This is a course designed to prepare students for Calculus or AP Calculus. The focus of this course will be to help the students develop the higher-level thinking skills needed to apply their mathematical knowledge to problems beyond the classroom. The first week will be spent honing their algebraic skills before launching into the world of functions and graph analysis. They will continue with a study of inverse functions, composite functions, and mathematical modeling, solving problems involving Hooke’s Law for springs, refrigeration, and cost. An in-depth examination of quadratic functions will provide the girls with a working knowledge of the position function and how it is applied to velocity and height of an object above the ground. Polynomials of higher degrees, rational functions, and inequalities will augment the students' understanding of the importance of domain and range as they apply these concepts to problems relating to population, economics, and enrollment. Previous concepts of inverse and composite functions will be needed for the exciting study of exponential and logarithmic functions as the girls delve into practical applications of bacteria growth, radioactive decay, earthquake magnitudes, depreciation, inflation, population growth, and compound interest.
The course will culminate with a rigorous study of trigonometry during which time the girls will become familiar with The Unit Circle and its relationship to the real numbers and the six trigonometric functions. They will be able to identify and sketch the graphs of all six functions, solve practical problems involving right triangles, verify all types of trigonometric identities, and ultimately solve a variety of trigonometric equations.
Prerequisites: Algebra II and Geometry