SANTA BARBARA CITY COLLEGE
ASSOCIATE
DEGREE CREDIT COURSE OUTLINE
Department: Mathematics
Subject
Area and Course Number: Mathematics 111
Course
Title: Intermediate Algebra for Math, Science and Business Majors
Discipline:
Mathematics
Units: 5
Repeatability: None
Catalog
Course Description: Second course in algebra, including
algebraic manipulation of polynomials, rational expressions, exponents,
radicals, linear equations, ratio and proportion, inequalities, word problems,
complex numbers, quadratic equations, and systems of linear and nonlinear
equations. 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, complex numbers, quadratic equations, systems of linear and
nonlinear equations. Introduction to functions, exponential exponentials, and
logarithmic functions.
Introduction to graphing calculators. A prerequisite for Math 130 and 137.
Lecture
Hours per Week: 5.3 (80-90
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
and English 103
Course
Advisories: Math 100, with a grade of ŇBÓ or
better.
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.
Review and
Extension of Elementary Algebra Topics
a. The
Real Number System
i)
organization of
real number system: natural
numbers, integers, rational numbers, irrational numbers, real numbers.
ii)
absolute value,
algebraic and geometric interpretations
b. polynomials
i)
review of
terminology and basic operations
ii)
special products
iii)
binomial theorem
using PascalŐs triangle
iv)
factoring
techniques including common factors, difference of squares, sum and difference
of cubes, trinomials, grouping,
and algebraic expressions which can be factored using substitution
c. review
of first degree equations and inequalities in one variable
i) solving
equations and inequalities, solution sets, literal equations,
ii) absolute
value equations and inequalities
iii)
word problems
including estimation and
approximation
d. rational
expressions
i) review
of basic operations
ii)
extensions to
more complicated expressions
iii)
complex rational
expressions
iv)
rational
equations, and applications
e. Direct,
inverse and joint variation
2.
Exponents and
Radicals
a. review
of integer exponents
i) simplifying
expressions using laws of exponents
ii) scientific
notation
b. rational
exponents and roots
i) n-th
roots; comparison of odd vs. even roots
ii) definition
and properties of rational exponents
iii) simplifying
expressions
iv) radicals
and their relation to rational exponents
v) simplifying
and rationalizing radicals
vi) addition,
subtraction, and multiplication of radicals
3.
Complex Numbers
a.
definition
(rectangular form only)
b.
simplifying
square roots of negative numbers
c.
arithmetic of
complex numbers (addition, subtraction, and multiplication)
4.
Equations in two
variables
a. linear
equations and their graphs
i)
equations of
lines -- standard form, point slope form, slope intercept form
ii)
parallel and
perpendicular lines
5.
Introduction to
Functions and their graphs
a.
definition,
notation
b.
evaluating
functions
c.
addition,
subtraction, multiplication and division of functions
d.
composition of
functions
e.
inverse
functions
f.
translations and
reflections
6.
Quadratic
Equations and Functions
a.
solve by
factoring
b.
solve by
completing the square
c.
solve by using
the quadratic formula
i)
proof of formula
ii)
use of
discriminant
iii)
literal
quadratic equations
d.
complex
solutions
e.
equations quadratic in form
f.
graphs of
quadratic functions
g.
applied
maximum/minimum problems
h.
radical
equations
7.
Systems of
Equations
a.
Review of 2 x 2
linear systems
b.
3 x 3 linear
systems
c.
word problems
d.
systems
involving non-linear equations
8.
Exponential and
Logarithmic Functions
a.
exponential
functions
i) definition
and graph
ii) applications
-- exponential growth and decay
b.
logarithmic
functions
i) definition
and graph, including common and natural logarithms
ii) properties
of logarithm -- exponential and logarithm equivalences
iv)
converting to
other bases
c.
solving exponential
and logarithmic equations
9.
Conics
a.
standard form
for circles
b.
standard form
for parabolas
c.
ellipses and
hyperbolas
d.
putting
equations of conic sections in standard form by completing the square
10.
Sequences and
Series (optional)
a.
notation,
definition (including recursive definition) of sequences
b.
partial sums and
sigma notation
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.
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:
Larson, Hostetler, Neptune, Intermediate
Algebra: Graphs and Functions,
3rd Ed., Houghton Mifflin Publishing, 2003
TI-84 Graphing Calculator
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, complex numbers, inverse variation, complex
fractions, and 3X3 systems of equations.
3.
Interpret
the specific properties of linear, quadratic, exponential, logarithmic, or
rational functions and their graphs within the context of the problem.
4.
Solve
equations with exponentials, logarithms, and square roots.
5.
Identify
conic sections and construct graphs from their equations, and solve nonlinear
systems involving conic sections.
IA/mej
Revised
August 2006; 5/13/09; 8/24/09
FRC
(WPC)