1) Graphing basic logarithmic functions



[NAME OF PROGRAM: ACCESS ACADEMY][COURSE CODE – MATH0100: COURSE NAME – PRECALCULUS]ACADEMIC YEAR 2018-2019[SEMESTER – SPRING]COURSE SYLLABUSCOURSE INFORMATIONClasses held:6th January, 2019 Credits : 4Prerequisite: Higher Secondary MathematicsFACULTY INFORMATIONFaculty Name: Faiz AhmadEmail: faiz.ahmad@auw.edu.bdOffice Location: H 518Office Hours: 4 Hours Qualifications: M.Sc. in Physics, University of Chittagong, Bangladesh B.Sc. in Physics, University of Chittagong, BangladeshAreas of Expertise: Pre-calculus, Calculus, Newtonian Mechanics, Nuclear Physics, and Astrophysics.Profile:Faiz served as a Senior Instructor in Mathematics, Pathways for Promise at AUW from Summer II 2016 to Fall 2017 and then in AA as Instructor (Pre-Calculus) from 2018 Spring Semester. He graduated from the University of Chittagong (Bangladesh), in Physics with both first class results. Before joining AUW, he worked for Presidency International School (Cambridge affiliated) and Bangladesh Elementary School (NC English medium) for 5 years. He actively participated in numerous training sessions conducted by local and international experts on teaching methods, lesson planning, class room management, student psychology etc. He is also one of the 29 listed junior researchers from South Asia selected by NABIC & BCAS (Dhaka) and NERSC (Bergen, Norway). In 2017 he successfully completed AuthorAID (based in Oxford, UK) grant proposal and research writing online course and obtained Merit grade.TEXT AND OTHER COURSE MATERIALSRequired Text: Michael Sullivan Pre-calculus.Other necessary course materials will be providing in the class room.COURSE OBJECTIVES AND DESCRIPTIONCourse Description: Pre-calculus is a one year course of mathematics. Pre-calculus exposes students to a rigorous level of mathematics, essential to the study of UG level courses under Liberal arts and Sciences. The pace of the class and depth of the material may be different than those encountered in previous education. The focus of this course is primarily on various types of functions: polynomial, rational, exponential, logarithmic and trigonometric. The student will also learn about the behavior of functions through graphs and transformations; they will gain insight into the properties of these functions and their inverse forms. At the end of the course, students will be able to apply a variety of techniques to abstract and real-life problems alike. They will also use "Khan Academy Videos/ Resources" in this course in a blended learning and assessing approach.Course Objectives:Gaining factual knowledge (Essential) Learning fundamental principles, generalizations or theories (Important)Learning to apply course material (to improve thinking, problem solving, and decisions) (Important) Spring SemesterLearning Goals:Exponential and Logarithmic Functions One-to-One FunctionsInverse FunctionsExponential Equation/Function and its properties.Logarithmic Equation/Function and its properties.Applications of Exponential and Logarithmic FunctionsTrigonometric FunctionsTypes of Trigonometric FunctionsProperties of the Trigonometric FunctionsAnalytic Trigonometry Trigonometric Identities Sum and Difference FormulasDouble-angle and Half-angle Formulas Product to Sum and Sum to Product Formulas Systems of EquationsMatrix Algebra.Describing Data SetsCharacterizing Data.LEARNING OUTCOMESStudent Learning OutcomesMethod of Assessment1) Demonstrate the fundamental concept of a mathematical function and all of its properties.Quiz based upon class lecturer, Assigned homework exercises, and exam.2) Solve equations and inequalities both algebraically and graphically.Quiz based upon class lecturer, Assigned homework exercises, and exam.3) Find zeros of polynomials and the zero product property. Quiz based upon class lecturer, Assigned homework exercises, and exam.4) Graph polynomial, absolute value, square root, rational function and polynomial functions.Quiz based upon class lecturer, Assigned homework exercises, and exam.5)Identify some connection between the mathematics at this level and the real worldQuiz based upon class lecturer, Assigned homework exercises, and exam.ATTENDANCE REQUIREMENT & GRADING POLICYAn “A” designates truly excellent and outstanding work and an “F” represents complete lack of effort resulting in unacceptable work.A+ 4.3 (96.68-100)A 4.0 (93.33-96.67)A- 3.7 (90.00-93.32)B+ 3.3 (86.68-89.99)B 3.0 (83.33-86.67)B- 2.7 (80.00-83.32)C+ 2.3 (76.68-79.99)C 2.0 (73.33-76.67)C- 