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H2M 2019 P2 Q11: Exploring Normal Distribution and Exponential Functions

H2M 2019 P2 Q11: Exploring Normal Distribution and Exponential Functions
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2020-07-05 20:28
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①This GeoGebra example demonstrates an interactive simulation of a comprehensive math problem (H2M 2019 P2 Q11) involving normal distribution, exponential and logarithmic functions, scatter plots, and polygons, with dynamic buttons for exploration. ②Core mathematical concepts include normal distribution (using InverseNormal), random sampling, exponential/logarithmic function fitting, frequency distribution, and construction of 3D objects like spheres, circles, and cylinders, bridging probability/statistics with function graphing. ③Construction highlights: The summary shows commands such as Random and InverseNormal for generating random normal samples, Sphere, Circle, and Cylinder for 3D geometric elements, and If for conditional logic; multiple buttons (button1, button2) control updates, while objects like n1, a1, c1, x1 store numerical values and coordinates, and text objects display results, making the applet highly interactive. ④This is suitable for senior high school students (e.g., A-Level or H2 Mathematics) and teachers for reviewing probability and function modeling, and as a reference for designing dynamic GeoGebra lessons that combine random simulation with mathematical visualization.

GeoGebra Commands & Parameters

  1. Random(4, 5) → a2
  2. Random(2, 3) → b2
  3. Random(2, 2) → n2
  4. Random(3, 3) → n3
  5. InverseNormal(e1, e2, p1) → iii
  6. Sphere((0, 0, 0), 1) → c
  7. Circle((0.8, 0, 0), 0.2, xAxis) → d
  8. Cylinder(d, 1.2) → e, e_2, e_3
  9. Circle((0, 0.8, 0), 0.2, yAxis) → f
  10. Cylinder(f, 1.2228520705420156) → g, h, i
  11. Circle((0, -0.8, 0), 0.2, yAxis) → k
  12. Cylinder(k, -1.2) → j, p, l
  13. Circle((-0.8, 0, 0), 0.2, xAxis) → q
  14. Cylinder(q, -1.2) → m, r, n
  15. Sphere((2.3, 0, 0), 0.5) → s
  16. Sphere((-2.3, 0, 0), 0.5) → t
  17. Sphere((0, -2.3, 0), 0.5) → u
  18. Sphere((0, 2.3, 0), 0.5) → v
  19. If(n1 ≟ 3, text2a, text2b) → text2