# MCR3U Functions – Grade 11 (University)

## Course Details

• 3. Grade 11

PREREQUISITE: Principles of Mathematics, Grade 10, Academic

AVAILABILITY: Full-time – All Campuses, Part-time – All Campuses, Private – All campuses, Blyth Academy Online

THE ONTARIO CURRICULUMMathematics

## Course Overview

MCR3U online 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 MCR3U online, students will reason mathematically and communicate their thinking as they solve multi-step problems. As this is a course designed for university preparation, the skills learned in MCR3U will hone skills needed for academic and professional programs at the university level. The Grade 11 Functions course can also be used as a prerequisite for Grade 12 – University courses necessary for certain university programs. Whether you choose to take MCR3U online or on campus, the course will help prepare you for the next steps you take in applying for university programs and beyond.

## Course Outline

Below is a course outline for the online MCR3U course offered by Blyth Academy. As the Ontario MCR3U curriculum is set by the Ontario Ministry of Education, the course and skills learned remain the same whether you take it in person or online.

MCR3U aims to help students use the language of mathematics confidently, flexibly, and skillfully. The course incorporates a variety of instructional strategies in order to offer learning opportunities that accommodate different learning styles, ability levels, and interests. Students will gain facility with solving problems, selecting tools and computational strategies, connecting concepts to real-world applications, using various representations (including concrete, visual, and symbolic), and self-assessing understanding of concepts learned throughout the duration of the course.

### 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.

### Assessment

The final grade will be based on a student’s achievement of curriculum expectations as well as demonstrating the skills required for effective learning. The final percentage grade each student receives reflects the quality of the individual student’s overall achievement, showing how the student has mastered course expectations. The final grade is broken down in the following manner:

70% of the grade: This portion of the final percentage grade will be based on evaluations conducted throughout the MCR3U course. This component of the grade reflects a student’s most consistent achievement level, though special consideration may be given to recent evidence of further achievement.

30% of the grade: This portion of the final percentage grade will come from final evaluations, to be administered at the conclusion of the MCR3U course. The final assessment for the Blyth Academy course is comprised of two parts: A culminating project, which is worth 10% of the overall final course grade, and a final proctored exam, which is worth 20% of the overall final course grade. Expectations for both the culminating project and final exam are described below.

Please consult our Frequently Asked Questions Page or the Exam section within your course for more details on final exams and the exam fee. More information can also be found in our Student Handbook

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