SANTA BARBARA CITY COLLEGE

ASSOCIATE DEGREE CREDIT COURSE OUTLINE

 

 

Department:  Mathematics

Subject Area and Course Number:  MATH 87

Course Title:  Intermediate Algebra Refresher

Discipline:  Mathematics

Units:   1

Repeatability:  None

Catalog Course Description:  Short course intended for those students who have assessed into Math 107 and wish to improve their assessment level; those who have successfully completed Math 107 but need more review; or students who unsuccessfully attempted Math 120 and need review of intermediate algebra skills.  Features a computer program to refresh those concepts identified as needed for each student, plus weekly contact with the instructor. Successful completion of this course may serve as a petition to challenge Math 107.   Course does not replace a failing grade in Math 107.

Description for Schedule of Classes: Intermediate algebra refresher for students who desire higher placement; students who have completed Math 107 but need review; or those who have attempted Math 120 and need review. 

Lecture Hours per Week:  18 Hours Total (Short Course)

Laboratory Hours per Week:  None

Plus Hours:  None

Prerequisite:  None

Co-requisites:  None

Skills Advisories:    None

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.          The Real Number System

a.          Organization of real number system: natural numbers, integers, rational numbers, irrational numbers, real numbers

b.         Axioms for the real numbers

 

2.          Linear Equations and Inequalities

a.          Solving equations and inequalities

b.         Literal equations

c.          Ratio and proportion

d.         Word problems

e.          Graphing linear equations, slope intercept approach

f.          Finding equations of straight lines given one point and the slope or given two points

g.         Interpretation of slope, units for slope

3.          Systems of Linear Equations

a.          Systems with two unknowns

i.           Solution by graphing, substitution and elimination

ii.         Inconsistent and dependent systems

b.         Systems with three unknowns

c.          Word problems

4.          Function and Their Graphs

a.          Definition and notation

b.         Domain and range

c.          Evaluation

d.         Addition, subtraction, multiplication and division of functions

5.          Exponential and Logarithmic Functions

a.          Properties of exponents, negative and fractional exponents

b.         Exponential and logarithmic functions-definitions and graphs

c.          Properties of logarithmic functions-exponential and logarithmic equations

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

6.          Quadratic Functions

a.          Review of special products and basic factoring

b.         Graphing parabolas in standard form using symmetry properties

c.          Solving quadratic equations by factoring

d.         Derivation and the use of the quadratic formula

e.          Word problems and the Pythagorean theorem

7.          Rational Expressions and Functions

a.          Multiplication, division and reduction of rational expressions

b.         Addition and subtraction of rational expressions

c.          Complex fractions

d.         Equations involving rational expressions

8.          Variation

a.          Direct

b.         Inverse

9.          Radicals

a.          Review of exponents-scientific notation

b.         Properties of radicals

c.          Addition and multiplication of radicals

d.         Radical equations

10.       Sequences

a.          Arithmetic sequences-relationship to linear functions

b.         Geometric sequences-relationship to exponential functions

c.          Summation notation

 

Methods of Instruction:  The course will include use of email, ALEKS computer-based tutorials, interactive computer-based activities, and regular computer-based assessment tests. 

 

Required Assignments:   Students will do the assigned components of ALEKS (which is equivalent to regular homework assignments) and take the assigned assessments at the appropriate level.

 

Methods of Evaluation: Students' grades will be based on their performance on the assigned components of ALEKS, the assigned assessments at the appropriate level and an in-class Math 107 final exam.

 

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:  

Software: ALEKS, McGraw Hill, 2.0 ed

ALEKS is a diagnostic and tutorial software package which will be adjusted to cover the specific topics in this course.  The software can be downloaded from the web and students will enroll via a password from the instructor.

 

Textbook: (Not Mandatory)

Lehmann, Jay.  Intermediate Algebra: Functions and Authentic Applications, Prentice Hall, 2007.

 

 

PG/mej

Approved September 24, 2007

FRC (10/19/07 gb)