Course Prefix & Number: MATH 040 F
CC Approved: 04/25/10
DCCC Approved: 10/08/08
Board Approved: 11/12/08
EFFECTIVE TERM: Fall 2010
FULLERTON COLLEGE
COURSE OUTLINE
Division:
FC Math & Computer Science
Department/Subject Area:
Mathematics
Course Prefix:
MATH
Course Number:
040 F
Course Title:
Intermediate Algebra
Units:
4
Lec Hours: Full Term Hrs/Wk.
4
Lab Hours: Full Term Hrs/Wk.
1
Assignment Preparation Hours:
8
Prerequisite(s):


A minimum grade of 'C' in MATH 020 F
or math skills clearance
Corequisite(s):

None
Advisory(ies):

None
Repeatability

I.
Not designed as repeatable
DESCRIPTIONS
1.
CATALOG DESCRIPTION
Four hours of lecture and one hour arranged per week. This course includes products and
factoring, exponents and radicals, fractions, functions and graphs, linear and quadratic
equations, linear inequalities, logarithms, and related
topics at an intermediate level. Calculators will be used for selected topics. (Degree Credit)
AA GE
2.
SCHEDULE DESCRIPTION (max 2 lines):
This course includes at an intermediate level: factoring, exponents, radicals, rational
expressions, functions and graphs, linear and quadratic equations, inequalities, logarithms,
conic sections.
II.
ENTRY LEVEL SKILLS AND KNOWLEDGE (To be completed if required by Prerequisite Policy)
Upon entering this course, the student needs to be able to:
1.
Identify and successfully complete operations on rational and irrational numbers.
2.
Create equivalent simplified polynomial, rational and radical expressions and
evaluate polynomial, rational and radical expressions.
3.
Perform multiplication and factoring of polynomials.
4.
Solve linear, quadratic, and rational equations, and check their solutions.
5.
Construct mathematical models of business, chemistry and physics applications and
solve verbal problems.
6.
Construct the graphs of linear equations and identify the features of a line.
7.
Construct the graphs of quadratic equations and identify the concavity of a
parabola.
8.
Solve linear inequalities in one variable and construct their graphs.
9.
Solve systems of linear equations.
III.
INSTRUCTIONAL OBJECTIVES (Use measurable objectives only)
Upon completion of this course, the student will be able to:
1.
Perform arithmetic operations on real numbers, polynomials and rational
2.
3.
4.
5.
6.
7.
8.
9.
10.
IV.
expressions.
Solve linear, quadratic, radical, rational, exponential, logarithmic and literal
equations.
Solve linear inequalities and express the solutions in interval notation or by
graphing.
Construct the graphs of linear functions using x- and y-intercepts or slope and yintercept.
Convert rational exponents to their equivalent radical notation.
Solve systems of linear equations by graphing, substitution or elimination.
Solve applications of linear, quadratic, exponential and logarithmic functions.
Use a scientific calculator to perform basic operations, including evaluating
exponential and logarithmic functions.
Construct the graphs of parabolas, circles, ellipses (centered at the origin) and
hyperbolas (centered at the origin).
Solve non-linear systems of equations by graphing.
COURSE CONTENT AND SCOPE (instructional topics or units)
1.
2.
3.
4.
5.
Factoring
1.
Review greatest common factor, GCF
1.
Monomial GCF
2.
Binomial GCF
2.
Review difference of two squares
1.
Monomial factors
2.
Binomial factors
3.
Review trinomials
1.
Leading coefficient is 1
2.
Leading coefficient is not 1
4.
Factoring by grouping
5.
Sum and difference of two cubes
Rational Expressions
1.
Simplify
2.
Add and subtract
3.
Multiply and divide
4.
Complex fractions
Long Division of Polynomials
1.
Synthetic Division
Exponents
1.
Natural, integer and rational
2.
Properties of exponents
3.
Review scientific notation
Radicals
1.
Simplify variable radicands, principal roots
2.
Add and subtract
3.
Multiply and divide
4.
6.
7.
8.
9.
10.
11.
Rationalize denominators
1.
Monomial denominators
2.
Binomial denominators
5.
Convert radical notation to exponential notation
Complex Numbers
1.
Definition of i, standard form of complex number
2.
Add and subtract
3.
Multiply and divide
Solving Equations
1.
Rational
2.
Absolute Value
3.
Quadratic by factoring
4.
Quadratic by completing the square
5.
Quadratic by the Quadratic Formula
1.
Complex roots
6.
"Quadratic in Form" using a u-substitution
7.
Radical
8.
Literal
9.
Variation
1.
Direct
2.
Joint
3.
Inverse
4.
Combinations of the above
10.
Miscellaneous applications
Solving Inequalities
1.
Quadratic
1.
Use a number line for its solution
2.
Rational
1.
Use a number line for its solution
3.
Interval notation or set notation
4.
Linear in two variables
1.
