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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

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