Problem Samples for GGB Classroom

Arthur Lee, Jun 25, 2021

Problem Set

Table of Contents

  1. Problems
    1. Make a quadratic graph
    2. quadratic pattern
    3. Parabola and triangle area
    4. compare quadratic expressions
    5. Line and Parabola
    6. fit a circle
    7. angles
    8. tasks about a cube
    9. Circle and tangent problem
    10. Stormy Night
    11. make a pentagon
    12. triangle fold
    13. isosceles hunt 1
    14. make your number machine
    15. successive percentage changes
    16. polygon patterns making
  2. supplementary
    1. parabola and triangle area (hint1)
    2. parabola and triangle area (hint2)

1.

Problems

  • 1. Make a quadratic graph
  • 2. quadratic pattern
  • 3. Parabola and triangle area
  • 4. compare quadratic expressions
  • 5. Line and Parabola
  • 6. fit a circle
  • 7. angles
  • 8. tasks about a cube
  • 9. Circle and tangent problem
  • 10. Stormy Night
  • 11. make a pentagon
  • 12. triangle fold
  • 13. isosceles hunt 1
  • 14. make your number machine
  • 15. successive percentage changes
  • 16. polygon patterns making

1.1.

Make a quadratic graph

This can be used as a template for making different examples of quadratic graphs (by dragging the free points A,B,C).[br][br]It can also be turned into an open activity in the GeoGebra Classroom. A simple question can be:[br][br]Show me a quadratic graph/function that:[br][br][list][*]touches the x-axis and has a positive y-intercept;[/*][*]has a maximum point and cut the x-axis on different sides of the y-axis;[/*][*]has a positive discriminant and a negative sum of roots;[/*][*]......[/*][/list]
– Arthur Lee

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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1.12.

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1.13.

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1.14.

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1.15.

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1.16.

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2.

supplementary

  • 1. parabola and triangle area (hint1)
  • 2. parabola and triangle area (hint2)

2.1.

parabola and triangle area (hint1)

[color=#6aa84f]This page provides supplementary materials for a problem from another page:[br][url=https://www.geogebra.org/m/gdz2hbze]https://www.geogebra.org/m/gdz2hbze[/url] [/color]
D is a point on AB, vertically above C. The length of CD is shown. When you drag the point C, you can see that the triangle area divided by CD gives a constant. [color=#ff0000]Do you expect this? Can you explain how this constant is related to any part of this figure? [/color][br][br]If the area of the triangle is proportional to CD, we can make CD as long as possible to get the maximum area. [color=#ff0000]So, how can you get the longest CD? [/color]
Continue to explore this problem with more suggestion in another page:[br][url=https://www.geogebra.org/m/vqf8tcyf]https://www.geogebra.org/m/vqf8tcyf[/url]
– Arthur Lee

2.2.

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