Course Syllabus
Southeast Missouri State University
Department of Mathematics
Title of Course: Precalculus
I.
Course No.: MA137
New: Fall 2014
Catalog Description and Credit Hours of Course:
In-depth study of polynomial, rational, exponential, logarithmic and trigonometric
functions and equations with applications. Credit may not be received for MA 137 and
any of the following: MA 133, MA 134 or MA 135. (5 hours)
II.
Prerequisite(s):
MA 102 or MA 106 with a grade of ‘CR’ or a grade of ‘C’ or higher or MA 095 with a
grade of 'C' or higher, or ACT Math sub-score of 22 or higher.
III.
Objective of Course:
This course will provide an in-depth study of selected topics in Precalculus to prepare
students for a first semester science and engineering calculus course. The primary
objectives of this course are to:
A. Identify, find domains, graph, and perform transformations on a library of parent
functions.
B. Add, subtract, multiply and divide polynomial and rational expressions.
C. Recognize and evaluate exponential functions for a given base, graph exponential
functions having the 1-to-1 property, use exponential functions to model and solve
real-life problems, use the change-of-base formula to evaluate logarithmic
expressions and use logarithmic functions to model real-life situations.
D. To evaluate trigonometric functions on the unit circle, describe and use angles to
model and solve real-life problems, sketch graphs of the sine and cosine functions.
E. Identify and solve linear and non-linear systems of equations using algebraic,
graphical and substitution methods; use systems of equations to solve real-world
problems.
F. Use sequence notation to write the terms of a sequence, use summation notation to
write sums, find the sum of a series, use series and sequences to solve real-life
problems.
IV.
Student Learning Outcomes:
A. Students will be able to construct and simplify a difference quotient.
B. Students will be able to solve exponential and logarithmic equations.
C. Students will be able to simplify expressions involving trigonometric and inverse
trigonometric functions.
V.
Expectations of Students:
A.
B.
C.
D.
VI.
Attend classes.
Participate in classroom activities.
Complete assigned homework.
Satisfactory performance on quizzes and tests.
Course Outline:
Topic
Functions and Their Graphs.
Rectangular Coordinates; Graphs of Equations;
Linear Equations in Two Variables; Analyzing
Graphs of Functions; A Library of Parent
Functions; Transformations of Functions;
Combinations of Functions: Composite
Functions; Inverse Functions.
Polynomial and Rational Functions.
Quadratic Functions and Their Models;
Polynomial Functions of Higher Degree;
Polynomial Division, Rational Functions.
Exponential and Logarithmic Functions.
Exponential Functions and Their Graphs;
Logarithmic Functions and Their Graphs;
Properties of Logarithms; Exponential and
Logarithmic Equations; Exponential and
Logarithmic Models
Trigonometry.
Radian and Degree Measure; Trigonometric
Functions: The Unit Circle; Right Triangle
Trigonometry; Trigonometric Functions of
Any Angle; Graphs of Sine and Cosine
Functions; Graphs of Other Trigonometric
Functions; Inverse Trigonometric Functions;
Applications and Models.
Analytic Trigonometry.
Using Fundamental Identities; Verifying
Trigonometric Identities; Solving
Trigonometric Equations; Sum and Difference
Formulas; Multiple-Angle and Product-to-Sum
Formulas.
Additional Topics in Trigonometry.
Law of Sines; Law of Cosines.
Systems of Equations and Inequalities.
Class
Hours
8
8
10
14
10
4
6
Linear and Nonlinear Systems of Equations;
Two-Variable Linear Systems; Partial
Fractions.
Sequences, Series, and Probability.
Sequences and Series; Arithmetic Sequences
and Partial Sums; Geometric Sequences and
Series.
Examinations.
Reviews.
Total
VII.
6
5
4
75
Textbook and Course Materials:
Larson, Ron. (2007) Precalculus, (Ninth Ed.), Boston, MA, Brooks/Cole, Cengage
Learning.
Every student in MA 137 is required to have a graphing calculator. There is no required brand
of graphing calculator. The University has a calculator rental program, located at Textbook
Services. Calculators with Computer Algebra Systems (CAS) and/or Internet access are
not allowed
VIII. Basis of Student Evaluation:
A. 4 Unit examinations – 60%
B. 10 Quizzes, 10 homework assignments, and class participation – 20%
C. Comprehensive Final examination– 20% The final is mandatory, a grade of X will
be assigned if the final is not taken.
