cheat page sketchpad

Geometer's Sketchpad Done & Old Stuff

Notes & TOC    Listed by Focus    Listed Alphabetically    Old Stuff    GSPfa21.htm

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Summer 2021 - Fall 2023 New Stuff
Backstory webpage

Before Precalc
  • line   -- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
    -- slide points A and B and generate equation of the line in 4 forms.
    -- computes slopes and writes lines by sliding and by parameters
    1 - drag segment endpoints to compute midpoint and distance
    2 - show how the distance formula computes
    3 - find a perpendicular w/input coordinates
    4 - find parallel w/input coordinates
  • 2graphs.gsp  -- 1,2 graphed functions, piece-wise, composite ready to edit, link to "coordinate" and more history, table of f(x) gps files
  • make.hexagon.gsp -- construct a hexagon, and also consider other polygons w/a look towards pi
Functions, Lines, Circles
  • Cartesian -- definition and analytic history web page
  • ssong.gsp -- slope from history, to sound, to words & numbers, through examples, to computation
    0 - toc, history
    1 - only 1 function
    2 - parabola w/tangent line
    3 - cubic w/tangent line
    4 - polynomial
    5 - rational
    6 - compute slope drag 2 points
    7 - dy/dx by definition
    8 - m= given A, B
    9 - 3 points define a parabola
    10 - notes on 3 points define a parabola
  • circle.tangent.normal.gsp
    1 drag center & radius 2 create equation
    2 enter h, k, r
    3 perpendicul w/input coordinates
    4 slide tangent then compute & write
  • circleFormula.gsp --
  • inverse.gsp
    0 - vertical, horizontal line tests
    1 - square root fx
    2 - any function
    3 - sqrt fx by parameters
    4 - restricted domain on inverse
    5 - arcsine
    6 - arctangent
    7 - f and inverse
    8 - f, inverse, tangents --
Polynomial and Rational Functions
  • compositeFX.gsp --
  • parabola.gsp --
  • compositeFx.poly.ratl.gsp
    0 - graph of 1 function
    1 - graphs of 2 functions
    2 - composite of 4 functions
    3 - polynomial. links to polynomial, dilations gif, quatratic.htm, equation, discriminant
    4 - rational, rational function features & how to find them
    5 - end behavior, battle of (Ax^m)/(Bx^n)
Right Triangle & Trig
  • standardPosition.gsp
    1 standard position angle central angle, negative & positive angle measures
    2 angles coterminal?
  • radianSector.gsp
    1 intro angles degrees radians
    2 radian questions
    3 arc length angular speed sector area
    4 sector and area
  • veronica.gsp
    1 - 1 standard position angle
    2 - angles coterminal?
    3 - 1 veronica angles -- trig fx of angles is 4 quadrants
    4 - 2 veronica angles
    5 - extra 2 veronica angles
  • elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
Calculus
Limits
  • limit   -- limit by epsilon-delta, by dragging x, by approach from L & R, by table
    0 -The Modern Evolution of Limit and Its Symbols
    1 - approach by dragging x
    2 - by above & below x
    3 - table of x, f(x), f'(x), f''(x) w/tangent line
    4 - limit, as x goes to infinity, (Ax^m)/(Bx^n) battle pix, emd behavior
    5 - limit as h goes to 0, derivative by limit of difference quotient
    6 - by solpe of secant
    7 - webpage sample epsilon-delta
    8 - simple sample limit questions
    9 - by epsilon-delta
    10 - Squeeze to take a limit, link to proof Dx(sin(x) = cos(x)
  • limh4Dx.gsp
  • limitWquestions.gsp
Derivatives
      Derivatives Web Page
  • DerAnyFx.gsp
    1 - fx w/tangent line & tan line equation
    2 - sqrt(x) & TRACE
    3 - sqrt(x), tan, TRACE f '(x)
    4 - EMOJI, x, fx, f'x f''x, tan line
    5 - table, x, fx, f'x, f''x
  • emoji.gsp
    0 - toc - Links to: dictionary, algebra notes, precalc notes, calc 1 notes
    1 - f' by tangent, x, fx, f'x, f''x
    2 - trig f' by tangent, x, fx, f'x, f''x
    3 - polynomial
    4 - rational
          http://www.mathnstuff.com/math/gsp/sumr19/su19newgsp/fX.f'X.f''X.intX.dy.gsp
  • 3
    0 - resources including: derivative definition, calc cheat sheet, link to derivative calculator, link to integration calculator, derivative connect-the-dots, integration connecet-the-dots
    1 - f'(x), tan line, TRACE f'(x), table
    2 - Leibnitz, Newton pix
    3 - limit as h goes to 0
    4 - no table x, f(x), f'(x), f''(x), tangent line included
    5 - build table x, f(x), f'(x), f''(x)
    6 - hand-plot sums
    7 - extra hand-plot
    8 - auitomatic 2 fx plot
    9 secant images, link to wikipedia
  • Mean.Rolle.f'(x).f''(x).gsp
    0 - by secant & lim as h --> 0 of DQ
    1 - fx w/tangent line
    2 - just c on interval
    3 - tan line f(x), f'(x), f''(x)
    4 - f, f', TRACE, table
    5 - sine emoji, w/tan & trace, f', f''
    6 - fx tan & trace emoji, f f', f''
    7 - Mean Value Theorem. slide [a,b]
    8 - Roll's Theorem, slide [a, b]
    9 - derivative tests, f, f', f'', emoji
    10 - s(t), s'(t), s''(t), RED
    11 - no table x, fx, f'x, f''x
    12 - extra Rolle's
    13 - x,f,f',f'',RIGHT&LEFT
  • tracef.f1.f2.f3.f4.gsp
  • DerAnyFx.gps -- Derivative of Any Function
    * One may trace the function and see coordinates displayed.
