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Grade 12 Essential Mathematics (40S)

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Grade 12 EssentialMathematics (40S)A Course for Independent Study

Gr ade 12 EssentialM a t h e m a t i c s (4 0 S )A Course for Independent Study2014M a ni t o b a E d u c a t i o n a n d A d v a n c e d L e a r nin g

Manitoba Education and Advanced Learning Cataloguing in Publication DataGrade 12 essential mathematics (40S) : a course for independentstudyISBN: 978-0-7711-5838-41. Mathematics—Study and teaching (Secondary).2. Mathematics—Study and teaching (Secondary)—Manitoba.3. Mathematics—Programmed instruction.4. Distance education—Manitoba.5. Correspondence schools and courses—Manitoba.I. Manitoba. Manitoba Education and Advanced Learning.510Copyright 2014, the Government of Manitoba, represented by the Ministerof Education and Advanced Learning.Manitoba Education and Advanced LearningSchool Programs DivisionWinnipeg, Manitoba, CanadaEvery effort has been made to acknowledge original sources and to complywith copyright law. If cases are identified where this has not been done, pleasenotify Manitoba Education and Advanced Learning. Errors or omissions willbe corrected in a future edition. Sincere thanks to the authors, artists, andpublishers who allowed their original material to be used.All images found in this document are copyright protected and should notbe extracted, accessed, or reproduced for any purpose other than for theirintended educational use in this document.Any websites referenced in this document are subject to change withoutnotice.Disponible en français.Available in alternate formats upon request.

t Will You Learn in This Course?3How Is This Course Organized?3What Resources Will You Need for This Course?5Who Can Help You with This Course?5How Will You Know How Well You Are Learning?6How Much Time Will You Need to Complete This Course?11When and How Will You Submit Completed Assignments?13What Are the Guide Graphics For?161Module 1: Home FinanceModule 1 Introduction3Module 1 Cover Assignment: Investments Using Spreadsheets5Lesson 1: Affordability and Initial Costs9Lesson 2: Mortgages43Lesson 3: Home Insurance and Property Tax75Lesson 4: Home Maintenance97Lesson 5: Buying Compared to Renting a Home107Module 1 Summary133Module 1 Learning Activity Answer KeysContentsiii

Module 2: Geometry and Trigonometry1Module 2 Introduction3Module 2 Cover Assignment: Introduction to Circle Geometry5Lesson 1: Review of Geometry11Lesson 2: Polygons and Quadrilaterals21Lesson 3: Parallelograms41Lesson 4: Triangles53Lesson 5: Trigonometry: The Sine Law67Lesson 6: Trigonometry: The Cosine Law85Module 2 Summary101Module 2 Learning Activity Answer KeysModule 3: Business Finance1Module 3 Introduction3Module 3 Cover Assignment: Marginal Income Tax Rates5Lesson 1: Introduction to the Business World11Lesson 2: Profitability of a Small Business21Lesson 3: Income Tax37Module 3 Summary55Module 3 Learning Activity Answer KeysModule 4: ProbabilityModule 4 Introduction3Module 4 Cover Assignment: Applying Probability to Games7Lesson 1: Expressing Probability11Lesson 2: Comparing Probability and Odds23Lesson 3: Expected Value41Lesson 4: Making Decisions Based on Probability57Module 4 Summary75Module 4 Learning Activity Answer Keysiv1Grade 12 Essential Mathematics

1Module 5: Vehicle FinanceModule 5 Introduction3Module 5 Cover Assignment: Vehicle Analysis5Lesson 1: Purchasing a New Vehicle13Lesson 2: Leasing a New Vehicle31Lesson 3: Purchasing a Used Vehicle47Lesson 4: Costs Associated with Owning a Vehicle59Lesson 5: Insuring a Vehicle77Module 5 Summary91Module 5 Learning Activity Answer Keys1Module 6: Career LifeModule 6 Introduction3Module 6 Cover Assignment: Personal Costs and Taxes5Lesson 1: Self-Assessment13Lesson 2: Career Descriptions25Lesson 3: Education/Training Requirements33Lesson 4: What Do You Expect Your Life to Be Like?47Lesson 5: Resumé61Module 6 Summary691Module 7: StatisticsModule 7 Introduction3Module 7 Cover Assignment: Problem Analysis5Lesson 1: Review of Mean, Median, and Mode9Lesson 2: Outliers in Data17Lesson 3: Weighted Mean33Lesson 4: Advantages and Disadvantages of Using DifferentMeasures of Central Tendency47Lesson 5: Percentiles65Lesson 7 Summary83Lesson 7 Learning Activity Answer KeysContentsv

