Grand Traverse Academy 2018-19 Secondary Course Catalog 19 Mathematics Algebra I (Grade 9) It is expected that students entering Algebra I are able to recognize and solve mathematical and real-world problems involving linear relationships, and to make sense of and move fluently among the graphic, numeric, symbolic, and verbal representations of these patterns. Algebra I builds on this increasingly generalized approach to the study of functions and representations by broadening the study of linear relationships, to include systems of equations with three unknowns, formalized function notation, and the development of bivariate data analysis topics such as linear regression and correlation. In addition, their knowledge of exponential and quadratic function families is extended and deepened with the inclusion of topics such as rules of exponentiation (including rational exponents) and use of standard and vertex forms for quadratic equations. Students will also develop their knowledge of power (including roots, cubics, and quartics) and polynomial patterns of change and the applications they model. In addition to deepening and extending students’ knowledge of the algebra strand, Algebra I also draws upon and connects to topics related to number and geometry by including the formalized study of the real number system and its properties, and by introducing elementary number theory. Geometry (Grade 10) Prerequisite: Algebra I Students studying Geometry in high school further develop analytic and spatial reasoning. They apply what they know about two-dimensional figures to three- dimensional figures in real-world contexts, building spatial visualization skills and deepening their understanding of shape and shape relationships. Geometry includes a study of right triangle trigonometry that is developed through similarity relationships. These topics allow for many rich real-world problems to help students expand geometric reasoning skills. It is critical that connections are made from algebraic reasoning to geometric situations. Connections between transformations of linear and quadratic functions to geometric transformations should be made. Earlier work in linear functions and coordinate graphing leads into coordinate Geometry. The study of formal logic and proof helps students to understand the axiomatic system that underlies mathematics through the presentation and development of postulates, definitions, and theorems. It is essential that students develop deductive reasoning skills that can be applied to both mathematical and real-world problem contexts. Algebra II (Grade 11) Prerequisite: Algebra I The goal of Algebra II is to build upon the concepts taught in Algebra I and Geometry while adding new concepts to students’ repertoire of mathematics. In Algebra I, students studied the concept of functions in various forms such as linear, quadratic, polynomial, and exponential. Algebra II continues the study of exponential and logarithmic functions and further enlarges the catalog of function families to include rational and trigonometric functions. In addition to extending the algebra strand, Algebra II will extend the numeric and logarithmic ideas of accuracy, error, sequences, and iteration. The topic of conic sections fuses algebra with geometry. Students will also extend their knowledge of univariate and bivariate statistical applications. Functions, Statistics & Trigonometry (Grade 12) Prerequisite: Algebra II This is the fourth-year course for the college-bound or highly skilled workforce-bound student who has completed Algebra I, Geometry and Algebra II. Content presents topics from these three areas in a unified way to help students prepare for everyday life, with business applications. This is a class that is geared towards preparing students to have a better foundation for any college math class they may have to take. This course covers many things the students have seen in Algebra II but is used to expand on particular concepts. Pre-Calculus (Grade 11 or 12) Prerequisite: Algebra II Calculus is a powerful, useful, and versatile branch of mathematics. While the core ideas of calculus (derivatives and integrals) are not hard to understand, calculus is a demanding subject because it requires a broad and thorough background of algebra and functions. Study of the topics, concepts, and procedures of pre-calculus is very strongly recommended for all college-bound students. These topics, concepts, and procedures are prerequisites for many college programs