Grade 11 Function Analysis

PREREQUISITE: Principles of Mathematics, Grade 10, Academic

GRADE: 11 (University)

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

Grade 11 Function Analysis introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions, and develop facility in simplifying polynomial and rational expressions. In Grade 11 Function Analysis, students will reason mathematically and communicate their thinking as they solve multi-step problems.

UNIT ONE

Algebraic Tools

Essential Question: How can we decide when certain problem-solving strategies should be used over others?

  • In this unit, students will begin with a few review lessons to activate previous understanding of basic algebraic tools. They will then develop new algebraic skills that build off of these previous understandings.

UNIT TWO

Introduction to Functions

Essential Question: How can observed patterns be used to make predictions about unknown quantities?

  • In this unit, students will build on the algebraic skills they developed in the previous unit. Students will learn concepts such as domain and range, transformations of basic functions, and inverse functions. Most of these concepts are considered foundational skills that will be developed further throughout this course. This unit will also introduce new notation that uses the concept of the function.

UNIT THREE

Exponential Functions

Essential Question: What are the implications of using models to make predictions? Is it possible to have a model that is entirely accurate?

  • In this unit, students will identify specific characteristics of exponential functions that can be observed both graphically and in their equations and apply familiar transformations to the graphs of exponential functions. Students will solve exponential equations using algebraic strategies and exponent laws. Students will also analyze and solve real-world scenarios and problems using exponential functions.

UNIT FOUR

Trigonometry

Essential Question: What are the limitations of using models to make predictions?

  • In this unit, students will be reintroduced to the familiar concepts of SOH CAH TOA, Sine law and Cosine law. Students will build on them, leading to an introduction of trigonometric functions. By the end of this unit, students will have an understanding of trigonometric functions and how they can be used to model phenomenon such as the swinging of a pendulum.

UNIT FIVE

Sequences and Series

Essential Question: How can observed patterns be summarized in order to make informed predictions?

  • In this unit, students are introduced to a new type of function: the discrete function. In this course, discrete functions will take the form of sequences and series. A sequence is a list of numbers with some discernible pattern. Think back to your early studies of mathematics. You may recall problems that would present you with a list of numbers and it was your job to determine the pattern and maybe even predict the next three terms in the sequence. This unit will involve building on students knowledge of sequences like these, but they will be modelling them using functions that allow them to predict any term in the sequence.

UNIT SIX

Financial Applications

Essential Question: Can and should mathematical problem-solving strategies be used to make real-world decisions?

  • In this unit, students will connect and apply topics of study throughout the course to the concept of finance. The question every math teacher gets at least once per lesson is “when are we ever going to use this!?” The good news is this unit contains real-life applications of most concepts from this course! This unit will apply the knowledge students obtained from the following units: Algebraic Tools, Introduction to Functions and Exponential Functions.

CULMINATING PROJECT

10% of Final Grade

  • This project is one of the final evaluations of this course. This project will challenge students to use their knowledge of concepts learned throughout the course. This culminating project is worth 10% of the final grade.

FINAL EXAM

Proctored Exam20% of Final Grade

  • This exam is the final evaluation of this course. 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.