## AP Calculus Favorite web sites

Essence of Calculus: Great conceptual videos (they show why, not explain problems)

www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

Geogebra applets for Calculus, use Internet Explorer (try draw a graph of a derivative)

http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html

Get A Five, online practice, videos, practice tests

https://www.getafive.com/

Video Lectures by chapter/lesson for AP Calculus

http://www.centerofmath.org/video_ap.html

Khan Academy: videos on zillions of math topics

http://www.khanacademy.org/

Videos for Calculus (try #46, L'Hopital's Rule)

http://online.math.uh.edu/HoustonACT/videocalculus/

In particular, construct a derivative graph by estimating slopes of tangent lines

http://www.khanacademy.org/exercises?exid=derivative_intuition

Lots of interactive math

http://interactivemaths.net

Awesome site, huge, need to pick out specific applets

www.merlot.org

Student written wiki on AP Calculus topics

http://hkiscalc.wetpaint.com/

The Moving Man, download, needs Java

Flash movies explaining limit, continuity, IVT and derivative rules

http://www.calculus-help.com/funstuff/phobe.html

Nice applets on limits, derivatives and integration. Good for volumes of revolution. I like the graphical product rule, but students may find it complex

http://www.ies.co.jp/math/products/calc/menu.html

Nice lesson on IVT (go on to next lesson, too) with self-checking concept questions

http://oregonstate.edu/instruct/mth251/cq/Stage4/Lesson/IVT.html

Flash movies explaining limit, continuity, IVT and derivative rules

http://www.calculus-help.com/funstuff/phobe.html

Continuity of piece-wise defined functions,

http://www.mathdemos.org/mathdemos/piecewise/piecewise_continuity.html QuickTime movie

http://www.mathdemos.org/mathdemos/piecewise/Examples/Java_continuity.html Java applets

10 examples, print out equations, Launch MultiGraph applet, choose example at top of window, slide parameters to make the graph continuous

Instantaneous Rate of Change

https://www.youtube.com/watch?v=jTvTthjtIrk

Definition of Derivative, graphically

http://mathdemos.gcsu.edu/mathdemos/defofderiv/

ID-2/3

The Big Derivative Puzzle

https://www.univie.ac.at/moe/tests/diff1/ablerkennen.html

Scroll down to secants and tangents. I like the secant line behavior for non-differentiable functions. Also look at zooming in on a tangent line. Further down the page, check out a differentiable nowhere function.

www.math.psu.edu/dna/graphics.html

Motion along a line. Illustrations, explorations and problems about distance and velocity. Particularly recommended for students who are not taking physics.

http://webphysics.davidson.edu/physlet_resources/physlet_physics/contents/mechanics/one_d_kinematics/default.html

http://www.calculus-help.com/funstuff/phobe.html , chapter two, lesson 5, chain rule

Graphical visualization of derivative of inverse sin function

http://www.mph.net/coelsner/JSP_applets/InvFunThm.htm

Differentiability of piece-wise defined functions

https://www.desmos.com/calculator/c21eqg16lx

motion in 2D, design a roller coaster

http://www.funderstanding.com/k12/coaster/

Mean Value Theorem for Derivatives

http://www.teacherlink.org/content/math/interactive/flash/rolle/rolle.html

nice lesson on MVT with self-checking concept questions

http://oregonstate.edu/instruct/mth251/cq/Stage7/Lesson/MVT.html

Related Rates

http://mathdemos.gcsu.edu/relatedrates/relatedrates.html

Minimum Time for Different Terrains

http://illuminations.nctm.org/ActivityDetail.aspx?ID=124

I Will Derive Music Video

http://scienceblogs.com/purepedantry/2008/08/calculus_humor.php

Riemann sums applet, includes L, R, M, Trap and Simpson’s Rule

http://www.slu.edu/classes/maymk/Riemann/Riemann.html

Visualizing the Mean Value Theorem for Integrals

http://math.dartmouth.edu/~klbooksite/appfolder/403unit/MVTIntegrals.html

Graphing Antiderivatives: accumulation functions

http://www.math.uri.edu/~bkaskosz/flashmo/antplot/

Slope fields

http://alamos.math.arizona.edu/ODEApplet/JOdeApplet.html

Select JODE applet, then slope fields for f(x,y)

