Functions, Grade 11, University Prep.

Curriculum Policy:
https://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf
Course description:
This course introduces students to key principles of functions, building a foundation in various function types, trigonometry, and introductory calculus concepts. Students will deepen their understanding of mathematical models, exploring quadratic, trigonometric, polynomial, and rational functions. They will apply these models to solve real-world problems, enhancing skills in algebraic manipulation, graphical analysis, and rate of change concepts. By investigating the connections between different function types and their representations, students will develop critical thinking skills essential for advanced mathematics courses, preparing them for future studies in calculus, science, engineering, and business.

Chapters and Descriptions:

• Introduction to Functions
  Students explore the foundational concepts of functions, including function notation, domain, range, and transformations. This chapter introduces key features such as zeros, intercepts, and the effects of various transformations on graphs.
• Quadratic Functions
  In this chapter, students examine the properties of quadratic functions, including their standard and vertex forms. They learn to graph parabolas, solve quadratic equations, and apply these functions to model real-world scenarios.
• Polynomial Functions
  Students investigate polynomial functions of higher degrees, focusing on end behavior, zeros, and turning points. They explore the algebraic and graphical properties of these functions, analyzing how they can be applied in problem-solving.
• Rational Functions
  This chapter introduces rational functions and their unique characteristics, including asymptotes, discontinuities, and graphical behaviors. Students learn to simplify and analyze rational expressions and equations, applying their understanding to various contexts.
• Trigonometric Ratios and Functions
  Students explore trigonometric ratios and functions, focusing on their applications in right triangles and the unit circle. This chapter covers basic identities and transformations, building a foundation for further study in trigonometry.
• Advanced Trigonometric Functions
  Building on their understanding of trigonometric ratios, students delve into sinusoidal functions and their properties, including amplitude, period, phase shift, and vertical displacement. They apply these concepts to model periodic phenomena in real-life contexts.
• Exponential and Logarithmic Functions
  Students learn about exponential growth and decay, studying properties of exponential functions and their inverses, logarithmic functions. They explore real-world applications, such as compound interest, population growth, and pH measurement.
• Rates of Change
  This final chapter introduces the concept of average and instantaneous rates of change, setting the groundwork for calculus. Students apply these concepts to various functions, learning to interpret and solve problems involving rates of change in different contexts.