Functions and Applications (MCF3M)

In this first unit, students will build on their basic knowledge of functions and polynomial relationships to conduct a thorough exploration of quadratic functions. The focus will be on examining different forms of quadratic equations and mastering the techniques to translate these equations into graphs and back. Understanding the key features of quadratic functions is a central aspect of this unit.

Learners will develop an understanding of how quadratic functions can be represented numerically, graphically, and algebraically. They will also delve into the link between the roots of quadratic equations and their graphical representations. Additionally, the unit will cover the application of quadratic functions in various real-life situations, demonstrating their practical relevance.

This unit delves deeply into trigonometry, building on the basic introduction received in Grade 10. Trigonometric functions are vital in a range of practical scenarios, including navigation on land and sea, survival planning, construction project planning, analyzing cyclic phenomena, music production, and space exploration.

At the end of this unit, students will acquire a thorough knowledge of applying trigonometry in these varied contexts at a basic level. They will also learn to connect these real-world uses to the numerical, graphical, and algebraic representations of sine functions.

Throughout this unit, students will develop the ability to express and manipulate exponential functions. They will utilize diverse tools, including calculators, traditional paper and pencil, and graphing technology, to enhance their understanding. Building on the strategies acquired in previous units, there will be an exploration and comparison of exponential functions to those previously studied.

This unit also includes an in-depth look at various types of exponential functions, learning to establish their relationships through graphing and transformations, and recognizing different exponential functions. A key focus will be on applying these concepts to real-life situations involving growth and decay, giving students the opportunity to apply their knowledge of exponential functions in practical contexts.

The culminating Rich Summative Task, constituting 30% of the final grade, includes creating a Portfolio Website. This task involves assembling a Google Site, structured with separate tabs for each "artifact." Here, an artifact is any significant work, like projects, assignments, or tests. This digital portfolio is designed to be a detailed showcase, neatly organizing and displaying different artifacts under distinct tabs. It aims to provide a well-arranged summary of the student's accomplishments and efforts during the course.

This supervised exam accounts for 30% of the total grade.

• A device like a scanner or smartphone camera to upload handwritten or hand-drawn assignments.
• A laptop or desktop computer, ideally with Google Chrome or Mozilla Firefox installed.
• Tools for video recording and scanning of handwritten work, which can be done via a smartphone, tablet, iPad, or webcam.
• A reliable internet connection.
• A scientific calculator that is non-programmable and non-graphing.

• Access to Google Suites or Microsoft Education for word processing and presentation software, with accounts provided by the school.
• A variety of supplemental reading materials.
• Educational videos and step-by-step instructions via Screencast.
• Videos providing solutions to exercises and problems.
• Student accounts for educational platforms like Gizmos, Labster, Mathletics, GeoGebra, and Padlet, distributed by the school.

Note: The course is fully online and independent of textbooks.