MCR3U

Categories: Mathematics
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About Course

Functions, Grade 11, University Preparation

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.

Prerequisite: Principles of Mathematics, Grade 10, Academic

What Will You Learn?

  • MCR3U course is a Grade 11 Functions course which helps students at a university preparation level.

Course Content

Course Outline

  • Course Outline
  • Course Outline

Grade 11 Nelson Functions Book

Unit 1 Characteristics of Functions 30 Hours
The student will able to: ➢ Students will explore the concepts of relations and functions in this unit, their representations, their inverses, and how to make connections between the algebraic and graphical representations of functions using transformations. Students will learn how to apply and determine the different transformations that can be applied to functions using transformational parameters, along with learning to apply function and set notations, and graphing methods consistently. ➢ Students will explore properties of functions, in particular by determining 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.

Unit 2 Exponential Functions
The student will able to: ➢ 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 modelling and problem solving using these concepts

MCR3U Functions – Test 1

Unit 3 Trigonometric Functions and Graph 32.5 hrs
The student will able to: ➢ This unit concentrates students' attention on determining the values of the trigonometric ratios for angles less than 360° proving simple trigonometric identities and solving problems using the primary trigonometric ratios. The sine law and the cosine law are developed. Students will learn to demonstrate an understanding of periodic 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 real-world applications ➢ Students will investigate the relationship between the graphs and the equations of sinusoidal functions sketching and describing the graphs and describing their periodic properties.

MCR3U Functions – Test 2

Unit 4 Discrete Functions 25 hrs
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.

MCR3U Functions – Final Exam

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