Mathematics
HCC-Spring Branch Campus
Math 2412: Precalculus
CRN #73027 – Fall / 2015
Room 320 / 7:00 pm-9:00 pm / TT
4 hour lecture course / 64 hours per semester/ 16 Weeks
Textbook: Precalculus, 5rd Edition, by Robert Blitzer
ISBN-13: 9780321837349
Catalog Description: Precalculus. Topics include elementary theory of functions and
equations, analytic geometry, vectors, introductory logic, mathematical induction,
sequences and finite series.
4 credits. (4 lecture)
Prerequisites:
Instructor:
Math 1314: Pass with a “C” or better.
Math 1316: Pass with a “C” or better.
Oscar Castro
Email: oscar.castro@hccs.edu
Off. Hrs: By appointment only
Course Intent: This course is intended primarily to prepare students for calculus. It can
also be used for general mathematics credit.
Audience: This course is for students who need a background for taking a beginning
calculus course.
Course Objectives: Upon completion of this course, a student should be able to:
1.
Develop and use various problem-solving techniques.
2.
Recognize functions as ordered pairs.
3.
Determine the graph of an algebraic equation or function.
4.
Understand synthetic division.
5.
Develop partial fraction decomposition.
6.
Find the zeros of real functions
7.
Solve polynomial equations.
8.
Utilize the six basic trigonometric functions.
9.
Verify various trigonometric identities.
10.
Apply the Law of sines and the Law of cosines for various types of situations.
11.
Find the powers and roots of complex numbers using DeMoivre’s Theorem.
12.
Understand basic vectors (2 dimensional).
13.
Convert points in a rectangular coordinate system to polar coordinates.
14.
Recognize algebraic formulas relating to circles, parabolas, ellipses, and
hyperbolas.
15.
Use translation of axes, rotation of axes, and polar equations of conics.
16.
Recognize the use of arithmetic and geometric sequences.
17.
Use summation notation to represent a series.
18.
Understand and use the Binomial theorem.
19.
Understand mathematical induction.
20.
(Optional) Understand the basic concepts of limits.
Course Outline: Instructor will cover the course topics in the order listed below.
However, the instructor may choose to organize topics in any order, but all material must
be covered.
APPROXIMATE TIME
Unit I – Algebra (Review)
Unit I – Partial Fractions
(8 hours)
TEXT REFERENCE
Sections: {1.2 – 1.5, 1.7,
1.9, 2.4, 2.5, 2.6}
Section: 7.3
Topics include the following: Graphs and graphing utilities, lines in the plane, slope,
functions, polynomial functions of higher degree, synthetic division, real zeros of
polynomial functions, and the intermediate value theorem. The unit concludes with
partial fraction decomposition.
Unit II – Trigonometry (review) and Analytic Trigonometry
Sections: {4.2, 4.5, 4.6, 4.7}
5.1 – 5.5
(10 hours)
This unit contains Trigonometric Functions, the unit circle, graphs of the trigonometric
functions, inverse trigonometric functions, verifying identities, sum and difference
formulas, double angle and half-angle formulas, sum-to-product and product-to-sum
formulas, and solving trigonometric equations.
Unit III – Applications of Trigonometry
(10 hours)
Sections: Chapter 6
This unit includes Law of Sines, Law of Cosines, Polar coordinates, graphs of Polar
equations, DeMoivre’s Theorem, vectors, and the dot product.
Unit IV – Conic Sections and Analytic Geometry
Sections: Chapter 9
(12 hours)
Topics include the ellipse, the hyperbola, the parabola, rotation of axes, parametric
equations, and conic sections in polar coordinates.
Unit V – Sequences, Induction, and Probability
(14 hours)
Sections: 10.1 – 10.5
This unit contains Sequences and summation notation, arithmetic sequences, Geometric
Sequences and Series, Mathematical Induction, and The Binomial Theorem.
