Math 128 Precalculus and Trigonometry Great Basin College Fall Semester 2013 Math 128 Precalculus & Trigonometry Online Independent Study Section 1006 Class Key: gbcnv 3255 7303 5 credits CATALOG DESCRIPTION Equations, relations, functions, graphing; polynomial, rational, exponential, logarithmic, and circular functions with applications; coordinate geometry of lines and conics; analytic trigonometry; matrices, determinants; binomial theorem. Prerequisite: Math 096 within two years, sufficient placement test, or SAT/ACT score. COURSE DESCRIPTION This course serves as the bridge from algebra to calculus. We will cover all of the topics in our textbook, PreCalculus, 5th ed by J. Douglas Faires. Recorded lectures are available in WebCampus. LEARNING OUTCOMES Write the solution to inequalities in interval notation Solve nonlinear polynomial inequalities Solve inequalities that contain rational expressions Solve absolute value equations and inequalities Find the center and radius of a circle given the equation of the circle in standard form. Find the equation of a circle given the center and the radius Write the equation of a circle in standard form Find the equation and sketch the graph of a circle given the center and a point or the radius on the circle Sketch a region in the xy-plane bounded by a given inequality or inequalities Find the x- and y-intercepts of a given equation and describe any symmetry (x-axis, y-axis, or origin) the graph contains or if a function is even or odd Find the domain and range of a given function Find the difference quotient (average rate of change) and instantaneous rate of change of a given function Write the equation of a parabola in standard form Find the vertex given the equation of a parabola Find the maximum/minimum value of quadratic function Solve applications that are modeled by quadratic functions Graph basic functions including 𝑦 = 𝑥 2 , 𝑦 = √𝑥 , 3 𝑦 = 𝑥 3 , 𝑦 = √𝑥, 𝑦 = ⟦𝑥⟧, 𝑦 = |𝑥| Given the graph of y = f(x), find the graph of y =f(x+c), y =f(x)+c, y =cf(x), y =f(cx), y =-f(x), and y =f(-x) Find the x-intercepts of a quadratic function by using the quadratic formula Find the equation of a parabola given a vertex and a point on the parabola Given two functions, find the Chapter 1 Exam Ch 1 & 2 and 3 &4 Exams, Final Ch 1 & 2 Exam Ch 1& 2 Exam, Final Ch 1 & 2 Exam Ch 1 & 2 Exam Ch 1 & 2 Exam Ch 1& 2 Exam Ch 1 & 2 Exam Ch 1 & 2 Exam All Exams, Final Ch 1 & 2 Exam, Final Ch 1 & 2 Exam Ch 1 & 2 Exam Ch 1 & 2 Exam Ch 1 & 2 Exam Ch 1 & 2 Exam, Final All Exams, Final Ch 1 Exam Ch 1 Exam Ch 1 & 2 Exam 1 Math 128 Precalculus and Trigonometry sum/difference/product/quotient of the functions Given two functions, find the domain of the sum/difference/product/quotient of those functions Given the function 𝑦 = 𝑓(𝑥), graph its reciprocal Ch 1 & 2 Exam Ch 1 & 2 Exam 𝑔(𝑥) = 1⁄𝑓(𝑥) Given two functions find the composition of those functions and the domain of the composition Prove a function is one-to-one by showing 𝑓(𝑎) = 𝑓(𝑏) implies 𝑎 = 𝑏, the horizontal line test, or by stating the functions are increasing/decreasing Find the inverse of a one-to-one function Sketch the graph of the polynomial function by finding the axis intercepts, the intervals where f(x) > 0 and f(x) < 0, and end behavior Use long division to divide polynomials Use synthetic division to divide polynomials by the factor x - c Use the factor (or remainder) theorem to determine when the linear expression x – c is a factor of a given polynomial and factor the polynomial completely Use the Rational Zero Test to determine all of the possible rational zeros of a given polynomial function and to then factor a polynomial Find the vertical asymptotes of algebraic functions (including rational functions). Find the horizontal asymptote(s) of algebraic functions Sketch the graph of a rational function by finding zeros, asymptotes, and using a sign chart. Sketch the graph of an algebraic function by finding zeros, asymptotes, and using a sign chart Find a polynomial when given the zeros of the polynomial and a point on the graph of the polynomial Add/Subtract/Multiply/Divide complex numbers Find the conjugate of a complex number Find the radian measure of a given angle Find the reference angle of a given angle Find all six trigonometric ratios in a right triangle and use these