AP Calculus AB
Pre-Requisites: Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.
Estimated Completion Time: 2 segments/32-36 weeks
Students in this course will walk in the footsteps of Newton and Leibnitz.
An interactive course framework combines with the exciting on-line course delivery to make calculus an adventure. The course includes a study of limits, continuity, differentiation, integration, differential equations, and the applications of derivatives and integrals. An Advanced Placement (AP) course in calculus consists of a full high school year of work that is comparable to calculus courses in colleges and universities. It is expected that students who take an AP course in calculus will seek college credit, college placement, or both, from institutions of higher learning.
Most colleges and universities offer a sequence of several courses in calculus, and entering students are placed within this sequence according to the extent of their preparation, as measured by the results of an AP examination or other criteria.
Major Topics and Concepts
- Properties of Limits
- Determining and Estimating Limit Values Algebraically and from Graphs and Tables
- Limits Involving Infinity
- Continuity and Discontinuity
- Intermediate Value Theorem
- Rates of Change
- The Derivative
- Rules of Differentiation
- Trigonometric, Exponential, and Logarithmic Functions
- Implicit Differentiation
- Inverse Functions
- Distance, Velocity, Acceleration, and Rectilinear Motion
- Related Rates
- L'Hôpital's Rule
- The Mean-Value Theorem
- Function Behavior and Curve Sketching
- Area Approximation and Riemann Sums
- The Fundamental Theorem of Calculus
- Introduction to the Definite Integral
- Integrals and Antiderivatives
- Integration Using Substitution
- Integration Using Long Division and Completing the Square
- Differential Equations
- Slope Fields
- Separation of Variables
- Exponential Models
- Average Value of a Function and Rectilinear Motion Revisited
- Finding the Area Under and Between Curves
- Volumes with Discs
- Volumes with Washers
- Volumes with Cross Sections
To achieve success, students are expected to submit work in each course weekly. Students can learn at their own pace; however, “any pace” still means that students must make progress in the course every week. To measure learning, students complete self-checks, practice lessons, multiple choice questions, projects, discussion-based assessments, and discussions. Students are expected to maintain regular contact with teachers; the minimum requirement is monthly. When teachers, students, and parents work together, students are successful.