MATH120 College Algebra
Department of Science, Technology, Engineering & Mathematics: Mathematics
- I. Course Number and Title
- MATH120 College Algebra
- II. Number of Credits
- 4 credits
- III. Minimum Number of Instructional Minutes Per Semester
- 3000 minutes
- IV. Prerequisites
- Math Placement Test score of 7 or better or MATH103 (C or better)
- V. Other Pertinent Information
- A comprehensive departmental final is included in the course.
- VI. Catalog Course Description
- This course is designed to strengthen and increase the understanding of basic algebraic concepts before a student undertakes advanced study in mathematics. Topics include algebra of the real numbers, algebraic, exponential, and logarithmic functions and their graphs, systems of equations, inequalities, and absolute value.
- VII. Required Course Content and Direction
Learning Goals:Course Specific:
The student will be able to:
- develop an understanding and apply the concepts and procedures for solving equations and inequalities and for simplifying expressions.
- demonstrate the techniques of solving a variety of applications of equations.
- develop a proficiency in solving linear, quadratic, polynomial, and rational functions, and in mastering techniques for graphing these functions and describing their domain and range.
- develop skill in using a graphing calculator.
- accurately use logarithmic and exponential functions and develop the skill to graph and solve logarithmic and exponential equations.
- simplify algebraic expressions involving operations of arithmetic, exponents, radicals, fractions and factoring of polynomials.
- solve linear, quadratic, polynomial, absolute value, radical, exponential, logarithmic equations and systems of linear equations.
- solve applications of linear and quadratic equations.
- solve linear, quadratic, polynomial, absolute value, and rational inequalities and write the solutions in interval notation.
- graph linear, quadratic, polynomial, exponential, absolute value, radical, logarithmic, and rational functions and conic sections.
- perform operations of functions, find composition of functions, and describe increasing, decreasing, constant intervals, domain, range, and points of discontinuity.
- find equations of lines, given two points, a point and the slope, parallel or perpendicular lines, and a point.
- find the distance between, and the midpoint of, the segment, given two points.
Core Learning Goals:
Math or Science: The student will be able to:
- develop the ability to analyze, interpret, and apply quantitative information.
Core Learning Objectives:
Math or Science: The student will be able to:
- accurately translate descriptive problems into mathematical formulas and solve them. (1)
Critical Thinking/Problem Solving: The student will be able to:
- Demonstrate an understanding of solving problems by:
- recognizing the problem
- reviewing information about the problem
- developing plausible solutions
- evaluating the results
Planned Sequence of Topics and/or Learning Activities:The following is a list of the minimum amount of course material to be covered by the instructor. Accompanying each topic is an approximate number of lessons required to study the topic.
- Review Topics (12 lessons)
- The Real Numbers
- The Field Axioms
- Operations on Polynomials (+, -, x, /)
- Algebraic Fractions (reduction, +, -, x, /)
- Exponents (integer, rational)
- Radicals and Radical Expressions
- Complex Numbers
- Solution of Equations and Inequalities (12 lessons)
- First Degree Equations
- Formula Manipulation
- First Degree Inequalities (visualize solution set)
- Absolute Value Equations
- Absolute Value Inequalities
- Quadratic Equations (factoring, completing the square, quadratic formula)
- Quadratic Inequalities
- Radical Equations
- Applications (1st and 2nd degree)
- Rational Inequalities
- Relations and Functions (10 lessons)
- Cartesian Coordinate System and the Distance Formula
- Relations (domain, range, rule, graph)
- Functions (domain, range, rule, graph)
- Functional Notation
- Algebra of Functions (+, -, x, /)
- Composition of Functions
- Linear Functions (slope-intercept form, graphs)
- Quadratic Functions
- System of Equations (2x2, 3x3)
- Polynomial Functions (5 lessons)
- Division of Polynomials
- Synthetic Division
- Remainder and Factor Theorem
- Rational Root Theorem
- Graphs of Polynomial Functions
- Rational Functions
- Exponential and Logarithmic Functions (10 lessons)
- Inverse Functions (existence, rule, domain, range)
- Exponential Functions (rule, domain, range)
- Logarithmic Functions (rule, domain, range)
- Laws of Logarithms
- Logarithmic and Exponential Equations
- Applications of Logs
Assessment Methods for Core Learning Goals:All Core Critical Thinking and Problem Solving, College Level Mathematics or Science, and Discipline-Specific Course Objectives will be assessed as follows:
The student will apply mathematical concepts and principles to identify and solve problems presented through informal assessment, such as oral communication among students and between teacher and students and, for the core, formal assessment using open-ended questions reflecting theoretical and applied situations.
Reference, Resource, or Learning Materials to be used by Students:There is a departmentally selected textbook and calculator. The instructor will provide specific details for each section. See Course Format.
- VIII. Teaching Methods Employed
- Primary teaching methods are lecture, recitation, problem solving, and class discussion as appropriate.
Review/Approval Date - 3/06; Core Goals/Objectives added 4/04