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代数练习：三项式公式应用

代数练习：三项式公式应用
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2024-07-01 17:17
数列
所属专题 Binomische Formeln
该范例演示了三项式公式的推导、图形化展示和应用。涉及的核心数学概念包括三项式公式、代数表达式和练习。使用了GeoGebra命令如Element、Join、Sort等进行构造。适合7-8年级的学生学习和练习。

GeoGebra 命令及参数

  1. Element(Auswahl, questionCount) → randomQuestion
  2. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order01
  3. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(3\:a \cdot 4\:b \cdot 4\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:a + 4\:b\right) \cdot 2\)\vphantom{gb²}}$", "$\textsf{\(3\:a + 4\:b\)\vphantom{gb²}}$", "$\textsf{\(9\:a² + 24\:a\:b + 16\:b²\)\vphantom{gb²}}$"}, Order01) → dropdown01
  4. Join({Set1, Set2, Set3}) → Set123
  5. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order02
  6. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(25\:c² + 20\:a\:c + 4\:a²\)\vphantom{gb²}}$", "$\textsf{\(2 \cdot 5\:c + 2 \cdot 2\:a\)\vphantom{gb²}}$", "$\textsf{\(25\:c² - 20\:a\:c + 4\:a²\)\vphantom{gb²}}$", "$\textsf{\(25\:c² + 4\:a²\)\vphantom{gb²}}$"}, Order02) → dropdown02
  7. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order03
  8. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(4\:k² + 40\:k\:n + 100\:n²\)\vphantom{gb²}}$", "$\textsf{\(\left(2\:k\right)² + \left(10\:n\right)²\)\vphantom{gb²}}$", "$\textsf{\(2 \cdot 2\:k \cdot 10\:n\)\vphantom{gb²}}$", "$\textsf{\(2\:k \cdot 10\:n\)\vphantom{gb²}}$"}, Order03) → dropdown03
  9. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order04
  10. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(64\:g² - 48\:g\:f + 9\:f²\)\vphantom{gb²}}$", "$\textsf{\(64\:g² + 48\:g\:f + 9\:f²\)\vphantom{gb²}}$", "$\textsf{\(\left(8\:g + 3\:f\right)²\)\vphantom{gb²}}$", "$\textsf{\(8\:g²\)\vphantom{gb²}}$"}, Order04) → dropdown04
  11. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order05
  12. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(49\:y² - 28\:x\:y + 4\:x²\)\vphantom{gb²}}$", "$\textsf{\(\left(7\:y\right)² - \left(2\:x\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(7\:y + 2\:x\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(2\:x\right)² - \left(7\:y\right)²\)\vphantom{gb²}}$"}, Order05) → dropdown05
  13. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order06
  14. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(100\:u²\)\vphantom{gb²}}$", "$\textsf{\(10\:u - 3\:v\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:u + 3\:v\right)²\)\vphantom{gb²}}$", "$\textsf{\(100\:u² - 60\:u\:v + 9\:v²\)\vphantom{gb²}}$"}, Order06) → dropdown06
  15. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order07
  16. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(4\:k + 2\:l\right) \cdot \left(4\:k - 2\:l\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k + 2\:l\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k\right)² + \left(2\:l\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(4\:k - 2\:l\right)²\)\vphantom{gb²}}$"}, Order07) → dropdown07
  17. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order08
  18. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(3\:b + 4\:c\right) \cdot \left(3\:b + 4\:c\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:b + 4\:c\right)\:(3\:b - 4\:c)\)\vphantom{gb²}}$", "$\textsf{\(3\:b² + 4\:c \cdot \left(3\:b - 4\:c\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(3\:b - 4\:c\right)²\)\vphantom{gb²}}$"}, Order08) → dropdown08
