SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

Department:  Mathematics

Subject Area and Course Number:  Mathematics 107

Course Title:  Intermediate Algebra

Discipline:  Mathematics

Units:   4

Repeatability:  None

Catalog Course Description:  A second course in algebra, including algebraic manipulation of polynomials, rational expressions, exponents, radicals, linear equations, ratio and proportion, inequalities, word problems,  quadratic equations, systems of linear and quadratic equations, and sequences.  An introduction to functions and nonlinear equations.  Exponential and logarithmic functions and their applications.   Introduction to graphing calculators.

Description for Schedule of Classes:  Second course in algebra: inequalities, polynomials, quadratic equations, systems of linear and quadratic equations, sequences. Introduction to functions, exponential and logarithmic functions. Introduction to graphing calculators.

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

Laboratory Hours per Week:  None

Plus Hours:  None

Prerequisite:  Math 100, with a grade of "C" or better, OR qualifying score on SBCC placement exam.

Co-requisites:  None

Skills Advisories:    Eligibility for English 100, English 103

Course Advisories:       None

Limitation on Enrollment:       None

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

1.                  Demonstrate refined skills in algebraic manipulation and equation solving through extensions of techniques taught in Elementary Algebra by solving equations and systems of equations, and manipulating and simplifying algebraic expressions.

2.                  Apply the above skills while analyzing and finding solutions to word problems.

3.                  Demonstrate the ability to graph functions and relations involving two variables.

4.                  Demonstrate a basic understanding of the exponential and logarithmic functions.

5.                  Demonstrate ability to use graphing calculators appropriately.

Course Content and Scope:

1.         Linear Equations and Inequalities

a.         Brief review of linear equations, slope-intercept form, graphing lines, and finding equations of lines from descriptive data

b.         Using linear equations in word problems, and in application or modeling problems to give approximate values and predictions

c.         Solving linear inequalities in one variable.  Using linear inequalities in modeling situations.

2.         Systems of Linear Equations

a.         Brief review of solving 2x2 linear systems

b.         3x3 linear systems

c.         Using 2x2 and 3x3 systems in word problems and modeling problems

3.         Functions and Their Graphs

a.         Definition and notation

b.         Domain and range

c.         Evaluation

d.         Addition, subtraction, multiplication and division of functions

e.         Inverse functions

4.         Exponential and Logarithmic Functions

a.         Properties of exponents, negative and fractional exponents

b.         Exponential functions–definitions and graphs

c.         Logarithmic functions–definitions and graphs

d.         Properties of logarithmic functions–exponential and logarithmic equations

e.         Simplifying exponential and logarithmic expressions

f.          Exponential and Logarithmic equations

g.         Application of exponential and logarithmic functions to problems involving growth and decay

5.         Quadratic Functions

a.         Review of special products and basic factoring

b.         Graphing parabolas in vertex form

c.         Graphing parabolas in standard form using symmetry properties

d.         Solving quadratic equations by factoring

e.         Completing the square

f.          Derivation and the use of the quadratic formula

g.         Word problems and the Pythagorean theorem

h.         Modeling using quadratic equations

6.         Rational Expressions and Functions

a.         Domain of rational expressions

b.         Multiplication, division and reduction of rational expressions

c.         Addition and subtraction of rational expressions

d.         Complex fractions

e.         Solving rational equations

f.          Using rational equations to solve word problems

7.         Variation

a.         Direct

b.         Inverse

8.         Radicals

a.         Review of exponents–scientific notation

b.         Properties of radicals

c.         Addition and multiplication of radicals

d.         Radical equations

 

Method of Instruction:  Lecture is the primary activity to be used, along with student problem-solving.  Students are expected to work outside of class on assigned exercises as well as on supplementary reading from the text.

 

****A hybrid online version and a fully online version of this course are available.  See attached distance learning summary.

 

 

 

Required Assignments:

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

B.           Writing Assignments:  Students must work on 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.   Critical thinking will also be emphasized through numerous treatments of word problems.

 

Methods of Evaluation:  A student's grade will be based on multiple measures of performance in the solving of algebra problems.  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:

Lehmann, Jay.  Intermediate Algebra: Functions and Authentic Applications, 3rd ed., Prentice Hall, 2008.

Graphing Calculator

 

 

For online version:  Web browser, Netscape 4.0 or higher, MS Internet Explorer 4.0 or higher. PC compatible running Windows 95 or later, or Macintosh computer running OS7 or later.  Minimum 32 MB of RAM. Modem minimum speed of 33.6 (28.8).  Software: MyMathLab, Pearson Education, or similar product.

 

Student Learning Outcomes:

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

2.                  Broaden elementary algebra computational skills to include fractional exponents and the corresponding radical expressions, inverse variation, complex fractions, and 3x3 systems of equations.

3.                  Choose the appropriate linear, quadratic, exponential, logarithmic, or rational function to model data. 

4.                  Graph and interpret the specific properties of linear, quadratic, exponential, logarithmic, or rational functions within the context of the problem.

5.                  Solve equations with exponentials, logarithms, and square roots. 

 

 

 

CO/mej

Revised 3/03/08; 8/24/09

FRC (Word Proc Center)