Learning Recommendations: Designed for students who have a B average or better on assessments in Pre-Calculus. Students must have a strong foundation in algebra and pre-calculus math concepts, the ability to problem solve, think critically and creatively, persevere through challenges, and move quickly when working. Students must have a strong foundation in algebra and precalculus math concepts, the ability to problem solve, think critically and creatively, persevere through challenges, and move quickly when working. Students should enjoy working rigorous, demanding problems, and seek out challenging their abilities.
General Description: This one-year course develops the topics of limits, derivatives, and integration and their formulas for algebraic and transcendental functions. This class follows the College Board AP Calculus AB course guidelines for preparation of the AP Calculus AB exam.
Content: Topics that students will explore and understand in the course include:
I. Functions, Graphs, and Limits
- Analysis of graphs
- Limits of functions (including one-sided limits)
- Asymptotic and unbounded behavior
- Continuity as a property of 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
- Applications of antidifferentiation
- Numerical approximations to definite integrals
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 and topic (memory recall, lesson understanding, prior course, review activity, 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 is a portion of students’ grade because the intent is to encourage practice, problem solving, and for students to receive immediate feedback, not for assessing students’ daily skill and ability.
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 December through March. 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.