  19. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order09
  20. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(10\:r + 2\:s\right)²\)\vphantom{gb²}}$", "$\textsf{\(100\:r² + 2 \cdot 10\:r \cdot 2\:s - 4\:s²\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:r - 2\:s\right)\:\left(10\:r + 2\:s\right)\)\vphantom{gb²}}$", "$\textsf{\(\left(10\:r - 2\:s\right)²\)\vphantom{gb²}}$"}, Order09) → dropdown09
  21. If(randomQuestion ≟ 1, SelectedIndex[dropdown01], randomQuestion ≟ 6, SelectedIndex[dropdown06], randomQuestion ≟ 7, SelectedIndex[dropdown07], randomQuestion ≟ 8, SelectedIndex[dropdown08], SelectedIndex[dropdown09], randomQuestion ≟ 2, SelectedIndex[dropdown02], randomQuestion ≟ 3, SelectedIndex[dropdown03], randomQuestion ≟ 4, SelectedIndex[dropdown04], randomQuestion ≟ 5, SelectedIndex[dropdown05]) → actualIndex123
  22. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order10
  23. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(14 + 3,6\right)²\)\vphantom{gb²}}$", "$\textsf{\(3,6² + 14²\)\vphantom{gb²}}$", "$\textsf{\(3,6 + 14\)\vphantom{gb²}}$", "$\textsf{\(14 \cdot 3,6\)\vphantom{gb²}}$"}, Order10) → dropdown10
  24. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order11
  25. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(\left(30 - 12\right)²\)\vphantom{gb²}}$", "$\textsf{\(30² - 12²\)\vphantom{gb²}}$", "$\textsf{\(30² - 60 \cdot 12 + 12²\)\vphantom{gb²}}$", "$\textsf{\(30² - 12\)\vphantom{gb²}}$"}, Order11) → dropdown11
  26. Join({{1}, Shuffle[{2, 3, 4, 5}]}) → Order12
  27. Sort({"$\textsf{Wähle aus! \vphantom{gb²}}$", "$\textsf{\(22² - 3²\)\vphantom{gb²}}$", "$\textsf{\(19² + 3²\)\vphantom{gb²}}$", "$\textsf{\(\left(22 + 3\right)²\)\vphantom{gb²}}$", "$\textsf{\(\left(22 - 3\right)²\)\vphantom{gb²}}$"}, Order12) → dropdown12
  28. If(randomQuestion ≟ 10, SelectedIndex[dropdown10], randomQuestion ≟ 11, SelectedIndex[dropdown11], SelectedIndex[dropdown12]) → actualIndex4
  29. Textfield(InputFunc) → InputBoxFunc
  30. If(randomQuestion ≟ 23, (5.22, 1.8), (5.22, 1.98)) → PosA2
  31. Sequence(PosA2 + (k * Vector[PosA2, PosC2] / 8), k, 1, 7) → PosE22List
  32. Point(PosE22List) → PosE22
  33. Sequence(PosA2 + (k * Vector[PosA2, PosC2] / 10), k, 6, 13) → PosE23List
  34. Point(PosE23List) → PosE23
  35. If(randomQuestion ∈ Set123, actualIndex123 ≟ CorrectIndex123(randomQuestion), false, randomQuestion ∈ Set4, actualIndex4 ≟ CorrectIndex4(IndexOf[randomQuestion, Set4]), randomQuestion ∈ Set5, correctValue ∧ correctFactored ∧ correctNoSquare, randomQuestion ≟ 22, IndexOf[PosE22, PosE22List] ≟ 6, randomQuestion ≟ 23, IndexOf[PosE23, PosE23List] ≟ 5) → correct
  36. Element(randomQuestions, questionCount) → actualQuestion
  37. If(correctCount ≥ 5, (6.38, 2.6), (5, 2.6)) → PosBtnStartAgain
  38. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg041
  39. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg051
  40. Segment(PosA + ((-dis), 0), PosD + ((-dis), 0)) → seg061
  41. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg062
  42. Segment(PosD + (0, dis), PosC + (0, dis)) → seg091
  43. Segment((x(PosA), y(PosE3)) + ((-dis), 0), PosD + ((-dis), 0)) → seg092
  44. Segment(PosA2 - ((2 * dis), 0), (x(PosA2), y(PosE23)) - ((2 * dis), 0)) → seg231
  45. Segment(PosA2 - (0, (2 * dis)), (x(PosE23), y(PosA2)) - (0, (2 * dis))) → seg232
  46. If(randomQuestion ∈ Set123, actualIndex123 ≠ 1, true, randomQuestion ∈ Set4, actualIndex4 ≠ 1, randomQuestion ∈ Set5, Defined[InputFunc] ∧ (¬Defined[IndexOf[",", Text[InputBoxFunc]]]), randomQuestion ≟ 22, movedE22, randomQuestion ≟ 23, movedE23) → clickableBtnValidate
