Hello, I am a freshman in High School currently, I am in precalculus. I am intending to skip Calculus I over the summer. I know my school will test me with the AB Calculus APexam and I was planning on taking Calculus I through Columbia University's Summer Session. Will this be enough preparation, and will I be able to do well in Calculus II next year? Here is my High Schools Course Descriptions of Calc I and II "Description: AP Calculus I/AB is a rigorous college-level course which emphasizes a multirepresentational approach to calculus, with concepts, results, and problems being expressed geometrically, numerically, analytically, and verbally. Topics covered include the initial review of pre-calculus topics, limits, differentiation and its applications, and integration and its applications. There is an emphasis on problem solving, working collaboratively, and communicating mathematically in both written and oral form. Graphing calculators are used in class on a daily basis and are provided by the school. Since this is an Advanced Placement college-level course, students are expected to spend a considerable amount of time outside of class in homework preparation and daily studying. An Advanced Placement exam will be given through the College Board in May." "Description: Calculus II is a rigorous college level course that emphasizes a multirepresentational approach to calculus. Students learn to express mathematical concepts geometrically, numerically, analytically, and verbally. As a continuation of Calculus I, topics covered in this class include applications and techniques of integration, L’Hopitals’ Rule, improper integrals, an introduction to differential equations, infinite series and sequences, conic sections, parametric and polar equations. Students who enroll in Calculus II will be expected to participate in a collaborative learning environment. As in Calculus I, problem solving and mathematical communication in written and oral form are an essential component of this course. Graphing calculators are utilized extensively and are provided by the school. Calculus II is an Advanced Placement, college level course. Therefore, all students are expected to spend considerable time outside of class in homework preparation and daily study. An Advanced Placement exam will be given through the College Board in May." Columbia's Description of Calculus I "Course Description: Functions, limits, derivatives, introduction to integrals." and a sample syllabus http://www.math.columbia.edu/department/syllabi/CalcIsyllabus.html Thanks For your input! And if anyone has experience with Columbia's Summer Session, Private Message me por favor.