WILLIAM SCHOOL COURSE PROFILE/UNIT PLAN ! ! Course Name: Course Code: Teacher: Functions, Grade 11, University Preparation MCR3U Mr. Michael Kim ! OVERVIEW: This course introduces the mathema0cal concept of the func0on by extending students' experiences with linear and quadra0c rela0ons. Students will inves0gate proper0es of discrete and con0nuous func0ons, including trigonometric and exponen0al func0ons; represent func0ons numerically, algebraically, and graphically; solve problems involving applica0ons of func0ons; inves0gate inverse func0ons; and develop facility in determining equivalent algebraic expressions. Students will reason mathema0cally and communicate their thinking as they solve mul0-­‐step problems. ! ! Unit Description No. of Hours ! ! ! ! ! ! ! ! ! Unit No./Title Unit 1 – Characteristics of Functions Unit 2 – Exponential Functions Unit 3 -Trigonometric Ratios Students will explore functions in this unit, their representations, and their inverses, and how to make connections between the algebraic and graphical representations of functions using transformations. Students will learn how to 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. By the end of the unit students will be able to demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions This unit will explore several topics including evaluating powers with rational exponents, simplifying expressions containing exponents, and describing properties of exponential functions represented in a variety of ways. The emphasis will be on problem solving using these concepts. This unit concentrates students' attention on determining the values of the trigonometric ratios for angles less than 360º; proving simple trigonometric identities and solving problems using the primary trigonometric ratios. The sine law and the cosine law are developed. ! 25 hours 24.5 hours 15 hours ! ! ! ! ! ! ! ! ! Unit 4 – Trigonometric Functions Unit 5 -Discrete Functions Students will learn to demonstrate an understanding of periodic 18 hours relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions while solving problems involving sinusoidal functions, including problems arising from realworld applications. Students will also investigate the relationship between the graphs and the equations of sinusoidal functions sketching and describing the graphs and describing their periodic properties. The unit begins with an exploration of recursive sequences and how to represent them in a variety of ways. Making connections to Pascal's triangle, demonstrating understanding of the relationships involved in arithmetic and geometric sequences and series, and solving related problems involving compound interest and ordinary annuities will form the rest of the unit Review and Final Evaluation The final assessment task is a proctored two and half hour exam worth 30% of the student's final mark. 25 hours 2.5 hours ! ! ASSESSMENT AND EVALUATION METHODS: METHODS (MAY INCLUDE MAJOR EVALUATIONS) ! ! • • • • • Unit Activities Assignments Tests Quizzes Exam ASSESSMENT CATEGORIES AND WEIGHTS AND EVALUATION ACHIEVEMENT CHART CATEGORIES ! ! EVALUATION/WEIGHT OF MARKS Achievement Category Percentage Evaluation Percentage Knowledge 20 Term Evaluation 70 Thinking/Inquiry 30 Communication 20 Application 30 Final Evaluation Exam 30 Academic Dishonesty - Cheating and Plagiarism: Learning tasks that students complete, as well as all assignments, tests and exams which students submit for evaluation must be their own work. Cheating and plagiarism is a serious offence which will not be condoned. Academic consequences will result. ! ! Late and Missed Evaluations - Student Roles and Responsibilities Students are expected to: • be responsible for providing evidence of their achievement of the overall expectations within the time frame specified by the teacher, and in a form approved by the teacher; • understand that there will be consequences for not completing evaluations; • use class time productively; • in extenuating circumstances, request a deferment from the teacher before the due date.