ratios to solve applied problems involving right triangles Find the values of the six trigonometric functions 𝜋 𝜋 𝜋 𝜋 for the special angles 𝜃 = 0, , , , , 𝜋 and the Ch 1 & 2 Exam, Final Ch 1 & 2 Exam Ch 1 & 2 Exam, Final Ch 3 & 4 Exam, Final Ch 3 & 4 Exam Ch 3 & 4 Exam Ch 3 & 4 Exam Ch 3 & 4 Exam Ch 3 & 4 Exam Ch 3 & 4 Exam Ch 3 & 4 Exam, Final Ch 3 & 4 Exam Ch 3 & 4 Exam Ch Ch Ch Ch Ch 3 & 4 Exam 3 & 4 Exam 3 & 4 Exam 3 & 4 Exam 3 & 4 Exam, Final Ch 3 & 4 Exam, Final 6 4 3 2 multiples of these angles Solve equations involving the trigonometric functions. Sketch the graphs of the six basic trigonometric functions and these graphs with horizontal/vertical shifts, stretches/compressions, and reflections Memorize and use the Pythagorean Identities in solving equations Use the sum and difference formulas for sine, Ch 3 & 4, Finall Ch 3 & 4 Exam, Final Ch 3 & 4 Exam Ch 3 & 4 Exam 2 Math 128 Precalculus and Trigonometry cosine, and tangent Use the half-angle and double-angle formulas Find the exact value of expressions involving the inverse trig functions Solve triangles using the Law of Sines Solve triangles using the Law of Cosines Sketch the graph of an exponential function Find the future value using the compound interest formula Find the future value using the continuously compounding interest formula Sketch the graph of a logarithmic function Use the arithmetic properties of logarithms to rewrite logarithmic expressions as a single log. Use the arithmetic properties of logarithms to simplify logarithmic expressions and solve equations Solve exponential equations Use the exponential function to solve continuous and compound interest problems and to model population growth/decay Identify and sketch the graph of a conic section and label the vertex and foci of the conic section and find and write the equation in standard form Convert polar coordinates to rectangular coordinates and rectangular to polar Convert polar equations to rectangular equations Sketch the graph of a given polar equations Identify and sketch the graph of the conic section given by 𝑟 = 𝑒𝑑 1±𝑒 cos 𝜃 or 𝑟 = Ch 3 & 4 Exam Ch 3 & 4 Exam, Final Ch Ch Ch Ch 3 & 4 Exam, Final 3 & 4 Exam, Final 5 & 6 Exam, Final 5 & 6 Exam Ch 5 & 6 Exam Ch 5 & 6 Exam, Final Ch 5 & 6Exam Ch 5 & 6 Exam Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final Ch 5 & 6, Final Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final 𝑒𝑑 1±𝑒 sin 𝜃 Find the equation of a conic section in polar coordinates given the eccentricity and the equation of the directrix. Rewrite parametric equations as rectangular equations Sketch the curve described by parametric equations indicating where 𝑡 = 0 and the direction of increasing values of 𝑡. Demonstrate the appropriate mathematical format and notation in solving problems. Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final Ch 5 & 6 Exam, Final All Exams and Final INSTRUCTOR INFORMATION Instructor: Lynne Owens Address: Great Basin College Office: MCML 136 1500 College Pkwy Phone: (775) 753-2152 Elko, NV 89801 Fax: (775) 738-8771 E-mail: lynne.owens@gbcnv.edu (preferred method of contact; please do not e-mail me in WebAssign) Office hours: MW 12:30p – 3:00p or by appointment I will not check email or voice mail in the evenings, weekends, or holidays. REQUIRED MATERIALS The homework management system, Enhanced WebAssign and the ebook , Precalculus by J. Doublas Faires, 7th edition have been bundled together. This by far presents the cheapest option 3 Math 128 Precalculus and Trigonometry for students ISBN: 9781285858319. Even though it is not required for this course, you can get the hard copy of the text, but the ebook comes free with WebAssign, and hard copies of math textbooks are notoriously expensive. Scientific calculator Note: Use of graphing calculators is NOT allowed on exams. Internet access Access to a scanner GRADING Grades will be based on a syllabus quiz in WebCampus (5 points), 32 homework assignments (2 points per assignment), and three exams (100 points each )and a final exam (200 points). Your assignments are weighted as follows: syllabus quiz 2%, homework 18%, exams 80%. Grades are distributed as follows. 