Use graphing for its solutions
Solving Systems of Equations
1.
Review systems in two variables by substitution
2.
Review systems in two variables by addition or elimination
3.
Linear systems in three variables
4.
Graphing systems in two variables
5.
Consistent, inconsistent and dependent systems
6.
Parallel and perpendicular lines
7.
Non-linear systems of equations in two variables
Solving Systems of Inequalities by Graphing
1.
Systems of linear inequalities
2.
Systems of non-linear inequalities
Functions
1.
Definition
2.
Domain and range
3.
Evaluating f(x) and f(x+h) and f[g(x)]
4.
Inverses
5.
6.
12.
13.
14.
V.
Graphing functions such as absolute value or radical
Linear functions
1.
Slopes
2.
Intercepts
3.
Graphs
7.
Quadratic functions
1.
Zeros
2.
Maximums or minimums
3.
Graphs
Conic Sections
1.
Parabola
1.
Vertex
2.
Intercepts
3.
Graphs
2.
Distance formula
3.
Circle
1.
Center not at origin
2.
Radius
3.
Equation
4.
Graphs
4.
Ellipse with its center at the origin
1.
Equation
2.
Intercepts
3.
Graphs
5.
Hyperbola with its center at the origin
1.
Equation
2.
Intercepts
3.
Asymptotes
4.
Graphs
Exponential Functions
1.
Graph
2.
Use e as a base
3.
Solving exponential equations
4.
Applications including compound interest, growth and decay
Logarithmic Functions
1.
Properties of logarithms
2.
Natural and common logarithms
3.
Graphs
4.
Solving logarithmic and exponential equations
5.
Applications including compound interest, growth and decay
INSTRUCTIONAL METHODOLOGIES (instructor initiated learning strategies):
A. Lecture/discussion
B.
C.
D.
E.
Demonstration
Observation
Lecture sessions with question and answer periods
Use of presentation media including chalkboard/whiteboard, overhead projector, videos
and/or DVDs, computer presentations, calculators, manipulatives
F. Group and cooperative learning activities
G. Formal and informal student presentations of solutions to problems and/or assigned topics
H. Guided practice and/or individual instruction
I. Make available supplementary tutorial services including Math Lab and/or Tutoring Center,
computer tutorials online at publisher's website, video tapes and/or DVDs, individual
and/or small group tutoring by instructor
VI.
MULTIPLE METHODS OF EVALUATION (measurements of student achievement):
.
A.
B.
C.
D.
E.
Class Participation
Class Work
Projects
Quizzes
Homework assignments requiring demonstration of problem solving ability
Regular sectional or midterm examinations requiring demonstration of problem solving
ability
F. An on-campus/proctored comprehensive final examination requiring demonstration of
problem solving ability
VII.
LIST RECOMMENDED TEXTBOOKS:
Texts such as the following are appropriate:
0. Lial, Margaret L., John E. Hornsby and Terry McGinnis. Intermediate Algebra, 10th ed.
Boston: Pearson Addison Wesley, 2008 Recommended
1. Bittinger, Marvin L. and David J. Ellenbogen. Intermediate Algebra: Concepts and
Applications, 8th ed. Boston: Pearson Addison Wesley, 2010 Recommended
VIII.
LIST SUPPLEMENTAL TEXTBOOKS OR MATERIALS:
Supplemental Reading or materials such as the following are appropriate:
IX.
ASSIGNMENTS:
0. WRITING ASSIGNMENTS AND/OR PROFICIENCY DEMONSTRATION (skill-based courses)
A. Problem sets that require complete written solutions
B. Examinations that require complete written solutions
C. Written reports and projects
D. Written self-evaluation
1. ASSIGNMENTS THAT DEMONSTRATE CRITICAL THINKING (Be specific when describing
student assignments and state in cognitive terms)
. Interpret an English phrase into an algebraic expression.
A. Construct sets using the correct roster and set-builder notation.
B. Distinguish between various kinds of real numbers.
C. Solve linear, quadratic, rational, exponential and logarithmic equations.
D. Construct the graph of linear and quadratic functions.
E. Identify the features of each conic section and sketch the graph of each.
F. Solve inequalities including inequalities with an absolute value.
G. Identify the properties of a line such as its slope and its intercepts.
H. Construct the graph of the solution to an inequality in two variables.
I. Solve a system of equations and apply that skill to problem solving.
J. Evaluate polynomials for specified values of the variable.
K. Create mathematical models to solve application problems.
L. Distinguish between meaningful and extraneous solutions to problems.
2. REQUIRED OUT-OF-CLASS ASSIGNMENTS (to be completed only if applicable)
. None
X.
GENERAL EDUCATION:
Associate Degree General Education Requirements
Associate Degree General Education
Requirements
XI.
3281
Area B2: Natural Sciences and MathematicsMathematics