1. GEOGEBRA A free downloadable web based program for both Interactive Geometry and Coordinate Geometry.

2. Finding Geogebra Either (a) Google Geogebra or (b) www.geogebra.orgwww.geogebra.org Then click “Download” followed by GeoGebra “Web Start”

3. Equations With Degree 1 or 2 (a) Equations of degree 1 or 2 can be entered either implicitly or as y = (b) For ease of use these equations should be given a name (a lower case letter) Eg: Entering a:2x+3y = 6 gives a straight line with name a Open a blank page

5. The “Command” Menu This gives 69 different commands that can be applied to the diagram. Format (a)Select a command (b)For simple commands enter the name of the object in the square brackets. Eg: To find the slope of the line, choose “slope” from the menu and type ‘a’ in the brackets

6. Drawing a perpendicular to a line from a point Choose point from the point menu (second from left) Click anywhere on the screen Choose perpendicular line (fourth menu from the left) Click on the point and then on the line

8. Using The Object List Right clicking on any object in the object list or on the diagram gives a choice that includes (a)deleting the object (b)editing the object (c)changing the format of an equation Eg: Right clicking on the equation of a straight line gives a choice of ax+by = c; y = mx +c or parametric form Using the mouse to point to any object on the list or on the diagram tells you what it is.

9. Using Sliders Sliders allow you to enter a pro-numeral as part of an equation and observe what happens as the pro-numeral changes Eg: Sliders can be used to observe what happens as values of m and c change when the equation y = m x + c is entered

10. The slider icon is in the measure menu (6 th icon from the left) Highlight this icon, then click anywhere to deposit the slider. Change setting if needed, then select “Apply” Repeat this process to create a second slider. Right click on the first slider, choose “rename” and change to m. Rename the second slider c Enter a:y = m*x +c Use your sliders to change the values of m and c Investigating y = mx +c

12. Investigating Circles Create three sliders and rename them h, k and r. Enter c: (x-h)^2+(y-k)^2=r^2 Observe what happens as h, k and r change Use commands to find the centre and the radius of your circle

13. The Circle

14. Cubics With the help of three sliders enter f(x) = (x-a)(x-b)(x-c) Investigate the effect of changing a, b and c

16. Trigonometric Functions Function notation must be used The argument of the trig function must be in brackets Right click on the x axis and choose – properties – units and select π Enter f(x) = a*sin(b*(x-h)) + k and play

17. A Trigonometric Example

18. Lower and Upper Sums Enter a slider with a range of values from 5 to 100, label it n Enter your function. Eg f(x) = 0.5x^2 + 2 To find a lower sum from 0 to 4 with n rectangles enter lowersum[f,0,4,n] Enter Uppersum[f,0,4,n] Play with the slider.

19. Integration Example

20. Demo: The angle in a semicircle Right click on the axes and turn them off Draw a circle (Circle menu) Draw a line through the centre and any point on the circle (Circle menu) Find the intersection points of the line and the circle (command menu) Draw a triangle through the points of intersection and any other point on the circle (line menu) Choose angle from the measure menu and click on any angle of the polygon Use the arrow (top left icon) to change the diagram

22. Descriptions of all Geogebra Commands with examples http://www.geogebra.org/en/wiki/index.php/Command_Descriptions Geogebra Introductory Workshop: http://wsdcff.wikispaces.com/geogebra?f=print Geogebra Applets: http://www.slu.edu/classes/maymk/GeoGebra/ Geogebra User Forum http://www.geogebra.org/forum/ license: http://creativecommons.org/licenses/by-sa/3.0/ Trig functions - graphical representations http://www.geogebra.org/en/upload/files/english/lewws/tr ig_functions_visualizations.html Circle: http://montanamath.org/geogebra/circle/circle.html Web Resources