  47. Element({600, 600, 625, 600, 550, 610, 610, 610, 650}, randomQuestion) → FBSet123PixX
  48. Segment(PosASol2 + (0, -0.2), PosASol2 + ((dim * sideLength2), -0.2)) → segSol231
  49. If(randomQuestion ≟ 22, PosE22, PosE23) → ArrowCenter
  50. Rotate(Segment[ArrowCenter + (arrowDistance, 0), ArrowCenter + (arrowDistance + arrowLength, 0)], arrowAngle + ((1 - 1) * (360°) / arrowNumber), ArrowCenter) → arrow1
  51. Rotate(Segment[ArrowCenter + (arrowDistance, 0), ArrowCenter + (arrowDistance + arrowLength, 0)], arrowAngle + ((2 - 1) * (360°) / arrowNumber), ArrowCenter) → arrow2
  52. If(randomQuestion ≟ 22, ¬movedE22, randomQuestion ≟ 23, ¬movedE23, false) → showArrows
  53. PolyLine(PosSB, Corner[txtStart, 1] + (0.5, -0.05), Corner[txtStart, 2] + (0.05, -0.05), Corner[txtStart, 3] + (0.05, 0.1), Corner[txtStart, 4] + (-0.05, 0.1), Corner[txtStart, 1] + (-0.05, 0.5), PosSB) → sb00
  54. PolyLine(PosSB, Corner[txtQuestionSet1, 1] + (-0.05 + 0.5, 0.1), Corner[txtQuestionSet1, 2] + (0.05, 0.1), Corner[txtQuestionSet1, 3] + (0.05, 0.1), Corner[txtQuestionSet1, 4] + (-0.05, 0.1), Corner[txtQuestionSet1, 1] + (-0.05, 0.5), PosSB) → sb01
  55. PolyLine(PosSB, Corner[txtQuestion10, 1] + (-0.05, 0.5), Corner[txtQuestion10, 1] + (-0.05, 0.1), Corner[txtQuestion10, 2] + (0.05, 0.1), Corner[txtQuestion10, 3] + (0.05, 0.1), Corner[txtQuestion10, 4] + (-0.05, 0.1), Corner[txtQuestion10, 1] + (-0.05, 1), PosSB) → sb10
  56. PolyLine(PosSB, Corner[txtQuestion11, 1] + (-0.05, 0.5), Corner[txtQuestion11, 1] + (-0.05, 0.1), Corner[txtQuestion11, 2] + (0.05, 0.1), Corner[txtQuestion11, 3] + (0.05, 0.1), Corner[txtQuestion11, 4] + (-0.05, 0.1), Corner[txtQuestion11, 1] + (-0.05, 1), PosSB) → sb11
  57. PolyLine(PosSB, Corner[txtQuestion12, 1] + (-0.05, 2.5), Corner[txtQuestion12, 1] + (-0.05, 0.1), Corner[txtQuestion12, 2] + (0.05, 0.1), Corner[txtQuestion12, 3] + (0.05, 0.1), Corner[txtQuestion12, 4] + (-0.05, 0.1), Corner[txtQuestion12, 1] + (-0.05, 3), PosSB) → sb12
  58. PolyLine(PosSB, Corner[txtQuestionSet5, 1] + (-0.05 + 0.5, 0.1), Corner[txtQuestionSet5, 2] + (0.05, 0.1), Corner[txtQuestionSet5, 3] + (0.05, 0.1), Corner[txtQuestionSet5, 4] + (-0.05, 0.1), Corner[txtQuestionSet5, 1] + (-0.05, 0.5), PosSB) → sb13
  59. PolyLine(PosSB, Corner[txtQuestion22, 1] + (-0.05, 1.25), Corner[txtQuestion22, 1] + (-0.05, 0.1), Corner[txtQuestion22, 2] + (0.05, 0.1), Corner[txtQuestion22, 3] + (0.05, 0.1), Corner[txtQuestion22, 4] + (-0.05, 0.1), Corner[txtQuestion22, 1] + (-0.05, 1.75), PosSB) → sb22
  60. PolyLine(PosSB, Corner[txtQuestion23, 1] + (-0.05, 1.25), Corner[txtQuestion23, 1] + (-0.05, 0.1), Corner[txtQuestion23, 2] + (0.05, 0.1), Corner[txtQuestion23, 3] + (0.05, 0.1), Corner[txtQuestion23, 4] + (-0.05, 0.1), Corner[txtQuestion23, 1] + (-0.05, 1.75), PosSB) → sb23
  61. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg023
  62. Segment(PosD + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg024
  63. Segment(PosC + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg031
  64. Segment(PosD + ((-dis), 0), (x(PosA), y(PosE3)) + ((-dis), 0)) → seg071
  65. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE3)) + ((-dis), 0)) → seg072
  66. Segment(PosD + (0, dis), (x(PosE3), y(PosD)) + (0, dis)) → seg073
  67. Segment(PosC + (0, dis), (x(PosE3 + y(PosE3 - PosA)), y(PosC)) + (0, dis)) → seg074
  68. Segment((x(PosA), y(PosE3)) + (0, (-dis)), PosE3 + (0, (-dis))) → seg081
