Grade 11, University Preparation (MCR3U)
Course Title: Functions, Grade 11, University Preparation(MCR3U)
Course Name: Functions
Course Code: MCR3U
Course Type: University Preparation
Credit Value: 1.0
Prerequisite: Principles of Mathematics, Grade 10,Academic
Curriculum Policy Document: Mathematics, The Ontario Curriculum, Grades 11 and 12, 2010 (Revised)
This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discreteand 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.
Titles and Descriptions
Time and Sequence
Characteristics of Functions
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 minimumofaquadraticfunction,andsolveproblemsinvolving quadraticfunctions,includingproblemsarisingfromreal-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 rationalexpressions.
Thisunitwillexploreseveraltopicsincludingevaluatingpowers with rational exponents, simplifying expressions containing exponents, and describing properties of exponential functions represented in a variety of ways. The emphasis will beon problem solving using theseconcepts.
Theunitbeginswithanexplorationofrecursivesequencesand 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 restof the unit.
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. Students will learn to demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical,andalgebraicrepresentationsofsinusoidalfunctions whilesolvingproblemsinvolvingsinusoidalfunctions,including problems arising from real-worldapplications.
Transforming Trigonometric Functions
Students will investigate the relationship between the graphs and the equations of sinusoidal functions sketching and describing the graphs and describing their periodic properties.
The final assessment task is a three hour exam worth 30% of the student’s final mark.