1.7 (70.00-73.32) *D+ 1.3 (66.68-69.99)D 1.0 (63.33-66.67)D- 0.7 (60.00-63.32)F 0 (59 .99 or below)* Any grade below C- (70%) requires remedial work. A course of action will be decided in agreement between the student, teacher, and an academic administrator. CONTACT WITH YOUR PROFESSORIf you face any problem you can contact me during my office hours or by appointment.Students are expected to check their email at least twice daily, preferably in the morning and evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements.COURSE SCHEDULE*Please see Khan Academy Video links provided at last 4 pages of this plan booklet. Also, note that you can watch much more that fits our lesson objectives and we may update (include/exclude) the list as Khan Academy also uploads new videos time to time and to make the links more useful for our students and lesson. I may send you all the links in your email as well so that you can click and go to the link directly.??Spring Semester Pre-Calculus Lesson PlanWeek 11st Class 2nd class 3rd class Objectives Introducing the Spring SyllabusDetermine whether the function is one-to-one.Draw the graph of inverse function, Check the inverse function algebraically and state domain and range. Class OutlineAn hour long discussion on Spring Syllabus and course planI will show how to work with problems 10,12,16,18,20,22,26,30,32,36 38 and 40 from exercise 5.2 (Sullivan Book) then Ss will have to solve few problems individually and answer will be given on the board. I will show how to work with problems 48, 58 and 66 from exercise 5.2 (Sullivan Book) then Ss solve most of the problems individually and answer will be written on the board. HandoutsSpring SyllabusEx;5.2 N/AHomeworkNone Some problems from Exercise-5.2 based on those conceptions.All odd number exercises from (47-58) and (59-70).Evaluation N/A Students will solve some problems based on the conceptions. Some students might straggle with problems 36 and 40. Students will solve some problems based on the conceptions.Week 21stclass2nd class3rd classObjectives Study two Transcendental functions: the Exponential function and Logarithmic function. Determine whether the given data represent exponential functions or not. Use the transformation to draw exponential graphs and then find out domain and range.Change exponential expressions to logarithmic expression, evaluate logarithmic functions. Quiz test 1Class OutlineEvaluate exponential functions, Graph exponential functions; laws of exponents and define the number ‘e’. ?I will show some problems from Ex: 5.3 (Sullivan Book). Most of the problems will complete by the students. Review of the Chapter(Use of Khan Academy videos/Resources)HandoutsSome Vocabulary to familiar with.Ex:5.3(Sullivan Book)Ex:5.4 (Sullivan Book)HomeworkSome problems from Larson’s Precalculus BookAll Odd numbers exercises from ex: 5.3.N/AEvaluation Some Students may work out problems based on the conceptions correctly, however they might have some confusion especially on exponential graphs.Most of the students are expected to respond well.Students will be asked to solve random problems by themselves.Week 3 & 41st and 2nd class3rd and 4th class5th and 6th classObjectivesSWBAT determine the domain of logarithmic function and graph logarithmic function.Discussing the Quiz-1 mistakes.SWBAT learn how to solve logarithmic equations SWBAT Identify the logarithmic expression as a single logarithm and evaluate logarithm whose base is neither 10 nor e.Class Outline First 30 minutes I will discuss the mistakes which Ss did on the Quiz-1.Then I will show how to find out the domain of the logarithmic function and how to graph. I will solve 44, 48 and 68 and will ask Ss to solve?38, 40, 42, 46, 50, 54, 56, 64, 66, and 70. Ss will go through the problems individually and I will roam to see Ss work.I will give an example and then I asked to solve 88,90,92,94,96,98,100,102,104,106,108 and 110. (Ex: 54 from Sullivan Book) Ss start to solve individually and answer will be given on the board.Students will see Khan Academy videos/Resources for more clear concepts.HandoutsN/AN/AN/AHomework37,39,41,43,47,51,53,55,61,63,65,67,69 ( Ex:5.4 Sullivan)Solve Worksheet.N/AEvaluationSs can easily understand my solution and easily solve problems.Ss can easily understand?and solve application problems.Students will have to solve some random problems.?????????????????????????????????????????????Week 5 & 61st and 2nd class3rd and 4th class5th and 6th classObjectivesSWBAT use the properties