US 1. Extensive Course Description:
The primary purposes of Precalculus are to develop problem-solving capabilities that follow
logical patterns and to provide the essential algebraic and trigonometric background for
work in science and technology fields and prepare students for a first semester science and
engineering calculus course. The main mathematical topics in this course are functions and
graphs, polynomial and rational functions, exponential and logarithmic functions, sequences
and series, systems of linear and non-linear equations, and trigonometric relations and
identities. The historical development of these topics, as well as applications to real-life
situations, will be emphasized in the course.
The students will work problems from the problem sets in the textbook as well as other
problems presented by the instructor. Students will be encouraged to use technology in the
form of graphing calculators and the internet to find information on the history or the
solution of a particular problem. (5)
US 2. Interdisciplinary Nature of the Course:
US 3. Purposes of Objectives of the Course:
This course will provide an in-depth study of selected topics in Precalculus to prepare
students for a first semester science and engineering calculus course. The primary
objectives of this course are to:
A. Identify, find domains, graph, and perform transformations on a library of parent
functions. (University Studies Objectives 1, 2, 3 and 4)
B. Add, subtract, multiply and divide polynomial and rational expressions. (University
Studies Objectives 2 and 3)
C. Recognize and evaluate exponential functions for a given base. Graph exponential
functions having the 1-to-1 property. Use exponential functions to model and solve
real-life problems. Use the change-of-base formula to evaluate logarithmic
expressions and use logarithmic functions to model real-life situations. (University
Studies Objectives 1, 2, and 3)
D. To evaluate trigonometric functions on the unit circle; describe and use angles to
model and solve real-life problems; sketch graphs of sine and cosine functions.
(University Studies Objectives 1, 2, 3 and 4)
E. Identify and solve linear and non-linear systems of equations using algebraic,
graphical and substitution methods; use systems of equations to solve real-world
problems. (University Studies Objectives 1, 2, and 3)
F. Use sequence notation to write the terms of a sequence; use summation notation to
write sums; find the sum of a series; use series and sequences to solve real-life
problems. (University Studies Objectives 1, 2, 3 and 4)
US 4. Student Learning Outcomes:
A. Students will be able to construct and simplify a difference quotient. (US obj. 2, 3)
B. Students will be able to solve exponential and logarithmic equations. (US obj. 1, 2, 3)
C. Students will be able to simplify expressions involving trigonometric and inverse
trigonometric functions. (US obj. 1, 2, 3)
US 5. Course Outline:
University
Topic
Studies Obj.
1, 2, 3, 4
Functions and Their Graphs.
Rectangular Coordinates; Graphs of Equations;
Linear Equations in Two Variables; Analyzing
Graphs of Functions; A Library of Parent
Functions; Transformations of Functions;
Combinations of Functions: Composite
Functions; Inverse Functions.
2, 3
Polynomial and Rational Functions.
Quadratic Functions and Their Models;
Polynomial Functions of Higher Degree;
Polynomial Division, Rational Functions.
1, 2, 3
Exponential and Logarithmic Functions.
Exponential Functions and Their Graphs;
Logarithmic Functions and Their Graphs;
Properties of Logarithms; Exponential and
Logarithmic Equations; Exponential and
Logarithmic Models
1, 2, 3, 4
Trigonometry.
Radian and Degree Measure; Trigonometric
Functions: The Unit Circle; Right Triangle
Trigonometry; Trigonometric Functions of
Any Angle; Graphs of Sine and Cosine
Functions; Graphs of Other Trigonometric
Functions; Inverse Trigonometric Functions;
Applications and Models.
1, 2, 3
Analytic Trigonometry.
Using Fundamental Identities; Verifying
Trigonometric Identities; Solving
Trigonometric Equations; Sum and Difference
Formulas; Multiple-Angle and Product-to-Sum
Formulas.
1, 2, 3
Additional Topics in Trigonometry.
Law of Sines; Law of Cosines.
1, 2, 3
Systems of Equations and Inequalities.
Linear and Nonlinear Systems of Equations;
Two-Variable Linear Systems; Partial
Fractions.
1, 2, 3, 4
Sequences, Series, and Probability.
Sequences and Series; Arithmetic Sequences
Class
Hours
8
8
10
14
10
4
6
6
and Partial Sums; Geometric Sequences and
Series.
Examinations.
Reviews.
Total
5
4
75
US 6. Justification for Inclusion in the University Studies Program:
US Objective 1: Demonstrate the ability to locate and gather information
Emphasis: Some
A. Precalculus gives some emphasis to locating and gathering information. Much of the
location of needed information pertains to other content and methods internal to the
discipline when applied to problem solving. The content of the precalculus course
requires the use of previously developed mathematical methods. Not all can be retained
mentally, but must be searched for by the student using appropriate sources.