Unit VI – Introduction to Calculus (Optional)
(6 hours)
Sections: 11.1 – 11.4
This optional unit contains an introduction to limits using tables and properties,
continuity, and an introduction to derivatives.
Departmental Policies:
1. Each instructor must cover all course topics by the end of the semester. The final
exam is comprehensive and questions on it can deal with any of the course
objectives.
2. Each student should receive a copy of the instructor’s student syllabus for the
course during the first week of class. The syllabus should also be available online.
3. A minimum of three in class tests and a comprehensive final examination must be
given. The final examination must be taken by all students.
4. All major tests should be announced at least one week or the equivalent in
advance.
5. The final exam must count between 25 percent and 40 percent of the final grade.
6. The final course average will be used in the usual manner (A = 90–100; B = 8089; C = 70-79; D = 60-69; F = below 60).
7. An open book or a take home major test may be given at the discretion of the
instructor.
8. Any review sheet should be comprehensive and the student should not feel that
classroom notes, homework, and test may be ignored in favor of the review sheet
for any examination.
Resource Materials: Any student enrolled in Math 2412 at HCCS has access to the
Academic Support Center where they may get additional help in understanding the theory
or improving their skill. The Center is staffed with mathematics faculty and student
assistants, and offers tutorial help. A Chapter Tests preparation video CD comes with the
text.
Suggested Methods: It is helpful to begin each class with questions concerning the
material discussed and the assigned homework problems. In presenting new material, it is
suggested that an explanation be followed by students working examples in class.
Students should be encouraged to work the review exercises at the end of each chapter.
Also, they should be encouraged to visit the Academic Support Center at their respective
colleges.
Americans With Disabilities Act (ADA): Any student with a documented disability
(e.g. physical, learning, psychiatric, vision, hearing, etc.) who needs to arrange
accommodations must contact the Disability Services Office at their respective college at
the beginning of each semester. Faculty are authorized to provide only the
accommodations requested by the Disability Support Services Office.
Student Conduct: Students will be expected to treat each other and the instructor
courteously and with respect. In class, please greet each other pleasantly, refrain from
activities which may be distracting to others, and participate honestly in group work and
exams. If you are dissatisfied with any aspect of the instructor or with other students,
please discuss your concerns with the instructor. If such discussion does not produce a
resolution to your concern, feel free to contact the department chair. Any student who
proves to be disruptive to the learning process of others will be removed from class and
dealt with by the administration.
Student Responsibilities: Consider being a student as a part-time or full-time job. It is
each student’s job to learn. With this job, the student has the responsibility to participate
in class, ask relevant questions, seek help when needed, and submit assignments when
they are due. Treat each deadline as you would an interview: do not miss a deadline.
Expect to spend a minimum of 2-6 hours per week, in addition to class time, studying
mathematics. If you miss class, it is your responsibility to make up any work assigned,
get notes or handouts, and determine if any pertinent announcement were made during
your absence.
Academic Honor: Every student in the class is expected to exhibit a high degree of
ethical standards as concerns the work in this class. Every graded assignment in this
course(homework/quiz, library assignment, or test) is to be entirely your own work
unless otherwise stated. Any violation of this policy will result in a minimum penalty of
failure of the assignment and a maximum penalty of expulsion from the college. If you
are uncertain as to whether you may work with another person on an assignment, ask
the instructor. It is also expected that if you see another person cheating in any way, you
will report it to the instructor.
Makeup Exams/Quizzes: Makeups are given at the discretion of the instructor and only
in the case of verified medical or other documented emergencies. Notify your instructor,
if possible, before the test is given. Makeups for major test ONLY. If the event is not an
emergency, you must notify the instructor in advance to request a makeup.
REMEMBER: The instructor is not required to accommodate you.
Final Grade: The final grade will be based on the following method:
E = Exam Average
Q = Daily Average(includes quizzes, daily work, etc.)