    * One may edit the function.
    * One may graph the approximate derivative function.
    1 - f(x) w/tangent line
    2 - f(x) & TRACE
    3 - any f(x): x, f(x), f'(x), f''(x)
    4 - sin(x): x, f(x), f'(x), f''(x)
  • tracef.f1.f2.f3.f4.gsp
  • derivativeTests.gsp
  • DERlnx.gsp --
  • for related rates, use elevation.gsp - angle of elevation, depression, ladders w/h(x), y(x), and h(y), x(y), and h as variable, and h s a constant
Reimann Sums & Antiderivatives
  • Intro2AntiDerivative.gsp
    0 - intro relation between sum and integral. Includes link to
          http://www.mathnstuff.com/math/gsp/sumr19/su19newgsp/ReimannSums.gsp
    0.5 - summary notation.
    1 - partition
    2 - subscript x0 start
    3 - subscript x1 start
    4 - left boxes n=4, x0
    5 - Reimann sums
    6 - see n [a,b]
    7 - int(x) plus c
    8 - by plotint(x) green dots
    9 - extra - h(x) input [a,b]
  • fX.f'X.f''X.intX.dy.gsp
    0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
    1 - limit by approach
    2 - limit as h goes
    3 - emoju&f' by m of tan line
    4 - trig derivatives trick
    5 - partition & sums 4 boxes
    6 - Reimann & sums
    7 - n=8 RLM
    8 - sums f(x) - g(x)
    9 - cummulative prob distr
    10 - HISTORY sum to integral
    11 - INTEGRATION only 1st + c
    12 - INTEGRATION FTCI FTCII
    13 - f(g) INTEGRATION
    14 - EXTRA Notes on integration by dots
  • fX.f'X.f''X.intX.gsp
    0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
    1 - limit by approach
    2 - limit as h goes
    3 - emoju&f' by m of tan line
    4 - trig derivatives trick
    5 - partition & sums 4 boxes
    6 - Reimann & sums
    7 - n=8 RLM
    8 - sums f(x) - g(x)
    9 - cummulative prob distr
    10 - HISTORY sum to integral
    11 - INTEGRATION only 1st + c
    12 - INTEGRATION FTCI FTCII
    14 - EXTRA Notes on integration by dots
  • fX.f'X.f''X.intX.dy.gsp
    0 - toc - dx, graphing; derivitive.htm; Reimann.gsp & notes; intro 2 anti, calculators;
    1 - limit by approach
    2 - limit as h goes
    3 - emoji &f' by m of tan line
    4 - trig derivatives trick
    5 - partition & sums 4 boxes
    6 - Reimann & sums
    7 - n=8 RLM
    8 - sums f(x) - g(x) input [a,b]
    9 - cummulative prob distr
    10 - HISTORY sum to integral
    11 - INTEGRATION only 1st + c
    12 - INTEGRATION FTCI FTCII
    13 - f(g) INTEGRATION
    14 - EXTRA Notes on integration by dots
  • ReimannSums.gsp -- partitions, boxes, area by sum, antiderivative by dots
    Reimann Boxes & Sums, and Integration Teacher's Manual contains:
    0 - toc
    1a - background limit by approach
    1b - LIMIT by definition, secant
    1c - partition
    1d - 1st page notes
    1e - 2nd page notes
    2 - PARTITION & SUMS 4 boxes
    3a - REIMANN & SUMS
    3b - subscript x1 start
    4 - n=8 RLM
    5 - Hump areas
    6 - area f(x)- g(x), input [a,b] in the boxes for a and b
    6b - probability distribution
    7 - sum to integral
    8 - INTEGRATION only 1st plus c
    8a - building the points (xi, sumi)
    8b - Notes green dots integration
  • absement.gsp -- the nth derivatives of displacement
    "Absement and 'nth Derivatives of Displacement' Presented Dynamically & Analytically" at MATYCNJ- MAA-NJ Joint Meeting, Kean University contains:
    0 - toc
    0 - 1 - time, t
    0 - 2 - displacement, distance, s(t)
    0 - 3 - definition of derivative
    0 - 4 - s(t), s'(t)
    0 - 5 - s(t), s'(t), s''(t)
    0 - 6 - emojis, f, f', f'', tangent line
    0 - 7 - trace derivatives
    0 - 8 - PARTITION & SUMS 4 boxes
    0 - 9 - Reimann & Sums
    0 - 10 - SUMS absement, input [a,b]
    0 - 11 - absement, n=32
    0 - 12 - absement plus c
    0 - 13 - play absement plus c
    0 - 14 -arcsine actual fx graphed
    0 - 15 - arcsine mesh - useF(x) plot to plot arcsine
  • JUSTdots.gsp -- Plots points on an antiderivative, no support pages
  • Justderivatives.gsp -- derivatives by definition, by tangent line, by traces of f', f'', f''', f''' (ideal for the trig cycle and for y=ex)
