# Grade 12 Essential Mathematics (40S) A Course for Independent Study

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1 Grade 12 Essential Mathematics (40S) A Course for Independent Study

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3 G r a d e 1 2 E s s e n t i a l M a t h e m a t i c s ( 4 0 S ) A Course for Independent Study 2014 Manitoba Education and Advanced Learning

5 C o n t e n t s Acknowledgements v Introduction 1 Overview 3 What Will You Learn in This Course? 3 How Is This Course Organized? 3 What Resources Will You Need for This Course? 5 Who Can Help You with This Course? 5 How Will You Know How Well You Are Learning? 6 How Much Time Will You Need to Complete This Course? 11 When and How Will You Submit Completed Assignments? 13 What Are the Guide Graphics For? 16 Module 1: Home Finance 1 Module 1 Introduction 3 Module 1 Cover Assignment: Investments Using Spreadsheets 5 Lesson 1: Affordability and Initial Costs 9 Lesson 2: Mortgages 43 Lesson 3: Home Insurance and Property Tax 75 Lesson 4: Home Maintenance 97 Lesson 5: Buying Compared to Renting a Home 107 Module 1 Summary 133 Module 1 Learning Activity Answer Keys Contents iii

6 Module 2: Geometry and Trigonometry 1 Module 2 Introduction 3 Module 2 Cover Assignment: Introduction to Circle Geometry 5 Lesson 1: Review of Geometry 11 Lesson 2: Polygons and Quadrilaterals 21 Lesson 3: Parallelograms 41 Lesson 4: Triangles 53 Lesson 5: Trigonometry: The Sine Law 67 Lesson 6: Trigonometry: The Cosine Law 85 Module 2 Summary 101 Module 2 Learning Activity Answer Keys Module 3: Business Finance 1 Module 3 Introduction 3 Module 3 Cover Assignment: Marginal Income Tax Rates 5 Lesson 1: Introduction to the Business World 11 Lesson 2: Profitability of a Small Business 21 Lesson 3: Income Tax 37 Module 3 Summary 55 Module 3 Learning Activity Answer Keys 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 iv Grade 12 Essential Mathematics

7 Module 5: Vehicle Finance 1 Module 5 Introduction 3 Module 5 Cover Assignment: Vehicle Analysis 5 Lesson 1: Purchasing a New Vehicle 13 Lesson 2: Leasing a New Vehicle 31 Lesson 3: Purchasing a Used Vehicle 47 Lesson 4: Costs Associated with Owning a Vehicle 59 Lesson 5: Insuring a Vehicle 77 Module 5 Summary 91 Module 5 Learning Activity Answer Keys Module 6: Career Life 1 Module 6 Introduction 3 Module 6 Cover Assignment: Personal Costs and Taxes 5 Lesson 1: Self-Assessment 13 Lesson 2: Career Descriptions 25 Lesson 3: Education/Training Requirements 33 Lesson 4: What Do You Expect Your Life to Be Like? 47 Lesson 5: Resumé 61 Module 6 Summary 69 Module 7: Statistics 1 Module 7 Introduction 3 Module 7 Cover Assignment: Problem Analysis 5 Lesson 1: Review of Mean, Median, and Mode 9 Lesson 2: Outliers in Data 17 Lesson 3: Weighted Mean 33 Lesson 4: Advantages and Disadvantages of Using Different Measures of Central Tendency 47 Lesson 5: Percentiles 65 Lesson 7 Summary 83 Lesson 7 Learning Activity Answer Keys Contents v

8 Module 8: Precision Measurement 1 Module 8 Introduction 3 Module 8 Cover Assignment: Puzzles in Design 5 Lesson 1: Accuracy vs. Precision 13 Lesson 2: Uncertainty 25 Lesson 3: Calipers and Micrometers 37 Lesson 4: Tolerance 55 Lesson 8 Summary 77 Lesson 8 Learning Activity Answer Keys Appendix A: Glossary 1 Bibliography 1 vi Grade 12 Essential Mathematics

