AP* CALCULUS
Calculus BC
Summer Institute Outline

BC Calculus -- This Institute will focus on the Calculus curriculum as outlined by The College Board. It will include a study of the five major components: limits, rates of change, indefinite integrals, accumulation using definite integrals, and series. Because this is a BC Calculus session, the majority of time will be spent on series, vectors, and parametric functions.

We will investigate the concepts using numerical, graphical, symbolic, and verbal perspectives. Concepts and lessons that promote student understanding of major ideas will be emphasized. Each participant will receive classroom-tested worksheets, programs, and activities. Special attention will be given to assessment of written student responses in light of current AP* scoring standards. The TI-83/84 graphing calculator will be used for instruction. Each participant should bring his/her text and graphing calculator.

Pre-Calculus Review

• Summer worksheet
• Calculator activities

Limits

• Definition
  
• Representations

The Derivative

• Introduction Activity
• Graphical representation
• Difference quotients
  
• Formal definition
  
• Rules for differentiation
  

Applications of the Derivative

• Curve analysis
  
  • Max and Min
    
  • Increasing and decreasing behavior
    
  • Inflection points
    
  • Concavity
    
• Tangent and normal lines
  
  • Local linearization
    
• Optimization problems
  
• Motion in the plane
  
  • Particle motion
    
  • Parametric functions
    
  • Vector functions
• Related rates
  
• Student Activities
  
  • Card match
    
  • Calculus Reaction Course
    
  • Relay races

Anti-Derivatives

• Differential equations
  
• Slope fields
  
• Euler's method
  
• Logistic growth functions

The Definite Integral

• Riemann Sums
  
• Trapezoidal Rule
  
• Fundamental Theorem of Calculus
  
• Accumulation functions
  
  • Area using rectangular functions
    
  • Area using polar functions
    
  • Volumes of solids of revolution
    
  • Volumes of solids with known cross section
    
    • Model activity
      
• Arc length
  
• Vector Functions

Series

• Power series
  
• Taylor series
  
• Maclaurin series
  
• Interval and radius of convergence
  
• Testing for convergence at endpoints
  

Preparing for the AP* Exam

• Time lines
  
• The AP* Philosophy
  
• Past Exams

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