  • JUSTdotsWreview.gsp -- Plots points on an antiderivative, includes some support pages


Listed by Focus - INCOMPLETE LIST
    Before Precalc
  • starPix   -- one clean picture with just 5-pointed stars
  • STARS   -- 4-, 5-, 6-pointed stars with instructions
  • complsuppl   -- just complementary & supplementary angles
  • transversal   -- corresponding, alternate interior, vertical angles and a transversal
  • circleFormula   -- writes the formula for the depicted circle
  • circleTangent   -- writes the tangent to a given circle
  • distance   -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
  • NewCentral   -- An angle in standard position.
  • polyLengthArea   -- polygon pictures, notes on area and length measurement
  • table   -- build and edit a table of data
  • trace   -- creates point defined by an x-intercept and a calculated value for y of point
    then traces the path of the point controlled by the x-intercept
    Functions, Lines, Circles
  • 2graphs.gsp  -- 1,2 graphed functions, piece-wise, composite ready to edit
  • absValu.gsp  -- 2 absolute value functions controlled by parameters
  • sqrt   -- 2 square root functions defined by easy-edit parameters
  • line   -- slide points A and B and generate equation of the line in 4 forms.
  • [[x]].gsp -- greatest integer function, also a[[bx+c]] + k
  • piecewise   -- graphs a piecewise defined function when left function and right function and the x-value for the boundary are edited -- endpoints are not shown.
  • parentFX   -- function "manipulatives" -- curve shift to graph functions, many functions provided
  • parentFX2   -- revised function "manipulatives"
  • generator   -- used to make the parent function sketch pad
  • compositeFX.gsp  -- build 2 functions using other functions
  • inverse.gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
  • GraphGivenCircle   -- Graph a circle by graphing + and - functions defined by parameters.
        * Also states equation of circle.
    Polynomial and Rational Functions
  • parabola   -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,
        * both generated by equations defined by parameters.
        * WITH SHOW/HIDE ACTION BUTTON
        * graphs of 2 parabolas: 1 in general form, 1 in standard forms,
        * 1 parabola, set a, then generat parabola w/2 points.
        * 1 parabola controlled by 3 points, used for determinant analysis
        * 1 vertical axis of symmetry, 1 horizontal "axis of symmetry
  • TracePoly   -- drag point f(x) to state and show new ( x, f(x))
  • recipfx   -- graph of parameter-defined reciprocal function,
        * with slide-able tangent line,
        * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
    Transendentals, Exponentials, Logs
  • logs   -- Multi page: 2 logs, log w/exponential
  • Dere2x -- Derivative of the exponential
  • Derlnx -- Derivative of the Natural Log
  • e2xSums -- The Antiderivative of ex
    Right Triangle Trig
  • cosplay   -- just right triangle cosine
  • TraceSin   -- just graph with a slideable point to display coordinates
  • sinplay   -- just right triangle sine
  • tanplay   -- just right triangle cosine
    Unit Circle and Identities
  • unitfx   -- 6 functions with a unit circle
  • unitSinCosTriangle   -- sine & cosine functions with a unit circle
  • unitTanSec   -- tangent & secant functions with a unit circle
  • unitCotCsc   -- cotangent & cosecant functions with a unit circle
  • Pythagorean   -- using only figure to adjust angle
  • PythagorIdentities   -- using either figure or parameter theta to adjust angle
    Trig
  • 2TrigGraphs.gsp  -- 1 blank function, 1 parameter-driven function on a "trig plane"
  • sinplay   -- just right triangle sine
  • cosplay   -- just right triangle cosine
  • tanplay   -- just right triangle tangent
  • TraceSin   -- drag point f(x) to state and show new ( x, f(x))
  • TraceCos   -- drag point f(x) to state and show new ( x, f(x))
  • TraceTan   -- just graph with a slideable point to display coordinates
  • SinCosTan1stDay   -- Just sine, cosine, tangent of right triangle angles.
