Whether teaching calculus at the introductory or AP level, at a high school or college, there is no better way to explore this rich study of movement and change than through interactive animation.  Calculus In MotionTM animations are packaged on a CD-ROM (the basic license is for 1 computer, but other licenses also are available).  They perform equally well on either the Windows or Macintosh platform.  Although a detailed instruction manual is included on the CD-ROM (PDF format), most of the animations can be successfully run simply using the on-screen information.
NOTE:   The animations are data files written in The Geometer’s Sketchpad so Sketchpad must reside on your computer for the files to run – see full explanation in “Requirements” on the home page.

Galleries below are titled:
Arc Length
Area Between 2 Curves
Def. of a Derivative / Def. of Integrations / Inverse Functions
Graphers
Limits & Continuity
Maclaurin & Taylor Series
Optimization
Related Rates
Riemann Sums
Slope Fields & Euler’s Method
Theorems
Volumes on a Base
Volumes by Revolution
Animations to AP Calculus AB & BC Exams’ Released Free Response Questions 2018-1997  (Jump to FRs)

 

ARC LENGTH
Develop the idea of arc length using any f(x), parametric, or polar curve & any number of partitions.

 

AREA BETWEEN 2 CURVES
Sweeping horizontally or vertically, the first animation explains the main idea, then 8 specific examples
follow with changeable intervals, and finally, 2 animations (one for vertical sweeps and one for horizontal)
you can enter any desired curves as well as the boundaries of integration.

 

DEFINITION OF A DERIVATIVE  ~  DEFINITION OF INTEGRATION  ~  INVERSE FUNCTIONS

 

GRAPHERS
Explore slope using animated tangent lines. See any desired combination of f ‘, f ‘’, area, and F.
“Morph” each graph using sliders. A 7th animation (not shown below) allows the user to enter any
desired function and applies all of the same animated features to it. (*also for precalculus)

 

LIMITS AND CONTINUITY
Explore the ε, ∂ definition of limits and the definition of continuity.
Evaluate the limits (full, left-hand or right-hand) of any function (including piece-wise defined) as x →a or as x→±∞

 

 

MACLAURIN AND TAYLOR SERIES
Enter any f(x). Overlay a Maclaurin or Taylor Series polynomial of degree n & use it to approximate the value of f(x) at any point t. Vertical gray bands show where the power series is within a chosen tolerance to f(x). As n increases, the band widens.

 

 

OPTIMIZATION
Interact with various classic applications to find the most, lerasdy, cheapest, fastest, etc.
Graphed data includes tangent line & derivative analysis.

RELATED RATES
A click of a button advances time to commence the action to these classic problems.
Other buttons reveal the values and graphs of the rates.

 

RIEMANN SUMS
Choose rectangles using left endpoints, right endpoints, or midpoints; or trapezoids to approximate an integral for any number
partitions from 1 to 80!  Functions can be morphed by dragging sliders, or use the first page to type in any desired function for f(x).

 

SLOPE FIELDS & EULER’S METHOD
To introduce what a slope field is, use the graph of f ’ to see its values controlling a gliding dynamic “slope column”.
Snapshots of this column are the slope field. A tangent segment “pilots” the field to draw f.
Once understood, a different animation allows any differential equation to be entered and generates the slope field.
Manually follow the field to draw f or use Euler’s Method (includes explanation of E.M. and numerical table of data). Easily adjustable.

 

THEOREMS
Mean-Value Theorem for Derivatives, Mean-Value Thm. for Derivatives vs. Rolle’s Thm., Intermediate-Value Theorem
Mean-Value Theorem for Integrals (a little game),1st Fundamental Theorem of Calculus (a visual proof)
Connect the 1st FTC to both Mean-Value Theorems

 

VOLUMES ON A BASE
Visualize these shapes one step at a time. Start by rotating the xy-plane to horizontal.
View a few stationary slices, then a sweeping slice, and finally, an accumulating slice.
Rotate the solid any time for other viewing angles. Choose from an assortment of bases and cross-sections.

 

VOLUMES BY REVOLUTION
These animations cover both the disk/washer technique and the cylindrical shell technique.
Develop the process by first revolving one lone rectangle. Next, revolve several rectangles in a region and stack or nest the results.
Finally, revolve any desired region (bounded by 1 or 2 functions of choice) on an interval of choice, about any horizontal or vertical axis.

—-

 

169 ANIMATIONS OF AP CALCULUS AB & BC EXAMS’
RELEASED FREE RESPONSE QUESTIONS  2018 – 1997

Click below to link to AP Central for statements of the Free Response Questions from the exams for …

AP CALCULUS AB 2017 & 2018          AP CALCULUS AB 2016 & older

AP CALCULUS BC 2017 & 2018          AP CALCULUS BC 2016 & older

2018

2017  animations to AP Calculus AB/BC Exams’ FRs

2016  animations to AP Calculus AB/BC Exams’ FRs

2015  animations to AP Calculus AB/BC Exams’ FRs

2014  animations to AP Calculus AB/BC Exams’ FRs

2013  animations to AP Calculus AB/BC Exams’ FRs

2012  animations to AP Calculus AB/BC Exams’ FRs

2011  animations to AP Calculus AB/BC Exams’ FRs

2010  animations to AP Calculus AB/BC Exams’ FRs

2009  animations to AP Calculus AB/BC Exams’ FRs

2008  animations to AP Calculus AB/BC Exams’ FRs

2007  animations to AP Calculus AB/BC Exams’ FRs

 

2006  animations to AP Calculus AB/BC Exams’ FRs

 

2005  animations to AP Calculus AB/BC Exams’ FRs

 

2004  animations to AP Calculus AB/BC Exams’ FRs

 

2003  animations to AP Calculus AB/BC Exams’ FRs

 

2002  animations to AP Calculus AB/BC Exams’ FRs

 

2001  animations to AP Calculus AB/BC Exams’ FRs

 

2000  animations to AP Calculus AB/BC Exams’ FRs

 

1999  animations to AP Calculus AB/BC Exams’ FRs

 

1998  animations to AP Calculus AB/BC Exams’ FRs

 

1997  animations to AP Calculus AB/BC Exams’ FRs

 

 

 

 

 

Close Menu