Mathematics Department Victoria Park Collegiate Institute

FUNCTIONS

GRADE 11 - UNIVERSITY Preparation

Ministry of Education Document: The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Course Code:MCR3U1Credit Value:1 Credit

Textbook:Functions 11; McGraw-Hill Ryerson; 2009

Replacement Cost is $80

Prerequisite:Grade 10 Academic (MPM2D)

DESCRIPTION (as per The Ontario Curriculum, Grades 11 and 12):

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 GOALS:

By the end of this course, students will:

  • demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations;
  • 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;
  • demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.
  • evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways;
  • make connections between the numeric, graphical, and algebraic representations of exponential functions;
  • identify and represent exponential functions, and solve problems involving exponential functions, including those arising from real-world applications.
  • demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to Pascal’s triangle;
  • demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series, and solve related problems;
  • make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.
  • 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;
  • demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions;
  • identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including those arising from real-world applications.

COMMUNICATION:

Teachers are available for extra help by appointment or during announced scheduled times.

Mathematics Office:Room 225

Telephone number:(416) 395-3310, extension 20080

The best time to call is before 8:45 am.

Absences & Evaluations

  1. If you know prior to the evaluation that you will be absent, make other arrangements with your teacher regarding that particular assessment.
  2. If for some reason you are absent on the day of an evaluation:
  3. Call the Math Office before 8:45 am and speak with your teacher or leave a message for him/her.
  4. On the first day back, a note from your parent/guardian is required.

TEACHING, ASSESSMENT & EVALUATION STRATEGIES:

Throughout this course, students will develop their understanding of essential mathematical knowledge and procedures. This knowledge becomes meaningful in reasoning, communicating, and solving problems based on real-life situations. Technology, calculators and/or computer software, will be used to compliment the teaching and application of mathematical skills and explore concepts where appropriate.

Student success is greatly enhanced by good attendance, behaviour, and class participation. Completion of daily homework exercises and writing all evaluations will provide feedback on student learning. For courses with multiple sections, summative evaluations will assess common expectations.

Quizzes and assignments will be scheduled throughout the course. A summative test will conclude a unit or a group of related units. Below is a list of anticipated evaluations. This list may be modified to accommodate circumstances that arise throughout the semester.

TASK / ACHIEVEMENT CATEGORIES / DATE
Unit 1: Functions (10-12 periods)
Quiz: Solving Quadratic Equations / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 2: Transformations of Functions (12-15 periods)
Investigation: All types of transformations / Knowledge/Application/Communication
Quiz: Translations of Functions / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 3: Exponential Functions (12-15 periods)
Investigations: All types of transformations / Knowledge/Application/Communication
Quiz: Negative Exponents / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 4: Trigonometry (10-12 periods)
Quiz: Special Angles / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 5: Trigonometric Functions (10-12 periods)
Investigations: Graphing all Trigonometric Functions / Knowledge/Application/Communication
Quiz: Modelling Periodic Behaviour / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 6: Discrete Functions (10-12 periods)
Quiz: Arithmetic and Geometric Sequences / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking
Unit 7: Compound Interest and Annuities (10-12 periods)
Quizzes: Calculating Compound Interest and Annuities / Knowledge/Application/Communication
Investigations: Word Problems / Knowledge/Application/Communication
Test / Knowledge/Application/Communication/Thinking

Mathematics Department Victoria Park Collegiate Institute

TERM MARK (70% OF FINAL GRADE):

KNOWLEDGE30%

APPLICATION30%

COMMUNICATION20%

THINKING20%

SUMMATIVE MARK (30% OF FINAL GRADE):

FINAL EXAM30%

LEARNING SKILLS:

Works Independently

Teamwork

Organization

Work Habits / Homework

Initiative

Self Regulation

Categories evaluated as Needs Improvement, Satisfactory, Good, or Excellent.

Mathematics Department Victoria Park Collegiate Institute

EVALUATION POLICY

Please refer to the Student Agenda.