90 –100% 80 – 89% 70 – 79% 60 – 869% Below 60 A B C D F Withdrawing from class If you decide that you need to drop or withdraw from this class, make sure you fill out the required paperwork. Monday, October 28, 2013 is the last day you can withdraw from this class. If you fail to turn in your paperwork on or before that date, you will receive the grade you are earning in the class. This bears repeating. You are responsible for withdrawing yourself from this class. I will not assign grades of W; if you simply stop attending class without turning in your drop/withdraw form to Admissions and Records, you will get the grade you have earned at the end of the semester. Please consult the Great Basin College catalogue for further information on "I" and "W" grades. HOMEWORK To access your homework go to https://www.webassign.net/login.html and click on “I have a class key.” You will see three boxes. In the first box type gbcnv, in the second box put 3255, and in the third box 7303. Note WebAssign is NOT WebCampus. Your homework, exams, and grades are not in Webcampus. They are in WebAssign. Homework is due on Mondays at 11:55pm, except on those weeks with a Monday holiday-then homework is due on Sunday. Late homework is not accepted. A reminder: Once again, your homework, exams, and grades live on Webassign, not WebCampus. They are different systems. If at any time you want to check your current grade, go to Webassign. EXAMS Your exams, except for the final, will be due on the Thursdays of the weeks where you have completed a two-chapter chunk. Your final is due on Tuesday, December 10, 2013. All exams are due by 11:55 PM, but please check the days and times your local test center (or your proctor) is open for testing and schedule your exams appropriately. Make sure you bring a photo ID to your test site. You may not use a graphing calculator on your exams, nor may you use the calculator in your cell phone or a website on the computer. You may only access WebAssign and no other websites during your test. Your exams are timed—4 hours for each exam. It is unlikely that you will need the full 4 hours for your exam, but I wanted to ensure that you did not feel a time crunch to complete your exam. You may not use books or notes on your exam. For the chapters 3 & 4 exam and the final, the proctor will provide you with a sheet of formulas. Late exams are not accepted. I want to see the work for your exams, so in that sense you should treat it like a regular pencil and paer exam. Your work must be legible and organized with all of the problems numbered. To get your work to me, you will need to scan it, save it as a jpg, and upload it to the test dropbox in WebCampus. If your scanner does not provide you with the option of saving your work as a jpg, you will need to do this yourself by using http://sourceforge.net/projects/pdf-to-jpg/ or 4 Math 128 Precalculus and Trigonometry http://www.zamzar.com/url/ to convert your pdf file to a jpg. If your work is not legible and organized with the problems numbered, or if it is not in the jpg format, I will not accept your work. PROCTORS Your exams need to be supervised by a proctor. If you live near a GBC campus in Elko, Winnemucca, Battle Mountain, Ely, or Pahrump, or if you are a high school student in these areas or at Nevada State High School, there are proctors already set up for you at those campuses. If you live outside of these areas, you will need to provide me with an e-mail address of someone (not a relative or spouse) who would be willing to serve as your proctor and vouch for the security of your exams. Only the proctors have the passwords which will enable you to sign on to your exams. If you will be testing in Elko, please use the Testing Center located in the Academic Success Center (ASC), EIT building, room 114 on our campus. The hours for the ASC and the Testing Center are 9am-8pm Monday-Thursday and 9-4 on Friday. The number for the ASC is 775-753-2149. ACCESSIBILITY STATEMENT Great Basin College is committed to providing equal educational opportunities to qualified students with disabilities in accordance with state and federal laws and regulations, including the Americans with Disabilities Act of 1990 and Section 504 of the Rehabilitation Act of 1973. A qualified student must furnish current verification of disability. This course is designed to be compatible with most universal screen readers. If you are a student needing video and/or audio captioning, GBC's