Indiana Virtual School [Home]

AP Calculus AB

Subject: Mathematics

Course Description:

An interactive text, graphing software and math symbol software combine with the exciting on-line course delivery to make Calculus an adventure. This course is designed to prepare the student for the AP Calculus AB exam given each year in May. With continuous enrollment, students can start the course and begin working on Calculus as early as spring of the previous year!

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:

Segment 1:

  • Review of Precalculus topics, including Trigonometry
  • Finding Limits Graphically and Numerically
  • Evaluating Limits Analytically
  • Continuity and One-Sided Limits
  • Infinite Limits
  • Differentiation
  • The Derivative and Tangent Line Problem
  • Basic Differentiation Rules and Rates of Change
  • The Product and Quotient Rules and Higher Order Derivatives
  • The Chain Rule
  • Implicit Differentiation
  • Related Rates
  • Applications of Differentiation
  • Extrema on an Interval
  • Rolle's Theorem and the Mean Value Theorem
  • Increasing and Decreasing Functions and the First Derivative Test
  • Concavity and the Second Derivative Test
  • Limits at Infinity
  • Summary of Curve Sketching
  • Optimization Problems
  • Differentials and Linear Approximation

Segment 2:

  • Integration
  • Antiderivatives and Indefinite Integration
  • Area
  • Riemann Sums and Definite Integrals
  • The Fundamental Theorem of Calculus
  • Average Value of a function and the Mean Value Theorem for Integrals
  • Integration by Substitution
  • Numerical Integration
  • The Integral as a Function
  • Logarithmic, Exponential, and Other Transcendental Functions.
  • The Natural Logarithmic Function and Differentiation
  • The Natural Logarithmic Function and Integration
  • Inverse Functions
  • Exponential Functions:  Differentiation and Integration
  • Bases other than e and Applications
  • Inverse Trigonometric Functions and Differentiation
  • Differential Equations: Slope Fields
  • Differential Equations: Growth and Decay
  • Differential Equations: Separation of Variables
  • Applications of Integration
  • Area of Region between Two Curves
  • Volume: Disk Method
  • Basic Integration Rules
  • Integration Techniques
  • Indeterminate Forms and L'Hopital's Rule
  • AP Exam Review and Test Taking Tips and Practice

Participation Requirements:

Besides engaging students in challenging curriculum, INVS guides students to reflect on their learning and evaluate their progress through a variety of assessments. Assessments can be in the form of self-checks, practice lessons, multiple choice questions, free-response questions, matching questions discussion based oral assessments, and written discussions. Included throughout the course are AP style questions so that students gain practice with the AP Exam format. Instructors evaluate progress and provide interventions through the variety of assessments built into a course, as well as through contact with the student in other venues.

College Board has authorized INVS to use the AP designation. AP and Advanced Placement are registered trademarks of The College Board.

Back To Course Listings

Course Details

  • Course Code:
  • Course Credits: 2.0

Algebra I, Geometry, Algebra II, Pre-Calculus or Trigonometry/Analytical Geometry.

Estimated Completion:
2 segments / 32-36 weeks