AP CALCULUS
PROJECTS

Sandra Halfacre, teacher
White Station High School
Memphis, Tennessee

  • PRECALCULUS TOPICS

    • The Cost of Expansion (precalculus)
    How Many Trees Fit in a Greenhouse (precalculus creating & interpreting functions)
    Into the World of Art (precalculus exponentials)
    Fire Swamps and Rodents and Snakes (Oh my) (fitting trig functions to data)
    Confusion in Beverly Hills (geometry, trigonometry)
    Sufferin' Succotash (geometry, trigonometry)
     
  • APPROXIMATING DERIVATIVES WITH TABLES

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  • DIFFERENCE QUOTIENTS

    • Terminal Velocity (difference quotients)
     
  • AVERAGE RATES OF CHANGE

    • The Case of the Dead Doornail (average velocities--average rates of change)
     
  • RELATED RATES

    • Dealing with Small Leaks (related rates)
     
  • OPTIMIZATION

    • The Continued Cost of Expansion (optimization)
    Crash Course in Calculus (optimization)
    Tunnel Vision (optimization)
    An Illuminating Project (optimization)
    Visions Spinning Around and Around (optimization)
    Facing Some Resistance (optimization)
    In and Out of the Gutter (optimization)
    When Do Newborn Babies Start to Grow (optimization)
    The Greenhouse Effect (trigonometry, optimization)
    Watch Out QVC (trigonometry, optimization)
    A Dorm Room's a Dorm Room, No Matter How Small (optimization)
    Designing a Greenhouse (geometry & optimization)
     
  • RIEMANN SUMS

    • The Area of Leaves (Riemann Sums)
    The Broad Side of the Barn (Riemann Sums to find area)
    A Question of Carpeting (Riemann Sums & Error Bounds)
    Sherlock Holmes' Train Adventure (Numerical Integration, lefthand approximation)
    Sherlock Holmes' Real Train Adventure (Numerical Integration, midpoint approximation,
                                                                              trapezoidal rule, and Simpson's rule)
     
  • FUNDAMENTAL THEOREM OF CALCULUS

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  • EXPONENTIALS

    • The General Spore (modeling exponential growth)
    The Case of the Jiggling Jello ( Newton's Law of Cooling)
    Constructing Freedom (optimization/exponentials)
    Coffee to Go (Newton's Law of Cooling)
    The Case of the Jello Jumper (Newton's Law of Cooling)
     
  • DISTANCE, VELOCITY, & ACCELERATION

    • A Bit of Profligate Consumption (distance, velocity, & acceleration integrals)
    The Case of the Dropped Baton (distance, velocity, & acceleration integrals)
    The Case of the Fall from Grace (motion and timing of a falling body)
    The Case of the Crushed Clown (projectile motion -- integrals)
    Average Height of a Weird Trapezoidal Object
     
  • VOLUME

    • The Case of the Murky Well (volume of solid of revolution)
    The Great Escape (volume by revolution)
    The Great Escape -- Volume 2 (volume by revolution)
    Experiment with volume -- demonstration
    Volume of a Water Tank I
    Volume of a Water Tank II
    Houdini's Escape
     
  • SURFACE AREA

    • Still Living in an Industrial World (surface area and work)
     
  • ARC LENGTH

    • I guess Leonardo DiCaprio was Booked (Arc-length, volume and surface area of a surface of revolution,
           Archimedes' Principal )
     
  • WORK

    • Out of the Gutter Again (work)
    Not Really a Drag (velocity and force)
     
  • DIFFERENTIAL EQUATIONS

    • Rural Agriculture in Skanebra (differential equations)
    The Case of the Falling Grapefruit (differential equations)
    The Case of the Lead Poisoning (differential equations)
    Vaporous Emissions (differential equations/exponentials)
    A Leg Up On Legal Issues (differential equations)
    Clean Up a Pollen Spill (differential equation)
     
  • SERIES

    • The Case of the Space Signal (Taylor's Polynomials)
    While Visions of Roadrunners Danced in His head (Infinite Series)
    Tripple Trouble (Sequences, Infinite Series, Differential Equations)
    Pi in the Sky (Infinite Series, Taylor Series, Estimation, Error Approximation,Taylor's Theorem with Remainder)
    The Race (Sequences, Infinite Series, Geometric Series)
    Medical Dosage (Geometric Series)
    Taylor Series Cookbook (Power Series, Taylor Series, Interval of Convergence)
    The Calculator Puzzler (Taylor Series, Taylor's Theorem)
     
  • LOGISTIC EQUATIONS

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  • PARAMETRICS

    • A Matter of Utmost Gravity (Parametric Equations in the Plane)
     
  • POLAR TOPICS

    • The Case of Darlene's Rose (area in polar coordinates)
    Roses are Violet (area in polar coordinates)
    Ya' Gotta Love Parametric Equations (Parametric & Polar Plots)
     


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    Questions or comments may be e-mailed to Mrs. Sandra L. Halfacre