F = Final Exam Score
Grade = 0.25Q + 0.50E + 0.25F
By the second week of school, each student will have a calendar to cover all quizzes,
exams, and the final exam. Grades of A, B, C, D, or F will be assigned according to
departmental policy. The grade of ‘I’ is given only in exceptional circumstances. When a
student for good reason misses too much work or the final exam and notifies the
instructor promptly, the instructor may give the grade ‘I’(incomplete) and specify what
work should be completed to remove the ‘I’ grade. The ‘I’ will become an ‘F’ if not
replaced after one full semester.(Refer to the student handbook.)
INFORMATION CONCERNING STUDENT DISCIPLINE AND
CONDUCT NOT COVERED CAN BE LOCATED IN THE STUDENT
HANDBOOK. ALL MATERIAL CONTAINED THEREIN WILL
APPLY TO THIS CLASS.
Tentative Instructional Outline: PRECALCULUS
FALL , 2013
Week
Number
1
8/27
Activities
and Assignment
Aug 25
Oscar J. Castro
O
and Details
1.1(11n), Read Sections 1 to 4
Last day(online only) for Drop/Add/Swap
Intro, Sec. 1.1
Example:11n, Start with n=1 and do every 11th
Secs 1.2 to 1.3
1.2(7n)
1.3(7n)
9/3
Secs 1.4 to 1.5
1.4(7n)
1.5(2n)
9/5
Secs 1.7 & 1.9
!.7(8n)
1.9(6n)
9/10
Sec 2.4
2.4(4n)
Quiz on all Chap 1 sections above
9/12
Secs 2.5 & 2.6
2.5(4n)
2.6(6n)
9/17
Sec 7.3
Quiz #2
7.3(3n) Quiz on Chap 2 sections above
9/19
Sec 4.2
Test #1
4.2(5n) Test on Chaps 1,2,7 sections
8/29
1,4(7n)
2
3
Quiz #1
4
5
9/24
Secs 4.5 & 4.6
4.5(6n)
4.6(5n)
9/26
Secs 5.1-4.7 & Quiz #3
4.7(6n) 5.1(4n)
10/1
Secs 5.2 & 5.3
5.2(5n)
5.3(5n)
10/3
Secs 5.4 & 5.5 Quiz #4
5.4(4n)
5.5(7n)
10/8
Test #2
Test on C4 secs and C5 secs
10/10
Sec 6.1 & 6.2
6.1(4n)
6.2(4n)
10/15
Secs 6.3 & 6.4
6.3(6n)
6.4(3n)
10/17
Sec 6.5 & Quiz #5
6.5(6n)
Quiz on 4.2, 4.5, 4,6
6
Quiz on 5.1 to 5.3
7
8
Quiz on 6.1 to 6.4
9
10/22
Secs 6.6 & 6.7
6.6(5n)
6.7(4n)
10/24
Secs 9.1 & 9.2
9.1(4n)
9.2(4n)
10/29
Sec 9.3
9.3(4n)
Quiz on 6.5 to 6.7 and 9.1 to 9.2
10/31
35
Secs 9.4 & 9.5
9.4(4n)
9.5(5n)
11
11/1 4:30 PM
Last day for student adm. withdrawal
9.6(2n)
10
Quiz #6
11/5
Secs 9.6
Problems
11/7
Test #3
Test on Chapters 6 and 9
11/12
Secs 10.1 & 10.2 &
10.3
10.1(5n) 10.2(5n)
11/14
Secs 10.4 & 10.5
10.4(2n)
10.5(4n)
11/19
Sec 11.1
11.1(4n)
Quiz on C10
11/21
Sec 11.2 & 11.3
11.2(4n)
11.3(3n)
11/26
Sec 11.4
11.4(3n)
11/28
Nov 28 – Dec 1
Office closed – Thanksgiving Holiday. No class
12/3
Test #4
Chaps 10 & 11
12/5
Final Exam Review
All Sections
FINAL EXAM(7-9pm)
Comprensive, Scantron is required
12
10.3(6n)
13
Quiz #6
14
15
Makeup work
16
12/12
12/20
GRADES AVAILABLE TO STUDENTS