Blue Ridge Community College/Stuarts Draft High School MTH 163-91 Pre-calculus I Spring 2012 INSTRUCTOR: Kathryn Childress (kchildress@augusta.k12.va.us) COURSE DESCRIPTION: Presents college algebra, matrices and algebraic, exponential, and logarithmic functions. Prerequisites: a placement recommendation for MTH 163 and Algebra I, Algebra II, and Geometry or equivalent. (Credit will not be awarded for both MTH 163 and MTH 166) STUDENT PERFORMANCE OBJECTIVES: Upon the completion of this course, the student should be able to: 1. 2. 3. 4. 5. 6. Use the distance and midpoint formulas Graph equations by plotting points and by intercepts Test an equation for symmetry with respect to the x-axis, the y-axis, and the origin Recognize the equation of a circle and be able to find its center and radius Sketch graphs of circles Sketch graphs of lines given slope and point, given two points, or given slope and intercept 7. Write the equation of a line in slope-intercept or general form 8. Find the equation of parallel and perpendicular lines 9. Use graphing calculator to find line of best fit for a scatter diagram 10. Distinguish between functions and relations 11. Find the value, the domain, the range, and the inverse of a function 12. Identify even or odd functions from a graph or equation 13. Determine where on a graph a function is decreasing or is constant and locate local maxima and minima by hand and by using the graphing calculator 14. Graph piece-wise functions 15. Graph functions using vertical and horizontal shifts, reflections about the x-axis and yaxis and using compressions and stretches 16. Solve applications problems involving constructing and analyzing functions 17. Graph a quadratic function using its vertex, axis, intercepts, and transformations 18. Solve applied problems by using maximum or minimum values 19. Use graphing calculator to find the quadratic function of best fit 20. Identify and graph polynomial functions 21. Identify the zeros of a polynomial function and their multiplicity 22. Find the domain, the vertical, horizontal, or oblique asymptotes of a rational function 23. Analyze the graphs of polynomial and rational functions 24. Solve polynomial and rational inequalities 25. Use the Remainder and Factor Theorems, Descartes’ Rule of Signs or the Rational Zeros Theorem to find the real zeros of a polynomial function 26. Solve polynomial equations 27. Find complex zeros of a polynomial 28. Form a composite function and find its domain 29. Determine and graph the inverse of a function 30. Evaluate and graph exponential functions 31. Define the number e 32. Solve exponential and logarithmic equations 33. Solve application problems dealing with exponential functions 34. Solve systems of equations by substitution and elimination 35. Solve system of equation with three variables 36. Identify inconsistent systems of equations containing two or three variables 37. Use Cramer’s Rule to solve a system of equations containing two or three variables 38. Perform matrix operations 39. Solve a system of inequalities by substitution or elimination 40. Graph a system of inequalities 41. Solve a linear progression problem ATTENDANCE POLICY: The Stuarts Draft High School Student Handbook explains their attendance policy, which this class will follow. The student is expected to attend all classes. It is the student’s responsibility to get work missed from an absence. All work is to be made up within 3 days. Make up work is graded as zero after 3 unexcused absences. In addition, you need to be aware that BRCC expects you to attend every class. School related absences (i.e. sports, choir, etc.) are not recognized by BRCC. Keep absences to a minimum. Notify the instructor and get any work needed before the absence. In a college course, make-up work and tests are given and/or accepted at the sole discretion of the instructor. In case of snow days, work is to continue. Online assignments will be given to keep students up to date. GRADING POLICY: o 80% of the grade is from 7 tests each worth 100 points, various quizzes each worth 50 points, and several projects worth varying amounts of points o 10% of the grade is from homework that is done on line or checked in class o 10% of the grade is from class participation where 100 points are assigned and points are deducted for rule infractions and absences. o The grading scale will be based on percentages as follows: 90% - 100% 80% - 89% 70% - 79% 60% - 69% Below 60% A B C D F There will be an exam that will count as 2 test grades. TEXT: Precalculus, 9th Edition, Sullivan; Pearson/Prentice-Hall, 2012 My Math Lab – Internet software with problems that coordinate to the text INSTRUCTIONAL MATERIALS: Graphing Calculator will be used extensively in the class. These are available in the classroom for in room use, but the student would benefit from having their own calculator. The student also needs a 3-ring binder or spiral notebook, whichever he/she is best at organizing. The student will also need internet access to do the online homework assigned. CLASS SCHEDULE AND SEQUENCE OF INSTRUCTION: The following is a tentative schedule, and