• COURSE DESCRIPTION

     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 EXPECTATIONS

    The Ontario Curriculum Grades 11 and 12: Mathematics identifies overall expectations, which describe in general terms the knowledge and skills that students are expected to demonstrate by the end of this course.  This course is broken down into four different strands: characteristics of functions, exponential functions, discrete functions and trigonometric functions.

     For the following strands, it is expected that students will:

     Characteristics of Functions 

    • 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 problems arising from real-world applications;
    • demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

     Exponential Functions 

    • 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 problems arising from real-world applications.

    Discrete Functions 

    • 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.

     Trigonometric Functions 

    • use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity;
    • solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
    • solve problems involving acute triangles, using the sine law and the cosine law.