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MAT 150
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I. TITLE: Algebra and Trigonometry
II. CATALOG DESCRIPTION:
Modern college algebra and plane trigonometry . Restriction:
A student who receives credit for MAT 150 may not receive credit for MAT
130 , 140 or 145. (Credit for the combination of MAT 140 and MAT 145 will
substitute for MAT 150.)
III. PURPOSE:
It is critical in todays world that one be able to deal effectively
in the area of problem solving. Since many problems are addressed
in mathematical/analytic form , it becomes clear that a knowledge of the
techniques and procedures of algebra and trigonometry is essential.
In order to understand the scientific methodologies and the necessary
critical thinking involved in many academic disciplines, one must be able
to employ algebraic/trigonometric techniques and concepts. Mathematics
is a universal language and is used in almost all communications involving
scientific methodology and critical thinking. The solutions studied
in MAT 150 requires one to engage in analyzing problems and developing
logical steps to arrive at a conclusion.
IV. COURSE OBJECTIVES:
Students will develop critical thinking and problem solving skills
by analyzing problems and determining solution techniques.
V. CONTENT OUTLINE :
A. Fundamentals
1. Review of
the real numbers , subsets of real numbers and the properties of the
arithmetic of real numbers
2. Ordering
and absolute value
3. Polynomials
- Addition , subtraction , multiplication and factorization
4. Rational
expressions - Multiplication , division , addition and subtraction
5. Radicals
and rational exponents
6. Complex numbers
and the arithmetic of complex numbers
B. Equations and inequalities in one variable
1. Solutions
of equations in one unknown
(a) linear
(b) literal equations - formulas
(c) equations involving rational expressions
(d) absolute value equations
(e) quadratic equations
(f) applications
2. Solutions
of linear , absolute value and nonlinear inequalities and applications
C. Functions
1. Graphing
in a rectangular coordinate system
2. Algebra of
functions
3. Linear and
Quadratic functions and their graphs
D. Graphing techniques
1. parabolas
and circles
2. symmetry
and translations
3. inverse functions
4. variations
E. Polynomial and rational functions
1. Synthetic
division
2. Remainder
and Factor Theorems
F. Exponential and logarithmic functions
1. Exponential
functions and their graphs
2. Logarithmic
functions and their graphs
3. Solutions
of exponential and logarithmic equations
G. Systems of equations
1. Systems of
linear equations in two and three variables
2. Systems of
nonlinear equations in two variables
H. Trigonometric functions
1. Measurements
of angles
2. Trigonometric
functions of angles
3. Fundamental
identities - Reciprocal , ratio and Pythagorean
4. Trigonometric
function values
5. Graphs of
the trigonometric functions
6. Right triangles
and their applications
I. Analytic trigonometry
1. Additional
identities
(a) sum and difference of two angles
(b) double and half-angle
(c) product and sum
2. Solutions
of trigonometric equations
3. Inverse trigonometric
functions
J. Triangle solutions
1. Law of sines
2. Law of cosines
VI. INSTRUCTIONAL ACTIVITIES
This course is a thematic problem-solving course meant to develop students'
ability to logically and independently analyze and solve algebraic and
trigonometric problems. In the classroom an interactive format is
used in that instructors use a question/answer, discussion approach.
Participation in class discussions and the presentation of homework problems
are activities which develop the students’ reasoning and communication
skills. Frequent testing develops the students' abilities in reading
, critical thinking and writing. Problem sessions are used to encourage
students to accept a shared responsibility for learning.
VII. FIELD AND CLINICAL EXPERIENCES : none
VIII. RESOURCES :
The textbook and a scientific calculator are required. Handouts
and additional exercise sets are frequently used to augment the instruction.
IX. GRADING PROCEDURES :
The course grade is determined by the student's performance on homework/quizzes,
several hourly exams, a comprehensive final exam, and other in class activities
such as presenting their solution to a problem on the board and verbally
explaining their solution. Critical thinking, problem solving skills, and
writing skills will be evaluated on each exam. Homework is typically
checked by the use of quizzes. A group project is generally included
as a part of the homework component. Various instructors assign different
weights to factors used in determining grades, but ranges are usually:
homework/quizzes/in class activities 10% - 17%
hourly exams 50% - 70%
comprehensive final exam 20% - 33%
Grades are assigned according to the following scale:
A 90% and above
B 80 - 89 %
C 70 - 79 %
D 60 - 69 %
E below 60 %
X. ATTENDANCE POLICY :
Regular attendance is expected. Attendance records are kept and
reports will be made to the First Year Experience Office. The student
is responsible for missed work. Penalties for the lack of attendance
may vary with instructors.
XI. HONESTY POLICY :
Any instance of academic dishonesty , as determined by the instructor
( in compliance with the Board of Regents Policy on Academic Integrity
- Feb. 1975), will result in zero points for the assignment, or a grade
of E for the course.
XII. TEXT AND REFERENCES : Current
XIII. PREREQUISITES :
Mathematics ACT of at least 21.
Last updated February 14, 2000. Designed and maintained
by Kyosung Koo