Disabilities Office will provide captioning for you in this course. The Students with Disabilities Office, located in Berg Hall, will assist qualified students with disabilities in securing the appropriate and reasonable accommodations, auxiliary aids, and services. For more information or further assistance, please call 775-753-2271. ACADEMIC DISHONESTY The University and Community College System of Nevada expressly forbids all forms of academic dishonesty, including (but not limited to) all forms of cheating, copying, and plagiarism. Plagiarism is presenting someone else’s word, ideas or data as one’s own. When a student submits work that includes the words, ideas, or data of others, the source of that information must be acknowledged through complete, accurate, and specific references; and if verbatim statements are included, through quotation marks as well. In academically honest writing or speaking, the students will acknowledge the source whenever: Another person’s actual words are quoted Another person’s idea, opinion or theory is used, even if it is completely paraphrased in the student’s own words Facts, statistics, or other illustrative materials are borrowed, unless the information is common knowledge. Students who are discovered cheating will be subject to discipline as outlined in the Great Basin College catalog. In an online setting, academic dishonesty also includes the use of websites to find or check solutions to your exam questions while you are taking the exam. RESOURCES There are videos for this course that I have recorded . They are available in WebCampus. These recordings are to be used only by students in this class and are not allowed to be copied, reproduced, or shared with people outside of this course. Academic Success Center (ASC) EIT Building Room 114, 753-2149 For those of you in Elko, the ASC provides free tutoring. They also have computers that you can use for your homework. ASC hours: 9am-8pm Monday-Thursday and 9-4 on Friday. 5 Math 128 Precalculus and Trigonometry The ASC also offers online tutoring. Send an email to tutor@gbcnv.edu for assistance. TROUBLESHOOTING Because of the nature of an online course, we rely heavily on three technology systems to deliver course materials: WebCampus and WebAssign. Unfortunately, technology can fail and often at inopportune moments. Should you experience technical difficulties, please get help from the appropriate source as quickly as possible. Product WebCampus WebAssign Support helpdesk@gbcnv.edu or 775-753-2167 Webassign.net, click on “student support” or 800-955-8275 COMPUTER ASSIGNMENTS and EXAMS DUE DATES Section Due Date Syllabus quiz Sunday September 1, 2013 1.2 –1.4 Sun. Sept. 1 1.5 – 1.8 (omit 1.5) Mon. Sept. 9 2.2 – 2.4 Mon. Sept. 16 2.5 – 3.3 Mon. Sept. 23 CHAPTERS 1 & 2 Exam Thursday, Sept. 26 3.4 – 3.6 Mon. Sept. 30 4.2 – 4.4 Mon. October 7 4.5 – 4.7 Mon. Oct. 14 4.8 – 5.2 Mon. Oct. 21 CHAPTERS 3 & 4 EXAM Thurs. Oct. 24 Official Course Drop Mon. Oct. 28 Deadline 5.3 – 5.4 Mon. Nov. 4 6.2 – 6.3 Mon. Nov. 11 6.4 – 6.5 Mon. Nov. 18 6.6 Mon. Nov. 25 6.7 Mon. December 2 CHAPTERS 5 & 6 EXAM Thursday, Dec. 5 FINAL EXAM Tues. Dec.10 All homework/exams are due by 11:55pm of the due date. Of course, check the availability of your proctor/testing center on exam day. They may not choose to be available until 11:55pm. TIPS FOR SUCCESS While precalculus can be a difficult subject to master, the burden of learning is on you; therefore, you must be your own advocate. Here are some steps you can take that may increase the probability of your success. If you don’t understand a concept, get some help and get it fast. Do not sit like a bump on a log suffering in silence. Go to the Academic Success Center for free tutoring if you live in Elko. Take advantage of our LiveNet capabilities to ask me a question. Be cognizant of class policies and due dates. For example, what are the policies regarding late work? Do your homework. Math is not a subject that can be skimmed. You learn by doing. Do some math every day. Math is like a language and your proficiency will increase if you expose yourself to some math every day. Do not procrastinate with the computer homework. Technology is our friend and enemy. Allow yourself enough time to complete the homework in case you run into technological difficulties. 6