Mathematics

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students’ proficiency in applying them must be developed in all strands of a mathematicscourse. Teachers should ensure that students develop their ability to apply these processesin appropriate ways as they work towards meeting the expectations outlined in thestrands.When developing detailed courses of study from this document, teachers are expected toweave together related expectations from different strands, as well as the relevant processexpectations, in order to create an overall program that integrates and balances conceptdevelopment, skill acquisition, the use of processes, and applications.Many of the specific expectations are accompanied by examples and/or sample problems.These examples and sample problems are meant to illustrate the kind of skill, the specificarea of learning, the depth of learning, and/or the level of complexity that the expectationentails. Some examples and sample problems may also be used to emphasize the importanceof diversity or multiple perspectives. The examples and sample problems areintended only as suggestions for teachers. Teachers may incorporate the examples andsample problems into their lessons, or they may choose other topics, approaches, orproblems that are relevant to the expectation.COURSES AND STRANDSThe courses in the Grade 11–12 mathematics curriculum are briefly described below, bycourse type. The strands in each course are listed in the graphic provided in each section,and their focus is discussed in the following text.University Preparation CoursesGrade 12ADVANCED FUNCTIONS(MHF4U)Grade 12CALCULUS AND VECTORS(MCV4U)THE ONTARIO CURRICULUM, GRADES 11 AND 12 | <strong>Mathematics</strong>Grade 11FUNCTIONS (MCR3U)A. Characteristics ofFunctionsB. Exponential FunctionsC. Discrete FunctionsD. Trigonometric FunctionsA. Exponential andLogarithmic FunctionsB. Trigonometric FunctionsC. Polynomial and RationalFunctionsD. Characteristics ofFunctionsGrade 12MATHEMATICS OF DATAMANAGEMENT (MDM4U)A. Counting and ProbabilityB. Probability DistributionsC. Organization of Data forAnalysisD. Statistical AnalysisE. Culminating DataManagementInvestigationA. Rate of ChangeB. Derivatives and TheirApplicationsC. Geometry and Algebra ofVectors12
The Grade 11 university preparation course, Functions, builds on the concepts and skillsdeveloped in the Grade 9 and 10 academic mathematics courses. The course is designedto prepare students for Grade 12 mathematics courses that lead to one of many universityprograms, including science, engineering, social sciences, liberal arts, and education.The concept of functions is introduced in the Characteristics of Functions strand of thiscourse and extended through the investigation of two new types of relationships in theExponential Functions and Trigonometric Functions strands. The Discrete Functionsstrand allows students, through the study of different representations of sequences andseries, to revisit patterning and algebra concepts introduced in elementary school andmake connections to financial applications involving compound interest and ordinarysimple annuities.The Grade 12 university preparation course Advanced Functions satisfies the mathematicalprerequisite for some universities in areas that include business, social science,and health science programs. The strands in this course help students deepen theirunderstanding of functions by revisiting the exponential and trigonometric functionsintroduced in Grade 11 to address related concepts such as radian measure and logarithmicfunctions and by extending prior knowledge of quadratic functions to explore polynomialand rational functions. The Characteristics of Functions strand addresses someof the general features of functions through the examination of rates of change andmethods of combining functions.The Grade 12 university preparation course Calculus and Vectors is designed to preparestudents for university programs, such as science, engineering, and economics, thatinclude a calculus or linear algebra course in the first year. Calculus is introduced in theRate of Change strand by extending the numeric and graphical representation of rates ofchange introduced in the Advanced Functions course to include more abstract algebraicrepresentations. The Derivatives and Their Applications strand provides students withthe opportunity to develop the algebraic and problem-solving skills needed to solveproblems associated with rates of change. Prior knowledge of geometry and trigonometryis used in the Geometry and Algebra of Vectors strand to develop vector concepts thatcan be used to solve interesting problems, including those arising from real-worldapplications.The Grade 12 university preparation course <strong>Mathematics</strong> of Data Management isdesigned to satisfy the prerequisites for a number of university programs that mayinclude statistics courses, such as those found in the social sciences and the humanities.The expectations in the strands of this course require students to apply mathematicalprocess skills developed in prerequisite courses, such as problem solving, reasoning, andcommunication, to the study of probability and statistics. The Counting and Probabilitystrand extends the basic probability concepts learned in the elementary school programand introduces counting techniques such as the use of permutations and combinations;these techniques are applied to both counting and probability problems. The ProbabilityDistributions strand introduces the concept of probability distributions; these include thenormal distribution, which is important in the study of statistics. In the Organization ofData for Analysis strand, students examine, use, and develop methods for organizinglarge amounts of data, while in the Statistical Analysis strand, students investigate anddevelop an understanding of powerful concepts used to analyse and interpret largeamounts of data. These concepts are developed with the use of technological tools suchTHE PROGRAM IN MATHEMATICS13
Page 3 and 4: CONTENTSINTRODUCTION 3Secondary Sch
Page 5 and 6: INTRODUCTIONThis document replaces
Page 7 and 8: and art. It is important that these
Page 9 and 10: THE PROGRAM INMATHEMATICSOVERVIEW O
Page 11 and 12: Courses in Mathematics, Grades 11 a
Page 13: Half-Credit CoursesThe courses outl
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
Page 53 and 54: 2. Investigating Arithmetic andGeom
Page 55 and 56: D. TRIGONOMETRIC FUNCTIONSOVERALL E
Page 57: Sample problem: The relationship be
Page 60 and 61: MATHEMATICAL PROCESS EXPECTATIONSTh
Page 62 and 63: Grade 11, University/College Prepar
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Grade 11, University/College Prepar
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MATHEMATICAL PROCESS EXPECTATIONSTh
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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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MATHEMATICAL PROCESS EXPECTATIONSTh
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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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