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					Chabot College                                                                                     Fall 2008

                                    Course Outline for Mathematics 31
                                          COLLEGE ALGEBRA

Catalog Description:

31 – College Algebra                                                                                  3 units

    Preparation for Calculus for Business and Social Science students. Functions and graphs:
    polynomials, rational functions, exponential and logarithmic functions, circles, parabolas, binomial
    theorem, sequences and series. Solving rational, radical, quadratic in form, exponential and
    logarithmic equations. Prerequisite: Mathematics 54, 54L, 55, 55L or 55B (completed with a grade of
    C or higher) or an appropriate skill level demonstrated through the Mathematics Assessment process.
    3 hours.
    [Typical contact hours: 52.5]

Prerequisite Skills:

    Before entering this course the student should be able to:

    1.    solve systems of linear equations and interpret the solutions;
    2.    graph polynomial, rational, exponential, and logarithmic functions;
    3.    solve exponential equations;
    4.    find inverse functions and apply their properties;
    5.    perform function composition;
    6.    solve quadratic equations;
    7.    apply the properties and perform operations with radicals;
    8.    apply the properties and perform operations with rational exponents;
    9.    apply the properties and perform operations with logarithms;
    10.   apply the concepts of exponential functions.

Expected Outcomes for Students:

    Upon completion of the course the student should be able to:

    1.    graph given algebraic functions and relations;
    2.    sketch the graphs of circles and parabola;
    3.    find the equation of circles and parabolas;
    4.    sketch the graphs of logarithmic and exponential functions involving translations of basic graphs;
    5.    solve exponential and logarithmic equations;
    6.    apply the concepts of logarithmic and exponential functions to other fields;
    7.    find specified terms and sums of arithmetic and geometric progressions;
    8.    expand a power of a binomial and find a specified term in a binomial expansion:
    9.    solve nonlinear inequalities.

Course Content:

    1. Review of functions and graphs
       a. Definition
       b. Operations
       c. Inverse functions
       d. Linear functions
       e. Quadratic functions
    2. Graphing factorable polynomial functions of degree three or higher
       a. Intercepts
       b. Signed charts
Chabot College
Course Outline for Mathematics 31, page 2
Fall 2008

   3. Graphing rational functions
       a. Intercepts
       b. Sign charts
       c. Vertical and horizontal asymptotes
   4. Solving equations
       a. Review linear
       b. Review quadratic and quadratic in form
       c. Polynomial
       d. Rational
       e. Radical
       f. Exponential and logarithmic
   5. Solving inequalities
       a. Review linear
       b. Polynomial
       c. Rational
       d. Absolute value
   6. Exponential and logarithmic functions
       a. Definition
       b. Graphing, including translations of basic graph
       c. Applications
   7. Circles and parabolas
       a. Find equations
       b. Graphing, including translations
   8. Sequences and series
       a. Summation notation (sigma)
       b. Arithmetic
       c. Geometric
   9. Binomial theorem
   10. Systems of equations

Methods of Presentations:

   1.   Lectures
   2.   Collaborative small groups
   3.   Class discussion
   4.   Audio-visual materials

Assignments and Methods of Evaluating Student Progress:

   1. Typical Assignments
      a. Homework
          1) Section 3.7: Read the definitions of rational function, asymptotes. Work out problems 1,
              5, 9, 10, 11, 13, 15, 21, 23: submit detailed graphs of # 45, 65. The graphs should be on
              graph paper.
          2) Read 8.1. Learn all the definitions. Work out problems 1 – 27 every other odd, 29 – 33
              odds, 35 – 45 all, and 47 – 57 odds.
      b. Collaborative Assignments using a small mirror and a yard stick, work with your group to find
          the height of a tree or a building.

   2. Methods of Evaluating Student Progress
      a. Homework
      b. Collaboratives
      c. Quizzes
      d. Midterms
Chabot College
Course Outline for Mathematics 31, page 3
Fall 2008

          e. Final Exams

Textbook(s) (Typical):

     College Algebra, Stewart/Redlin/Watson, Brooks Cole, 2004

Special Student Materials:

     None




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Revised: 10/05/04

				
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