Grade 11 : Functions of Mathematics
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.
Unit Content and Courses of Delivery
Introduction to Functions (11 hours)
Students will learn to identify a function as a special type of relation, recognize functions in various representations, and make connections between the algebraic and graphical representations of functions using transformations in this unit. They will also explore the properties of some basic functions and their inverses.
Quadratic Functions (14 hours)
Students will learn to graph and analyze the properties of quadratic functions in this unit. They will also determine the zeros and the maximum and minimum of quadratic functions. In addition, they will solve problems involving quadratic functions, including problems arising from real-world applications.
Exponential Functions (25 hours)
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 problem solving using these concepts.
Trigonometric Ratios (10 hours)
In this unit, students will learn to relate the six trigonometric ratios to the unit circle, solve real-life problems by using trigonometric ratios, properties of triangles, and the sine and cosine laws. They will also learn to prove simple trigonometric identities.
Sinusoidal Functions (20 hours)
Students will be able to demonstrate an understanding of periodic relationships and sinusoidal functions, make connections between the numeric, graphical, and algebraic representations of sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications in this unit. They will also understand the effect of applying transformations to the trigonometric functions.
Discrete Functions: Sequences and Series (15 hours)
This unit entails an exploration of recursive sequences and their representation in a variety of ways, an understanding of Pascal’s triangle and the relationships involved in arithmetic and geometric sequences and series.
Discrete Functions: Financial Applications (15 hours)
This unit involves the exploration of discrete functions’ related problems involving compound interest and ordinary annuities.
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