inequalities
Carson, 4.6
A system of inequalities is a group of two or more inequalities.
A system of two linear equations in two unknowns is called
either
 consistent - independent equations (one solution)
 consistent - dependent equations (infinitely many
solutions), or
 inconsistent (no solutions).
Solution or solution set of a system of inequalities
 Set of all ordered pairs in the region where the
individual inequalities‘ solution sets overlap
 Includes ordered pairs on the portion of any solid line
that touches the region of overlap.
To graph a system of inequalities:
1. Graph each inequality, shading the appropriate region.
2. The overlap of all shaded regions will be the solution of
the system of inequalities.
52
Calendars:
53
AUGUST 2011
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
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2
3
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5
6
7
8
9
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Classes Begin
MALL Hours 1 Starts
HW 1 Opens
QZ 1 Opens
Drop/Swap Deadline
27
Add Deadline
Orientation (MALL Hours 1) M - Th 10:00am - 6:30pm; Fri 10:00am - 5:30pm
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29
30
HW 1: DUE
MALL Hr 1 Due @ 10am
i>Clicker registration
DUE
www.iclicker.com
Orientation (MALL Hours 1) 9:00AM - 9:30AM only
S
M
3 4
10 11
17 18
24 25
31
31
July 2011
T W Th F
1
5 6 7 8
12 13 14 15
19 20 21 22
26 27 28 29
QZ 1: DUE
MALL Hours 2 Starts
HW 2 Opens
QZ 2 Opens
Sa
2
9
16
23
30
September 2011
M T W Th F Sa
1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
S
Notes:
www.vertex42.com
© 2009 Vertex42 LLC
SEPTEMBER 2011
Sunday
4
Monday
5
Labor Day
UCF CLOSED
MALL Closed
Tuesday
6
Wednesday
Thursday
7
HW 2: DUE
MALL Hours 2 Due
Friday
Saturday
1
2
3
8
9
10
15
16
17
22
23
24
QZ 2 Due
MALL Hours 3 Starts
HW 3 Opens
QZ 3 Opens
Practice Test 1:
Parts 1 & 2 Open
11
12
13
14
HW 3: DUE
MALL Hours 3 Due
Test 1 Sched.
Opens at 10:00 AM
QZ 3 Due
MALL Hours 4 Starts
HW 4 Opens
QZ 4 Opens
Prac Test 1: All Parts Open
18
19
20
Prac Test 1: DUE
Test 1 Sched.
Closes at 1:00 PM
25
26
21
HW 4: DUE
QZ 4 Due
HW 5 Opens
QZ 5 Opens
Test 1 - NO MALL HOURS CAN BE EARNED
27
28
HW 5: DUE
MALL Hours 4 Due
S
7
14
21
28
29
30
QZ 5 Due
MALL Hours 5 Starts
HW 6 Opens
QZ 6 Opens
August 2011
M T W Th F
1 2 3 4 5
8 9 10 11 12
15 16 17 18 19
22 23 24 25 26
29 30 31
Sa
6
13
20
27
S
October 2011
M T W Th F
2
9
16
23
30
3 4 5 6 7
10 11 12 13 14
17 18 19 20 21
24 25 26 27 28
31
Sa
1
8
15
22
29
Notes:
OCTOBER 2011
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
1
2
3
4
5
HW 6: DUE
MALL Hours 5 Due
Practice Test 2:
6
7
8
13
14
15
20
21
22
28
29
QZ 6 Due
MALL Hours 6 Starts
HW 7 Opens
QZ 7 Opens
Parts 1 & 2 Open
9
10
11
12
HW 7: DUE
MALL Hours 6 Due
Test 2 Sched.
Opens at 10:00 AM
QZ 7 Due
MALL Hours 7 Starts
HW 8 Opens
QZ 8 Opens
Prac Test 2: All Parts Open
16
17
18
Prac Test 2: DUE
Test 2 Sched.
