Accordingly, formal logic is studied early in the course and then used throughout. Starting with undefined terms, postulates, and definitions, the students follow the progressive development of theorems and their proofs to create a mathematical structure with rich aesthetic and practical value. In building this axiomatic structure, they improve their ability to recognize and organize the various relationships among points, lines, triangles, polygons, and circles in the plane. This course also includes the study of geometry with coordinates, the solid geometry of common shapes, and transformational geometry using a computerized dynamic geometry program. The Honors sections cover the material of Geometry at a faster pace to allow time for greater depth and enrichment.
Emphasis is placed on original proofs and abstract reasoning.
After a brief review of elementary algebra, this course proceeds to the study of linear functions and relations, systems of linear equations and inequalities, graphs, polynomials and rational algebraic expressions, radicals and irrational numbers, complex numbers and polynomial functions, quadratic relations and systems, exponents and logarithms, and a substantial treatment of trigonometry. Graphing calculators are used in the course to enhance understanding and to facilitate the investigation of more sophisticated problems. These courses may lead to a calculus elective in the senior year. Using a discovery approach and developing problem-solving skills, this course addresses such advanced topics as polynomial, trigonometric, exponential, and logarithmic functions, and transformations. The more abstract topics of a traditional precalculus course are omitted.