## Mathematics

- The Grade 9 Mathematics course (MTH1W) was revised in 2021. This course supersedes the two Grade 9 courses outlined in
*The Ontario Curriculum, Grades 9 and 10: Mathematics, 2005*, as well as*The Ontario Curriculum: Mathematics – Mathematics Transfer Course, Grade 9, Applied to Academic, 2006*. Effective September 2021, all mathematics programs for Grade 9 will be based on the expectations outlined in the course curriculum. - The 2005 Mathematics curriculum for Grade 10 and the 2007 Mathematics curriculum for Grades 11–12 remain in effect. All secondary mathematics courses for Grades 10–12 will continue to be based on those documents.
- All references to Grade 9 that appear in
*The Ontario Curriculum, Grades 9 and 10: Mathematics, 2005*and*The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007*have been superseded by*The Ontario Curriculum, Grade 9: Mathematics, 2021*. - Addenda have been issued to the Grade 10 MPM2D and MFM2P courses, to be implemented for the 2022–23 school year.

### Courses

Grade |
Course Name |
Course Type |
Course Code |
Credit Value |
Prerequisite |

9 | Mathematics | De-streamed | MTH1W | 1.0 | None |

10 | Principles of Mathematics | Academic | MPM2D | 1.0 | Grade 9 Mathematics, De-streamed (2021), or Grade 9 Principles of Mathematics, Academic (2005) |

10 | Foundations of Mathematics | Applied | MFM2P | 1.0 | Grade 9 Mathematics, De-streamed (2021), or Grade 9 Foundations of Mathematics, Applied (2005) |

11 | Functions | University | MCR3U | 1.0 | Grade 10 Principles of Mathematics, Academic |

11 | Functions and Applications | University/ College | MCF3M | 1.0 | Grade 10 Principles of Mathematics, Academic, or Grade 10 Foundations of Mathematics, Applied |

11 | Foundations for College Mathematics | College | MBF3C | 1.0 | Grade 10 Foundations of Mathematics, Applied |

11 | Mathematics for Work and Everyday Life | Workplace | MEL3E | 1.0 | Grade 9 Mathematics, De-streamed (2021), or Grade 9 Principles of Mathematics, Academic (2005), or Grade 9 Foundations of Mathematics, Applied (2005), or a Grade 10 Mathematics LDCC (locally developed compulsory credit) course |

12 | Advanced Functions | University | MHF4U | 1.0 | Grade 11 Functions, University, or Grade 12 Mathematics for College Technology, College |

12 | Calculus and Vectors | University | MCV4U | 1.0 | Grade 12 Advanced Functions, University, must be taken prior to or concurrently with Calculus and Vectors |

12 | Mathematics of Data Management | University | MDM4U | 1.0 | Grade 11 Functions, University, or Grade 11 Functions and Applications, University/College |

12 | Mathematics for College Technology | College | MCT4C | 1.0 | Grade 11 Functions and Applications, University/College, or Grade 11 Functions, University |

12 | Foundations for College Mathematics | College | MAP4C | 1.0 | Grade 11 Foundations for College Mathematics, College, or Grade 11 Functions and Applications, University/College |

12 | Mathematics for Work and Everyday Life | Workplace | MEL4E | 1.0 | Grade 11 Mathematics for Work and Everyday Life, Workplace |

### Prerequisite Chart

This chart maps out all the courses in the discipline and shows the links between courses and the possible prerequisites for them. It does not attempt to depict all possible movements from course to course.

* Note: *For students who completed any of the Grade 9 mathematics courses prior to September 2021, refer to the prerequisite chart on page 10 of

*The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007*.

### Course Descriptions

**Mathematics, Grade 9, De-streamed (MTH1W)**This course enables students to consolidate, and continue to develop, an understanding of mathematical concepts related to number sense and operations, algebra, measurement, geometry, data, probability, and financial literacy. Students will use mathematical processes, mathematical modelling, and coding to make sense of the mathematics they are learning and to apply their understanding to culturally responsive and relevant real-world situations. Students will continue to enhance their mathematical reasoning skills, including proportional reasoning, spatial reasoning, and algebraic reasoning, as they solve problems and communicate their thinking.

*Prerequisite*: None

**Principles of Mathematics, Grade 10, Academic (MPM2D)**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*: Grade 9 Mathematics, De-streamed (2021), or Grade 9 Principles of Mathematics, Academic (2005)

**Foundations of Mathematics, Grade 10, Applied (MFM2P)**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 hands-on activities. Students will develop and graph equations in 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 figures. Students will consolidate their mathematical skills as they solve problems and communicate their thinking.

*Prerequisite*: Grade 9 Mathematics, De-streamed (2021), or Grade 9 Foundations of Mathematics, Applied (2005)

**Functions, Grade 11, University (MCR3U)**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

**Functions and Applications, Grade 11, University/College (MCF3M)**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. Students will 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

**Foundations for College Mathematics, Grade 11, College (MBF3C)**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 financial problems connected with vehicle ownership; develop their ability to reason by collecting, analysing, and evaluating data involving one variable; connect probability and statistics; and 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

**Mathematics for Work and Everyday Life, Grade 11, Workplace (MEL3E)**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*: Grade 9 Mathematics, De-streamed (2021), or Principles of Mathematics, Grade 9, Academic, or Foundations of Mathematics, Grade 9, Applied, or a Grade 10 Mathematics LDCC (locally developed compulsory credit) course

**Advanced Functions, Grade 12, University (MHF4U)**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

**Calculus and Vectors, Grade 12, University (MCV4U)**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 refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields 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*: Note: Advanced Functions, Grade 12, University Preparation, must be taken prior to or concurrently with Calculus and Vectors.

**Mathematics of Data Management, Grade 12, University (MDM4U)**This course broadens students’ understanding of mathematics as it relates 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 find this course of particular interest.

*Prerequisite*: Functions, Grade 11, University Preparation, or Functions and Applications, Grade 11, University/College Preparation

**Mathematics for College Technology, Grade 12, College (MCT4C)**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

**Foundations for College Mathematics, Grade 12, College (MAP4C)**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

**Mathematics for Work and Everyday Life, Grade 12, Workplace (MEL4E)**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