9 A c k n o w l e d g e m e n t s Manitoba Education and Advanced Learning gratefully acknowledges the contributions of the following individuals in the development of Grade 12 Essential Mathematics (40S): A Course for Independent Study. Writers Megan Hudson Instructional Design Assistant Development Unit Instruction, Curriculum and Assessment Branch Amanda Konrad Instructional Design Assistant Development Unit Instruction, Curriculum and Assessment Branch Reviewer Irv Peters Independent Consultant Winkler Manitoba Education and Advanced Learning School Programs Division Staff Carole Bilyk Project Leader Louise Boissonneault Coordinator Ian Donnelly Consultant (since February 2012) Lynn Harrison Desktop Publisher Myrna Klassen Consultant Gilles Landry Project Manager Philippe Leclercq Conseiller pédagogique Susan Lee Coordinator Grant Moore Publications Editor John Murray Consultant (until August 2011) Development Unit Instruction, Curriculum and Assessment Branch Document Production Services Unit Educational Resources Branch Development Unit Instruction, Curriculum and Assessment Branch Document Production Services Unit Educational Resources Branch Distance Learning Unit Instruction, Curriculum and Assessment Branch Development Unit Instruction, Curriculum and Assessment Branch Conseiller pédagogique Mathématiques 9 à 12 Division du Bureau de l éducation française Division Distance Learning Unit Instruction, Curriculum and Assessment Branch Document Production Services Unit Educational Resources Branch Development Unit Instruction, Curriculum and Assessment Branch Acknowledgements vii

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11 G r a d e 1 2 E s s e n t i a l M a t h e m a t i c s ( 4 0 S ) Introduction

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13 I n t r o d u c t i o n t o t h e c o u r s e Overview Welcome to Grade 12 Essential Mathematics! This course is a continuation of the concepts you have been studying in previous years, as well as an introduction to new topics. As a student enrolled in a distance learning course, you have taken on a dual role that of a student and a teacher. As a student, you are responsible for mastering the lessons and completing the learning activities and assignments. As a teacher, you are responsible to check your work carefully, noting areas in which 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 knowledge and skills students gained while studying Grade 11 Essential Mathematics. You will put to use many of the skills that you have already learned to solve problems and do basic arithmetic operations. This course helps you develop the skills, ideas, and confidence that you will need to make decisions and solve problems related to consumer applications of mathematics. How Is This Course Organized? The Grade 12 Essential Mathematics course consists of the following eight modules: Module 1: Home Finance Module 2: Geometry and Trigonometry Module 3: Business Finance Module 4: Probability Module 5: Vehicle Finance Module 6: Career Life Module 7: Statistics Module 8: Precision Measurement Introduction 3

19 Midterm and Final Exams This course contains a midterm examination and a final examination. The 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 examination when you have completed Module 4. As a student, you can use your Midterm Exam Resource Sheet to bring any formulas you have not memorized into the exam with you. You will be required to bring the following supplies to the Midterm Examination: pens and 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 midterm examination: n Amortization Table n Manitoba Homeowner s Insurance Rates Table n Interest Rate Factor Table n Local Improvement Costs for Property Tax Credits Formulas are not included with the exam. Be sure to include these on the resource sheet. The final examination is based on Modules 5 to 8, and is worth 12.5% of your final mark in this course. You will write the final examination when you have completed Module 8. You can use your Final Exam Resource Sheet to bring any formulas you have not memorized into the exam with you. Formulas are not provided on the exam. You will be required to bring the following supplies to the final examination: pens and pencils (2 or 3 of each), blank paper, a scientific or graphing calculator, and your Final Exam Resource Sheet. The following tables from the course are attached to the back of the final examination: n Driver Safety Rating Chart n Amortization Table n MPI Passenger Vehicle Rate Groups Table n MPI Basic Rate Table Formulas are not included with the exam. Be sure to include these on the resource sheet. The two examinations are worth a total of 25% of your final course mark. You will write both examinations under supervision. Introduction 9

21 How Much Time Will You Need to Complete This Course? Learning through independent study has several advantages over learning in the classroom. You are in charge of how you learn and you can choose how quickly you will complete the course. You can read as many lessons as you wish in a single session. You do not have to wait for your teacher or classmates. From the date of your registration, you have a maximum of 12 months to complete this course, but the pace at which you proceed is up to you. Read the following suggestions on how to pace yourself. Chart A: Semester 1 If you want to start the course in September and complete it in January, you can follow the timeline suggested below. Module Module 1 Module 2 Module 3 Module 4 and Midterm Exam Module 5 Module 6 Module 7 Module 8 and Final Exam Completion Date Middle of September End of September Middle of October Early November Middle of November End of November Middle of December Middle of January Introduction 11

