Ministry of Education Course Title: Functions
Course Code: MCR3U
Grade Level: 11
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; and develop facility in simplifying polynomial and rational expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.
Overall Curriculum Expectation - all units are interrelated
Unit 1 Characteristics of Functions
- demonstrate an understanding of functions, their inverse, the impact of transformations and various ways of representing them;
- demonstrate facility with equivalent algebraic expressions involving polynomials, radicals and rational expressions;
- determine key features of quadratic functions and solve linear-quadratic systems.
Unit 2 Exponential Functions
- demonstrate an understanding of exponential functions;
- analyze and transform exponential functions;
- solve problems involving exponential growth and decay.
Unit 3 Discrete Functions
- demonstrate an understanding of recursive sequences, including the connection to Pascal’s Triangle;
- demonstrate an understanding of arithmetic and geometric sequences and series as discrete functions and determine the value of a term and the sum of a set of terms;
- demonstrate an understanding of the connection between sequences, series and financial applications and solve problems involving financial decision making, with and without technology.
Unit 4 Trigonometric Functions
- demonstrate the connection between the trigonometric ratios and the unit circle, and solve problems using the primary trigonometric ratios, the sine law and the cosine law;
- determine, through investigation, the relationship between the graphs and the equations of sinusoidal functions;
- solve problems involving models of sinusoidal functions drawn from a variety of applications.