Awesome applet for slope fields, you can draw a solution curve atop the slope field, it will compute the actual curve, it will show the family of curves, can choose preset diff. eqns or input your own

http://math.dartmouth.edu/~klbooksite/appfolder/301unit/SlopeField.html

Integral ApplicationsVolumes of revolution: Disks

http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_16a.htm

Volumes of revolution: Washers

http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_18a.htm

http://higheredbcs.wiley.com/legacy/college/anton/0470183454/applets/ch6/figure6_2_13/washer_ex4.htm

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2washer.htm

Common cross-sections:

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2xsection1.htm

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2xsection2.htm

http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/other/myXSection.htmVolumes of Known Cross Sections

http://mathdemos.gcsu.edu/sectionmethod/sectiongallery.html

Student Models of Volumes of Known Cross Sections

http://www.dade.k12.fl.us/msprings/skoski/calc/

Volumes of Revolution – disk method

http://mathdemos.gcsu.edu/diskmethod/diskmethod.html

Gallery of Shapes for volumes of revolution

http://mathdemos.gcsu.edu/diskmethod/diskmethodgallery.html

Washers

http://mathdemos.gcsu.edu/washermethod/

Short movies of graphical concepts, not interactive, not a lot of options , use for areas and volumes of revolutions, also has polar graphs

http://clem.mscd.edu/~talmanl/MathAnim.html

I like Volume of solid of revolution 2, slides showing volume of rotation with washers around a vertical line (not the y-axis), not interactive

http://www.convergesoftware.com/ choose slide shows, manual,

Download Winplot, an awesome, free, graphing program, graphs in 2D or 3D, graphs explicit and implicit functions and differential equations (slope fields)

http://math.exeter.edu/rparris/winplot.html

General Winplot tutorial

http://www2.spsu.edu/math/Dillon/Peanutdocs/GaWinPlotTutorial.pdf

Winplot: graph a solid with known cross sections

After graphing the 2 curves that form the base (use y = 0 for the x-axis if necessary) go to the pull down list called "TWO" and click on "Sections" and fill in the things there. Then click on "See Solid" and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.

Winplot: graph solids of revolution

Under the "ONE" list you can choose "Revolve Surface" to see solids of revolution and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.

Mean Girls video clip (http://www.youtube.com/watch?v=oDAKKQuBtDo) pause at 1:07 to see the function, limit as x --> 0 (ln (1-x) - sin x)/ (1 - (cos x)^ 2)

Operation Mother Hen (http://motherhen.eng.buffalo.edu) features streaming video clips of an instructor as she solves problems that illustrate basic calculus concepts, with close-ups of the problem so that students can see what she's doing as she explains. Math 141 is Calc AB with area/volume in Math 142. Math 142 continues with Calc BC topics. RealPlayer (free download) required.

Calculus on the Web (COW). You can register your class, they work on certain problems you've assigned, and you get a report of problems completed. Its EXCELLENT practice with immediate feedback for students - and easy for you to grade! Good practice for skill problems, step by step breakdowns

http://cow.math.temple.edu/

Stuff You Need to Know Cold

http://fc.woodberry.org/~david_mcrae/BC_Cal/apindex.html

Same sheet in color

http://cs3.covenantchristian.org/bird/Smart/Calc1/StuffMUSTknowColdNew.htm

Flash cram sheet, includes some non-AP Calc AB stuff

http://www.calculus-help.com/funstuff/cheatsheet.html

Problem of the week archive

http://www.calculus-help.com/oldproblems.html

Review questions and solutions by topic, both multiple choice and free response, great model cards

http://www.livebinders.com/shelf/search_author?terms=ryanjgrady

Calculus Carols

http://www.calculus-help.com/funstuff/carols.html

Calculus songs, poems and carols

http://www.wildstrom.com/susan/songs.htm

Here's a website for some songs.

