MCR3U COURSE OUTLINE

Course Title: Functions

Grade: 11

Ministry Course Code: MCR3U

Course Type: Academic

Credit Value: 1.00

Course Hours: 110

Department: Sciences

Revision Date: N/A

Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2007 (Revised)

http://www.edu.gov.on.ca/eng/curriculum/secondary/math1112currb.pdf

Domestic Student Price: $550
International Student Price: $799

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COURSE DESCRIPTION

This course 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; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

OVERALL EXPECTATIONS

Characteristics of Functions

By the end of this course, students will:

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.

Exponential Functions

By the end of this course, students will:

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.

Discrete Functions

By the end of this course, students will:

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.

Trigonometric Functions

By the end of this course, students will:

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.

OUTLINE OF COURSE CONTENT

TEACHING AND LEARNING STRATEGIES

A variety of teaching and learning strategies are used to allow students many opportunities to attain the necessary skills for success in this course and in future studies. In all activities, consideration will be taken to ensure that individual students’ multiple intelligences and learning strengths are addressed through the use of varied and multiple activities in each lesson.

STRATEGIES FOR ASSESSMENT AND EVALUATION OF STUDENT PERFORMANCE

The primary purpose of assessment and evaluation is to improve student learning. Assessment and evaluation is based on the Ministry of Education’s Growing Success policy document, which articulates the Ministry’s vision for how assessment and evaluation is practiced in Ontario schools.

Growing Success describes the three assessment types as follows:

Assessment as Learning: focuses on the explicit fostering of students’ capacity over time to be their own best assessors, but teachers need to start by presenting and modelling external, structured opportunities for students to assess themselves.
Assessment for Learning: the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go, and how best to get there.
Assessment of Learning: the assessment that becomes public and results in statements or symbols about how well students are learning.

ASSESSMENT AND EVALUATION

EVALUATION SCHEME

A final grade (percentage mark) is calculated at the end of the course and reflects the quality of the student’s achievement of the overall expectations of the course, in accordance with the provincial curriculum.

The final grade will be determined as follows:

Seventy percent (70%) of the grade will be based on evaluation conducted throughout the course. This portion of the grade should reflect the student’s most consistent level of achievement throughout the course, although special consideration should be given to more recent evidence of achievement.
Thirty percent (30%) of the grade will be based on a final evaluation administered at or towards the end of the course. This evaluation will be based on evidence from one or a combination of the following: an examination, a performance, an essay, and/or another method of evaluation suitable to the course content. The final evaluation allows the student an opportunity to demonstrate comprehensive achievement of the overall expectations for the course.

PLAGIARISM

Plagiarism is a serious offense. It is defined as taking words, phrasing, sentence structure, or any other element of the expression of another person’s ideas, and using them as if they were your own. Plagiarism is a violation of another person’s rights, whether the material taken is great or small.Students will be assisted in developing strategies and techniques to avoid plagiarism. They need to be aware that plagiarized term work will be penalized and could result in a mark of zero.