ࡱ> Y u;bjbj h h .kbkbg3 R!R!R!R!R!f!f!f!8!<!f!5#^$$$$$$$$$$$5555555$B9;p+5R!$$$$$+5R!R!$$$$@5&&&$jR!$$R!$$5&$5&&A3|E4$$Gai%v3.4V5053Zh<%h<$E4E4h<R!Y4&$$$+5+5&$$$5$$$$h<$$$$$$$$$B  : COLLEGE ALGEBRA AND TRIGONOMETRY The University of Toledo Mathematics & Statistics Department, College of Natural Sciences and Mathematics MATH1340-0XX, CRN XXXXX Instructor: (Insert Name] Class Location: (Insert Building/Room) Email: (Insert E-mail Address) Class Day/Time: (Insert Days/Time) Office Hours: (Insert Days/Time) Lab Location: (Insert Building/Office #, if applicable) Office Location: (Insert Building/Office Number) Lab Day/Time: (Insert Days/Time, if applicable) Office Phone: (Insert Phone Number) Credit Hours: 5 Term: (Insert Semester and Year) ___________________________________________________________________________________________________ COURSE DESCRIPTION Functions and graphs, exponential and logarithmic functions, trigonometric functions and applications, systems of equations and topics in analytic geometry. STUDENT LEARNING OUTCOMES Math 1340 focuses on the concept of a function and the solution of equations. Students will demonstrate skills verbally, numerically, graphically and algebraically. A more detailed list of learning objectives is given below. At least 70% of the course time will be devoted to these essential outcomes. These objectives are listed again in the chronological list of topics at the end of this syllabus. Representation: Graphical, algebraic, numerical, and verbal representation of linear, quadratic, polynomial, rational, root/radical/power, exponential, logarithmic, trigonometric, and piecewise-defined functions. Graphs: Determine whether an algebraic or trigonometric relation or given graph represents a function; perform transformations on graphs and operations with functions; determine intercepts, domain, range, intervals of monotonicity, vertex of a quadratic, asymptotes, symmetry; and match graphs to algebraic or trigonometric definitions. Remainder and Factor Theorems: Use the Remainder and Factor Theorems for polynomial functions. Inverse functions: Describe the relationship of the graph of a function to that of its inverse; determine the algebraic form of inverse functions. Trigonometric Definitions: Define the six trigonometric functions in terms of right triangles and the unit circle. Modeling: Use functions to model a variety of real-world problem-solving applications. Angles/Triangles: Solve right and oblique triangles in degrees and radians for both special and non-special angles, and solve application problems that involve right and oblique triangles. Equations: Recognize the difference between an algebraic equation and function; describe the relationship among the solutions of an equation and the zeros of the corresponding function; identify the coordinates of the x-intercepts of the graph of a function. Solutions of equations and inequalities: Solve a variety of equations, including polynomial, rational, exponential, and logarithmic, including equations arising in applications; solve a system of linear equations graphically and algebraically by substitution and elimination; and solve polynomial and rational inequalities graphically and algebraically. Conic Sections: Identify and express the conics (quadratic equations in two variables) in standard rectangular form, graph the conics, and solve applied problems involving conics. Trigonometric Identities: Verify trigonometric identities by algebraically manipulating trigonometric expressions using fundamental trigonometric identities, including the Pythagorean, sum and difference of angles, double-angle and half-angle identities. Sequences and Series: Represent sequences verbally, numerically, graphically and algebraically. Write series in summation notation, and represent sequences of partial sums verbally, numerically and graphically. Identify and express the general term of arithmetic and geometric sequences, and find the sum of arithmetic and geometric series. Vectors: Represent vectors graphically in both rectangular and polar coordinates and understand the conceptual and notational difference between a vector and a point in the plane. Perform basic vector operations both graphically and algebraically addition, subtraction and scalar multiplication. Solve application problems using vectors. PREREQUISITES Sufficient score on the