MalinC's GeoGebra-book

Malin Christersson, Feb 17, 2014

All worksheets from http://www.malinc.se/math/ divided into chapters according to the menu at the site.

Table of Contents

  1. Linear Algebra
    1. Curve of pursuit
    2. Two translations
    3. Adding vectors
    4. Linear combination
    5. Bound vectors
    6. Vector subtraction
    7. Equation of line in parametric form
    8. Determinant
    9. Linear transformations of curves
    10. Rotate cube
  2. Trigonometry
    1. Aristarchus' mistake
    2. Eratosthenes and the circumference of the earth
    3. Ptolemy
    4. Sextant
    5. Stellar Parallax
    6. Triangle definition
    7. Chords in Greece
    8. Half-chords in India
    9. Unit circle
    10. Unit circle and graphs
    11. Tangent and cotangent
    12. Graphs of tangent and cotangent
    13. Radians
    14. Epitrochoid
    15. Hypotrochoid
    16. Superposition of waves
    17. The sound of a sine function
    18. Play notes
    19. Play overtones
  3. Statistics
    1. Perpendicular fitting
    2. Vertical fitting
    3. Regression
    4. Normal distribution
    5. Binomial distribution
    6. Binomial and normal distribution
  4. Calculus
    1. Archimedes Pi
    2. Limit of sin(x)/x
    3. Derivative at point
    4. Derivative at point (with absolute value)
    5. Derivative as function
    6. Derivative of polynomial functions
    7. Derivative of sine and cosine
    8. Derivative of exponential function
    9. Derivative of logarithmic function
    10. Area under graph
    11. Distance, speed, time
    12. Fundalmental theorem of calculus
    13. Damped pendulum
    14. Cobweb plot
    15. Cobweb plot of linear function
  5. Functions
    1. Cartesian and non-Cartesian cars
    2. Find the formula
    3. Check the formula
    4. Slope and road signs
    5. Linear and exponential growth
    6. Annuity loan
    7. Completing the square
    8. Vertex form
    9. Translated graphs
    10. Factor form
    11. Inverse functions
    12. Composite functions
    13. Restricting the domain
  6. Geometry
    1. Dragging test
    2. Triangles
    3. Symmetries - reflection and rotation
    4. Shapes reflected in circles
    5. Circle mirror
    6. Summary - Angles
    7. Two angles in triangle
    8. Pythagorean theorem jigsaw puzzle
    9. The Pythagorean theorem
    10. Sun, earth and moon
    11. Similar triangles
    12. Angle bisector theorem
    13. Heights in triangles
    14. Midpoints on quadrilateral
    15. Soddy circles
    16. Square inscribed in triangle
  7. GeoGebra Tutorial
    1. Interactive GeoGebra logo
    2. Construct rectangle
    3. Cat on ladder
    4. Cats on ladder
    5. Wheel paradox
    6. Measuring angles
    7. Demonstrate addition
    8. Ellipse or hyperbola
    9. Parabola made using spreadsheet
    10. Polar flower
    11. Sun, earth, moon
    12. Lissajous
    13. Rotations, reflections, translations
    14. Dynamic tessellation made of points placed on triangles
    15. Symmetry lines
    16. Reflect triangle
    17. Symmetries made using lists
    18. Möbius Transformations of Doyle Circles
    19. Clock
    20. Keplers first law of planetary motion
    21. Cannon ball

1.

Linear Algebra

  • 1. Curve of pursuit
  • 2. Two translations
  • 3. Adding vectors
  • 4. Linear combination
  • 5. Bound vectors
  • 6. Vector subtraction
  • 7. Equation of line in parametric form
  • 8. Determinant
  • 9. Linear transformations of curves
  • 10. Rotate cube

1.1.

Curve of pursuit

– Malin Christersson

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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2.

Trigonometry

  • 1. Aristarchus' mistake
  • 2. Eratosthenes and the circumference of the earth
  • 3. Ptolemy
  • 4. Sextant
  • 5. Stellar Parallax
  • 6. Triangle definition
  • 7. Chords in Greece
  • 8. Half-chords in India
  • 9. Unit circle
  • 10. Unit circle and graphs
  • 11. Tangent and cotangent
  • 12. Graphs of tangent and cotangent
  • 13. Radians
  • 14. Epitrochoid
  • 15. Hypotrochoid
  • 16. Superposition of waves
  • 17. The sound of a sine function
  • 18. Play notes
  • 19. Play overtones

2.1.