22 Chart B: Semester 2 If you want to start the course in January and complete it in June, you can follow the timeline suggested below. Module Module 1 Module 2 Module 3 Module 4 and Midterm Exam Module 5 Module 6 Module 7 Module 8 and Final Exam Completion Date Middle of February End of February Early March Middle of March Early April Middle of April Early May End of May Chart C: Full School Year (Not Semestered) If you want to start the course in September and complete it in June, you can follow the timeline suggested below. Module Completion Date Module 1 Module 2 Module 3 Module 4 and Midterm Exam Module 5 Module 6 Module 7 Module 8 and Final Exam End of September End of October End of November Middle of January Middle of February Middle of March Middle of April End of May Timelines Do not wait until the last minute to complete your work, since your tutor/ marker may not be available to mark it immediately. It may take a few weeks for your tutor/marker to assess your work and return it to you or your school. If you need this course to graduate this school year, remember to schedule and complete your final examination by May Grade 12 Essential Mathematics

23 When and How Will You Submit Completed Assignments? When to Submit Assignments While working on this course, you will submit completed assignments to your tutor/marker eight times. Each time you submit assignments, you must include the applicable Cover Sheet, which you will find at the end of this Introduction. The following chart shows you exactly what assignments you will be submitting at the end of each module. Submission of Assignments Submission Assignments You Will Submit 1 Module 1: Home Finance Module 1 Cover Sheet Module 1 Cover Assignment: Investments Using Spreadsheets Assignment 1.1: Affordability, Initial Costs, and Mortgages Assignment 1.2: Insurance and Property Tax Assignment 1.3: Making Decisions 2 Module 2: Geometry and Trigonometry Module 2 Cover Sheet Module 2 Cover Assignment: Circle Geometry Assignment 2.1: Polygons Assignment 2.2: The Sine Law Assignment 2.3: Trigonometry 3 Module 3: Business Finance Module 3 Cover Sheet Module 3 Cover Assignment: Marginal Income Tax Rates Assignment 3.1: Profitability of a Small Business Assignment 3.2: Income Tax 4 Module 4: Probability Module 4 Cover Sheet Module 4 Cover Assignment: Applying Probability to Games Assignment 4.1: Expressing Probability and Odds Assignment 4.2: Applications of Probability 5 Module 5: Vehicle Finance Module 5 Cover Sheet Module 5 Cover Assignment: Vehicle Analysis Assignment 5.1: Financing a New Vehicle Assignment 5.2: Used Vehicles and Using Vehicles Assignment 5.3: Insurance Costs continued Introduction 13

24 Submission of Assignments (continued) Submission Assignments You Will Submit 6 Module 6: Career Life Module 6 Cover Sheet Module 6 Cover Assignment: Personal Costs and Taxes Assignment 6.1: Self-Assessment Report Assignment 6.2: Career Descriptions Assignment 6.3: Education/Training Requirements Assignment 6.4: Expected Lifestyle Report Assignment 6.5: Resumé and Reflection 7 Module 7: Statistics Module 7 Cover Sheet Module 7 Cover Assignment: Problem Analysis Assignment 7.1: Mean, Median, Mode, and Outliers Assignment 7.2: Five Measures of Central Tendency Assignment 7.3: Analyzing Percentiles 8 Module 8: Precision Measurement Module 8 Cover Sheet Module 8 Cover Assignment: Puzzles in Design Assignment 8.1: Accuracy, Precision, and Uncertainty Assignment 8.2: Measurements and Tolerances How to Submit Assignments In this course, you have the choice of submitting your assignments either by mail or electronically. Mail: Each time you mail something, you must include the print version of the applicable Cover Sheet (found at the end of this Introduction). Electronic submission: Each time you submit something electronically, you must include the electronic version of the applicable Cover Sheet (found in the Student Downloads section of the distance learning website at <www.edu.gov.mb.ca/k12/dl/downloads/index.html>) or you can scan the Cover Sheet located at the end of this Introduction. Complete the information at the top of each Cover Sheet before submitting it along with your assignments. 14 Grade 12 Essential Mathematics

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