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Course Description

 The Calculus and Vectors course 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. This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modeling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. 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.

Course Content

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Unit 1: Explore Rate of “Flow” Problems Using Non-algebraic Means
Unit 2: Derivative Functions from First Principles
Unit 3: Derivative Functions: Properties and their Applications
Unit 4: Derivatives in Rate of Change and Optimization Problems
Unit 5: Representing Vectors
Unit 6: Representing Lines and Planes
Final Exam
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