Aristarchus' mistake

– Malin Christersson

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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2.12.

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2.13.

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2.14.

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2.15.

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2.16.

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2.17.

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2.18.

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2.19.

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3.

Statistics

  • 1. Perpendicular fitting
  • 2. Vertical fitting
  • 3. Regression
  • 4. Normal distribution
  • 5. Binomial distribution
  • 6. Binomial and normal distribution

3.1.

Perpendicular fitting

– Malin Christersson

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Calculus

  • 1. Archimedes Pi
  • 2. Limit of sin(x)/x
  • 3. Derivative at point
  • 4. Derivative at point (with absolute value)
  • 5. Derivative as function
  • 6. Derivative of polynomial functions
  • 7. Derivative of sine and cosine
  • 8. Derivative of exponential function
  • 9. Derivative of logarithmic function
  • 10. Area under graph
  • 11. Distance, speed, time
  • 12. Fundalmental theorem of calculus
  • 13. Damped pendulum
  • 14. Cobweb plot
  • 15. Cobweb plot of linear function

4.1.

Archimedes Pi

– Malin Christersson

4.2.

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4.3.

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4.4.

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4.5.

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4.6.

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4.7.

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4.8.

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4.9.

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4.10.

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4.11.

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4.12.

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4.13.

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4.14.

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4.15.

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5.

Functions

  • 1. Cartesian and non-Cartesian cars
  • 2. Find the formula
  • 3. Check the formula
  • 4. Slope and road signs
  • 5. Linear and exponential growth
  • 6. Annuity loan
  • 7. Completing the square
  • 8. Vertex form
  • 9. Translated graphs
  • 10. Factor form
  • 11. Inverse functions
  • 12. Composite functions
  • 13. Restricting the domain

5.1.

Cartesian and non-Cartesian cars

– Malin Christersson

5.2.

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5.3.

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5.4.

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5.5.

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5.6.

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5.7.

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5.8.

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5.9.

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5.10.

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5.11.

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5.12.

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5.13.

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6.

Geometry

  • 1. Dragging test
  • 2. Triangles
  • 3. Symmetries - reflection and rotation
  • 4. Shapes reflected in circles
  • 5. Circle mirror
  • 6. Summary - Angles
  • 7. Two angles in triangle
  • 8. Pythagorean theorem jigsaw puzzle
  • 9. The Pythagorean theorem
  • 10. Sun, earth and moon
  • 11. Similar triangles
  • 12. Angle bisector theorem
  • 13. Heights in triangles
  • 14. Midpoints on quadrilateral
  • 15. Soddy circles
  • 16. Square inscribed in triangle

6.1.

Dragging test

A rectangle, rhombus, parallelogram and trapezium.
The main feature of dynamic (or interactive) geometry is that you should be [br]able change a geometrical object without changing the significant properties of the object. In the applet above, you can change the shapes but they are always a rectangle, rhombus, parallelogram and trapezium.
– Malin Christersson

6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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6.13.

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6.14.

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6.15.

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6.16.

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7.

GeoGebra Tutorial

  • 1. Interactive GeoGebra logo
  • 2. Construct rectangle
  • 3. Cat on ladder
  • 4. Cats on ladder
  • 5. Wheel paradox
  • 6. Measuring angles
  • 7. Demonstrate addition
  • 8. Ellipse or hyperbola
  • 9. Parabola made using spreadsheet
  • 10. Polar flower
  • 11. Sun, earth, moon
  • 12. Lissajous
  • 13. Rotations, reflections, translations
  • 14. Dynamic tessellation made of points placed on triangles
  • 15. Symmetry lines
  • 16. Reflect triangle
  • 17. Symmetries made using lists
  • 18. Möbius Transformations of Doyle Circles
  • 19. Clock
  • 20. Keplers first law of planetary motion
  • 21. Cannon ball

7.1.

Interactive GeoGebra logo

Drag the points!
– Malin Christersson

7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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7.10.

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7.11.

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7.12.

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7.13.

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7.14.

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7.15.

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7.16.

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7.17.

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7.18.

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7.19.

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7.20.

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7.21.

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