August 6-9, 2012

Location: Palos Verdes Peninsula High School

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Calculus BC

Taught by Larry Peterson

Outline

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.

Agenda

  • Pre-Calculus Review
    • Summer worksheet
    • Calculator activities
  • Student Activities
    • Card match
    • Calculus Reaction Course
    • Relay races
  • Anti-Derivatives
    • Differential equations
    • Slope fields
    • Euler's method
    • Logistic growth functions
  • The Definite Integral
    • Fundamental Theorem of Calculus
    • Accumulation functions
      • Area using rectangular functions
      • Area using polar functions
      • Vector functions
  • Series
    • Power series
    • Taylor series
    • Maclaurin series
    • Interval and radius of convergence
    • Testing for convergence at endpoints
  • Vectors, Parametric Functions, and Polar Functions
    • Tangent lines
    • Particle motion
    • Arc length
    • Area
  • Preparing for the AP Exam
    • Time lines
    • The AP Philosophy
    • Past Exams