cheat page sketchpad

Geometer's Sketchpad Done & Old Stuff

Notes & TOC    Listed by Focus    Listed Alphabetically    Old Stuff    GSPfa21.htm
Summer 2021, Fall 2022 New Stuff
Backstory webpage

Before Precalc
  • line   -- line segment by dragging & by coordinates, midpoint, distance formula, point-slope equation, perpendicular, parallel lines
  • 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 Polynomial and Rational Functions Right Triangle & Trig Mixed Calculus
  • absement.gsp -- nth derivatives -- absity, absement, displacement,velocity, acceleration, jolt, jounce, ...
  • Der.Anti.Tool.gsp --
  • JUSTdots.gsp -- antiderivative by cumulation function through dots
  • fX.f'X.f''X.intX.gsp  -- function, first derivative, Reimann Sums to areas, areas to antiderivatives
    The Lecture Version of fX.f'X.f''X.intX.gsp
    fX.f'X.f''X.intX.gsp - The Derivative & Antiderivative Sketchpad Teacher's Manual
    0 - Table of Contents, Links , A Function, Its Derivative, Its Antiderivative
    1 - Take a limit analytically by approach.
    2 - limit as a goes
    3 - emojis & f' by m of tangent
    4 - trig derivatives w/memory trick
    5 - partition & sums 4 boxes
    6 - Reimann & Sums
    7 - n=8 RightLM
    8 - Sums f(x) - g(x), input a, b
    9 - CUMULATIVE AREA probability fx
    10 - HISTORY sum to integral
    11 - INTEGRATION only, + c
    12 - INTEGRATION FTI FTII
    13 - g(x)
    14 - EXTRA Notes on integration by dots
  • 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
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 Reimann Sums & Antiderivatives
  • Intro2AntiDerivative.gsp
  • 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
  • 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
    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
  • 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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