Functions, Grade 11 - Canada Benson Academy

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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.
Prerequisite: Principles of Mathematics, Grade 10, Academic

Unit 1: Introduction to Functions

Students will explore the concepts of relations and functions in this unit, their representations, their inverses, and how to make connections between the algebraic and graphical representations of functions using transformations. Students will learn how to apply and determine the different transformations that can be applied to functions using transformational parameters, along with learning to apply function and set notations, and graphing methods consistently.

Unit 2: Equivalent Algebraic Expressions

. By the end of the unit, students will be able to demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions

Unit 3: Quadratic Functions

Students will explore properties of functions, by determining the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications. By the end of the unit, students will be able to demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

Unit 4: Exponential Functions

This unit will explore several topics including evaluating powers with rational exponents, simplifying expressions containing exponents, and describing properties of exponential functions represented in a variety of ways. The emphasis will be on modelling and problem solving using these concepts.

Unit 5: Trigonometric Ratios

This unit concentrates students' attention on determining the values of the trigonometric ratios for angles less than 360° proving simple trigonometric identities and solving problems using the primary trigonometric ratios. The sine law and the cosine law are developed. Students will learn to demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions while solving problems involving sinusoidal functions, including problems arising from real-world applications.

Unit 6: Sinusoidal Functions

Students will investigate the relationship between the graphs and the equations of sinusoidal functions sketching and describing the graphs and describing their periodic properties.

Unit 7: Sequences and Series

Students will demonstrate an understanding of relationships involved in arithmetic and geometric sequences and series and solve recursive sequences and apply these scenario to real life applications.

Unit 8: Financial Applications

Students will investigate the different aspects of financial mathematics. Investigate the effects of changing the conditions of investment. Use formulas and spreadsheet software to solve for future value, present value, interest rate and time for various type of investment. By the end of this unit students will be able to apply their financial literacy to real life applications.

Unit 9:Course Review and Final Exam

Students will be given time near the end of the course to review all the concepts they have learned throughout the course in preparation for the final exam that covers all overall expectations.

Unit Titles	Length
1:Introduction to Functions	14 hours
2:Equivalent Algebraic Expressions	12 hours
3:Quadratic Functions	16 hours
4:Exponential Functions	14 hours
5:Trigonometric Ratios	16 hours
6:Sinusoidal Functions	12 hours
7:Sequences and Series	10 hours
8:Financial Applications	10 hours
9: *Course Review and Final Exam* All strands are covered.	6 hours
Total	110 hours

A. CHARACTERISTICS OF FUNCTIONS
OVERALL EXPECTATIONS By the end of this course, students will:
1. demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;
2. determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications;
3. demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.
B. EXPONENTIAL FUNCTIONS
OVERALL EXPECTATIONS By the end of this course, students will:
1. evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;
2. make connections between the numeric, graphical, and algebraic representations of exponential functions;
3. identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.
C. DISCRETE FUNCTIONS
OVERALL EXPECTATIONS By the end of this course, students will:
1. demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;
2. demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;
3. make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities
D. TRIGONOMETRIC FUNCTIONS
OVERALL EXPECTATIONS By the end of this course, students will:
1. determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;
2. demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
3. identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.