Catalog Description: This course will give students
a rigorous preparation in
algebra. Topics include review of basic algebraic concepts, functions and
graphs,
polynomial, radical, rational, exponential and logarithmic functions ; equations,
inequalities,
systems of equations and inequalities; applications. Prerequisite: MATH
050 or mathematics placement .
Number of Credits : 4
Topics Covered:
Basic Concepts of Algebra
•Real Numbers and Their Properties
•Integral Exponents
•Rational Exponents and Radicals
•Polynomials: Basic Operations
•Polynomials: Factoring
• Rational Expressions : Basic Operations
Equations and Inequalities
• Linear Equations and Applications
o Solving linear equations
o Strategies for solving word problems
o Solving number and geometric problems
o Solving rate-time problems
o Solving mixture problems
• Linear Inequalities
o Inequality relations and interval notation
o Solving linear inequalities
•Absolute Value in Equations and Inequalities
o Definition and properties
o Solving absolute value equations and inequalities
•Complex Numbers
o Concepts and terminology
o Operations
o Complex numbers and radicals
o Solving equations involving complex numbers
• Quadratic Functions and Applications
o Factoring to solve quadratic equations
o Square root property to solve quadratics
o Completing the square
o Quadratic formula
o Applications
Graphs
•Cartesian Coordinate System
o Review of Cartesian Coordinate System
o Plotting points
o Using symmetry
•Distance in the Plane
o Distance between two points
o Midpoint of a line segment
o Circles
•Equation of a Line
o Graphing lines
o Finding slope of a line
o Special forms of the equation of a line
o Parallel and perpendicular lines
•Linear Equations and Models
o Slope as a rate of change
o Linear models
o Linear regression (optional)
Functions
•Functions
•Graphing Functions
•Transformations of Functions
o Vertical and Horizontal Shifts
o Reflections
o Stretching and Shrinking
o Even/Odd Functions
• Quadratic Functions
o Graphing quadratics
o Modeling with quadratics
o Solving quadratic inequalities
•Composite Functions
o Operations on functions
o Composition
o Modeling with composite functions
•Inverse Functions
Polynomial and Rational Functions
• Polynomial Functions and Models
o Graphs of Polynomial Functions
o Polynomial Division
o Remainder and Factor Theorems
o Zeroes of polynomials
•Rational Functions and Inequalities
o Rational functions and properties of their graphs
o Asymptotes
o Analyzing the graph of a rational function
o Rational inequalities
Introduction to Exponential and Logarithmic Functions
• Exponential Functions
•Logarithmic Functions
•Solving Exponential and Logarithmic Equations
•Applications
Additional Topics Time Permitting
Systems of Equations and Inequalities
•Systems of Linear Equations in Two Variables
•Systems of Linear Equations in Three Variables
• Inequalities and Systems of Inequalities in Two Variables
Introduction to Trigonometric Functions
•Angles and Radians
• Right Triangle Approach
•Unit- Circle Approach
•Properties of Trigonometric Functions
Listing of Sections in Departmental Text to be Covered (Name and Author of
Text Here):
Remarks:
Approximate pace of coverage:
Method of Instruction : The basic method of instruction will be lecture,
discussion,
problem sessions, and group work . In addition, students will likely have access
to
online learning resources available from most publishers of introductory
mathematics
texts and have additional help available through the departmental tutoring
program.
Evaluation Procedure: Course requirements will include homework
assignments,
quizzes, and exams. Students may also be required to complete outside work using
online learning resources.
This course would a mathematics basic skills course in
University Studies Program.
Last Revised: Oct. 2008, by Berry A. Peratt
