GRADE 11
GRADE 12
MCR3U: Functions and Relations, Grade 11, University Preparation
This course introduces some financial applications of mathematics, extends students' experiences with functions and trigonometry, and introduces second-degree relations. Many of the expectations of this course are based on direct extensions of concepts introduced in Grades 9 and 10. Having previously explored linear and quadratic relationships, students study polynomial and rational functions, and investigate the relationship between functions and their inverses. Students continue their study of trigonometry and discover new properties and contexts to which it can be applied. Graphing and algebraic skills are also consolidated and extended in this course. Identifying connections between the algebraic and graphic representations of functions continues to be an important skill.
Successful completion of MCR3U Functions and Relations will prepare students for any of the five Grade 12 University and College Preparation courses, and provides the necessary foundation for mathematically rich university programs. In particular, this course should be taken by students who are planning to study engineering, computer science, pure mathematics, or the physical sciences at the university level. This course shares a core set of expectations with the Grade 11 Functions course, MCF3M, which is comprised of three strands: Financial Applications of Sequences and Series, Trigonometric Functions, and Tools for Operating and Communicating with Functions. Completion of either of these two Grade 11 programs will prepare students for the Grade 12 courses Advanced Functions and Introductory Calculus (MCB4U), Mathematics of Data Management (MDM4U), Mathematics for College Technology (MCT4C), and College and Apprenticeship Mathematics (MAP4C). In addition to this common core, the Functions and Relations course contains some extension to the core plus a fourth strand, Investigations of Loci and Conics, which provides students with the knowledge and skills necessary for MGA4U, Geometry and Discrete Mathematics.
In addition to the Investigations of Loci and Conics strand and operations on complex numbers, the MCR3U course differs from the MCF3M course in timing and context. The pace of delivery in MCR3U will require students to consistently demonstrate the ability to:
In the Financial Applications of Sequences and Series strand, students will acquire the tools required to make sound personal financial decisions. Students will investigate and solve problems involving applications of sequences related to compound interest, annuities, and financial decision-making. In the Trigonometric Functions strand, students will investigate and apply properties of the primary trigonometric functions and develop a competency in the manipulation of these functions. This strand has been divided into two units: Trigonometry (covering radian measure and the sine and cosine laws) and Trigonometric Functions (with particular emphasis on the study of sinusoidal functions). The Tools for Operating and Communicating with Functions strand allows students to develop skills in operating with various algebraic expressions and to develop facility in using function notation and in communicating reasoning. This strand has also been divided into two units: Exploring Functions: Connecting Algebra and Geometry and Function Notation, Inverses, and Transformations. In the Investigations of Loci and Conics strand, students will extend their inquiry of loci into a study of conics. Students will become proficient in two- and three-dimensional modelling, which is essential to achieving success in MGA4U, Geometry and Discrete Mathematics.
MCF3M: Functions, Grade 11, University/College Preparation
This course extends student experiences with functions and trigonometry and introduces some financial applications of mathematics. Many of the expectations of this course are based on direct extensions of concepts introduced in Grades 9 and 10. Having previously explored linear and quadratic relationships, students study various polynomial and rational functions, and investigate the relationship of functions and their inverses. Students not only consolidate their previous study of trigonometry but also discover new properties and contexts to which they can be applied. Prior graphing and algebraic skills are consolidated and extended in this course. Identifying connections between the algebraic and graphical representations of functions continues to be an important skill.
Successful completion of MCF3M Functions will prepare students for the two Grade 12 University Preparation courses (Advanced Functions and Introductory Calculus, MCB4U and Mathematics of Data Management, MDM4U) and for the two Grade 12 College Preparation courses (Mathematics for College Technology, MCT4C and College and Apprenticeship Mathematics, MAP4C).
