MCR 3U2009-2010

Grade 11 Functions
Course Content

This course introduces the concepts of function and sequence, and applies them through the study of discrete functions, quadratics, rationals, radicals, trigonometry, and exponents. Students will develop their skill with the mathematical processes. They will reason mathematically and communicate their thinking as they investigate ideas and solve multi-step problems.

Sequence of Topics

  • Unit 1Introducing Sequences and Functions
  • Unit 2Quadratic Functions
  • Unit 3Rationals and Radicals
  • Unit 4Geometric Sequences and Exponential Functions
  • Unit 5Trigonometric Functions
  • Unit 6Sequences, Series and Financial Applications

Mathematical Processes

The Mathematical Processes are a set of interconnected thinking skills that support lifelong learning in mathematics. Students develop and apply these skills in all math courses as they work to achieve the expectations outlined within each course. These skills are developed through problem-solving experiences that incorporate a variety of approaches, including investigation. The mathematical processes are:

  • Problem Solving
  • Reasoning and Proving
  • Reflecting
  • Selecting Tools and Computational Strategies
  • Connecting
  • Representing
  • Communicating

Note: Students will find that the pace in MCR 3U is faster than in MPM 2D, and that a thorough understanding of the concepts from 2D is required to be successful in this course. The content is cumulative, so students will need to manage their learning carefully and seek help as soon as issues arise.

Evaluation

Students will be evaluated according to the categories of Knowledge and Understanding, Application, Communication, and Thinking as specified in the achievement chart of the Ministry of Education and Training curriculum documents. Evaluation should be viewed as an opportunity to demonstrate achievement of course expectations. Evaluation will be varied, and will include mastery tests, unit tests and performance assessments. It may also include other assignments, projects, investigations, and classroom activities.

Category / Weight (% of final) / Types of Assessments
Knowledge and Understanding / 30 / Mastery (10% of final mark)
Tests
Assignments / Projects
Application / 30 / Tests
Assignments / Projects
Communication / 20 / Tests
Assignments / Projects
Investigations
Performance Tasks
Thinking, Inquiry, Problem Solving / 20 / Tests
Assignments / Projects
Investigations
Performance Tasks

Summative Evaluation

The final mark has two components: term work (70%) and summative evaluation (30%). The summative evaluation occurs near the end of the course, and has two components: a final examination (20%) anda performance task(10%). Attendance is mandatory for both of these evaluations.

Learning Skills

Learning skills are student habits and behaviours that enable them to learn effectively and achieve their potential. They are critical to success in all subject areas. Work habits, team work, initiative, independent work, and organizational skills will be assessed throughout the course, and communicated on the report card.

Student Absences

Students are responsible for all work missed regardless of the reason for the absence. If you are away, you WILL miss something important! Work must be completed before return to school in order to remain connected to the development of the concepts.

Students who expect to miss school due to family vacations must notify the Principal in writing, in advance. Vacations cannot be recognized as legitimate reasons for exemption from formal evaluation.

Refer to Math Department policy on Missed / Late Assesments for more detailed information

Textbook and E-book

Your text is Functions 11 (Nelson). You must return it in the condition that you receive it or you will be charged a fee for damages. The text is available on CD. If you would like to borrow a copy, please see your teacher.

MCR3U: Funtions, Grade 11 Overall Expectations

(from Ministry of Education: The Ontario Curriculum Grades 11 and 12: Mathematics)

By the end of this course, students will:

A: Characteristics of Functions

1. demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;

2. determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications;

3. demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

B: Exponential Functions

1. evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;

2. make connections between the numeric, graphical, and algebraic representations of exponential functions;

3. identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications

C: Discrete Functions

1. demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;

2. demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;

3. make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

D: Trigonometric Functions

1. determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law;

2. demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;

3. identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.