MCR3U, Grade 11, Functions, University Preparation

Course Title/ Grade/ Course Type: Functions, Grade 11, University Preparation

Ministry Course Code: MCR3U

Curriculum Document: The Ontario Curriculum, Grades 11 to 12, Mathematics (Revised 2007); Ministry of Education: Growing Success Documents, 2010

Prerequisite: MPM2D, Principles of Mathematics, Grade 10, Academic

*If you are a current UMC High School student, please contact your advisor.

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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.


Outline of Course Content

Unit 1:  Introduction to Functions

By the end of this section, you will be able to, identify a function as a special type of relation. They will recognize functions in various representations and use function notation. You will Explore the properties of some basic functions and apply transformations to those functions, and investigate the inverse of a linear function and its properties.


Unit 2:  Equivalent Algebraic Expressions

By the end of this unit, you will be able to determine whether algebraic expressions are equivalent. Add, subtract, multiply, and factor polynomials. You will simplify rational expressions; and add, subtract, multiply, and divide rational expressions.


Unit 3:  Quadratic Functions

By the end of this section, you will be able to, graph and analyze the properties of a quadratic function. You will determine the zeros of quadratic functions. You will calculate the maximum or minimum values of quadratic function, and solve problems involving quadratic functions.


Unit 4: Exponential Functions

By the end of the section, you will be able to describe the characteristics of exponential functions and their graphs. You will compare exponential functions with linear and quadratic functions, and evaluate powers with integer and rational exponents and simplify expressions involving them. Lastly, you will use exponential functions to solve problems involving exponential growth and decay.


Unit 5: Trigonometric Ratio 

By the end of the section, you will be able to, relate the six trigonometric ratios to the unit circle, and solve real-life problems by using trigonometric ratios, properties of triangles, and the sine and cosine laws. Finally, you will prove simple trigonometric identities.


Unit 6: Sinusoidal Functions 

By the end of the section, you will be able to, identify situations that can be modeled using sinusoidal and other periodic functions, and interpret the graphs of sinusoidal and other periodic phenomena. You will understand the effect of applying transformations to the functions: fx=sin x and fx=cos x , where x is measured in degrees, and determine the equations of sinusoidal functions in real- world situations and use those equations to solve problems.


Unit 7: Sequences and Series 

By the end of the section, you will be able to identify and classify sequences and create functions for describing sequences and use the sequences to make predictions. You will investigate efficient ways to add the terms of a sequence and model real-life problems using sequences.


Unit 8: Discrete Functions – Financial Applications 

By the end of the section, you will be able to determine how interest is earned and charged and use the difference between future value and present value to solve problems. You will solve problems about money invested at regular intervals over a period of time and calculate payments that must be made when a purchase is financed over a period of time.



Final Mark will be determined following percentages:

70% Determined by the evaluations conducted throughout the duration of the course:

Products – Assignments, Essays, Journals, Portfolio

Observations – Presentations

Conversations – Conferences with the Teacher

30% Final Exam