of logarithm to find the exact value, express as a sum and/or difference and each expression as a single logarithm.One more lesson on logarithm.To make students familiar with Application based problems,To model a problem from data.Class Outline I will solve few problems from Ex: 5.5 then will ask the Ss to solve 8, 12, 16, 20, 22, 26, 28.30,36, 38, 44, 48, and 50. Answer will be given on the board.I will show problems no. 56, 64 and 70.Will ask to solve problems No 52,54,58,60,62,66,68 and 72. Answer will be given on the board.I will discuss some problems based on Economics & some problems based on Life Science.HandoutsSullivan ?Ex:5.5N/AApplication problems handoutsHomeworkRevise Ex: 5.2-5.4.Revise : Ex:5.5From handouts.EvaluationMost of the students might struggle with problems: 22, 48 and 50.Ss can easily understand?and will solve problems. At first few students struggle then they will get fun.Week 7 & 81st and 2nd class3rd and 4th class5th and 6th classObjectives To find the exact values of the trigonometric functions using a point on the unit circle.SWBAT learn properties of the trigonometric functions.Review of the trigonometric functions.Class OutlineWill show some numerical problems on finding trig. Values graphically and numerically.Determine the domain and range of trigonometric functions and period of trigonometric function and work with first six fundamental identities.After the discussion Ss will see Khan Academy videos/Resources for more clear concepts.HandoutsEx:6.2Ex:6.3N/AHomeworkExercise 6.2 (29-48) and (67-82) Sullivan Book.Exercise 6.3 (27– 34, 59 - 76)Sullivan book.N/AEvaluation Get few problems done by students, students may be confused on some problems related to Phi.Students will solve few problems from Exercise and will rectify the previous difficulties.Random questions will be asked to judge the level of understanding.Week 91st class2nd class3rd classObjectivesRevision for Midterm. Midterm Review of Mid-Term questions.Class Outline Revise all concepts in Midterms.Students will participate in the midterm exam.N/AHandoutsA work sheet Question paper.N/AHomeworkPreparation for Midterm.N/AN/AEvaluation Hope class will finish well.N/AN/AWeek 101st class2nd class3rd classObjectivesSWBT will use algebra to simplify trigonometric expression and establish identities.Second lesson on using algebra to simplify trigonometric expression and establish identities.Third lesson on using algebra to simplify trigonometric expression and establish identities.Class Outline Demonstrate algebraic techniques to simplify trigonometric expression .Then I ask to solve 10, 12 18,30,31,32 and 34. Ss will work with the problem. I will be checked each students answer when they will work.Ss will work with the problems 40 42, 44,46,48,50, 52,54,56,58,60,62,64,66,68,70 72and74. I will be checked each students answer when they will work.Ss will have to solve problems 76,78,80,82,84,86,88,90,92,94,96,98,100 and 102. I will be checked each students answer when they will work.HandoutsEx:7.3( Sullivan Book)N/AN/AHomeworkEx:7.3 (20,22,24,26,30,32,34,35,36,37,38) Ex:7.3(41,43,45,47,49,51,53,55,57,73)Ex: 7.3 All odd number exercises from 75-101.EvaluationSome of the students might struggle with applying techniques. Ss will easily solve the problems.Ss will easily solve problems.Week 111st class2nd class3rd classObjectivesProof the sum and difference formulas and use sum and difference formulas to find the exact values. SWBAT use sum and difference formulas and use sum and difference formulas to establish identities (Double angle and half angle formulas; Product to sum and sum to product formulas)SWBAT understand the graphing utility to find the line of best fit and second lesson on previous lesson. Class Outline Class will start with the some basic of Euclidian geometry then I will prove the sum and difference formulas. Ss will work with the problems. I will be checked each students answer when they will work.I will show few examples then ask to solve 46,48,50,52,56,58,60,62,64,68 and 70 from Ex: 7.4 (Sullivan Book) .I will be checked each students answer when they will work. ?In the class I will solve 18 (which was H.W) Then I will ask to solve 21 and 22.HandoutsEx:7.4Ex: 7.4N/AHomeworkEx:7.4 (All odd numbers from 9-38)Ex:7.4 ( all odd numbers from 45-69)Preparation for 2nd Quiz.EvaluationSs might confuse with geometry problems.Ss easily will solve the problems.Ss easily could understand the application problems and will get fun.Week 121st class2nd class3rd