Grade 12 Advanced Function Analysis

PREREQUISITE: Functions, Grade 11, University Preparation, or Mathematics for College Technology, Grade 12, College Preparation

GRADE: 12 (University)

AVAILABILITY: Full-time, Part-time, Private and Online

This course xtends students’ experience with functions. Students will investigate the properties of polynomial, rational, logarithmic, and trigonometric functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. Advanced Function Analysis is intended both for students taking the Calculus and Vector Analysis course as a prerequisite for a university program and for those wishing to consolidate their understanding of mathematics before proceeding to any one of a variety of university programs

UNIT ONE

Polynomials

Essential Question: How can characteristics of polynomials be used to make connections between functions and their graphical representations?

  • In this unit, students will investigate the key properties and characteristics of polynomials and use their findings to form connections between algebraic and graphical representations of polynomial functions. Students will develop skills that can be used to analyze and solve polynomial equations and inequalities.

UNIT TWO

Rational Functions

Essential Question: What patterns exist in rational functions and how can they be used to make predictions about their graphs?

  • In this unit, students will examine the key characteristics of rational functions and use them to develop an understanding of their graphical representations. Students will investigate the different cases where horizontal asymptotes occur and use their understanding to solve rational equations and inequalities.

UNIT THREE

Trigonometry

Essential Question: How can the properties of trigonometric functions be used to make predictions about real-world scenarios?

  • In this unit, students will build on their understanding of trigonometry acquired from previous studies of mathematics. Students will develop an understanding of radian measure and conceptualize special triangles and the unit circle in terms of radians. Students will explore advanced trigonometric identities and make connections to the graphs of sine and cosine. These graphs will be used to develop the graphs of tangent, cosecant, secant, and cotangent. Lastly, students will apply the understandings developed in this unit to solve trigonometric equations and real-world problems.

UNIT FOUR

Exponential and Logarithmic Functions

Essential Question: How can the relationship between exponential and logarithmic functions be used to solve real-world problems?

  • In this unit, students will review exponential functions and make connections to the logarithmic function by applying an understanding of inverse functions. Students will then learn to write expressions in both exponential and logarithmic form. Students will learn about the laws of logarithms and how they can be applied to solve logarithmic equations. Lastly, students will combine the understandings they develop throughout this unit and apply them to solve real-world problems that can be modelled using exponential and logarithmic functions.

UNIT FIVE

Combining Functions and Rates of Change

Essential Question: How can rates of change be used to make sense of motion in the world?

  • In this unit, students will begin by examining sums, differences, products, and quotients of functions. Students will then substitute functions into other functions in order to form composite functions. The domain, range, and key characteristics of combined functions will then be explored. Students will then turn their attention to rates of change of functions and investigate how the average rate of change can be used to approximate the instantaneous rate of change of a given function.

FINAL EXAM

Proctored Exam30% of Final Grade

  • This exam is the final evaluation of MHF4U online. Students need to arrange their final exam 10 days in advance. All coursework should be completed and submitted before writing the final exam, please be advised that once the exam is written, any outstanding coursework will be given a grade of zero. The exam will be two hours.