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元素判断随机练习 - Level 2

元素判断随机练习 - Level 2
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2022-09-05 14:44
函数几何作图滑块动画
所属专题 Ⓔ Zahlenmengen
本范例演示如何从一组几何对象中随机选取并判断元素归属。核心数学概念涉及集合论中的元素判断（Element命令）、条件逻辑（If命令）以及随机排序（Shuffle命令）。作图要点：使用Polygon命令构造多个四边形对象（P0-P20），通过Textfield显示对应的文本标签（text0-text20），利用Shuffle命令对对象索引进行随机打乱，再用Element命令按顺序提取元素，最后通过If条件判断实现交互式问答效果。本练习适合中学数学课程，可用于教授集合概念、元素与集合的关系判断，以及训练学生的逻辑思维能力，也可作为信息技术与数学学科融合的实践案例。

GeoGebra 命令及参数

  1. Join({{2}, Shuffle[{5, 4, 9, 7, 3, 6, 8, 1}]}) → randomNosForBsp
  2. Polygon(A, B, C, D) → region1, a, b, c, d
  3. Polygon(E, F, G, H) → region2, e, f, g, h
  4. If(bsp ≟ 1 ∧ IsInRegion[P20, region1], true, If[bsp ≟ 5 ∧ IsInRegion[P20, region1], true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P20, region1] ∨ IsInRegion[P20, region2])), true, If[bsp ≟ 9 ∧ IsInRegion[P20, region2], true, false]]]) → correct20
  5. If(bsp ≟ 1 ∧ IsInRegion[P19, region2], true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P19, region1] ∨ IsInRegion[P19, region2])), true, If[bsp ≟ 6 ∧ IsInRegion[P19, region1], true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P19, region1] ∨ IsInRegion[P19, region2])), true, false]]]) → correct19
  6. If(bsp ≟ 1 ∧ IsInRegion[P18, region1], true, If[bsp ≟ 5 ∧ IsInRegion[P18, region1], true, If[bsp ≟ 6 ∧ IsInRegion[P18, region1], true, If[bsp ≟ 9 ∧ IsInRegion[P18, region2], true, false]]]) → correct18
  7. If(bsp ≟ 1 ∧ IsInRegion[P17, region2], true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P17, region1] ∨ IsInRegion[P17, region2])), true, If[bsp ≟ 6 ∧ IsInRegion[P17, region1], true, If[bsp ≟ 7 ∧ IsInRegion[P17, region2], true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P17, region1] ∨ IsInRegion[P17, region2])), true, false]]]]) → correct17
  8. If(bsp ≟ 1 ∧ IsInRegion[P16, region1], true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P16, region1] ∨ IsInRegion[P16, region2])), true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P16, region1] ∨ IsInRegion[P16, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P16, region1] ∨ IsInRegion[P16, region2])), true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P16, region1] ∨ IsInRegion[P16, region2])), true, false]]]]) → correct16
  9. If(bsp ≟ 1 ∧ IsInRegion[P15, region2], true, If[bsp ≟ 3 ∧ IsInRegion[P15, region2], true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P15, region1] ∨ IsInRegion[P15, region2])), true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P15, region1] ∨ IsInRegion[P15, region2])), true, If[bsp ≟ 7 ∧ IsInRegion[P15, region2], true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P15, region1] ∨ IsInRegion[P15, region2])), true, false]]]]]) → correct15
  10. If(bsp ≟ 1 ∧ IsInRegion[P14, region1], true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P14, region1] ∨ IsInRegion[P14, region2])), true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P14, region1] ∨ IsInRegion[P14, region2])), true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P14, region1] ∨ IsInRegion[P14, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P14, region1] ∨ IsInRegion[P14, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P14, region1], true, If[bsp ≟ 9 ∧ IsInRegion[P14, region1], true, false]]]]]]) → correct14
  11. If(bsp ≟ 1 ∧ IsInRegion[P13, region2], true, If[bsp ≟ 3 ∧ IsInRegion[P13, region2], true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P13, region1] ∨ IsInRegion[P13, region2])), true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P13, region1] ∨ IsInRegion[P13, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P13, region1] ∨ IsInRegion[P13, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P13, region1], true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P13, region1] ∨ IsInRegion[P13, region2])), true, false]]]]]]) → correct13
  12. If(bsp ≟ 1 ∧ IsInRegion[P12, region1], true, If[bsp ≟ 2 ∧ (¬(IsInRegion[P12, region1] ∨ IsInRegion[P12, region2])), true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P12, region1] ∨ IsInRegion[P12, region2])), true, If[bsp ≟ 4 ∧ IsInRegion[P12, region1], true, If[bsp ≟ 5 ∧ IsInRegion[P12, region2], true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P12, region1] ∨ IsInRegion[P12, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P12, region1] ∨ IsInRegion[P12, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P12, region1], true, If[bsp ≟ 9 ∧ IsInRegion[P12, region1], true, false]]]]]]]]) → correct12
