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High AP Calculus BC

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Pre Requisites

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

Description

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, and integration of algebraic, trigonometric, and transcendental functions; the applications of derivatives and integrals; infinite series; parametric equations; and polar equations.

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.

Access the site link below to view the course description from the Florida Course Code directory.

http://www.cpalms.org/Public/PreviewCourse/Preview/117          

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

Segment 1:

  • Review of Function Terminology and More
  • Graphing Calculators
  • Compositions and Transformations of Functions
  • Some Common Functions
  • Introduction to Limits
  • Properties of Limits
  • Limits Involving Infinity
  • Continuity
  • Applications of Limits
  • The Derivative
  • Rules of Differentiation
  • Trigonometric Derivatives and the Chain Rule
  • Inverse Functions
  • Exponential and Logarithmic Functions
  • Derivatives of Exponential, Logarithmic, and Inverse Trig Functions
  • Implicit Differentiation
  • Analyzing Functions Part I: Curve Sketching
  • Analyzing Functions Part II: Maximums and Minimums
  • Applied Maximum and Minimum Problems
  • Distance, Velocity, Acceleration, and Rectilinear Motion
  • Related Rates
  • The Mean-Value Theorem and L'Hôpital's Rule
  • Linearization
  • Area Approximation and Riemann Sums
  • Introduction to the Definite Integral
  • The Fundamental Theorem of Calculus
  • Integrals and Antiderivatives
  • Integration by Substitution
  • The Definite Integral
  • Finding the Area Under and Between Curves
  • Volume by Discs (Slicing)
  • Average Value of a Function and Rectilinear Motion Revisited

Segment 2:

  • Differential Equations – An Introduction
  • Initial Value Problems and Slope Fields 
  • Numerical Approximation Methods with Integrals
  • Exploring the Graphs of f, f Prime, and f Double Prime
  • Relative Rates of Growth
  • Using Calculus with Data in a Table
  • Functions Defined by Integrals
  • Integration by Parts
  • Integration Using Partial Fractions
  • Improper Integrals
  • Parametric Curves
  • Polar Curves
  • Vector Curves
  • Length of Planar Curves
  • Area of Planar Curves (Polar Curves only)
  • Series
  • Convergence
  • Tests for Convergence Part I
  • Tests for Convergence Part II
  • Error Bound
  • Maclaurin Series
  • Taylor Series and Error Bound
  • Power Series
  • Radius and Interval of Convergence of Power Series
  • AP Exam Review and Test Taking Tips and Practice

 

Calculator approved for use on the AP exam
http://apstudent.collegeboard.org/apcourse/ap-calculus-bc/calculator-policy

Study Forge- Provided within the course.