SANTA BARBARA CITY COLLEGE

Associate Degree Credit Course Outline

Department: Mathematics

Subject Area and Course Number: Mathematics 120

Course Title: College Algebra

Discipline: Mathematics

Units: 4

Repeatability: None

Catalog Course Description: Study of functions and their graphs, including polynomial, rational, exponential and logarithmic functions. Systems of equations and conics.

Description for Schedule of Classes: College algebra, including polynomial, rational, exponential and logarithmic functions. Systems of equations and conics.

Lecture Hours per Week: 4.3 (64-72 Total Semester Hours)

Laboratory Hours per Week: None

Plus Hours: None

Prerequisites: Math 107 or Math 111, with grade of "C" or better or qualifying score on SBCC placement exam.

Co-requisite: None

Skills Advisories: Eligibility for English 100 or English 103

Course Advisories: None

Limitation on Enrollment: None

Course Objectives: By the end of the course, the student will be able to:

1. Demonstrate the ability to perform fundamental operations on algebraic expressions including polynomials, rational expressions, and expressions containing radicals or non-integer exponents.

2. Solve inequality statements, including linear, absolute value and more general non-linear inequality statements and graph their solutions.

3. Analyze and locate zeros of polynomial functions.

4. Determine whether a function is one to one and construct its inverse function.

5. Demonstrate familiarity with the main features of the conics: circles and ellipses, parabolas and hyperbolas.

6. Solve systems of equations.

7. Analyze and manipulate symbolically expressions representing sequences and series.

Course Content and Scope

A. Fundamental Concepts

1. Radicals and Rational Exponents

2. Fractional Expressions

B. Equations and Inequalities in one variable

1. Quadratic and absolute value equations and inequalities

2. Higher order equations with graphical emphasis

3. Zeros of Polynomials

C. Functions and Graphs

1. Notation

2. Combinations and Inverses

3. Quadratic and higher with graphing emphasis

4. Rational Functions

D. Exponential and Logarithmic Functions

1. Introduction to exponential and logarithmic functions

2. Solving exponential and logarithmic equations

3. Exponential and logarithmic models

E. Systems of Equations and Inequalities

1. Systems of linear equations (at least 2 and 3 variables)

2. Nonlinear systems

3. Systems of inequalities

F. Conics

1. Circles and parabolas in graphing form and standard form

2. Completing squares to obtain graphing form of circles and parabolas

3. Ellipses and hyperbolas

G. Sequences and Series

1. Sequence and Summation Notation

2. Arithmetic Sequences

3. Geometric Sequences

Method of Instruction: The method of instruction will be lecture, discussion, and group discussion. Traditional lecture will be supplemented with calculators and computers. Small group-work will also be emphasized. Students are expected to work outside of the class on assigned exercises as well as supplementary reading from the text. Online offering also available.

Required Assignments:

A. Appropriate Readings: Students are required to read assigned chapters in texts. Outside readings are generally not required.

B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols.

C. Appropriate Outside Assignments: Students will be expected to spend a sufficient amount of time outside of class to practice techniques taught during class time, read assigned materials, and complete frequent homework assignments.

D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills such as equation solving and graphing which involve analyzing information, recognizing concepts in new contexts, and drawing analogies.

Methods of Evaluation: A student's grade will be based on multiple measures of performance in the solving of algebra problems, preparation and analysis of graphs. Such measures will include at least three exams and a comprehensive final examination requiring demonstrations of problem-solving skills. In addition, instructors may make use of quizzes, written homework assignments, or other appropriate means to judge a student's dexterity with algebra skills and familiarity with mathematical vocabulary.

Instructors are required to provide students, in writing, with a course syllabus in accordance with district policy, which will include the specific procedures by which students will be evaluated. These procedures must be consistent with the objectives and course content stated above.

Appropriate Texts and Supplies

Dugopolski, College Algebra, 4^th Ed., Addison Wesley Publishing, 2005

TI-84 Graphing Calculator

Student Learning Outcomes:

1. Solve word problems involving linear, quadratic, exponential, and logarithmic functions.

2. Broaden algebra computational skills including fractional exponents and the corresponding radical expressions, complex numbers, and linear and nonlinear systems of equations.

3. Identify the specific properties of linear, quadratic, exponential, and rational functions and construct their graphs.

4. Solve equations with exponentials, logarithms, radical expressions, rational expressions, polynomials, and quadratic in form .

5. Identify conic sections and construct graphs from their equations.

CO/mej

Revised August 2006; 8/24/09

FRC (WPC)