math placement exam. REQUIRED MATERIALS ALEKS 360 access card for PreCalc. Online access is provided with an e-text and may be purchased from www.ALEKS.com (you need a credit card) or the bookstore. The course is based on: Precalculus, Miller 1st edition ISBN: 1259723321. You will receive details the first day of the class. Access to a PC or Mac connected to the web and on which you have privileges to install browser plug-ins. (for ALEKS, above) Calculator: You will need to own or have access to a scientific calculator that has the trigonometric function keys. A graphing calculator is helpful, but not required. Cell phones, smart phones, and graphing calculators are not allowed during quizzes and exams. UNIVERSITY POLICIES: POLICY STATEMENT ON NON-DISCRIMINATION ON THE BASIS OF DISABILITY (ADA) The University is an equal opportunity educational institution. Please read The University's Policy Statement on Nondiscrimination on the Basis of Disability Americans with Disability Act Compliance. ACADEMIC ACCOMMODATIONS The University of Toledo is committed to providing equal access to education for all students. If you have a documented disability or you believe you have a disability and would like information regarding academic accommodations/adjustments in this course please contact the Student Disability Services Office (Rocket Hall 1820; 419.530.4981; studentdisabilitysvs@utoledo.edu) as soon as possible for more information and/or to initiate the process for accessing academic accommodations. For the full policy see:  HYPERLINK "http://www.utoledo.edu/offices/student-disability-services/sam/index.html" http://www.utoledo.edu/offices/student-disability-services/sam/index.html ACADEMIC POLICIES: Student Privacy Federal law and university policy prohibits instructors from discussing a student's grades or class performance with anyone outside of university faculty/staff without the student's written and signed consent. This includes parents and spouses. For details, see the Confidentiality of student records (FERPA) section of the University Policy Page at  HYPERLINK "http://www.utoledo.edu/policies/academic/undergraduate/index.html"http://www.utoledo.edu/policies/academic/undergraduate/index.html Missed Class policy If you miss any graded item, then this item may only be made up in accordance with the Universitys Missed Class Policy. This policy requires that you contact me in advance by phone, e-mail or in person, provide official documentation for the absence, and make up the missed item as soon as possible. You can find the Universitys Missed Class Policy at  HYPERLINK "http://www.utoledo.edu/policies/academic/undergraduate/index.html" http://www.utoledo.edu/policies/academic/undergraduate/index.html ACADEMIC DISHONESTY Any act of academic dishonesty as defined by the University of Toledo policy on academic dishonesty (found at  HYPERLINK "http://www.utoledo.edu/dl/students/dishonesty.html"http://www.utoledo.edu/dl/students/dishonesty.html) will result in an F in the course or an F on the item in question, subject to the determination of the instructor. GRADING: Evaluation The evaluation for this course will be based upon a percentage of the total of homework, test and final exam scores: Quizzes and homework (Insert min percent) to (Insert max percent)% Midterms (Insert min percent) to (Insert max percent)% Final Exam (comprehensive) (Insert min percent) to (Insert max percent)% Total 100% Grades are based on the following percentages of total points: 100% - 90% A 89% - 80% B 79% - 70% C Pluses and minuses will be used using the policy of the University. 69% - 60% D Below 60% F Assessment of Student Learning Assessment will be based on a combination of homework, quizzes, midterms and a final exam. You will need to demonstrate the ability to apply mathematical reasoning and skills to solve problems in all the outcome areas listed above using correct mathematical notation. Responsibilities of the Student You are expected to attend each class session. If you attend class, it is assumed that you will participate actively by asking questions and participating in discussions. You are expected to prepare for class, to have read the indicated sections prior to the class session and have your homework completed by the indicated date. This is a three credit hour course and you should expect to spend 5 to 8 hours outside of class