Module 8: Precision Measurement1Module 8 Introduction3Module 8 Cover Assignment: Puzzles in Design5Lesson 1: Accuracy vs. Precision13Lesson 2: Uncertainty25Lesson 3: Calipers and Micrometers37Lesson 4: Tolerance55Lesson 8 Summary77Lesson 8 Learning Activity Answer KeysviAppendix A: Glossary1Bibliography1Grade 12 Essential Mathematics

AcknowledgementsManitoba Education and Advanced Learning gratefully acknowledges the contributions ofthe following individuals in the development of Grade 12 Essential Mathematics (40S): A Coursefor Independent Study.WritersReviewerManitoba Educationand Advanced LearningSchool Programs DivisionStaffMegan HudsonInstructional DesignAssistantDevelopment UnitInstruction, Curriculum and Assessment BranchAmanda KonradInstructional DesignAssistantDevelopment UnitInstruction, Curriculum and Assessment BranchIrv PetersIndependent ConsultantWinklerCarole BilykProject LeaderDevelopment UnitInstruction, Curriculum and Assessment BranchLouise BoissonneaultCoordinatorDocument Production Services UnitEducational Resources BranchIan DonnellyConsultant(since February 2012)Development UnitInstruction, Curriculum and Assessment BranchLynn HarrisonDesktop PublisherDocument Production Services UnitEducational Resources BranchMyrna KlassenConsultantDistance Learning UnitInstruction, Curriculum and Assessment BranchGilles LandryProject ManagerDevelopment UnitInstruction, Curriculum and Assessment BranchPhilippe LeclercqConseiller pédagogiqueConseiller pédagogique—Mathématiques 9 à 12Division du Bureau de l’éducation française DivisionSusan LeeCoordinatorDistance Learning UnitInstruction, Curriculum and Assessment BranchGrant MoorePublications EditorDocument Production Services UnitEducational Resources BranchJohn MurrayConsultant(until August 2011)Development UnitInstruction, Curriculum and Assessment BranchAcknowledgementsvii

Gr ade 12 EssentialM a t h e m a t i c s (4 0 S )Introduction

IntroductiontothecourseOverviewWelcome to Grade 12 Essential Mathematics! This course is a continuationof the concepts you have been studying in previous years, as well as anintroduction to new topics.As a student enrolled in a distance learning course, you have taken on a dualrole—that of a student and a teacher. As a student, you are responsible formastering the lessons and completing the learning activities and assignments.As a teacher, you are responsible to check your work carefully, noting areas inwhich you need to improve and motivating yourself to succeed.What Will You Learn in This Course?In this course, Grade 12 Essential Mathematics, builds on the knowledgeand skills students gained while studying Grade 11 Essential Mathematics.You will put to use many of the skills that you have already learned to solveproblems and do basic arithmetic operations. This course helps you developthe skills, ideas, and confidence that you will need to make decisions andsolve problems related to consumer applications of mathematics.How Is This Course Organized?The Grade 12 Essential Mathematics course consists of the following eightmodules:QQModule 1: Home FinanceQQModule 2: Geometry and TrigonometryQQModule 3: Business FinanceQQModule 4: ProbabilityQQModule 5: Vehicle FinanceQQModule 6: Career LifeQQModule 7: StatisticsQQModule 8: Precision MeasurementIntroduction3

Each module in this course consists of several lessons, which contain thefollowing components:Examples:QQQQQQQQQQQQLesson Focus: The Lesson Focus at the beginning of each lesson identifiesone or more specific learning outcomes (SLOs) that are addressed inthe lesson. The SLOs identify the knowledge and skills you should haveachieved by the end of the lesson.Introduction: Each lesson begins with an explanation of what you will belearning in that lesson.Lesson: The main body of the lesson is made up of the content that you needto learn. It contains text, explanations, images, diagrams, and completedexamples.Learning Activities: Many (most) lessons include one or more learningactivities that will help you learn about the lesson topics and prepare youfor the assignments, the midterm examination, and the final examination.Once you complete a learning activity, check your responses against thoseprovided in the Learning Activity Answer Key found at the end of eachapplicable module. You will not submit the completed learning activities toyour tutor/marker.Assignments: Assignments are found at the end of each lesson that hasan assignment. You will mail or electronically submit all your completedassignments to your tutor/marker for assessment at the end of each module.In total, all assignments are worth 75% of your final course mark.Summary: Each lesson ends with a brief review of what you just learned.This course also includes the following appendix:QQ4Appendix A: Glossary: The glossary at the end of the course providesdefinitions for an alphabetical list of the terms identified throughout thecourse. You can use the glossary to review terms used in the course.Grade 12 Essential Mathematics

