Advanced Functions(MHF4U)

In this engaging unit, learners will delve back into the essential elements of distance-time graphs, solidifying their grasp on this key type of graphical representation. The program includes an in-depth exploration of graph transformations and the significant effects they can have on various graphs. We'll also revisit critical concepts such as function notation, understanding relationships in mathematics, and the concepts of range and domain, ensuring a comprehensive understanding for all students.

As we approach the end of this unit, we'll introduce new strategies aimed at deepening students' understanding of rates of change. This is a pivotal component in the world of mathematics, and we equip our learners with the necessary tools to skillfully handle this aspect. Our holistic teaching approach aims to reinforce and enhance students' foundational knowledge in these fundamental mathematical principles in an interactive and engaging learning environment.

This unit introduces students to an in-depth study of polynomial and rational functions. Extending their knowledge from linear and quadratic functions, students will now explore the nuances of cubic, quartic, and quintic functions. They'll analyze the graphs and unique characteristics of these functions, learning to differentiate them from sinusoidal and exponential functions.

Students will engage in comparative analyses of polynomial function graphs versus other types of functions. A key part of this unit is the investigation, both with and without technology, into the essential features of rational function graphs, especially those functioning as reciprocals to linear and quadratic functions. These features encompass vertical and horizontal asymptotes, domain and range, intercepts, and intervals indicating positivity/negativity and increase/decrease.

The curriculum also covers the practical application of simple rational functions and equations, highlighting the distinction between solving one-variable equations and inequalities. Students will learn to verify solutions of inequalities and graphically determine solutions to straightforward rational inequalities, using graphing technology to identify intervals that satisfy these inequalities.

This unit introduces students to radians, a vital alternative to degrees for measuring angles. They'll learn how radian measures are determined by arc lengths in a unit circle and will explore the conversion between radians and degrees. Key activities include graphing the sine and cosine functions using radian-based angle measurements, focusing on understanding their fundamental properties like a 2π period and unit amplitude.

The unit also covers expressing sinusoidal functions as equations, utilizing radian measures. Students will engage with trigonometric identities, learning to prove and verify these using reasoning and technology. This module provides a comprehensive overview of trigonometric functions in the context of radian measurement.

In this unit, students will uncover the deep connection between logarithmic and exponential functions, understanding their interrelated nature. The focus will be on the relationship between the laws of exponents and logarithms, where students will engage in verifying these logarithmic principles, using technological tools as well as manual calculations.

Another key aspect of the unit is the practical application of logarithmic laws in simplifying and evaluating numerical expressions, and solving problems involving exponential and logarithmic equations. Students will also look into real-world scenarios where these equations are applicable, illustrating the practical significance of these mathematical concepts. The unit aims to provide a comprehensive blend of theory and practical application, laying a solid foundation in exponential and logarithmic functions.

The culminating evaluation for this course is a supervised final exam spanning three hours, accounting for 30% of the overall student grade.

• Scanner or smartphone camera for document uploads.
• Laptop or PC with Google Chrome or Mozilla Firefox.
• Video recording device (phone, tablet, webcam).
• Stable internet connection.
• Non-programmable scientific calculator.

• Google Suites or Microsoft Education access for word processing and presentation software (accounts provided by the school).
• Supplemental Readings.
• Tutorial Videos / Screencast Instructions.
• Solution Videos.
• Educational tools access: Gizmos, Labster, Mathletics, GeoGebra, Padlet (accounts provided by the school).