http://homework.zendog.org/songsfall2004.html

www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

**GENERAL**Geogebra applets for Calculus, use Internet Explorer (try draw a graph of a derivative)

http://webspace.ship.edu/msrenault/GeoGebraCalculus/GeoGebraCalculusApplets.html

Get A Five, online practice, videos, practice tests

https://www.getafive.com/

Video Lectures by chapter/lesson for AP Calculus

http://www.centerofmath.org/video_ap.html

Khan Academy: videos on zillions of math topics

http://www.khanacademy.org/

Videos for Calculus (try #46, L'Hopital's Rule)

http://online.math.uh.edu/HoustonACT/videocalculus/

In particular, construct a derivative graph by estimating slopes of tangent lines

http://www.khanacademy.org/exercises?exid=derivative_intuition

Lots of interactive math

http://interactivemaths.net

Awesome site, huge, need to pick out specific applets

www.merlot.org

Student written wiki on AP Calculus topics

http://hkiscalc.wetpaint.com/

**Motion Simulations**The Moving Man, download, needs Java

**Limits**Flash movies explaining limit, continuity, IVT and derivative rules

http://www.calculus-help.com/funstuff/phobe.html

Nice applets on limits, derivatives and integration. Good for volumes of revolution. I like the graphical product rule, but students may find it complex

http://www.ies.co.jp/math/products/calc/menu.html

**Continuity**Nice lesson on IVT (go on to next lesson, too) with self-checking concept questions

http://oregonstate.edu/instruct/mth251/cq/Stage4/Lesson/IVT.html

Flash movies explaining limit, continuity, IVT and derivative rules

http://www.calculus-help.com/funstuff/phobe.html

Continuity of piece-wise defined functions,

http://www.mathdemos.org/mathdemos/piecewise/piecewise_continuity.html QuickTime movie

http://www.mathdemos.org/mathdemos/piecewise/Examples/Java_continuity.html Java applets

10 examples, print out equations, Launch MultiGraph applet, choose example at top of window, slide parameters to make the graph continuous

Instantaneous Rate of Change

https://www.youtube.com/watch?v=jTvTthjtIrk

**Intro to Derivatives****ID-1**Definition of Derivative, graphically

http://mathdemos.gcsu.edu/mathdemos/defofderiv/

ID-2/3

The Big Derivative Puzzle

https://www.univie.ac.at/moe/tests/diff1/ablerkennen.html

**ID-4**Scroll down to secants and tangents. I like the secant line behavior for non-differentiable functions. Also look at zooming in on a tangent line. Further down the page, check out a differentiable nowhere function.

www.math.psu.edu/dna/graphics.html

**ID-9**Motion along a line. Illustrations, explorations and problems about distance and velocity. Particularly recommended for students who are not taking physics.

http://webphysics.davidson.edu/physlet_resources/physlet_physics/contents/mechanics/one_d_kinematics/default.html

**More Derivatives****MD-2**http://www.calculus-help.com/funstuff/phobe.html , chapter two, lesson 5, chain rule

**MD-6**

Visualization and proof of derivative of inverses

webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_inverse_functions.htmlVisualization and proof of derivative of inverses

webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_inverse_functions.html

Graphical visualization of derivative of inverse sin function

http://www.mph.net/coelsner/JSP_applets/InvFunThm.htm

**MD-8**Differentiability of piece-wise defined functions

https://www.desmos.com/calculator/c21eqg16lx

**Derivative Applications I**motion in 2D, design a roller coaster

http://www.funderstanding.com/k12/coaster/

**Derivative Applications II**Mean Value Theorem for Derivatives

http://www.teacherlink.org/content/math/interactive/flash/rolle/rolle.html

nice lesson on MVT with self-checking concept questions

http://oregonstate.edu/instruct/mth251/cq/Stage7/Lesson/MVT.html

Related Rates

http://mathdemos.gcsu.edu/relatedrates/relatedrates.html

Minimum Time for Different Terrains

http://illuminations.nctm.org/ActivityDetail.aspx?ID=124

I Will Derive Music Video

http://scienceblogs.com/purepedantry/2008/08/calculus_humor.php

**Definite Integrals**Riemann sums applet, includes L, R, M, Trap and Simpson’s Rule

http://www.slu.edu/classes/maymk/Riemann/Riemann.html

Visualizing the Mean Value Theorem for Integrals

http://math.dartmouth.edu/~klbooksite/appfolder/403unit/MVTIntegrals.html

Graphing Antiderivatives: accumulation functions

http://www.math.uri.edu/~bkaskosz/flashmo/antplot/

**Differential Equations and Modeling**Slope fields

http://alamos.math.arizona.edu/ODEApplet/JOdeApplet.html

Select JODE applet, then slope fields for f(x,y)