What Resources Will You Need for This Course?You do not need a textbook for this course. All the content is provided directlywithin the course. You will, however, need access to a variety of resources.The required and optional resources for this course are identified below.Required ResourcesFor this course, you will need access to the following resources. If you do nothave access to one or more of these resources, contact your tutor/marker.QQQQA calculator: Use a graphing or scientific calculator as you work throughthis course. You will need the calculator for the examination(s).A metric ruler, an imperial ruler, and a protractor: Use the rulers andprotractor as you work through this course. You will not need the rulers orprotractor for the examination(s).Optional ResourcesQQQQAccess to a computer with spreadsheet and graphing capabilities will be anadvantage but not a requirement. Use of the Internet may be suggested as aresource in some places, but if you do not have access to an online computeryou can still complete the related learning activities and assignmentswithout it.Access to a photocopier would be helpful because it would let you makea copy of your assignments before you send them to your tutor/marker.That way, if you and your tutor/marker want to discuss an assignment, youwould each refer to your own copy.Who Can Help You with This Course?Taking an independent study course is different from taking a course in aclassroom. Instead of relying on the teacher to tell you to complete a learningactivity or an assignment, you must tell yourself to be responsible for yourlearning and for meeting deadlines. There are, however, two people who canhelp you be successful in this course: your tutor/marker and your learningpartner.Introduction5

Your Tutor/MarkerTutor/markers are experienced educators who tutor ISO students andmark assignments and examinations. When you are having difficulty withsomething in this course, contact your tutor/marker, who is there to help you.Your tutor/marker’s name and contact information were sent to you with thiscourse. You can also obtain this information in the Who Is My Tutor/Marker?section of the distance learning website at www.edu.gov.mb.ca/k12/dl/iso/assistance.html .Your Learning PartnerAnother person who can help you with your course is a learning partner.A learning partner is someone you choose who will help you learn. It maybe someone who knows something about mathematics, but it doesn’t haveto be. A learning partner could be someone else who is taking this course,a teacher, a parent or guardian, a sibling, a friend, or anybody else whocan help you. Most importantly, a learning partner should be someone withwhom you feel comfortable and who will support you as you work throughthis course.Your learning partner can help you keep on schedule with your coursework,read the course with you, check your work, look at and respond to yourlearning activities, or help you make sense of assignments. You may evenstudy for your examination(s) with your learning partner. If you and yourlearning partner are taking the same course, however, your assignmentwork should not be identical.How Will You Know How Well You Are Learning?You will know how well you are learning in this course by how well youcomplete the learning activities, assignments, and examinations.Learning ActivitiesEach learning activity has two parts—Part A has BrainPower questions andPart B has questions related to the content in the lesson6Grade 12 Essential Mathematics

Part A: BrainPowerThe BrainPower questions are provided as a warm-up activity for you beforetrying the other questions. Each question should be completed quickly andwithout using a calculator, and most should be completed without usingpencil and paper to write out multiple steps. Some of the questions will relatedirectly to content of the course. Some of the questions will review contentfrom previous courses—content that you need to be able to answer efficiently.Being able to do these questions in a few minutes will be helpful to you asyou continue with your studies in mathematics. If you are finding it is takingyou longer to do the questions, you can try one of the following:nnnwork with your learning partner to find more efficient strategies forcompleting the questionsask your tutor/marker for help with the questionssearch online for websites that help you practice the computations so youcan become more efficient at completing the questions.None of the assignment questions or exam questions will require you to dothe calculations quickly or without a calculator. However, it is for your benefitto complete the questions as they will help you in the course. Also, beingable to successfully complete the BrainPower exercises will help build yourconfidence in mathematics. BrainPower questions are like a warm-up youwould do before competing in a sporting event.Part B: Course Content QuestionsOne of the easiest and fastest ways to find out how much you have learned isto complete Part B of the learning activities. These have been designed to letyou assess yourself by comparing your answers with the answer keys at theend of each module. There is at least one learning activity in each lesson. Youwill need a notebook or loose-leaf pages to write your answers.The learning activities in this course will help you to review and practisewhat you have learned in the lessons. You will not submit the completedlearning activities to your tutor/marker. Instead, you will complete thelearning activities and compare your responses to those provided in theLearning Activity Answer Key found at the end of each module.Make sure you complete the learning activities. Doing so will not only helpyou to practise what you have learned, but will also prepare you to completeyour assignments and the examination(s) successfully. Many of the questionson the examination(s) will be similar to the questions in the learningactivities. Remember that you will not submit learning activities to yourtutor/marker.Introduction7

