Page 15 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

The Grade 11 university preparation course, Functions, builds on the concepts and skills developed in the Grade 9 and 10 academic mathematics courses. The course is designed to prepare students for Grade 12 mathematics courses that lead to one of many university programs, including science, engineering, social sciences, liberal arts, and education.
The concept of functions is introduced in the Characteristics of Functions strand of this course and extended through the investigation of two new types of relationships in the Exponential Functions and Trigonometric Functions strands. The Discrete Functions strand allows students, through the study of different representations of sequences and series, to revisit patterning and algebra concepts introduced in elementary school and make connections to financial applications involving compound interest and ordinary simple annuities.
The Grade 12 university preparation course Advanced Functions satisfies the mathe- matical prerequisite for some universities in areas that include business, social science, and health science programs. The strands in this course help students deepen their understanding of functions by revisiting the exponential and trigonometric functions introduced in Grade 11 to address related concepts such as radian measure and logarith- mic functions and by extending prior knowledge of quadratic functions to explore poly- nomial and rational functions. The Characteristics of Functions strand addresses some of the general features of functions through the examination of rates of change and methods of combining functions.
The Grade 12 university preparation course Calculus and Vectors is designed to prepare students for university programs, such as science, engineering, and economics, that include a calculus or linear algebra course in the first year. Calculus is introduced in the Rate of Change strand by extending the numeric and graphical representation of rates of change introduced in the Advanced Functions course to include more abstract algebraic representations. The Derivatives and Their Applications strand provides students with the opportunity to develop the algebraic and problem-solving skills needed to solve problems associated with rates of change. Prior knowledge of geometry and trigonometry is used in the Geometry and Algebra of Vectors strand to develop vector concepts that can be used to solve interesting problems, including those arising from real-world applications.
The Grade 12 university preparation course Mathematics of Data Management is designed to satisfy the prerequisites for a number of university programs that may include statistics courses, such as those found in the social sciences and the humanities. The expectations in the strands of this course require students to apply mathematical process skills developed in prerequisite courses, such as problem solving, reasoning, and communication, to the study of probability and statistics. The Counting and Probability strand extends the basic probability concepts learned in the elementary school program and introduces counting techniques such as the use of permutations and combinations; these techniques are applied to both counting and probability problems. The Probability Distributions strand introduces the concept of probability distributions; these include the normal distribution, which is important in the study of statistics. In the Organization of Data for Analysis strand, students examine, use, and develop methods for organizing large amounts of data, while in the Statistical Analysis strand, students investigate and develop an understanding of powerful concepts used to analyse and interpret large amounts of data. These concepts are developed with the use of technological tools such
THE PROGRAM IN MATHEMATICS
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