  • SinCosTan6fx   -- All 6 functions in right triangle only.
  • SinCosTanAllNumbers   -- All 6 functions in right triangle and forall numbers,
        * controlled by figure for right triangle,
        * parameter-defined angle measure in degrees for all measures, and
        * parameter-defined angle measure in decimal number times pi for radian measures
  • sinNcos.gsp   -- sine and cosine in right triangle only
  • 2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison also h(x) = sine + cosine
  • SinTraceDerSums -- Sine from many views, right triangle, ABCD, derivative, antiderivative
  • polar.gsp -- r()=asin(b -c)+d
    Limits
  • limit   -- take a limit by dragging x -- drag x and see where f(x) is going or by epsilon-delta
    Derivatives
  • derivativeTests -- Derivative Tests & DerAnyFx
  • DerAnyFx -- Derivative of Any Function
  • DerCos -- Derivative of Cosine
  • Dere2x -- Derivative of the exponential
  • Derlnx -- Derivative of the Natural Log
  • DerReciprocal -- Derivative of the Reciprocal Function
  • DerSqrt -- Derivative of the Square Root
  • limh4Dx   -- Really shows the derivative is the limit of the direrence quotient. Use this one!!
  • DerReciprocal   -- by use of a tangent line
  • DerAnyFx   -- a function is graphed w/tangent line.
        * One may trace the function and see coordinates displayed.
        * One may edit the function.
        * One may graph the approximate derivative function.
  • DERe2x   -- by use of a tangent line
  • DerSqrt   -- simple curve and tangent. Could make it fancy.
  • DerSquare   -- simple graph w/tangent of x2. Could make it fancy.
    Trig Derivatives
  • DerCos   -- cosine graph, movable tangent line w/equation,
        * m derived by simple m formula (h=.01),
        * "derivative" may be graphed.
  • DerivCos   -- display cosine graph and entire difference quotient triangle (not the best)
  • DerivSin   -- full blown 4-page sketches ** Use this
  • DerSin   -- simple sine and tangent line. Use other DerivSin.
  • DerTan   -- tangent function & tangent line graphed, actual derivative function is provided & may be graphed.


Listed Alphabetically - INCOMPLETE LIST
  • 2graphs.gsp  -- 2 graphed functions ready to edit
  • 2parabolas.gsp  -- one in standard form, one in general form
  • 2 Sine Functions -- Asin(Bx-C) + D on 2 functions for comparison also h(x) = sine + cosine
  • 2TrigGraphs.gsp  -- 1 blank function, 1 parameter-driven function on a "trig plane"
  • absValu.gsp  -- 2 absolute value functions controlled by parameters
  • circleFormula   -- writes the formula for the depicted circle
  • circleTangent   -- writes the tangent to a given circle
  • complsuppl   -- just complementary & supplementary angles
  • compositeFX.gsp  -- build 2 functions using other functions
  • conics   -- circle, ellipse, hyperbola, eccentricity, parabola, family of parabolas, animation of "a," the parabola dilator
  • cosplay   -- just right triangle cosine
  • DerAnyFx -- Derivative of Any Function
  • DerCos -- Derivative of Cosine
  • Dere2x -- Derivative of the exponential
  • derivativeTests -- Derivative Tests & DerAnyFx
  • Derlnx -- Derivative of the Natural Log
  • DerReciprocal -- Derivative of the Reciprocal Function
  • DerSin -- Derivative of the Sine
  • DerSqrt -- Derivative of the Square Root
  • DerSquare -- Derivative of the Square
  • DerTan -- Derivative of the Tangent
  • DerAnyFx   -- a function is graphed w/tangent line.
        * One may trace the function and see coordinates displayed.
        * One may edit the function.
        * One may graph the approximate derivative function.
  • DerCos   -- cosine graph, movable tangent line w/equation,
        * m derived by simple m formula (h=.01),
        * "derivative" may be graphed.