AssignmentsEach module in this course contains assignments, which you will completeand submit to your tutor/marker for assessment. The assignments are worth atotal of 75% of your final course mark.There are two types of assignments that you must submit to your tutor/marker. Each module has a cover assignment, which you can complete atany time during the module. Lesson assignments are located throughoutthe modules, and include questions similar to the questions in the learningactivities of previous lessons. The cover assignments and lesson assignmentshave space provided for you to write your answers on the question sheets.You need to show all your steps as you work out your solutions, and makesure your answers are clear (include units, where appropriate).The tutor/marker will mark your assignments and return them to you.Remember to keep all marked assignments until you have finished the courseso that you can use them to study for your examinations.Resource SheetWhen you write your Midterm and Final Examinations, you will be allowedto take an Exam Resource Sheet with you into the exam. This sheet will beone letter-sized page, 8½ ‘’ by 11”, with both sides in your handwriting ortypewritten. It is to be submitted with your exam. The Exam Resource Sheetis not worth any marks.Creating your own resource sheet is an excellent way to review. It alsoprovides you with a convenient reference and quick summary of theimportant facts of each module. Each student is asked to complete a resourcesheet for each module to help with studying and reviewing.The lesson summaries are written for you to use as a guide, as are the modulesummaries at the end of each module. Refer to these when you create yourown resource sheet. Then, go to Appendix B: Glossary (at the end of thecourse) to check the information on your resource sheet.After you complete each module’s resource sheet, you should summarize thesheets from all of the modules to prepare your Exam Resource Sheet. TheMidterm Examination is based only on the first four modules of the course,while the Final Examination is based on Modules 5 to 8.8Grade 12 Essential Mathematics

Midterm and Final ExamsThis course contains a midterm examination and a final examination.QQThe midterm examination is based on Modules 1 to 4, and is worth 12.5%of your final mark in this course. You will write the midterm examinationwhen you have completed Module 4.As a student, you can use your Midterm Exam Resource Sheet to bring anyformulas you have not memorized into the exam with you. You will berequired to bring the following supplies to the Midterm Examination: pensand pencils (2 or 3 of each), blank paper, a scientific or graphing calculator,and your Midterm Exam Resource Sheet.The following tables from the course are attached to the back of the midtermexamination:nAmortization TablenManitoba Homeowner’s Insurance Rates TablenInterest Rate Factor TablenLocal Improvement Costs for Property Tax CreditsFormulas are not included with the exam. Be sure to include these on theresource sheet.QQThe final examination is based on Modules 5 to 8, and is worth 12.5% ofyour final mark in this course. You will write the final examination whenyou have completed Module 8.You can use your Final Exam Resource Sheet to bring any formulas youhave not memorized into the exam with you. Formulas are not provided onthe exam. You will be required to bring the following supplies to the finalexamination: pens and pencils (2 or 3 of each), blank paper, a scientific orgraphing calculator, and your Final Exam Resource Sheet.The following tables from the course are attached to the back of the finalexamination:nDriver Safety Rating ChartnAmortization TablenMPI Passenger Vehicle Rate Groups TablenMPI Basic Rate TableFormulas are not included with the exam. Be sure to include these on theresource sheet.The two examinations are worth a total of 25% of your final course mark. Youwill write both examinations under supervision.Introduction9

To do well on each examination, you should review all the work youhave completed from the modules, including all learning activities andassignments.Practice Examinations and Answer KeysTo help you succeed in your examinations, you will have an opportunity tocomplete a Midterm Practice Examination and a Final Practice Examination.These examinations, along with the answer keys, are found in the StudentDownloads section of the distance learning website at www.edu.gov.mb.ca/k12/dl/downloads/index.html . If you do not have access to the Internet,contact the Independent Study Option office at 1-800-465-9915 to obtain acopy of the prac

Module 4: Probability 1 Module 4 Introduction 3 Module 4 Cover Assignment: Applying Probability to Games 7 Lesson 1: Expressing Probability 11 Lesson 2: Comparing Probability and Odds 23 Lesson 3: Expected Value 41 Lesson 4: Making Decisions Based on Probability 57 Module 4 Summary 75 Module 4 Learning Activity Answer Keys