Closes at 1:00 PM
23
24
19
HW 8: DUE
QZ 8 Due
HW 9 Opens
QZ 9 Opens
Test 2 - NO MALL HOURS CAN BE EARNED
25
HW 9: DUE
MALL Hours 7 Due
30
31
Practice Test 3:
Parts 1 & 2 Open
27
QZ 9 Due
MALL Hours 8 Starts
HW 10 Opens
QZ 10 Opens
September 2011
M T W Th F Sa
1 2 3
4 5 6 7 8 9 10
11 12 13 14 15 16 17
18 19 20 21 22 23 24
25 26 27 28 29 30
S
Final Exam Sched.
Opens at 10:00 AM
26
S
6
13
20
27
Withdrawal Deadline
November 2011
M T W Th F
1 2 3 4
7 8 9 10 11
14 15 16 17 18
21 22 23 24 25
28 29 30
Sa
5
12
19
26
Notes:
NOVEMBER 2011
Sunday
Monday
Tuesday
Wednesday
1
2
HW 10 Due
MALL Hours 8 Due
6
Daylight Savings
7
Thursday
3
QZ 10 Due
MALL Hours 9 Starts
HW 11 Opens
QZ 11 Opens
8
9
HW 11: DUE
MALL Hours 9 Due
Prac Test 3: All Parts Open
Friday
4
Saturday
5
UCF Football Game
Campus Closes at 12:30pm
MALL Closes at 12:00pm
10
11
12
17
18
19
25
26
Veterans Day
UCF CLOSED
MALL Closed
QZ 11 Due
MALL Hours 10 Starts
HW 12 Opens
QZ 12 Opens
Test 3 Sched.
Opens at 10:00 AM
13
14
15
16
Prac Test 3: DUE
Test 3 Sched.
Closes at 1:00 PM
20
21
HW 12 Due
QZ 12 Due
HW 13 Opens
QZ 13 Opens
Test 3 - NO MALL HOURS CAN BE EARNED
22
23
HW 13: DUE
MALL Hours 10 Due
Cum HW Opens
Cum QZ Opens
27
28
29
Thanksgiving
UCF CLOSED
MALL Closed
UCF CLOSED
MALL Closed
30
HW 14: DUE
MALL Closed
24
QZ 13 Due
MALL Hours 11 Starts
HW 14 Opens
QZ 14 Opens
MALL Closes at 7:30pm
S
October 2011
M T W Th F
2
9
16
23
30
3 4 5 6 7
10 11 12 13 14
17 18 19 20 21
24 25 26 27 28
31
QZ 14 Due
HW 15 Opens
QZ 15 Opens
Sa
1
8
15
22
29
S
4
11
18
25
December 2011
M T W Th F
1 2
5 6 7 8 9
12 13 14 15 16
19 20 21 22 23
26 27 28 29 30
Sa
3
10
17
24
31
Notes:
www.vertex42.com
© 2009 Vertex42 LLC
DECEMBER 2011
Sunday
4
Monday
5
MALL Hours 11 Due
HW 15 & QZ 15: DUE
Cum HW & QZ: DUE
Final Exam Sched.
Closes at 1:00 PM
Tuesday
6
Wednesday
7
Thursday
Friday
Saturday
1
2
3
8
9
10
Final Exam Make-up
Final Exam Make-up
7:00 PM (20% penalty)
7:00 PM (20% penalty)
Final Exams - possible times offered: 7am, 10am, 1pm, 4pm, 7pm
Final Exam Make-up
10:00 AM (20% penalty)
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
S
6
13
20
27
November 2011
M T W Th F
1 2 3 4
7 8 9 10 11
14 15 16 17 18
21 22 23 24 25
28 29 30
Sa
5
12
19
26
S
1
8
15
22
29
January
M T W
2 3 4
9 10 11
16 17 18
23 24 25
30 31
2012
Th F
5 6
12 13
19 20
26 27
Sa
7
14
21
28
Notes:
www.vertex42.com
© 2009 Vertex42 LLC