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 = ax2 + 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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