Mathematics

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Antidiscrimination Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Literacy and Inquiry/Research Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36The Role of Information and Communication Technologyin Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Career Education in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37The Ontario Skills Passport and Essential Skills . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38Cooperative Education and Other Forms of Experiential Learning . . . . . . . . . . . . . . . . . . . 38Planning Program Pathways and Programs Leading to aSpecialist High-Skills Major . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Health and Safety in Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .39COURSES 41Grade 11Functions, University Preparation (MCR3U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Functions and Applications, University/College Preparation (MCF3M) . . . . . . . . . . . . . . 57Foundations for College Mathematics, College Preparation (MBF3C) . . . . . . . . . . . . . . . 67Mathematics for Work and Everyday Life, Workplace Preparation (MEL3E) . . . . . . . . . 77Grade 12Advanced Functions, University Preparation (MHF4U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Calculus and Vectors, University Preparation (MCV4U) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99Mathematics of Data Management, University Preparation (MDM4U) . . . . . . . . . . . . 111Mathematics for College Technology, College Preparation (MCT4C) . . . . . . . . . . . . . . . 123Foundations for College Mathematics, College Preparation (MAP4C) . . . . . . . . . . . . . . 135Mathematics for Work and Everyday Life, Workplace Preparation (MEL4E) . . . . . . . 147
INTRODUCTIONThis document replaces The Ontario Curriculum, Grade 11: Mathematics, 2006, and theGrade 12 courses in The Ontario Curriculum, Grades 11 and 12: Mathematics, 2000.Beginning in September 2007, all Grade 11 and Grade 12 mathematics courses will bebased on the expectations outlined in this document.SECONDARY SCHOOLS FOR THE TWENTY-FIRST CENTURYThe goal of Ontario secondary schools is to support high-quality learning while givingindividual students the opportunity to choose programs that suit their skills and interests.The updated Ontario curriculum, in combination with a broader range of learningoptions outside traditional classroom instruction, will enable students to better customizetheir high school education and improve their prospects for success in school and in life.THE IMPORTANCE OF MATHEMATICS IN THE CURRICULUMThis document provides a framework outlining what students are expected to know andbe able to do by the end of each of the courses in the Grade 11–12 mathematics curriculum.The required knowledge and skills include not only important mathematical facts andprocedures but also the mathematical concepts students need to understand and themathematical processes they must learn to apply.The principles underlying this curriculum are shared by educators dedicated to the successof all students in learning mathematics. Those principles can be stated as follows: 1Curriculum expectations must be coherent, focused, and well-articulated acrossthe grades.Learning mathematics involves the meaningful acquisition of concepts, skills, andprocesses and the active involvement of students in building new knowledge fromprior knowledge and experience.Learning tools such as manipulatives and technologies are important supports forteaching and learning mathematics.Effective teaching of mathematics requires that the teacher understand the mathematicalconcepts, procedures, and processes that students need to learn, and use avariety of instructional strategies to support meaningful learning.Assessment and evaluation must support learning, recognizing that students learnand demonstrate learning in various ways.1. Adapted from Principles and Standards for School Mathematics, developed by the National Council of Teachers ofMathematics (Reston, VA: NCTM, 2000).
Page 3: CONTENTSINTRODUCTION 3Secondary Sch
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Page 9 and 10: THE PROGRAM INMATHEMATICSOVERVIEW O
Page 11 and 12: Courses in Mathematics, Grades 11 a
Page 13 and 14: Half-Credit CoursesThe courses outl
Page 15 and 16: The Grade 11 university preparation
Page 17 and 18: Grade 11FOUNDATIONS FORCOLLEGEMATHE
Page 19 and 20: THE MATHEMATICALPROCESSESPresented
Page 21 and 22: REASONING AND PROVINGReasoning help
Page 23 and 24: Mental computation involves calcula
Page 25 and 26: ASSESSMENTAND EVALUATIONOF STUDENTA
Page 27 and 28: THE ACHIEVEMENT CHART FOR MATHEMATI
Page 29 and 30: course and reflects the correspondi
Page 31 and 32: Categories 50−59%(Level 1)60−69
Page 33 and 34: The approaches and strategies used
Page 35 and 36: If the student requires either acco
Page 37 and 38: use of a variety of instructional s
Page 39 and 40: THE ROLE OF INFORMATION AND COMMUNI
Page 41: they need to be aware of harassment
Page 45 and 46: Functions, Grade 11University Prepa
Page 47 and 48: A. CHARACTERISTICS OF FUNCTIONSOVER
Page 49 and 50: 2.5 solve problems involving the in
Page 51 and 52: 2.2 determine, through investigatio
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D. TRIGONOMETRIC FUNCTIONSOVERALL E
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Sample problem: The relationship be
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MATHEMATICAL PROCESS EXPECTATIONSTh
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Grade 11, University/College Prepar
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THE ONTARIO CURRICULUM, GRADES 11 A
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2. Comparing Financial Services 3.
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Grade 11, Grade University/College
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Mathematics for Work andEveryday Li
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A. EARNING AND PURCHASINGOVERALL EX
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B. SAVING, INVESTING, ANDBORROWINGO
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C. TRANSPORTATION AND TRAVELOVERALL
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Advanced Functions,Grade 12Universi
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A. EXPONENTIAL AND LOGARITHMICFUNCT
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B. TRIGONOMETRIC FUNCTIONSOVERALL E
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C. POLYNOMIAL AND RATIONALFUNCTIONS
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Sample problem: Investigate, using
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D. CHARACTERISTICS OF FUNCTIONSGrad
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2.3 determine, through investigatio
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Calculus and Vectors,Grade 12Univer
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A. RATE OF CHANGEOVERALL EXPECTATIO
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B. DERIVATIVES AND THEIRAPPLICATION
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joules the bird gets if it spends t
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2.3 solve problems involving the ad
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Mathematics of DataManagement, Grad
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A. COUNTING AND PROBABILITYOVERALL
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B. PROBABILITY DISTRIBUTIONSOVERALL
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2.7 make connections, through inves
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2.3 describe how the use of random
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as a measure of the fit of the data
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Mathematics for CollegeTechnology,
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A. EXPONENTIAL FUNCTIONSOVERALL EXP
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B. POLYNOMIAL FUNCTIONSOVERALL EXPE
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3.6 determine the value of a variab
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2.2 sketch the graphs of f(x) = sin
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D. APPLICATIONS OF GEOMETRYOVERALL
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Foundations for CollegeMathematics,
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A. MATHEMATICAL MODELSOVERALL EXPEC
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Years after 1955 Population of Gees
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payable monthly. Use a given amorti
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etween the two variables (i.e., by
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Grade 12, Workplace Preparationmont
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The Ministry of Education wishes to
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Mathematics

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