Awesome applet for slope fields, you can draw a solution curve atop the slope field, it will compute the actual curve, it will show the family of curves, can choose preset diff. eqns or input your own

http://math.dartmouth.edu/~klbooksite/appfolder/301unit/SlopeField.html

Integral ApplicationsVolumes of revolution: Disks

http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_16a.htm

Volumes of revolution: Washers

http://higheredbcs.wiley.com/legacy/college/mccallum/0470131586/applets/ch8/hh_fig_8_18a.htm

http://higheredbcs.wiley.com/legacy/college/anton/0470183454/applets/ch6/figure6_2_13/washer_ex4.htm

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2washer.htm

Common cross-sections:

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2xsection1.htm

http://web.monroecc.edu/manila/webfiles/pseeburger/secure/MyLarson/ch7/LC7_2xsection2.htm

http://web.monroecc.edu/manila/webfiles/calcNSF/JavaCode/other/myXSection.htmVolumes of Known Cross Sections

http://mathdemos.gcsu.edu/sectionmethod/sectiongallery.html

Student Models of Volumes of Known Cross Sections

http://www.dade.k12.fl.us/msprings/skoski/calc/

Volumes of Revolution – disk method

http://mathdemos.gcsu.edu/diskmethod/diskmethod.html

Gallery of Shapes for volumes of revolution

http://mathdemos.gcsu.edu/diskmethod/diskmethodgallery.html

Washers

http://mathdemos.gcsu.edu/washermethod/

Short movies of graphical concepts, not interactive, not a lot of options , use for areas and volumes of revolutions, also has polar graphs

http://clem.mscd.edu/~talmanl/MathAnim.html

I like Volume of solid of revolution 2, slides showing volume of rotation with washers around a vertical line (not the y-axis), not interactive

http://www.convergesoftware.com/ choose slide shows, manual,

Download Winplot, an awesome, free, graphing program, graphs in 2D or 3D, graphs explicit and implicit functions and differential equations (slope fields)

http://math.exeter.edu/rparris/winplot.html

General Winplot tutorial

http://www2.spsu.edu/math/Dillon/Peanutdocs/GaWinPlotTutorial.pdf

Winplot: graph a solid with known cross sections

After graphing the 2 curves that form the base (use y = 0 for the x-axis if necessary) go to the pull down list called "TWO" and click on "Sections" and fill in the things there. Then click on "See Solid" and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.

Winplot: graph solids of revolution

Under the "ONE" list you can choose "Revolve Surface" to see solids of revolution and you'll get a 3D picture that can be rotated with the arrow keys on your keyboard.

**L'Hopital's Rule**Mean Girls video clip (http://www.youtube.com/watch?v=oDAKKQuBtDo) pause at 1:07 to see the function, limit as x --> 0 (ln (1-x) - sin x)/ (1 - (cos x)^ 2)

**Review**Operation Mother Hen (http://motherhen.eng.buffalo.edu) features streaming video clips of an instructor as she solves problems that illustrate basic calculus concepts, with close-ups of the problem so that students can see what she's doing as she explains. Math 141 is Calc AB with area/volume in Math 142. Math 142 continues with Calc BC topics. RealPlayer (free download) required.

Calculus on the Web (COW). You can register your class, they work on certain problems you've assigned, and you get a report of problems completed. Its EXCELLENT practice with immediate feedback for students - and easy for you to grade! Good practice for skill problems, step by step breakdowns

http://cow.math.temple.edu/

Stuff You Need to Know Cold

http://fc.woodberry.org/~david_mcrae/BC_Cal/apindex.html

Same sheet in color

http://cs3.covenantchristian.org/bird/Smart/Calc1/StuffMUSTknowColdNew.htm

Flash cram sheet, includes some non-AP Calc AB stuff

http://www.calculus-help.com/funstuff/cheatsheet.html

Problem of the week archive

http://www.calculus-help.com/oldproblems.html

Review questions and solutions by topic, both multiple choice and free response, great model cards

http://www.livebinders.com/shelf/search_author?terms=ryanjgrady

**Calculus Songs**Calculus Carols

http://www.calculus-help.com/funstuff/carols.html

Calculus songs, poems and carols

http://www.wildstrom.com/susan/songs.htm

Here's a website for some songs.

http://homework.zendog.org/songsfall2004.html