Credit Value: 1.0
Department: Mathematics
Prerequisite(s): Grade 10 Academic Mathematics
Policy Documents
The Ontario Curriculum: Grades 11 and 12: Mathematics (2007)
Ontario Secondary Schools 9 to 12 – Program and Diploma Requirements (1999)
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 Curriculum Expectations and Summative Tasks
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 those 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:
4. evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways
5. make connections between the numeric, graphical, and algebraic representations of exponential
6. identify and represent exponential functions, and solve problems involving exponential functions, including those arising from real–world applications
Discrete Functions
By the end of this course, students will:
7. demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle
8. demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems
9. 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:
10. determine the values of the trigonometric ratios for angles less than 360 degrees; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law
11. demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions
12. identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including those arising from real–world applications
Your Report Card Grade will be determined as follows:
| Term work: 70% of your grade will be based on all of the evidence you have provided. It will reflect your most consistent level of achievement with special consideration given to more recent evidence. | 20% Knowledge & Understanding: Knowledge of content and the understanding of mathematical concepts. 20% Application: the application of knowledge and skills in familiar contexts; transfer of knowledge and skills to new contexts; making connections within and between various contexts. 20% Thinking: use of planning and processing skills; use of critical and creative thinking processes. 10% Communication: Expression and organization of ideas and mathematical thinking, communication for different audiences/purposes and use of conventions, vocabulary and terminology of the discipline … all using oral, visual and written forms. |
| Final Evaluation: 30% of your grade will be determined at the end of the course. | 10% Culminating Task: Consisting of a mathematical investigation or contextual, open-ended problematic situation suited to a variety of approaches including use of technology where appropriate. |
| 20% Exam: Consisting of a variety of question types (e.g. short answer, multiple choice, extended tasks) sampling all strands and categories of 2.5 hours duration or less. | |
| Your final grade will be calculated by combining your Term (70%) grade and your Exam and Performance Task Evaluations (30%). | |
Textbook: Nelson Functions 11
Additional Resources: Teacher’s notes and handouts