Advanced Functions, Grade 12, University Preparation
Curriculum Policy

Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)

Course Description:
This course builds on students’ previous knowledge of functions, enabling them to explore the properties of polynomial, rational, logarithmic, and trigonometric functions. Students will enhance their ability to combine functions and deepen their understanding of rates of change while mastering the application of these concepts and skills. The course emphasizes refining essential mathematical processes that are critical for success in advanced mathematics. It is designed for students preparing for the Calculus and Vectors course as a prerequisite for university programs, as well as for those looking to solidify their mathematical foundation before pursuing a variety of university pathways.

Chapters and Descriptions:

• Foundational Skills Refresher
  This unit revisits essential concepts covered in prerequisite math courses, reinforcing the definition of a function, function notation, and key properties. Students will also explore function transformations and inverse functions. The unit assessment measures their proficiency in effective communication, formatting, and technical skills, which will be crucial for success in subsequent assignments throughout the course.
• Understanding Polynomial Functions
  In this unit, students will identify and describe key features of polynomial functions while making connections between their numerical, graphical, and algebraic representations. This understanding enables students to manipulate polynomial functions in various ways and apply their skills to solve real-world problems, with an emphasis on strategies that enhance comprehension of rates of change.
• Rational Functions and Inequalities
  Students begin this unit by exploring the defining characteristics of rational functions. They will learn to represent and manipulate these functions to address real-life problems, employing both graphical and algebraic methods. Additionally, this unit introduces inequalities and examines how they yield different solutions compared to equations.
• Exponential and Logarithmic Functions
  This unit starts with a review of exponential functions, their properties, and real-world applications. Students will then delve into logarithmic functions, learning about their properties and how to apply their knowledge of both exponential and logarithmic functions to solve practical problems.
• Exploring Trigonometry
  In this unit, students will investigate radian measure, which allows for solving complex situations with exact values. They will connect trigonometric ratios with the graphical and algebraic representations of corresponding trigonometric functions, using these connections to tackle problems involving trigonometric equations and to prove identities.
• Trigonometric Functions and Their Graphs
  This unit deepens students’ understanding of trigonometry by focusing on the functions associated with trigonometric ratios. They will analyze trigonometric functions and their reciprocals, study their key properties and behaviors, and learn how to transform these functions to model a diverse range of data.
• Operations with Functions
  Building on their study of various types of functions and transformations, this final unit emphasizes the theory and practice of performing arithmetic operations on entire functions. Students will explore the algebraic, graphical, and practical implications of these operations, deepening their understanding of the significance of differential rates of change in functions.