  13. If(bsp ≟ 2 ∧ IsInRegion[P11, region1], true, If[bsp ≟ 3 ∧ IsInRegion[P11, region2], true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P11, region1] ∨ IsInRegion[P11, region2])), true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P11, region1] ∨ IsInRegion[P11, region2])), true, If[bsp ≟ 6 ∧ IsInRegion[P11, region2], true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P11, region1] ∨ IsInRegion[P11, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P11, region1], true, If[bsp ≟ 9 ∧ (¬(IsInRegion[P11, region1] ∨ IsInRegion[P11, region2])), true, false]]]]]]]) → correct11
  14. If(bsp ≟ 2 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 5 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 6 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P10, region1] ∨ IsInRegion[P10, region2])), true, false]]]]]]) → correct10
  15. If(bsp ≟ 2 ∧ IsInRegion[P7, region2], true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P7, region1] ∨ IsInRegion[P7, region2])), true, If[bsp ≟ 4 ∧ IsInRegion[P7, region2], true, If[bsp ≟ 7 ∧ IsInRegion[P7, region1], true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P7, region1] ∨ IsInRegion[P7, region2])), true, false]]]]) → correct7
  16. If(bsp ≟ 2 ∧ (¬(IsInRegion[P8, region1] ∨ IsInRegion[P8, region2])), true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P8, region1] ∨ IsInRegion[P8, region2])), true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P8, region1] ∨ IsInRegion[P8, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P8, region1] ∨ IsInRegion[P8, region2])), true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P8, region1] ∨ IsInRegion[P8, region2])), true, false]]]]) → correct8
  17. If(bsp ≟ 2 ∧ IsInRegion[P9, region1], true, If[bsp ≟ 3 ∧ (¬(IsInRegion[P9, region1] ∨ IsInRegion[P9, region2])), true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P9, region1] ∨ IsInRegion[P9, region2])), true, If[bsp ≟ 6 ∧ IsInRegion[P9, region2], true, If[bsp ≟ 7 ∧ IsInRegion[P9, region1], true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P9, region1] ∨ IsInRegion[P9, region2])), true, false]]]]]) → correct9
  18. If(bsp ≟ 2 ∧ IsInRegion[P5, region2], true, If[bsp ≟ 3 ∧ IsInRegion[P5, region1], true, If[bsp ≟ 4 ∧ IsInRegion[P5, region2], true, If[bsp ≟ 7 ∧ IsInRegion[P5, region1], true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P5, region1] ∨ IsInRegion[P5, region2])), true, false]]]]) → correct5
  19. If(bsp ≟ 2 ∧ IsInRegion[P4, region2], true, If[bsp ≟ 3 ∧ IsInRegion[P4, region1], true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P4, region1] ∨ IsInRegion[P4, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P4, region2], true, false]]]) → correct4
  20. If(bsp ≟ 2 ∧ (¬(IsInRegion[P3, region1] ∨ IsInRegion[P3, region2])), true, If[bsp ≟ 3 ∧ IsInRegion[P3, region1], true, If[bsp ≟ 4 ∧ IsInRegion[P3, region2], true, If[bsp ≟ 8 ∧ (¬(IsInRegion[P3, region1] ∨ IsInRegion[P3, region2])), true, false]]]) → correct3
  21. If(bsp ≟ 2 ∧ IsInRegion[P6, region2], true, If[bsp ≟ 3 ∧ IsInRegion[P6, region1], true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P6, region1] ∨ IsInRegion[P6, region2])), true, If[bsp ≟ 7 ∧ (¬(IsInRegion[P6, region1] ∨ IsInRegion[P6, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P6, region2], true, false]]]]) → correct6
  22. If(bsp ≟ 1 ∧ IsInRegion[P1, region1], true, If[bsp ≟ 2 ∧ (¬(IsInRegion[P1, region1] ∨ IsInRegion[P1, region2])), true, If[bsp ≟ 4 ∧ IsInRegion[P1, region2], true, false]]) → correct1
  23. If(IsInRegion[P0, region1] ∨ IsInRegion[P0, region2], false, true) → correct0
  24. If(bsp ≟ 2 ∧ (¬(IsInRegion[P2, region1] ∨ IsInRegion[P2, region2])), true, If[bsp ≟ 4 ∧ (¬(IsInRegion[P2, region1] ∨ IsInRegion[P2, region2])), true, If[bsp ≟ 8 ∧ IsInRegion[P2, region2], true, false]]) → correct2
  25. Textfield(aInput) → InputBox1
  26. Textfield(bInput) → InputBox2
  27. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  28. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {7, 9, 5, 6, 9, 1, 2, 10, 5, 0, 4, 5, 10, 3, 2, 2, 4, 9, 10, 7, 2, 2, 0, 4, 8, 8, 2, 1, 0, 4, 3, 6, 3, 10, 0, 9, 10, 2, 0, 9, 5, 8, 7, 5, 7, 6, 0, 8, 7, 9, 4, 9, 7, 5, 5, 7, 9, 1, 5, 6, 6, 3, 8, 4, 0, 9, 5, 0, 5, 3, 6, 5, 3, 1, 10, 9, 8, 6, 3, 9, 3, 6, 5, 9, 6, 9, 1, 0, 6, 4, 6, 2, 2, 9, 3, 5, 6, 4, 3, 2}
  29. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  30. If(bsp ≟ 3 ∨ bsp ≟ 6 ∨ bsp ≟ 8, Pos2, Pos1) → Position1
  31. If(bsp ≟ 2 ∨ bsp ≟ 5, Pos4, Pos3) → Position2

AI 绘图提示语参考

创建两个四边形，随机打乱编号并依次检查编号对应的点是否在四边形内，通过条件判断显示结果，并用文本框输入答案，根据答案反馈绘制正确答案的矩形。
以上提示语为根据原始绘图命令整理而来，仅供参考。