NVCC
COLLEGE-WIDE COURSE CONTENT SUMMARY
MTH 60 -
INTRODUCTION
TO COLLEGE ALGEBRA (3 CR.)
COURSE
DESCRIPTION
Reviews the
fundamental
ideas of algebra including the real number system, polynomials,
rational
expressions, graphing, equations and inequalities, relations and
functions,
and systems of first degree equations and inequalities. Lecture 3 hours
per week.
GENERAL COURSE
PURPOSE
This course is
designed
to provide a bridge for students who have completed the prerequisite
courses
for either MTH 163 - "Precalculus I" or MTH 166 - "Precalculus with
Trigonometry"
but have not been able to obtain a satisfactory score of the
proficiency
examination for either of those courses. Grades given will be S, R, or
U. Successful completion of this course will provide the student with
the
skills necessary for MTH 163 or MTH 166.
ENTRY LEVEL
COMPETENCIES
Prerequisites are
a
satisfactory score on an appropriate proficiency examination and MTH 3
- "Algebra I" and MTH 4 - "Algebra II" or equivalent. The
student must also obtain a score in a designated range on the
proficiency
examination that tests for competency.
COURSE
OBJECTIVES
As a result of
the
learning experiences provided in this course, the student should be
able
to:
A. perform
operations on polynomials and rational expressions
B. solve linear
and
quadratic equations
C. graph lines and
parabolas on the Cartesian plane
D. solve linear
inequalities
algebraically and graphically
E. solve systems
of
linear equations and inequalities
F. state the
definition
of a function and give examples of functions
G. evaluate
logarithmic
and exponential expressions
MAJOR TOPICS TO
BE
INCLUDED
A.
Algebraic
Expressions
1. Exponents
a.
Definitions of
integral, rational, and negative exponents
b. Laws of
operations
with exponents
c. Radical
expressions
using exponents
d. Simplication
and
operations
2. Polynomials
a. Operations:
+,-,x,/
b.Factorization (sum
and difference of cubes, expressions reducible by substitution and
grouping)
c. Evaluation
3. Rational
Expressions
a. Operations:
+,
-, x, /
b. Reducing to
lowest
terms and evaluation
B. Equations
1. Solutions of
linear
equations
2. Solutions of
quadratic
equations (by factoring, by completing the square, and by using the
quadratic
formula)
3. Solutions of
equations
containing rational expressions
4. Absolute value
(linear)
5. Radical equations
6. Literal equations
7. Application
problems
throughout
When possible,
include
problems that will help students to remember basic geometric facts like
perimeter, area, and volume formulas, angle relationships in triangles,
angles formed with intersecting lines, angles formed with parallel
lines
cut by a transversal, similar and congruent triangles, Pythagorean
theorem.
C.
Inequalities
1.
Algebraic/graphical
solution of linear inequalities in one variable
2.
Algebraic/graphical
solution of linear inequalities in two variables
3. Factorable
quadratic
inequalities in one variable
4. Absolute value
inequalities in one variable
D. Equations in two
variables
1. Linear
a. slope,
intercepts,
slopes of parallel, and perpendicular lines
b. finding
equations,
given point-slope, two points
c. graphing
2. Quadratic:
graphing
parabolas of the form y = ax^{2}
+ bx + c
3. Solution of
systems
of linear equations (2 x 2, 3 x 3)
E.
Functions/relations
1. Definition
and
terminology
2. Domain and
Range
3. Computing
functional
values
4.
Graphic
recognition of quadratic, square root, absolute value, and linear
functions
F.
Logarithms
1. Definition
2. Review scientific
notation
3. Use of log button
and its inverse on calculator
4. Properties:
product, quotient, and power rules
5. Graph of log base
_{10}
x
6. Logarithmic and
exponential equations
EXTRA TOPICS
(optional)
A. Use
of
Graphing calculator
B. Complex numbers
C. Rational
inequalities
Revised 12/00;
reviewed
02/01
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