Functions and Applications, Grade 11, University/College Preparation
Curriculum Policy
Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)

Course description:
This course provides students with an introduction to essential features of functions, building on their understanding of quadratic relations. It emphasizes quadratic, trigonometric, and exponential functions, exploring their applications in real-world contexts. Students will learn to represent functions in numerical, graphical, and algebraic forms; simplify expressions; and solve equations. Through hands-on problem-solving, students will develop their mathematical reasoning skills and effectively communicate their thought processes as they tackle multi-step problems related to various applications.

Chapters and descriptions:

• Revisiting Mathematical Foundations
  In this initial unit, students will refresh their understanding of arithmetic and key mathematical concepts acquired in previous grades. They will focus on polynomials, emphasizing operations on polynomial equations. This foundational knowledge will lead to a deeper exploration of functions, enabling students to tackle problems involving rational expressions using the skills developed throughout the module.
• In-Depth Study of Quadratic Functions
  With a solid grasp of functions and polynomial relations, students will delve into quadratic functions, examining their various forms in detail. They will employ strategies to convert equations into graphs and vice versa, highlighting the significance of quadratic characteristics. Connections among numeric, graphical, and algebraic representations will be emphasized, as students relate the roots of quadratic equations to their graphical counterparts. Additionally, students will explore the applicability of quadratic functions in modeling diverse real-world scenarios.
• Real-World Financial Applications
  This unit centers on the practical application of mathematics in financial contexts, particularly in understanding and managing money. Students will focus on exponential functions, first using them to model real-world phenomena like population growth and radioactive decay. They will then apply their knowledge to financial mathematics, including simple interest, compound interest, and annuities. Through this exploration, students will solve realistic financial problems, linking numeric, graphical, and algebraic representations of exponential functions.
• Exploring Trigonometric Functions
  In this comprehensive unit, students will engage deeply with trigonometry, which was briefly introduced in Grade 10. They will learn how trigonometric functions are utilized in various real-world applications, such as navigation, construction planning, and analyzing cyclic phenomena. By the end of this unit, students will be equipped with a foundational understanding of these applications, relating them to the numeric, graphical, and algebraic representations of sine functions.