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AP Calculus BC

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 BC 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. Students with AP Calculus BC examination credit are generally awarded 2 semesters of College Calculus credit.

Access the site below to view the course description from the College Board:

http://apcentral.collegeboard.com/apc/public/repository/ap08_calculus_coursedesc.pdf

Major Topics:

Segment 1:

  • 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
  • Logarithmic 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
  • 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: Euler’s Method
  • Differential Equations: Growth and Decay
  • Differential Equations: Logistic Equations
  • Differential Equations: Separation of Variables

Segment 2:

  • Applications of Integration
  • Area of Region between Two Curves
  • Volume: Disk Method
  • Volume: Shell Method
  • Arc length
  • Work
  • Basic Integration Rules
  • Integration by Parts
  • Integration using Partial Fractions
  • Indeterminate Forms and L'Hopital's Rule
  • Improper Integrals
  • Sequences
  • Series and Convergence
  • Integral Test and p-series
  • Comparison of Series
  • Alternating Series
  • Ratio and Root Test
  • Taylor Polynomials and Approximations
  • LaGrange Error
  • Power Series
  • Representation of Functions by Power Series
  • Taylor and Maclaurin Series
  • Plane Curves and Parametric Equations
  • Differentiation and Integration of Parametric Equations
  • Arclength of a curve described by parametric equations
  • Polar Coordinates and Polar Graphs
  • Area and Arc length in Polar Coordinates
  • Vector-valued Functions
  • Differentiation and Integration of Vector-valued functions
  • Velocity and Acceleration: motion
  • Tangent and Normal Vectors
  • Arclength of a vector valued function
  • 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.

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Course Details

  • Course Code:
  • Course Credits: 2.0

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

Estimated Completion:
2 segments / 32-36 weeks