MCF3M, Functions, Grade 11, University/College Preparation, (1 credit)

What You Will Learn:
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.

Course Outline:

Units:

• Tools for Operating and Communicating with Functions: manipulate polynomials, rational expressions, and exponential expressions; understand inverses and transformations of functions and function notation; communicate mathematical reasoning.
• Trigonometric Functions: solve problems involving the sine law and the cosine law in oblique triangles; apply radian measure; determine the relationships between the graphs and equations of sinusoidal functions; solve problems involving models of sinusoidal functions drawn from a variety of applications.
• Financial Applications of sequences and Series: solve problems involving arithmetic and geometric sequences and series.

Resources/ materials used:

• Class handouts, textbook.

Emphasis also 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.

Because of the intended destination of students enrolled in MCF3M, the contextual examples and activities are drawn from a wide variety of areas with minimal emphasis on areas that are generally mathematically intensive (e.g., engineering, computer science, pure mathematics, etc.).

In the Financial Applications of Sequences and Series strand, 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 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 more easily visualize concepts.

Related Courses:

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 technology to allow fast visualization of graphs of various functions.

Further information