The majority of university-bound students and students planning to study technology or apprenticeship programs at college are expected to take the MCF3M Functions course. In the delivery of the program emphasis must be placed on helping the students to build solid foundations so that they will keep open doors to their own futures. Emphasis must also be placed on:
In the Financial Applications of Sequences and Series strand, students acquire the tools required to make sound personal financial decisions. Students investigate and solve problems involving applications of sequences related to compound interest, annuities, and financial decision-making. In the Trigonometric Functions strand, students investigate and apply properties of the primary trigonometric functions and develop a competency for the manipulation of these functions. This strand has been divided into two units: Trigonometry (including radian measure and the sine and cosine laws) and Applied Trigonometry (with emphasis on the study of sinusoidal functions). The Tools for Operating and Communicating with Functions strand, which has been divided into two units: Algebraic Manipulation of Functions and Function Notation, Inverses and Transformations. This allows students to develop skills in operating with various algebraic expressions and to develop facility in using function notation and in communicating reasoning.
An emphasis on technology allows students to investigate efficiently and effectively. Appropriate technology enables students to more easily visualize concepts and also allows for more time for consolidation, practice and the necessary remediation of skills.
MBF3C: Mathematics of Personal Finance, Grade 11, College Preparation
This course promotes the development of problem-solving and decision-making skills in a realistic financial context. The concepts of exponential growth, sequences, and series are studied. These concepts are explored through the concrete applications of interest, investments, living accommodation, transportation, and budgets. The financial framework of the course utilizes individual career paths and projected incomes established using each student's Annual Education Plan (AEP). Course activities incorporate the technological tools appropriate for financial analysis. Upon successful completion of the course, students will have the skills necessary to make sound financial decisions in both post-secondary endeavors and personal life situations.
MEL3E: Mathematics for Everyday Life, Grade 11, Workplace Preparation
This course prepares students for the world of work and for the Grade 12 Mathematics for Everyday Life course. This course is intended for students who have, at minimum, successfully completed a Grade 9 Mathematics course. It enables students to broaden their understanding of mathematics as it applies to real-life financial contexts. Students use current information and technology to solve problems and make comparisons leading to informed decisions. Assessment and evaluation are done using a wide variety of strategies with an emphasis on performance-based approaches.
This course introduces some financial applications of mathematics, extends students' experiences with functions and trigonometry, and introduces second-degree relations. Many of the expectations of this course are based on direct extensions of concepts introduced in Grades 9 and 10. Having previously explored linear and quadratic relationships, students study polynomial and rational functions, and investigate the relationship between functions and their inverses. Students continue their study of trigonometry and discover new properties and contexts to which it can be applied. Graphing and algebraic skills are also consolidated and extended in this course. Identifying connections between the algebraic and graphic representations of functions continues to be an important skill.
Successful completion of MCR3U Functions and Relations will prepare students for any of the five Grade 12 University and College Preparation courses, and provides the necessary foundation for mathematically rich university programs. In particular, this course should be taken by students who are planning to study engineering, computer science, pure mathematics, or the physical sciences at the university level. This course shares a core set of expectations with the Grade 11 Functions course, MCF3M, which is comprised of three strands: Financial Applications of Sequences and Series, Trigonometric Functions, and Tools for Operating and Communicating with Functions. Completion of either of these two Grade 11 programs will prepare students for the Grade 12 courses Advanced Functions and Introductory Calculus (MCB4U), Mathematics of Data Management (MDM4U), Mathematics for College Technology (MCT4C), and College and Apprenticeship Mathematics (MAP4C). In addition to this common core, the Functions and Relations course contains some extension to the core plus a fourth strand, Investigations of Loci and Conics, which provides students with the knowledge and skills necessary for MGA4U, Geometry and Discrete Mathematics.
In addition to the Investigations of Loci and Conics strand and operations on complex numbers, the MCR3U course differs from the MCF3M course in timing and context. The pace of delivery in MCR3U will require students to consistently demonstrate the ability to:
- investigate and construct mathematical concepts independently;
- conjecture and, through inquiry, test a hypothesis;
- generate multiple types of solutions to complex problems which may cross strands, require the use of appropriate technology, and require abstract thinking (e.g., the consideration of cases);
- expand the depth of their inquiry in order to solve higher-order problems;
- analyze and design proofs from multiple perspectives.