  69. Segment((x(PosB), y(PosE3)) + (0, (-dis)), PosE3 + (0, (-dis))) → seg082
  70. Segment(PosC + (0, dis), PosC - (x(PosE3 - PosA), 0) + (0, dis)) → seg083
  71. Segment(PosD + (0, dis), PosC - (x(PosE3 - PosA), 0) + (0, dis)) → seg084
  72. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE3)) + ((-dis), 0)) → seg085
  73. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg011
  74. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE12)) + ((-dis), 0)) → seg012
  75. Segment(PosD + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg021
  76. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg022
  77. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg032
  78. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg042
  79. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg043
  80. If(randomQuestion ≟ 10, 14 / 17.6, randomQuestion ≟ 11, 12 / 30, 19 / 22) → parSkizze
  81. Segment(PosSkizze + (0, dimSkizze + dis), PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis)) → segSkizze101
  82. Segment(PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis), PosSkizze + (dimSkizze, dimSkizze + dis)) → segSkizze102
  83. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze103
  84. Segment(PosSkizze + ((-dis), 0), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze104
  85. Segment(PosSkizze + (0, dimSkizze + dis), PosSkizze + ((parSkizze * dimSkizze), dimSkizze + dis)) → segSkizze111
  86. Segment(PosSkizze + (0, dimSkizze + dis + 0.65), PosSkizze + (dimSkizze, dimSkizze + dis + 0.65)) → segSkizze112
  87. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * (1 - parSkizze)))) → segSkizze113
  88. Segment(PosSkizze + ((dimSkizze * parSkizze), dimSkizze + dis), PosSkizze + (dimSkizze, dimSkizze + dis)) → segSkizze121
  89. Segment(PosSkizze + (0, dimSkizze + dis + 0.65), PosSkizze + (dimSkizze, dimSkizze + dis + 0.65)) → segSkizze122
  90. Segment(PosSkizze + ((-dis), dimSkizze), PosSkizze + ((-dis), (dimSkizze * parSkizze))) → segSkizze123
  91. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg052
  92. Segment(PosC + (0, dis), (x(PosE12), y(PosC)) + (0, dis)) → seg053
  93. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg063
  94. Segment((x(PosA), y(PosE3)) + ((-dis), 0), PosA + ((-dis), 0)) → seg093
  95. Text("\textsf{\bold{Zieh mich!}}", PosE22, false, true, -1, 1) → CapZiehMich22
  96. Text("\textsf{\bold{Zieh mich!}}", PosE23, false, true, -1, 1) → CapZiehMich23
  97. Segment(PosA2 + (x((5 * Vector[PosA2, PosC2] / 10)), 0) + (0, -0.15), (x(PosE23), y(PosA2)) + (0, -0.15)) → seg233
  98. Segment(PosA2 + (0, y((5 * Vector[PosA2, PosC2] / 10))) + (-0.15, 0), (x(PosA2), y(PosE23)) + (-0.15, 0)) → seg234
  99. Segment(PosASol2 + (0, ((dim * sideLength2) * 5 / 10)) + (-0.15, 0), PosASol2 + (0, ((dim * sideLength2) * 10 / 10)) + (-0.15, 0)) → segSol232
  100. Point(Line[PosImgFuchsHappy21, xAxis]) → PosImgFuchsHappy22
  101. Join({Random[2, 2, 12], Random[1, 1, 9], {2, 2}}) → AttemptCountStartList
  102. Segment(PosD + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg013
  103. Segment(PosC + (0, dis), (x(PosE12), y(PosD)) + (0, dis)) → seg014
  104. Segment(PosA + ((-dis), 0), (x(PosA), y(PosE12)) + ((-dis), 0)) → seg033
  105. Segment(PosD + ((-dis), 0), (x(PosD), y(PosE12)) + ((-dis), 0)) → seg034

AI 绘图提示语参考

绘制一个代数练习界面，包含多个下拉选择题，每个题目展示一个代数表达式，选项为相关的展开式或因式分解形式。界面顶部有标题，下方有输入框和验证按钮。图形区域包含坐标轴和若干线段构成的几何示意，用于辅助理解公式。整体布局清晰，适合学生练习。
以上提示语为根据原始绘图命令整理而来，仅供参考。