## Course Descriptions & Syllabi

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 COURSE NUMBER: MATH111 COURSE TITLE: College Algebra DIVISION: Sciences IAI CODE(S): SEMESTER CREDIT HOURS: 5.0 DELIVERY MODE: Face to Face

COURSE DESCRIPTION:

A review of the fundamental topics of algebra, including the real and complex number systems, simplification and manipulation of algebraic expressions involving polynomials, rational exponents, radicals, and fractions, and the solution of polynomial equations and inequalities.  Emphasis is placed on the study of the following functions: polynomial, rational, exponential, and logarithmic and their applications. These will be explored using traditional graphing techniques and also using graphing calculators.
PREREQUISITES:

Place into MATH111 with approved and documented math placement scores or by completing MATH105 with a grade of C or better.

NOTES:

COURSE OBJECTIVES / GOALS:

The student should be able to:
• Represent subsets of the real number system using set notation, interval notation, and graphing on the real number line.
• Demonstrate knowledge of general algebraic skills in the following areas:
• Simplifying algebraic expressions involving polynomials, rational exponents, radicals,absolute value and fractions
• Factoring polynomials
• Basic operations and simplification of numbers in the complex number system
• Solving linear and quadratic equations in one or more variables
• Solving applications of linear and quadratic equations
• Solving linear equations and inequalities involving absolute value
• Solving compound inequalities
• Solving quadratic and rational inequalities using sign graph method
• Use formulas associated with the co-ordinate plane to calculate the following:
• Distance between two points
• Midpoint between two points
• Slope of a line
• Given two points on the line
• Given the equation of line
• Equation of a line given a point on the line and the slope
• Equation of a line given the slope and y intercept
• Equations of vertical and horizontal lines
• Demonstrate knowledge of the general principles of functions:
• Defining a function algebraically and graphically
• Determining the domain and range of a function
• Using function notation
• Identifying intervals over which a function is increasing, decreasing, and/or constant
• Determining symmetry with respect to y axis and origin
• Performing operations with functions
• Graph the following in a co-ordinate plane: These will be explored with traditional graphing methods or by using graphing calculators.
• Points
• Circles
• Inequalities
• Linear functions
• Polynomial functions
• Rational functions
• Exponential functions
• Logarithmic functions
• Functions and their inverses
• Systems of equations and inequalities
• Apply concepts of variation to application problems.
• Use translations to sketch the graph of a function.
• Determine the complex roots of higher order polynomial equations using appropriate tools.
• Work applications using formulas involving variable exponents and logarithms.
• Solve linear systems of equations:
• Using algebraic methods
• Using methods of matrices and determinants
• Solve non-linear systems of equations.
A student should obtain a 60% competency in the mentioned objectives.  A student who is taking this course as a prerequisite for another math course should receive a 70% competency before taking the succeeding course.

TOPICAL OUTLINE:

Set notation, interval notation, graphical notation, and conversion from one form to another.
Fundamental algebraic skills:
• Addition, subtraction, multiplication, and division of polynomials
• Addition, subtraction, multiplication, and division of fractional expressions
• Evaluation and simplification of expressions with rational exponents
• Factoring polynomials
• Solving equations:
• Linear equations (with and without absolute value)
• Quadratic equations using methods of square root property, factoring, completing the square, and the quadratic formula
• Rational equations
• Equations with rational exponents
• Solving application problems, including the following types: number, mixture, geometry,consecutive integer, money, uniform motion, investment.
• Solving inequalities:
• Linear inequalities using rules for inequalities
• Linear inequalities with absolute value
• Compound inequalities
• Quadratic inequalities using sign graph method
• Rational inequalities using sign graph method
• Formulas of the co-ordinate plane:
• Distance between two points
• Midpoint between two points
• Slope of a line: given two points on the line, and given equation of line
• Equation of a vertical line
• Equation of a horizontal line
• Equation of a line given slope of the line and a point on the line
• Equation of a line given slope of a line and the y intercept of the line
• Slopes of parallel lines and perpendicular lines
• Graphing relations in the co-ordinate plane:
• Points
• Circles
• Inequalities
• General Topics on Functions:
• Definition
• Function notation
• Domain and range of functions
• Graphing linear functions using slope and y intercept
• Determining vertex, and axis of symmetry
• Determining maximum and minimum values
• Determining domain, range, increasing and decreasing intervals
• Sketching the graph
• Applications
• Other standard functions:
• Absolute value function
• Squaring function
• Cubing function
• Square root function
• Graphing concepts of functions:
• Vertical line test for functions
• Increasing, decreasing, and constant functions
• Symmetry
• One-to-one functions and horizontal line test for functions
• Inverse functions
• Transformations:
• Vertical and horizontal shifts
• Reflections
• Stretching and shrinking
• Operations with functions:
• Subtraction
• Multiplication
• Division
• Composition
• Polynomial functions:
• Synthetic division
• Finding zeros using the following tools:
• Factoring
• Rational root theorem
• Descartesâ€™ rule of signs
• Upper and lower bound theorem
• Conjugate zero theorem
• Graphing techniques.
• Rational functions:
• Vertical, horizontal and slant asymptotes
• Sketching rational functions using asymptotes
• Exponential functions:
• Definition
• Exponential functions with base e
• Graphs of exponential functions with base greater than 1 and base between 0 and 1
• Logarithmic functions:
• Definition
• Natural vs common logarithms
• Graphs of logarithmic functions with base greater than 1 and base between 0 and 1
• Equations using logarithms and exponents:
• Converting equations form logarithmic form to exponential form and vice versa
• Applying laws of logarithms in solving exponential and logarithmic equations
• Applications; exponential growth and decay, pH scale, Richter scale, decibel scale, interest
• Systems of equations:
• Solution of linear equations using the following methods:
• Graphing
• Substitution
• Matrices
• Determinants and Cramers rule
• Solution of nonlinear systems using substitution or elimination
• Solution of systems of inequalities by graphing
• Graphing functions, solving equations, and algebraic manipulations using Mathematica

TEXTBOOK / SPECIAL MATERIALS:
• College Algebra, 5th Edition, by Mark Dugopolski, Published by Addison-Wesley, 2003  ***Some instructors may use the 4th edition
• Calculator (Graphing calculator desirable)

EVALUATION:
• Quizzes and homework.
• At least five 50 minute exams.
• Comprehensive final exam.
• Determination of grade is according to the following scale:
• A = 90% - 100%
• B = 80% - 89%
• C = 70% - 79%
• D = 60% - 69%

BIBLIOGRAPHY:
• College Algebra, 10th Edition, by Margaret L. Lial, John Hornsby, and David I. Schneider, 2008

REVISION:
Fall 2012

RECORD UPDATED:
2012-09-28 15:25:00