Santa Barbara City College Course Outline

MATH 137 - College Algebra

MATH 137
College Algebra
Disciplines
Mathematics (Masters Required)
5.000
0 - May not be repeated
Extensive treatment of functions and graphing techniques, including translations, symmetries, reflections, and graphs of inverse functions. Analysis and applications of polynomial, rational, absolute value, exponential and logarithmic functions. Systems of equations and inequalities, conics, and sequences and series.
80.000-90.000 Total Hours
Total Hours
160.000-180.000 Total Hours
80.000-90.000 Total Hours
Prerequisite: MATH 107 or equivalent based on SBCC's Assessment Center placement via multiple measures.
Prerequisite or Corequisite: None
Concurrent Corequisite: None
Course Advisories: None
Limitation on Enrollment: None
Course Objectives:
Analyze and solve problems involving algebraic fundamentals, functions, and graphs.
Solve inequality statements, including linear, absolute value and more general non-linear inequality statements and graph their solutions.
Describe the main features of conics: circles and ellipses, parabolas and hyperbolas.
Solve systems of equations and inequalities.
Analyze and manipulate symbolically expressions representing sequences and series.
Demonstrate a beginning ability to present clear and logical solutions to the above problems.
Student Learning Outcomes
MATH137 SLO1 - Solve application problems involving linear, polynomial, exponential, and logarithmic functions.
MATH137 SLO2 - Identify properties of functions and their graphs and inverses, including linear, polynomial, exponential, and rational functions and construct their graphs.
MATH137 SLO3 - Identify conic sections and construct graphs from their equations.
MATH137 SLO4 - Solve systems of linear and nonlinear equations, and apply these methods to solve application problems.

  1. Algebraic fundamentals

    1. Exponents, including negative and fractional

    2. Radicals

    3. Absolute value

    4. Complex numbers

  2. Functions and graphing

    1. Graphs, functions and relations

    2. Notation

    3. Translations

    4. Symmetry/Even and odd functions, algebraically and graphically

    5. Expansions and contractions

    6. Algebra of functions, function composition

    7. Inverse functions

    8. Piecewise-defined functions

  3. Linear and Polynomial Functions

    1. Linear and polynomial equations and  inequalities

    2. Polynomial division

    3. Finding zeros of polynomials, including complex zeros

    4. Graphs of polynomial functions

  4. Rational Functions

    1. Rational equations and inequalities

    2. Graphs of rational functions

    3. Modeling, including variation

    4. Partial fraction decomposition (optional)

  5. Absolute Value Functions

    1. Absolute value equations and inequalities

    2. Graphs of absolute value functions

  6. Exponential and Logarithmic Functions

    1. Exponential functions and their graphs

    2. Logarithmic functions and their graphs

    3. Exponential and logarithmic equations

    4. Modeling, including growth and decay

  7. Systems of Equations and Inequalities

    1. Linear systems

    2. Nonlinear systems

    3. Modeling

  8. Conics

    1. Distance formula

    2. Midpoint

    3. Circles, parabolas, ellipses, hyperbolas

    4. Completing squares to obtain graphing form of conic sections

  9. Sequences and Series

    1. Sequence and summation notation

    2. Arithmetic Sequences

    3. Geometric Sequence

Methods of Instruction
Directed Study
Discussion
Distance Education
Lecture
Lecture is the primary activity, along with student problem-solving activities. Students are also expected to work outside of class on assigned exercises and supplemental reading from the text.
Applications of Exponential and Logarithmic Functions 1. Mark Anthony once loaned the City and People of Rome 100,000 talents of gold with the stipulation that the city pay compound interest at a rate of 1.5% each month. How much did Rome owe her favorite son after six months? After one year? After a year and a half? 2. When Benjamin Franklin died in 1790, he bequeathed a sum of $1000 to “his beloved City of Philadelphia” with the codicil that this remain on deposit in an account that paid 4% compound interest each year for two centuries. On July 4th, 1990, the city of Philadelphia closed this account. How much money did Ben Franklin give to the citizens of Philadelphia two hundred years after his death?
A. Appropriate Readings: Students are required to read assigned sections in text or supplements. B. Writing Assignments: Students must work assigned mathematical problems requiring the manipulation of abstract symbols. C. Appropriate Outside Assignments: Students are expected to spend a sufficient amount of time outside of class to practice techniques presented during class time, read assigned materials, and complete frequent homework assignments. D. Appropriate Assignments that Demonstrate Critical Thinking: Students must demonstrate mathematical skills which involve analyzing information, recognizing concepts in new contexts, and drawing analogies. They must also analyze using both inductive and deductive reasoning within a logical system.
A student’s grade will be based upon multiple measures of performance in the solving of algebraic problems, in the preparation and in the analysis of graphs, and analysis of logical arguments. Such measures may include at least four one-hour exams (or equivalent) 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. In accordance with district policy, instructors are to provide students a written course syllabus 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.
    PrecalculusOpenstax, Openstax, 2014PrecalculusCohen, Cengage, 2012
  • TI-84 Graphing Calculator
11/05/2018
Board of Trustees: 12/13/2018
CAC Approval: 12/03/2018