This course is for students who previously completed Calculus AB. The course provides a brief review of Calculus AB and an extended study of the subsequent Calculus BC topics plus extensive preparation for the AP Calculus BC exam. In this course, calculus is explored using multiple representations including analytic, algebraic, numerical, graphical, and technological techniques. Students will examine the limit and continuity of functions along with the two main functions of calculus: the derivative and the integral. Derivatives will be explored as a point and as functions, along with second derivatives and applications in optimization, linearization, and related rates. Interpretations and properties of integration will be presented, including Riemann’s Sums and applications of motion, area under curves, and volumes of unusual shapes. The Fundamental Theorem of Calculus will be used for analytical and graphical analysis of functions. Students will investigate infinite series and polynomial approximations using Taylor and Maclaurin series, vector-valued functions, and polar curves. Students will also practice AP-style questions to familiarize themselves with the format and grading techniques. The teacher will reinforce commonly difficult concepts, address general concept questions, strengthen weak areas, host collaborative problem-solving among the students, and provide additional AP prep problems.