Prerequisite Course: Principles of Mathematics Grade 10, Academic

Description and Overall Expectations: This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will 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.

Math Processes: The mathematical processes will be integrated into student learning throughout the course and include: problem-solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating.

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, & solve problems involving exponential functions, including problems arising from real-world applications.
• Discrete Functions: demonstrate an understanding of recursive sequences, represent them 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: determine the values of the trigonometric ratios for angles less than 360°; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law; demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions; identify and represent sinusoidal functions, and solve problems involving them, including problems arising from real-world applications.