Catalog Description: This course covers the study of quadratics; polynomial, rational, logarithmic, and exponential functions; systems of equations; progressions; sequences and series; and matrices and determinants.
Lecture Hrs = 4, Lab Hrs = 0
Semester Credit Hours: 4 Lecture Hours per Week: Contact Hours per Semester: 64 State Approval Code: 2701015400
Course Subject/Catalog Number: MATH1414
Course Title: College Algebra
Core Curriculum: State Criteria
Basic Intellectual Competencies (Those marked with a √ reflect the state-mandated
competencies taught in this course.)
Perspectives (Those marked with a √ reflect the state-mandated perspectives
taught in this course.)
Establish broad and multiple perspectives
on the individual in relationship to the larger society and world in which
he/she lives, and to understand the responsibilities of living in a culturally
and ethnically diversified world.
Stimulate a capacity to discuss and
reflect upon individual, political, economic, and social aspects of life in
order to understand ways in which to be a responsible member of society.
Recognize the importance
of maintaining health and wellness.
Develop a capacity to use knowledge
of how technology and science affect their lives.
Develop personal values for ethical
behavior.
Develop the ability to make
aesthetic judgments.
Use logical reasoning in problem solving.
Integrate knowledge and understand
the interrelationships of the scholarly disciplines.
Exemplary Objectives (Those marked with a √ reflect state-mandated exemplary
objectives taught in this course.)
Mathematics: The objective of the mathematics component
of the core curriculum is to develop a quantitatively literate college graduate. Every
college graduate should be able to apply basic mathematical tools in the
solution of real-world problems.
To apply arithmetic, algebraic, geometric, higher-order thinking and
statistical methods to modeling and solving real-world situations.
To represent and evaluate basic mathematical information verbally,
numerically, graphically, and symbolically.
To expand mathematical reasoning skills and formal logic to develop
convincing mathematical arguments.
To use appropriate technology to enhance mathematical thinking and
understand and to solve mathematical problems and judge reasonableness
of the results.
To interpret mathematical models such as formulas, graphs, tables
and schematics, and draw inferences from them.
To develop the limitations of mathematical and statistical models.
To develop the view that mathematics is an evolving discipline interrelated
with human culture, and understand its connections to other disciplines.
Instructional Goals and Purposes:
Lee College's instructional goals include 1) creating an academic atmosphere
in which students may develop their intellects and skills and 2) providing
courses so students may receive a certificate/an associate degree or transfer
to a senior institution that offers baccalaureate degrees.
General Course Objectives:
Successful completion of this course will promote the general student learning
outcomes listed below. The student will be able
To apply problem-solving skills through solving application
problems.
To demonstrate arithmetic and algebraic manipulation skills.
To read and understand scientific and mathematical literature
by utilizing proper vocabulary and methodology.
To construct appropriate mathematical models to solve applications.
To interpret and apply mathematical concepts.
To use multiple approaches - physical, symbolic, graphical, and
verbal - to solve application problems.
Specific Course Objectives:
Upon successful completion of the course, the student will be able
To evaluate a function from its graph, formula, or equation.
To determine if a relation is a function and state its domain
and range given the graph or equation.
To perform algebraic operations and compositions with functions.
To categorize basic functions given their graphs or equations.
To graph the inverse of a function whose graph is given.
To solve logarithmic, exponential, absolute value, radical
and miscellaneous higher order equations.
To solve polynomial and rational inequalities.
To graph rational, polynomial, piecewise, exponential and
logarithmic functions and selected inverses.
To use symmetry and transformations to sketch graphs.
To solve linear and nonlinear systems of equations.
To set up and solve applications involving functions and relations.
Course Content:
Students will be required to do the following:
FUNCTIONS AND GRAPHS
Define a relation.
Define a function.
Evaluate functions.
Determine domain and range.
Use the vertical line test.
Graph functions and relations.
Identify increasing or decreasing functions.
Graph transformations of functions.
Identify increasing or decreasing functions.
Graph transformations of functions.
Form combinations of functions.
Form the compositions of functions.
Find and give definition of the inverse of functions.
POLYNOMIAL AND RATIONAL FUNCTIONS
Analyze graphs of polynomials using end-behavior, leading coefficient
test.
Perform synthetic division.
State and use the Remainder Theorem.
State and use the Factor Theorem.
State and use the Rational Zero Theorem.
State and use Descartes Rule of Signs.
Find bounds on the roots of a polynomial equation.
State and use the Intermediate value theorem.
Solve polynomial equations.
Graph rational functions.
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Define the exponential function.
Graph exponential functions.
Use exponential models to solve problems.
Define the logarithmic function.
Identify properties of the logarithmic function.
Graph the logarithmic function.
Use logarithmic models to solve problems.
Solve logarithmic or exponential equations.
MATRICES AND LINEAR SYSTEMS
Define a matrix.
Solve a linear system using the Gauss-Jordan Method.
Model stated problems using matrices.
Find solutions to dependent systems.
Perform operations on matrices.
Find the inverse of a matrix.
Solve a linear system using the inverse.
Evaluate determinants.
Decompose rational expressions into partial fractions.
SEQUENCES AND SERIES
Define a sequence.
Define an arithmetic sequence.
Find the nth term and the nth partial sum of an arithmetic sequence.
Model problems using arithmetic sequences.
Define a geometric sequence.
Find the nth term and the nth partial sum of a geometric sequence.
Find the sum of certain infinite geometric series.
State and use the principle of mathematical induction.
Perform proof by mathematical induction.
State and use the Binomial Theorem.
Methods of Instruction/Course Format/Delivery:
Faculty may choose from but are not limited to the following methods of instruction: lecture,
discussion, Internet, video, television, demonstrations, field trips, collaboration,
readings.
Assessment:
Faculty may assign both in- and out-of-class activities to evaluate students'
knowledge and abilities. Faculty may choose from the following methods:
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