The use of GeoGebra at the exams in Norway

Arne Amdal Norwegian University of Science and

Technology (NTNU)Trondheim, Norway

• This is the new new model: • The most theoretical courses in upper secondary:– 3 hours with pencil and paper– 2 hours with all tools

• specific requirements regarding which tools in certain excercises

• CAS and grapher

The other courses in upper secondary, and also lower secondary :– 2 hours with pencil and paper– 3 hours with all tools • specific requirements regarding which tools in certain

excercises• spreadsheet and grapher

• CAS can trivialize problems• CAS in time consuming problems• CAS in «impossible» problems

b) Jeg skrev likningene inn i CAS-delen i GeoGebra.Jeg markerte dem og klikket på x=Trekanten har lengder 15/2, 10 og 25/2.

• There are three trees in the schoolyard. They are corners in a triangle. Petter measures the distances between them to be 14,0m, 20,0m and 24,0m

• Use CAS to determine the area of the triangle

• I use the law of cosines to find the angle opposite the 24,0m-side. I use the triangle area formula to find the area. The area is 139,64

The function

The point A has coordinates (0,0), the point B is on the x-axis, the point C is on the graph of and Use CAS to decide the exact value of x such that the area is as small as possible.What is the area for this value of x?

2

10( ) 5 , 0f x x

x

90B