  • DERe2x   -- by use of a tangent line
  • DerivCos   -- display cosine graph and entire difference quotient triangle (not the best)
  • DerivSin   -- full blown 4-page sketches ** Use this
  • DERlnx   -- by use of a tangent line
  • DerReciprocal   -- by use of a tangent line
  • DerSin   -- simple sine and tangent line. Use other DerivSin.
  • DerSqrt   -- simple curve and tangent. Could make it fancy.
  • DerSquare   -- simple graph w/tangent of x2. Could make it fancy.
  • DerTan   -- tangent function & tangent line graphed, actual derivative function is provided & may be graphed.
  • distance   -- start w/a segment, coordinatize it, build triangle, use Pythagorean Theorem to find distance
  • e2xSums -- The Antiderivative of ex
  • elevation   -- angles of elevation and depression and geometry on angle created by transversal
  • generator   -- used to make the parent function sketch pad
  • GraphGivenCircle   -- Graph a circle by graphing + and - functions defined by parameters.
        * Also states equation of circle.
  • [[x]].gsp -- greatest integer function, also a[[bx+c]] + k
  • inverse.gsp -- take an inverse of an invertable fdunction, horizontal & vertical line tests
  • limit   -- take a limit by dragging x -- drag x and see where f(x) is going or by epsilon-delta
  • limh4Dx   -- Really shows the derivative is the limit of the direrence quotient. Use this one!!
  • line   -- slide points A and B and generate equation of the line in 4 forms.
  • logs   -- Multi page: 2 logs, log w/exponential
  • NewCentral   -- An angle in standard position.
  • parabola   -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,
        * both generated by equations defined by parameters.
        * WITH SHOW/HIDE ACTION BUTTON
        * graphs of 2 parabolas: 1 in general form, 1 in standard forms,
        * 1 parabola, set a, then generat parabola w/2 points.
        * 1 parabola controlled by 3 points, used for determinant analysis
        * 1 vertical axis of symmetry, 1 horizontal "axis of symmetry
  • parentFX   -- function "manipulatives" -- curve shift to graph functions, many functions provided
  • parentFX2   -- revised function "manipulatives"
  • piecewise   -- graphs a piecewise defined function when left function and right function and the x-value for the boundary are edited -- endpoints are not shown.
  • polar.gsp -- r()=asin(b -c)+d
  • polyLengthArea   -- polygon pictures, notes on area and length measurement
  • Pythagorean   -- using only figure to adjust angle
  • PythagorIdentities   -- using either figure or parameter theta to adjust angle
  • radianSector   -- arc length, sector area, radians
  • recipfx   -- graph of parameter-defined reciprocal function,
        * with slide-able tangent line,
        * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER!
  • ReimannSumANSWERS.pdf -- answers only to student notes/questions
  • ReimannSumNotes.pdf -- for taking notes in class and 4 questions (graphics included)
  • ReimannSums.gsp -- n=8 and 32 LEFT, RIGHT, MIDPOINT slide [a,b] and set [a,b]
  • SinCosTan1stDay   -- Just sine, cosine, tangent of right triangle angles.
  • SinCosTan6fx   -- All 6 functions in right triangle only.
  • SinCosTanAllNumbers   -- All 6 functions in right triangle and forall numbers,
        * controlled by figure for right triangle,
        * parameter-defined angle measure in degrees for all measures, and
        * parameter-defined angle measure in decimal number times pi for radian measures
  • sinNcos.gsp   -- sine and cosine in right triangle only
  • sinplay   -- just right triangle sine
  • SinTraceDerSum -- Sine from many views
  • sqrt   -- 2 square root functions defined by easy-edit parameters
  • starPix   -- one clean picture with just 5-pointed stars
  • STARS   -- 4-, 5-, 6-pointed stars with instructions
  • table   -- build and edit a table of data
  • tanplay -- -- just right triangle tangent
  • trace   -- creates point defined by an x-intercept and a calculated value for y of point
    then traces the path of the point controlled by the x-intercept
  • TraceCos   -- drag point f(x) to state and show new ( x, f(x))
  • TracePoly   -- drag point f(x) to state and show new ( x, f(x))
  • TraceSin   -- just graph with a slideable point to display coordinates
  • transversal   -- corresponding, alternate interior, vertical angles and a transversal
  • unitCotCsc -- Unit circle, cosine, cosecant only
  • unitTanSec -- Unit circle, tangent, secant only
  • unitSinCosTriangle-- Unit circle, sine, cosine only
  • unitfx   -- 6 functions with a unit circle


Old Stuff



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