Course Syllabus Southeast Missouri State University Department of Mathematics Course No.: MA137 Title of Course: Precalculus New: Fall 2014 I. 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. Attend classes. B. Participate in classroom activities. C. Complete assigned homework. D. Satisfactory performance on quizzes and tests. VI. 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. Class Hours 8 Systems of Equations and Inequalities. 6 8 10 14 10 4
Linear and Nonlinear Systems of Equations; Two-Variable Linear Systems; Partial Fractions. Sequences, Series, and Probability. 6 Sequences and Series; Arithmetic Sequences and Partial Sums; Geometric Sequences and Series. Examinations. 5 Reviews. 4 Total 75 VII. 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. 5 Reviews. 4 Total 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.