# Mathematics

The mathetmatics courses are based on principles that are consistent with those that underpin the elementary program, facilitating the transition from elementary school. These courses reflect the belief that students learn mathematics effectively when they are given opportunities to investigate new ideas and concepts, make connections between new learning and prior knowledge, and develop an understanding of the abstract mathematics involved. Skill acquisition is an important part of the learning; skills are embedded in the contexts offered by various topics in the mathematics program and should be introduced as they are needed. The mathematics courses in this curriculum recognize the importance of not only focusing on content, but also of developing the thinking processes that underlie mathematics. By studying mathematics, students learn how to reason logically, think critically, and solve problems – key skills for success in today’s workplaces.

**MATHEMATICS**

**MPM1D Principles of Mathematics, Grade 9**

Academic This course enables students to develop understanding of mathematical concepts related to algebra, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will investigate relationships which they will then generalize as equations of lines and will determine the connections between different representations of a relationship. They will also explore relationships that emerge from the measurement of three-dimensional objects and twodimensional shapes. Students will reason mathematically and communicate their thinking as they solve multi-step problems. Successful completion of this course prepares students for Principles of Mathematics, Grade 10, Academic (MPM2D) or Foundations of Mathematics, Grade 10, Applied (MFM2P). Learning through abstract reasoning is an important aspect of this course. **Prerequisite: None**

**MFM1P Foundations of Mathematics, Grade 9**

Applied This course enables students to develop understanding of mathematical concepts related to introductory algebra, proportional reasoning, and measurement and geometry through investigation, the effective use of technology, and handson activities. Students will investigate real-life examples to develop various representations of linear relationships, and will determine the connections between the representations. They will also explore certain relationships that emerge from the measurement of three-dimensional objects and two-dimensional shapes. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. Successful completion of this course prepares students for Foundations of Mathematics, Grade 10, Applied (MFM2P). (Note: Students who wish to take Principles of Mathematics, Grade 10, Academic (MPM2D) after completing this course will need to take a transfer course.) Learning through hands-on activities and the use of concrete examples is an important aspect of this course. **Prerequisite: None**

**MAT1L Mathematics, Grade 9**

Locally Developed Compulsory Credit Course This course emphasizes further development of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, in the Grade 10 LDCC course. The course is organized by three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on developing and consolidating key foundational mathematical concepts and skills by solving authentic, everyday problems. Students have opportunities to further develop their mathematical literacy and problem-solving skills and to continue developing their skills in reading, writing, and oral language through relevant and practical math activities. **Prerequisite: None**

**MPM2D Principles of Mathematics**

Grade 10, Academic This course enables students to broaden their understanding of relationships and extend their problem-solving and algebraic skills through investigation the effective use of technology, and abstract reasoning. Students will explore quadratic relations and their applications; solve and apply linear systems; verify properties of geometric figures using analytic geometry; and investigate the trigonometry of right and acute triangles. Students will reason mathematically and communicate their thinking as they solve multi-step problems.** Prerequisite: Mathematics, Grade 9, Academic, or Mathematics Grade 9, Applied AND Mathematics Transfer course, Grade 9, Applied to Academic**

**MFM2P Foundations of Mathematics **

Grade 10, Applied This course enables students to consolidate their understanding of linear relations and extend their problem-solving and algebraic skills through investigation, the effective use of technology, and handson activities. Students will develop and graph equations and analytic geometry; solve and apply linear systems, using real-life examples; and explore and interpret graphs of quadratic relations. Students will investigate similar triangles, the trigonometry of right triangles, and the measurement of three-dimensional fi gures. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. **Prerequisite: Principles of Mathematics, Grade 9, Academic or Foundations of Mathematics, Grade 9, Applied**

**MAT2L Mathematics, Grade 10**

Locally Developed Compulsory Credit Course This course emphasizes the extension of mathematical knowledge and skills to prepare students for success in their everyday lives, in the workplace, and in the Grade 11 Mathematics Workplace Preparation course. The course is organized by three strands related to money sense, measurement, and proportional reasoning. In all strands, the focus is on strengthening and extending key foundational mathematical concepts and skills by solving authentic, everyday problems. Students have opportunities to extend their mathematical literacy and problem-solving skills and to continue developing their skills in reading, writing, and oral language through relevant and practical math activities. **Prerequisite: A Grade 9 Mathematics credit**