is subject to change at any time. Week 1: January 18 - 20 1.1 Rectangular Coordinates 1.2 Graphs of Equations in two variables 1.3 Lines 1.4 Circles Week 2: January 23 - 27 Quiz on Chapter 1 2.1 Functions 2.2 The Graph of a Function 2.3 Properties of Functions 2.4 Library of Functions: Piecewise-defined Functions 2.5 Graphing Techniques: Transformations 2.6 Mathematical Models Week 3: January 30 – February 3 TEST on Chapters 1 and 2 – Graphs and Functions 3.1 Linear Functions and their properties 3.2 Building Linear functions from data 3.3 Quadratic functions and their properties 3.4 Quadratic Models: Building quadratic functions from data Week 4: February 6 – 10 3.5 Inequalities Involving Quadratic functions Test on Chapter 3 4.1 Polynomial functions and models 4.2 and 4.3 Properties of rational functions Week 5: February 13 – 17 4.4 Polynomials and rational inequalities 4.5 Real zeros of a polynomial function 4.6 Complex zeros: Fundamental Theorem of Algebra Test on Chapter 4 Week 6: February 21 – 24 5.1 Composite functions 5.2 Inverse functions Quiz – functions 5.3 Exponential functions 5.4 Logarithmic functions Week 7: February 27 – March 2 5.5 Properties of Logarithms 5.6 Logarithmic and exponential equations Quiz – Logs 5.7 Compound Interest 5.8 Exponential growth and decay: models TEST – Chapter 5 Week 8: March 6 - 9 11.1 Systems of linear equations: substitution and elimination 11.2 Systems of linear equations: matrices 11.3 Systems of linear equations: determinants Quiz – System of equations 11.4 Matrix algebra Week 9: March 12 - 16 11.6 Systems of non-linear equations 11.7 Systems of inequalities 11.8 Linear Programming TEST – Chapter 11 EXAM: March 23 HONOR CODE The functioning of an academic community depends on the integrity of all of its members. Blue Ridge Community College values truthfulness, respect for the property of others, and honesty in academic work. Violations of these values may result in permanent dismissal from the College. The Statement on Student Rights and Responsibilities, located in the Catalog and Student Handbook, and the Statement on Academic Honesty below, provide specific guidelines which encompass this code. Academic Honesty When College officials award credit, degrees, diplomas, and certificates, they must assume the absolute integrity of the work done by students; therefore, it is important that each student maintains the highest standard of honor in his or her scholastic work. Academic dishonesty cannot be condoned. When such misconduct is established as having occurred, students are subject to possible disciplinary actions ranging from admonition to dismissal, along with any grade penalty the instructor may impose in accord with their syllabus and college policies. Procedural safeguards of limited due process and appeal are available to students in disciplinary matters. Grade disputes about a grade assigned as a result of academic dishonesty can only be resolved through the grade appeal procedure. No withdrawal policy outlined in the College Catalog and Student Handbook can supersede a grade penalty assigned as a consequence of an academic honesty violation. Academic dishonesty includes, but is not limited to, one of the following acts: 1. Cheating on an examination or quiz, including the giving, receiving or soliciting of information, the unauthorized use of notes or other materials during the examination or quiz. 2. Buying, selling, stealing or soliciting any material purported to be the unreleased contents of a forthcoming examination, or the use of such material. 3. Substituting for another person during an examination and/or quiz, including online exams or quizzes, or allowing such substitution for one’s self. 4. Plagiarism. This is the act of using content and/or ideas from the work of another individual, either word for word or in substance, and representing them as one’s own work. This includes any submission of written work other than one’s own. There are three types of plagiarism as listed in Donald A. Sears’ book Harbrace Guide to the Library and Research Paper, 3rd Edition (New York: Harcourt, 1972, p. 45). They are: a. Word-for-word plagiarism: The submission of the work of another source without proper acknowledgment of that source by footnote, bibliography or reference in the paper. b. Patchwork plagiarism: Submitting a work that is stitched together from a variety of sources that does not indicate direct quotes or acknowledgment of those sources. c. Unacknowledged paraphrase: Restatement or rewording of another author’s original thought or idea must be acknowledged. Restatement by means of paraphrase does not remove the necessity of giving credit to original sources. Refer to the Library website for more information on plagiarism. (http://www.brcc.edu/library/) 5. Collaboration with another person in the preparation or editing of assignments submitted for credit without advance approval from the instructor. 6. Knowingly furnishing false information to the College including, but not limited to, forgery, alteration or use of College documents, or instruments of identification with intent to defraud.