MCR3U – Functions – Grade 11
This course introduces the mathematical concept of the function by extending student’ 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.
₹450.00
*Course outline is subject to change
Overall Curriculum Expectations
By the end of this course, students will :
Characteristics of Functions
- A.1 – Demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations
- A.2 – Determine the zeros and maximum and minimum of quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications
- A.3 – Demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions
Exponential Functions
- B.1 – Evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways
- B.2. – Make connections between the numeric, graphical, and algebraic representations of exponential functions
- B.3 – Identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications
Discrete Functions
- C.1 – Demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle
- C.2 – Demonstrate an understanding of the relationship involved in arithmetic and geometric sequences and series, and solve related problems
- C.3 – Make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities
Trigonometric Functions
- D.1 – Determine the values of the trigonometric rations for angles less than 360°; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law and the cosine law
- D.2 – Demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions
- D.3 – Identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications
Outline of Course Content
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.
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
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.
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.
Trigonometric Ratios:
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.
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.
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.
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.
The final assessment task is a broken down into a conversation portion worth 10% and a written exam worth 20% of the student’s final mark.