**MCR3U Functions, Grade 11**

University Preparation This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems. **Prerequisite: Principles of Mathematics, Grade 10, Academic**

**MCF3M Functions and Applications, Grade 11**

University/College Preparation This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modelling real-world situations. Studentswill represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems. **Prerequisite: Principles of Mathematics, Grade 10, Academic, or Foundations of Mathematics, Grade 10, Applied**

**MBF3C Foundations for College Mathematics, Grade 11, College Preparation **

This course enables students to broaden their understanding of mathematics as a problem-solving tool in the real world. Students will extend their understanding of quadratic relations; investigate situations involving exponential growth; solve problems involving compound interest; solve fi nancial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and will solve problems in geometry and trigonometry. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. **Prerequisite: Foundations of Mathematics, Grade 10, Applied**

**MEL3E Mathematics for Work and Everyday Life, Grade 11, Workplace Preparation**

This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will solve problems associated with earning money, paying taxes, and making purchases; apply calculations of simple and compound interest in saving, investing, and borrowing; and calculate the costs of transportation and travel in a variety of situations. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. **Prerequisite: Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a Ministry-approved locally developed Grade 10 Mathematics course.**

**MCV4U Calculus and Vectors, Grade 12, University Preparation **

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refi ne their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fi elds such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course. **Prerequisite: Advanced Functions, Grade 12, University Preparation. Note: The new Advanced Functions course must be taken prior to or concurrently with MCV4U. **

**MHF4U Advanced Functions, Grade 12**

University Preparation This course extends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended both for students taking the Calculus and Vectors course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs. **Prerequisite: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation**

**MDM4U Mathematics of Data Management, Grade 12, University Preparation **

This course broadens students’ understanding of mathematics as itrelates to managing data. Students will apply methods for organizing and analysing large amounts of information; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Students planning to enter university programs in business, the social sciences, and the humanities will fi nd this course of particular interest. **Prerequisite: Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/ College Preparation**

**MCT4C Mathematics for College Technology, Grade 12, College Preparation **

This course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for a variety of college technology programs. **Prerequisite :Functions and Applications, Grade 11, University/ College Preparation, or Functions, Grade 11, University Preparation**

**MAP4C Foundations for College Mathematics, Grade 12, College Preparation **

This course enables students to broaden their understanding of real-world applications of mathematics. Students will analyse data using statistical methods; solve problems involving applications of geometry and trigonometry; solve financial problems connected with annuities, budgets, and renting or owning accommodation; simplify expressions; and solve equations. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This course prepares students for college programs in areas such as business, health sciences, and human services, and for certain skilled trades. **Prerequisite: Foundations for College Mathematics, Grade 11, College Preparation, or Functions and Applications, Grade 11, University/ College Preparation**

**MEL4E Mathematics for Work and Everyday Life, Grade 12**

Workplace Preparation This course enables students to broaden their understanding of mathematics as it is applied in the workplace and daily life. Students will investigate questions involving the use of statistics; apply the concept of probability to solve problems involving familiar situations; investigate accommodation costs, create household budgets, and prepare a personal income tax return; use proportional reasoning; estimate and measure; and apply geometric concepts to create designs. Students will consolidate their mathematical skills as they solve problems and communicate their thinking. **Prerequisite: Mathematics for Work and Everyday Life, Grade 11, Workplace Preparation**

**MPM1H Mathematics Transfer Course, Grade 9**

Applied to Academic This transfer course will provide students who have successfully completed Foundations of Mathematics, Grade 9, Applied with an opportunity to achieve the expectations not covered in that course but included in Principles of Mathematics, Grade 9, Academic. On successful completion of this transfer course, students may proceed to Principles of Mathematics, Grade 10, Academic (MPM2D). This transfer course focuses on developing number sense and algebra, linear relations, analytic geometry, and measurement and geometry through investigation, the effective use of technology, and abstract reasoning. Students will reason mathematically and communicate their thinking as they solve multi-step problems. **Prerequisite: Foundations of Mathematics, Grade 9, Applied (MFM1P) Credit Value: 0.5**