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GeoGebra

GeoGebra. Mathematics Cookies Term 2 Sabbatical Hwa Chong Institution. a free interactive geometry software started the in 2001 by Markus Hohenwarter at the University of Salzburg. What is GeoGebra ?. user friendly & convenient few system requirements (only requires Java)

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GeoGebra

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  1. GeoGebra Mathematics Cookies Term 2 Sabbatical Hwa Chong Institution

  2. a free interactive geometry software • started the in 2001 by Markus Hohenwarterat the University of Salzburg What is GeoGebra?

  3. user friendly & convenient • few system requirements (only requires Java) • new online or WebStart version does not need installation • when doing your project GC design on the 4th day you can use it to graph your draft out either the equations or the shapes then retrieve the equations first Why use GeoGebra?

  4. Use it online (Online Version): • http://www.geogebra.org/webstart/geogebra.html • Use the applet downloaded directly from internet (WebStart Version) • http://www.geogebra.org/webstart/geogebra.jnlp • Download and install it onto your computer (Installer Version) • http://www.geogebra.org/cms/en/installers • Download it onto your thumbdrive (Portable Version): • http://www.geogebra.org/cms/en/portable How to get GeoGebra?

  5. HOW TO USE GEOGEBRA?

  6. Spreadsheet View (Not often used) Algebra View Toolbar Chart View Components of GeoGebra Input bar for equations

  7. Lists all objects there are on the chart • Free objects – User defined functions (e.g. linear functions) • Dependent objects – Objects drawn with reference to free objects (e.g. quadrilateral plotted from 4 user-defined points) • Auxiliary objects – Objects classified by the user as auxiliary (no specific use) Algebra View

  8. Shows the chart & its objects • To change the properties of a function or shape, right click on them • Polar coordinates – change the object fromCartesian to Polar • Trace to Spreadsheet – records the x & y valuesof the object into the spreadsheet view • Auxiliary Object – classify the object as auxiliary • Copy to Input Bar – copy the formula of theobject to the input bar • Object Properties – format the object Chart View

  9. Line: y=mx+c • Quadratic: y=ax2+bx+c or y=a(x-h)2+k (derived from completing the square) • Cubic: y=px3+qx2+rx+c • Circle/Eclipse: (x-a)2+(y-b)2=r2 • where r is radius of circle & the centre’s coordinates are (a,b) • Trigonometry: y=sin(x), y=cos(x), y=tan(x) • You can also input other equations (need not be y=something), but for Graphical Calculators remember to make y the subject Functions commonly used & their equations

  10. Functions involving x • func(x) • x surrounded by round brackets • func is the short function name, common ones are: • sine – sin(x) • tangent – tan(x) • cosine – cos(x) • square root – sqrt(x) • cube root – cbrt(x) • absolute value – abs(x) • natural logarithm - ln(x) • common logarithm – lg(x) • Other functions • input as normal with exceptions • powers (x to the power of y) – x^y Inputing functions into GeoGebra

  11. A limitation in GeoGebra is that domains are hard to set • Domains are used if you only want a function to be visible at a certain range (of x or y values) • e.g. a line y=0 drawn from x=0 to x=5 has a domain of x<=5 & x>=0 • There are many methods tried out using IF Loops • GeoGebra IF Loop: If[<Condition>,<Statement if true>,<Optional Statement if false>] • However, the main objective of GeoGebra in this sabbatical is to design the draft of the GC design, so the domain can be ignored as it can be set later in the Graphic Calculator. Setting domains in GeoGebra

  12. EXAMPLEOlympic Logo Theme: YOG

  13. We only want to use the positive values for x & y. Move the drawing pad so that only the positive region of the graph can be seen. click on this then drag to this positive region Step 1

  14. Draw a circle • Click on circle tool • Select middle point then hover the cursor away from it to set the radius of the circle select the middle point click on this then hover the cursor here to set radius Step 2

  15. Repeat the process for the other 4 rings • Copy the generated equation in the algebra view into the input bar & create an identical circle • Use the move tool to move the circle (click on the circle’s perimeter) rightclickhere then click here… Step 3 and the equation is here

  16. Repeat the process for the other 4 rings • Generate the other 4 circles • Resize where appropriate depending your preferred range of x & y values • To select a circle from 2 identical circles you either: • click the circles and choose the one you want to select; or • hide one of the circles in Algebra View, then drag the visible one out Step 3 continued

  17. The End Any Questions? Help & Support: http://www.geogebra.org/cms/en/help

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