Information on the background of how the content applies to real-life situations is also
required.
B. Teaching Strategies: Students will be encouraged to search for needed information when
completing problem assignments. Suggestions will be made as to where various
formulas or other information may be found.
C. Student Assignments: Students will be given assignments which will require them to
demonstrate knowledge of concepts, as well as require them to consult sources other
than the textbook.
D. Student Evaluation: Collected assignments will be evaluated.
US Objective 2: Demonstrate capabilities for critical thinking, reasoning and
analyzing
Emphasis: Significant
A. Content: This is one of the most significant emphases of precalculus addressed by all
components of the course. The need to understand and graph several types of functions,
to solve equations by different methods and to reach reasonable and consistent solutions
to problems requires the instruction of the topics to be approached from several widely
varying viewpoints. Furthermore, the students will be increasing their problem solving
skills as they develop solutions to problems being worked in class, on assignments, and
on tests. This will require a high degree of critical analysis and reasoning by the
students.
B. Teaching Strategies: Class lectures will stimulate critical thinking. Problems will be
posed and various methods of solving them will be considered. Students will be
encouraged to be involved in the classroom discussions. Problem assignments will be
discussed and student solution processes shared after students have completed their
work.
C. Student Assignments: Students will complete homework problems to demonstrate their
knowledge of using various strategies and abilities for critical analysis of a problem and
their solutions.
D. Student Evaluation: Assignments will be collected, evaluated and returned, or will be
discussed carefully in class to verify that the students have mastered the concepts.
Successful completion of an assignment will necessitate the student’s demonstration of
correct use of concepts through problem solving. Quizzes and exams will also be used to
evaluate student progress.
US Objective 3: Demonstrate effective communication skills
Emphasis: Significant
A. Content: This is another significant emphasis of precalculus. Students are introduced to
many basic mathematics symbols and terminology that are essential to meaningful
communication, discussion, and proper solutions of problems encountered. The role and
language of mathematics in many of the natural and technical sciences dictate the
necessity of proper use of mathematical symbolism. Thus, students are expected to
demonstrate a mastery of essential mathematical symbols and terms on assignments and
tests in order to communicate mathematically with peers and superiors.
B. Teaching Strategies: Instructors will model proper mathematical terminology and
demonstrate the correct usage of the symbols and language of mathematics. Students
will be called upon to give written as well as oral explanations for problem solutions.
C. Student Assignments: Problems will be assigned regularly. The assignments are
designed to give students practice in organizing, solving, and presenting mathematical
writing.
D. Student Evaluation: Students’ progress in communicating mathematics will be evaluated
by checking assignments, and grading quizzes and exams.
US Objective 4: Demonstrate an understanding of human experiences and the ability
to relate them to the present
Emphasis: Some
A. Content: Historical perspectives surface in both the content and teaching strategies of
precalculus. The development of mathematical thinking is a building process. As such, it
depends in large measure on the advances and discoveries made in the past, from
antiquity to the present day. The historical background and the cultural setting for many
problems are studied and discussed.
B. Teaching Strategies: Mathematics has been a driving force in the molding of modern
culture and a major element of that culture. This course draws attention to that theme.
When needed, references are made to convey the true spirit of mathematics and the role
mathematics has played in the development of our civilization and today’s modern
world.
C. Student Assignments: Students will learn of contributions made to mathematics by
considering the lives of mathematicians of the past, as well contemporaries.
D. Student Evaluation: Students’ progress will be evaluated by class discussions.
US Objective 5: Demonstrate an understanding of various cultures and their
interrelationships
Emphasis: Not emphasized
US Objective 6: Demonstrate the ability to integrate the breadth and diversity of
knowledge and experience
Emphasis: Not emphasized
US Objective 7: Demonstrate the ability to make informed, intelligent value decisions
Emphasis: Not emphasized
US Objective 8: Demonstrate the ability to make informed, sensitive aesthetic
responses
Emphasis: Not emphasized
US Objective 9: Demonstrate the ability to function responsibly in one’s natural,
social and political environment
Emphasis: Not emphasized
US 7. Background:
The expertise and background required of the faculty members who teach this course is at a
minimum a Master’s Degree in Mathematics or Mathematics Education.
US 8. Class Size:
Maximum optimal class size for MA137 is 25 due to the high demand for the instructor to
interact with the students in a rich, problem solving environment.