In the Financial Applications of Sequences and Series strand, students will acquire the tools required to make sound personal financial decisions. Students will investigate and solve problems involving applications of sequences related to compound interest, annuities, and financial decision-making. In the Trigonometric Functions strand, students will investigate and apply properties of the primary trigonometric functions and develop a competency in the manipulation of these functions. This strand has been divided into two units: Trigonometry (covering radian measure and the sine and cosine laws) and Trigonometric Functions (with particular emphasis on the study of sinusoidal functions). The Tools for Operating and Communicating with Functions strand allows students to develop skills in operating with various algebraic expressions and to develop facility in using function notation and in communicating reasoning. This strand has also been divided into two units: Exploring Functions: Connecting Algebra and Geometry and Function Notation, Inverses, and Transformations. In the Investigations of Loci and Conics strand, students will extend their inquiry of loci into a study of conics. Students will become proficient in two- and three-dimensional modelling, which is essential to achieving success in MGA4U, Geometry and Discrete Mathematics.
MCF3M: Functions, Grade 11, University/College Preparation
This course extends student experiences with functions and trigonometry and introduces some financial applications of mathematics. Many of the expectations of this course are based on direct extensions of concepts introduced in Grades 9 and 10. Having previously explored linear and quadratic relationships, students study various polynomial and rational functions, and investigate the relationship of functions and their inverses. Students not only consolidate their previous study of trigonometry but also discover new properties and contexts to which they can be applied. Prior graphing and algebraic skills are consolidated and extended in this course. Identifying connections between the algebraic and graphical representations of functions continues to be an important skill.
Successful completion of MCF3M Functions will prepare students for the two Grade 12 University Preparation courses (Advanced Functions and Introductory Calculus, MCB4U and Mathematics of Data Management, MDM4U) and for the two Grade 12 College Preparation courses (Mathematics for College Technology, MCT4C and College and Apprenticeship Mathematics, MAP4C).
The majority of university-bound students and students planning to study technology or apprenticeship programs at college are expected to take the MCF3M Functions course. In the delivery of the program emphasis must be placed on helping the students to build solid foundations so that they will keep open doors to their own futures. Emphasis must also be placed on:
- practice and consolidation of skills;
- applications that address a broad scope of scenarios;
- diagnosis, identification, and remediation of skill weaknesses;
- reflection on and summary of new learning;
- explorations and activities that help students become more independent problem solvers.
In the Financial Applications of Sequences and Series strand, students acquire the tools required to make sound personal financial decisions. Students investigate and solve problems involving applications of sequences related to compound interest, annuities, and financial decision-making. In the Trigonometric Functions strand, students investigate and apply properties of the primary trigonometric functions and develop a competency for the manipulation of these functions. This strand has been divided into two units: Trigonometry (including radian measure and the sine and cosine laws) and Applied Trigonometry (with emphasis on the study of sinusoidal functions). The Tools for Operating and Communicating with Functions strand, which has been divided into two units: Algebraic Manipulation of Functions and Function Notation, Inverses and Transformations. This allows students to develop skills in operating with various algebraic expressions and to develop facility in using function notation and in communicating reasoning.
An emphasis on technology allows students to investigate efficiently and effectively. Appropriate technology enables students to more easily visualize concepts and also allows for more time for consolidation, practice and the necessary remediation of skills.
MBF3C: Mathematics of Personal Finance, Grade 11, College Preparation
This course promotes the development of problem-solving and decision-making skills in a realistic financial context. The concepts of exponential growth, sequences, and series are studied. These concepts are explored through the concrete applications of interest, investments, living accommodation, transportation, and budgets. The financial framework of the course utilizes individual career paths and projected incomes established using each student's Annual Education Plan (AEP). Course activities incorporate the technological tools appropriate for financial analysis. Upon successful completion of the course, students will have the skills necessary to make sound financial decisions in both post-secondary endeavors and personal life situations.
MEL3E: Mathematics for Everyday Life, Grade 11, Workplace Preparation
This course prepares students for the world of work and for the Grade 12 Mathematics for Everyday Life course. This course is intended for students who have, at minimum, successfully completed a Grade 9 Mathematics course. It enables students to broaden their understanding of mathematics as it applies to real-life financial contexts. Students use current information and technology to solve problems and make comparisons leading to informed decisions. Assessment and evaluation are done using a wide variety of strategies with an emphasis on performance-based approaches.
MATH CONTESTS
EXAM PREP CENTRE
GRADE 11
NORTHVIEW HEIGHTS S.S. - MATHEMATICS
