MATHEMATICS ALGEBRA II / TRIGONOMETRY
This course extends the concepts studied in earlier courses by presenting a formal treatment of functions and their graphs, along with some use of a graphics calculator as an aid for exploration and discovery. The concepts include exponential, logarithmic, trigonometric, polynomial, and rational functions. The course stresses real-life applications in order to teach the concepts involved in mathematical modeling. Year-long major – offered at the basic, regular, and honors levels; prerequisites Algebra I, Geometry
TOPICS IN PRECALCULUS
Topics in Precalculus focuses on the most essential topics in Precalculus with the aim of laying a solid foundation for the further study of calculus. Considerable emphasis is placed on strengthening students’ algebraic skills and deepening their understanding of the core conceptual ideas. The unifying theme of this course is the analysis of functions – polynomial, rational, exponential, logarithmic, and trigonometric – through graphical, numerical, and symbolic perspectives. Wherever possible, students are exposed to the application of these functions in modelling real-world phenomena. Graphing calculators are required and will be used extensively throughout the year. Year-long major – prerequisite Algebra II / Trigonometry
HONORS PRECALCULUS CONT.
By the end of the year, students will be able to comprehend how the graph of a tangent line, the slope written as a difference quotient, and the instantaneous rate of change attained through limits all relate to the notion of the first derivative. Honors Precalculus AB prepares students to advance to AP Calculus AB the following year. Honors Precalculus BC, which moves at an accelerated pace and covers additional topics (mathematical induction, properties of limits, probability, matrices, parametric equations, and the area under the curve) prepares students to advance to AP Calculus BC. Graphing calculators are required and are used extensively throughout the year. Year-long major – by permission of the department; prerequisite Algebra II / Trigonometry
CALCULUS
Calculus serves as an appropriate capstone course for those students who are considering further study of science, engineering, technology, finance, or other field not necessarily exclusively mathematical. The syllabus includes a review of the topics from algebra, trigonometry, and analytical geometry that are necessary for success in the course and contains an in-depth coverage of most of the topics normally taught in the first semester and part of the second semester of a three-semester college calculus sequence. Year-long major – prerequisite Precalculus
PRECALCULUS
This course is designed to further students’ algebraic development and mathematical thinking by laying a strong foundation for the further study of calculus. The unifying theme of this course is the analysis of functions – polynomial, rational, exponential, logarithmic, and trigonometric – through graphical, numerical, and symbolic perspectives. Wherever possible, students are exposed to the application of these functions in modelling realworld phenomena. If time permits, additional topics include sequences and series, polar coordinates, complex numbers, and vectors. A key concept of calculus, the first derivative, is introduced utilizing the difference quotient. Graphing calculators are required and are used extensively throughout the year.
AP CALCULUS AB
Year-long major – prerequisite Algebra II / Trigonometry
Year-long major – by permission of the department
HONORS PRECALCULUS
AP CALCULUS BC
Designed to prepare the student to advance to AP Calculus or a similar rigorous course in college, students entering this course should demonstrate independence of thought, creativity in problem solving, and intellectual curiosity. In addition to the topics mentioned in Precalculus, the following concepts are supplemented in Honors Precalculus: conic sections, advanced trigonometry, inverse relations, and an introduction to limits.
Calculus AB follows the Advanced Placement curriculum outlined by the College Board and is comparable to a college-level calculus course. The prerequisites outlined by this curriculum should be covered before or during the course. The course focuses on developing students’ understanding of the concepts of calculus and providing experience with its methods and applications. The course emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. The connections among these representations also are important. The course prepares students for the AP Calculus AB examination.
Calculus BC is an extension of Calculus AB rather than an enhancement; the common topics require a similar depth of understanding. While most students come from Calculus AB, that course is not a prerequisite. Students taking Calculus BC should have covered all the prerequisites outlined by the Advanced Placement curriculum before taking the course. The course prepares students for the AP Calculus BC examination. Year-long major – by permission of the department
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