Learning Recommendations: Designed for students who earned a C+ or better in AP Calculus AB or have easily excelled on assessments in Pre-Calculus and want a rigorous, fast-paced mathematical course. Students must have a strong foundation in algebra and pre-calculus math concepts, the ability and desire to solve challenging problems, the capacity to think quickly, critically, and creatively, the willingness to persevere through intellectual challenges, and the dedication to both learn material quickly and deeply, and work independently to master that material.
General Description: This one-year course develops the topics of limits, derivatives, integration, polynomial approximations and series, and their formulas for algebraic and transcendental functions. This class follows the College Board AP Calculus BC course guidelines, which covers topics in the AP Calculus AB course, and develops the topics beyond that course for preparation of the AP Calculus BC exam.
I. Functions, Graphs, and Limits
- Analysis of graphs
- Limits of functions
- Parametric, polar, and vector functions
- Concept of the derivative
- Derivative at a point
- Derivative as a function
- Second derivatives
- Applications of derivatives
- Computation of derivatives
- Interpretations and properties of definite integrals
- Applications of integrals
- Fundamental Theorem of Calculus
- Techniques of antidifferentiation
- Numerical approximations to definite integrals
IV. Polynomial Approximations and Series
- Concept of Power Series
- Taylor and Maclaurin Series
- Convergence of Series
Strategies: Students will learn through a combination of:
- Teacher-Centered (direct instruction or demonstrative)
- Learner-Centered (discovery or inquiry-based)
- Interactive (participation/group work)
Homework: Homework for this class is nightly practice problems. Work done at home can vary between 15 minutes - 45 minutes depending on the student (memory recall, lesson understanding, prior course, etc.). Studies suggest that daily small doses of practice is better for learning math. Practice problems revisit and expands concepts learned in math class in order to solidify the learning. Homework Quizzes will assess students' knowledge and ability to apply learning from daily homework practice problems.
Course Fee / Materials: Graphing calculator required. The TI-84 is recommended. Fee for the AP Exam.
AP courses at IHS challenge students with rigorous college-level work. By succeeding in college-level work while still in high school, students in AP courses develop confidence in their own abilities and learn essential time management and study skills needed for college and career success.
AP courses provide the opportunity for students to earn college credits. In order to earn college credit, students must register for the AP exam for this course. AP exam fees vary each year. Scholarships are available for students who qualify. AP exam registration takes place in September and October. College credit can be earned with a passing score on the AP exam, but what the score qualification and amount of credit earned varies by college.