classObjectives2nd Quiz Proof the sum and difference formulas and use those to establish identities.Proof the product to sum and sum to product formulas and use those to establish identities.Class Outline N/AClass will start with formulas proof then I will solve and explain problem no. 64 Ex: 7.5 from Sullivan book .Then I will ask to solve all even numbers from 48-68. I will check each and every one answers. Class will start with formulas proof then I will solve and explain problem no. 28 Ex: 7.6 from Sullivan book .Then I will ask to solve all even numbers from 20-36. I will check each and every one answers.HandoutsN/AEx: 7.5Ex:7.6HomeworkN/AEx:7.5 ( all odd numbers)Ex:7.6 ( all odd numbers)EvaluationHope most of the student will do better.Ss will easily solve the problems.Ss will easily understand the problems.Week 131st class2nd class3rd classObjectivesBasic concept on matrix with definition and Types of matrix. Will learn how to find the sum and difference of two matrices and scalar multiples of a matrix.Will learn how to find the product of two matrices.Class Outline N/AClass will start with formulas proof then I will solve and explain problem no. 7, 8, and 9 Ex: 11.4 from Sullivan book .Then I will ask to solve all even numbers from 10-22. I will check?each and every one answers. Class will start with formulas proof then I will solve and explain then I solved and explain problem no. 23 Ex: 11.4 from Sullivan book .Then I will ask to solve all even numbers from 24-28. I will check each and every one answers.HandoutsEX:11.4N/AN/AHomeworkExamples:1,2Examples: 3,4,5Examples: 6,7,8,9,10EvaluationHope most of the students will do better.Ss will easily solve the problems.Ss easily could understand the problems.Week 141st class2nd class3rd classObjectivesWill learn how to find the inverse of a matrix.Solve a system of linear equations using an inverse matrix.Application of Matrices.Class Outline Class will start with the Quiz-2 problems and then some basic discussion on inverse matrix. Will show few examples. Then will ask to solve skill building problems from Ex: 11.4 (29, 36).Answer will be written on the board.Ex: 11.4 (39, 40) Ss will solve the problems and Match answers.I will solve 73 for the students and will ask the students to solve ?74,75 from Ex:11.4 ( Sullivan Book )(Also see Khan Academy videos /Resources for more clear concepts)HandoutsN/AN/AN/AHomeworkEx: 11.4 ( 30-38)Ex:11.4(41-58)Ex: 11.4 (76,77)EvaluationSome of the students might struggle with some problems.Some of the students might struggle.Ss will easily understand the problems.Week 151st class2nd class3rd classObjectives Will discuss on the Characterizing Data.Will solve application problems from the provided worksheet.Revision Class Class Outline I will discuss some problems based on Characterizing Data. I will discuss some problems based on Economics & some problems based on Life Science.Revision ClassHandoutsOne worksheet will handout.N/AN/AHomeworkWill solve problems from the provided worksheet.N/AN/AEvaluationStudents will do some problems based on the conceptions.Ss will easily solve the problems.Hope everything will go smoothly.ASSESSMENT METHODSThere will be a number of different ways that your learning will be assessed this year:Participation (25%)The participation mark is divided into three areas: Attendance – 5% If you have no or one unexcused absence/late then you will receive the full 10% attendance mark. However, for two late attendances will be counted as one day absence. Three days of absence will result in the lose 60% of your marks. For example a student with 3 unexcused absences will receive an attendance mark of 2.Lesson Contribution/Class Participation – 10% The lesson contribution mark can be achieved by speaking at the board (50%), answering questions and other contributions (50%). 3. Assignments/ Homework – 10%Quizzes (20%) There will be three or four quizzes in Spring – one for each Chapter that is covered in Sullivan Pre-calculus. Each quiz will be equal in weighting. Mid-Term Exam (25%) The Mid-Term exam will test all of the content covered by the end of February. Final Exam (30%) The Final Exam will test all of the content covered by the end of Spring semester (April).KEY DATES & DEADLINESMid-Term Exam: Between 24th to 28th February.Final Exam: Between 22nd to 25th April.PLAGIARISM & ACADEMIC INTEGRITYAll members of the AUW Community are bound by the Academic Honor Code published in the Academic Bulletin (). The integrity of students’ academic