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)