reading, studying and doing homework problems. The syllabus schedule indicates the order in which the sections will be discussed. If you must miss a class, it is your responsibility to find out what you missed including any announcements which were made. IMPORTANT DATES *The instructor reserves the right to change the content of the course material if he perceives a need due to postponement of class caused by inclement weather, instructor illness, etc., or due to the pace of the course. MIDTERM EXAM: FINAL EXAM: OTHER DATES The last day to drop this course is: ________________ The last day to withdraw with a grade of W from this course is: ___________________ STUDENT SUPPORT SERVICES Free math tutoring on a walk-in basis is available in the Math Learning and Resources Center located in Rm B0200 in the lower level of Carlson Library (phone ext 2176). The Center operates on a walk-in basis. MLRC hours can be found at  HYPERLINK "http://www.math.utoledo.edu/mlrc/MLRC.pdf" http://www.math.utoledo.edu/mlrc/MLRC.pdf Topics to be Covered: TopicBook SectionLearning ObjectiveHoursSolving Systems of Linear Equations - Graphically7.1Solving Systems of Linear Equations0.5Solving Systems of Linear Equations - Elimination Method7.2Solving Systems of Linear Equations0.5Solving Systems of Linear Equations - Substitution Method7.1Solving Systems of Linear Equations0.5Solving Systems of Linear Equations - Modeling Problems7.1, 7.2Solving Systems of Linear Equations, Modeling1Conics Parabolas10.2Conic Sections1Conics Ellipses10.3Conic Sections1Conics Hyperbolas10.4Conic Sections1Conics - Modeling Problems10.2, 10.3, 10.4Conic Sections, Modeling1.5Relationships and Functions1.4, 1.5, 1.6Graphs, Equations1Transformations of Functions - Stretching and Shrinking1.7Functions, Graphs1Transformations of Functions - Translations1.7Functions, Graphs1Transformations of Functions Reflections1.7Functions, Graphs1Operations with Functions - Addition and Subtraction1.8Functions1Operations with Functions - Multiplication and Division1.8Functions1Operations with Functions - Composition1.8Functions1Quadratic Functions - Finding the Vertex2.1Functions, Graphs0.5Quadratic Functions - x- and y-intercepts2.1Functions, Graphs0.5Quadratic Functions - The Quadratic FormulaA48, 2.4Solutions of Equations1Quadratic Functions - Modeling with Quadratic Functions2.1Modeling1Polynomial Functions - Graphs of Polynomials2.2Graphs2Polynomial Functions - The Remainder Theorem2.3Remainder Theorem1Polynomial Functions - The Factor Theorem2.3Factor Theorem1Polynomial Functions - Zeros of Polynomials2.5Solutions of Equations1Rational Functions2.6Graphs2Modeling with Polynomial and Rational Functions2.2, 2.6Modeling1Solving Nonlinear Inequalities - Graphically2.7Solving Inequalities1Solving Nonlinear Inequalities - Algebraically2.7Graphing, Solving Inequalities1Inverse Functions1.9Inverse Functions1Exponential Functions3.1, 3.4Graphs, Functions2Logarithmic Functions3.2, 3.3, 3.4Graphs, Functions2Modeling with Exponential and Logarithmic Functions3.5Modeling1Sequences9.1, 9.2, 9.3Sequences1Series9.1Series1Arithmetic Series9.2Series1Geometric Series9.3Series1Total Hours for College Algebra:37Radian and Degree Measure4.1Angles1The Six Trigonometric Functions in Terms of a Right Triangle4.3Triangles, Modeling1.5Applications Involving Right Triangles4.8Modeling1.5Definition of the Six Trigonometric Functions Using the Unit Circle4.2Definitions1.5Reference Angles4.4Definitions1.5Coterminal Angles4.1, 4.2Definitions1.5The Graphs of the Trigonometric Functions4.5, 4.6Graphs3The Inverse Trigonometric Functions4.7Definitions, Modeling3The Graphs of the Inverse Trigonometric Functions4.7Graphs2Fundamental Trigonometric Identities5.1, 5.2Identities2Pythagorean Identities5.1, 5.2Identities2Solving Trigonometric Equations5.3Equations, Modeling2Sum and Difference Formulas5.4Identities1.5Double-Angle Formulas5.5Identities1.5Half-Angle Formulas5.5Identities1.5The Law of Sines6.1Identities, Modeling1.5The Law of Cosines6.2Identities, Modeling1.5Vectors6.3Vectors, Modeling3Total Hours for Trigonometry:33 4-5 hours (depending on holidays) for review, quizzes, and midterms     !    # ( 8 : J K [ \ d T V ^ h m o  Q  &»³¤wwh`t56B*\]^Jphh`th`tB*^Jphh`t5B*CJ\aJphhHL5B*CJ\aJphh`tmH sH hcl5\ h`t5\h?h`tCJaJh h`tCJaJh`tCJaJh h`tCJaJh<]h`t5CJ aJ .!:*  ? 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