work is very important to AUW faculty. Universities are based upon the fundamental principle that the work presented truly belongs to the author, because the academic community revolves around ideas and creativity. Each person’s ideas are his or her contribution to the academic community. Therefore, taking another person’s ideas and representing them as one’s own is a serious form of dishonesty. Similarly, cheating (copying someone else’s work, asking for answers, sharing answers, etc.) and other forms of dishonesty (falsifying data, making up references, etc.) are also serious breaches of this honor code.Plagiarism is intentionally or unintentionally taking credit for another’s words or ideas. You may not plagiarize in your academic work, and you must adhere to the following:When you use someone else’s words (whether they are from a distinguished author or a classmate’s paper), place the words you have copied in quotation marks and provide the appropriate citation of author and source. A good guideline to use to avoid plagiarism is to make sure quotes of three or more sequential words from someone else are put into quotation marks. If you paraphrase (reword) another person’s ideas, then you must also cite the source. Paraphrasing must involve changing the words and sentence structure of the original source. Cite materials you copy or paraphrase from the Internet, even if the author is not identified. The various academic disciplines (humanities, social sciences, sciences) use slightly different formats for footnotes, endnotes, and bibliographies. Your professor for a particular class will tell you which format he or she wants you to use in that class.Copying, asking for answers, sharing answers, and any other form of cheating (misrepresenting your own work and knowledge) on exams or quizzes are all forms of academic dishonesty.Other Forms of Academic DishonestyMaking up references, quoting wrong sources, etc. Falsifying data. Misrepresenting your situation to be excused from academic work. Submitting the same paper in more than one class. Informing a student in a later class about questions on tests or quizzes. Misrepresenting your academic work or qualifications in any way. STRATEGIES TO PREVENT PLAGIARIM& VIOLATIONS OF ACADEMIC INTEGRITY Students will not plagiarise –please see the Student Handbook.CLASS BEHAVIOURYou are expected to be in class on time.You should participate in class discussions and contribute to the class goal of learning Pre-calculus.Read your class notes over within 24 hours (or at least once before the next class).Students will complete all home works and assignments given by the required deadlines. Mobile phones and similar electronic devices such as MP3 players, laptops, and so on should be switched off and put away at the beginning of class. You will treat others in this class with respect.Students are expected to check their email at least twice daily, preferably in the morning and evening. Students are advised that a majority of faculty answer email within a 24 hour period during the week and a 48 hour period during weekends. Please be aware that students who do not check email regularly may miss important class announcements. Useful links from Khan AcademyExponential and Logarithmic Functions1) Graphing basic logarithmic?functions of the video (minutes. seconds): 9.092) Graphs of logarithms &?exponentials of the video (minutes. seconds): 5.423) Surjective (onto) and injective (one-to-one)?functions of the video (minutes. seconds): 9.314) Intro to inverse?functions of the video (minutes. seconds): 9.05Trigonometric Functions1) Graph of?y=sin(x) of the video (minutes. seconds): 9.212) Limits of trigonometric?functions of the video (minutes. seconds): 6.05Analytic Trigonometry1) Sine & cosine identities:?symmetry of the video (minutes. seconds): 7.572) Using trig angle addition identities: manipulating?expressions of the video (minutes. seconds): 6.113) Proof of the Pythagorean trig?identity of the video (minutes. seconds): 6.114) Trig word problem: modeling annual?temperature of the video (minutes. seconds): 7.08● Systems of Equations1) Adding & subtracting?matrices of the video (minutes. seconds): 5.342) Matrix product examples of the video (minutes. seconds): 18.13Describing Data Sets1) Statistics intro: Mean, median, &?mode of the video (minutes. seconds): 8.322) Impact on median & mean: removing an?outlier of the video (minutes. seconds): 5.36 ................
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