This is a complete course in high school Calculus which will cover fundamental concepts and provide a solid foundation of mathematical literacy, problem solving, reasoning, and critical thinking skills that are necessary for the exploration of more advanced and rigorous topics in mathematics. Topics in Calculus include limits of functions (one-sided and two-sided limits, limits at infinity and infinite limits, limits of sequences, and continuity of functions), derivatives (various definitions of derivatives, estimating derivatives from tables and graphs, rules of differentiation, properties of derivatives, separable differential equations, and the Mean Value Theorem), applications of derivatives (related rates, optimization, and exponential growth and decay models), integrals (basic techniques of integration including basic antiderivatives and substitution), applications of integrals (in finding areas and volumes, describing motion, and as accumulation functions), and the Fundamental Theorem of Calculus. Students will explore these topics through class discussions, practice problems, and open-ended problem-solving.
Prerequisite: Students should have a solid foundation PreCalculus in order to take this class.
Level: This course is offered at two levels, Honors and Advanced Placement (AP). The scope and sequence are identical, however AP students may have additional practice problems. Students who wish to take the AP exam must register and pay for their own exam through the College Board in fall 2020 for the May 2021 exam.
Workload: Students should expect to spend 1.25-1.75 hours per day on reading, review, and homework on most non-class days. Homework assignments will run on a 13-day cycle in this class with: a new unit introduced on a Friday (day 1), lecture on Tuesday (day 6), questions and answers on the next Friday (day 8), and homework due the next Tuesday (day 13). After introduction of a new topic (day 1), students will be expected to read the assigned section and look through worked, sample problems before the lecture the following Tuesday (day 6). Solutions will be provided for some homework problems, but students are expected to show all steps of all work.
Assignments: The Canvas online class management system will be used to post assignments and scores. Students should have their own e-mail address in order to be set up as users of the Canvas system. Parents can also be set up as Canvas guests/observers for purposes of tracking the student's progress and workload.
Assessments: In this class, the instructor will assess a student's progress by checking that weekly homework sets are complete and giving periodic take-home tests; class participation is also strongly encouraged. Parents will be able to view accumulated points awarded in the class for the purpose of determining a parent-awarded course grade.
Textbook: Students should purchase or rent the required textbook for this class: Calculus: Single Variable/Early Transcendentals, 8th edition by James Stewart (ISBN-13 9781305270336). A scientific calculator similar to the Casio fx-115ES PLUS is required for this class, and it is highly recommended that students preparing for the AP exam have a graphing calculator similar to the TI-83. Students without a graphing calculator must have access to desmos.com and/or wolframalpha.com for graphing assignments.
Credit: Homeschool families may wish to count this course as a complete credit in Calculus for purposes of a high school transcript.