Geogebra is a geometry program. It's free! Try it. I suggest using the offline installer, otherwise it downloads itself every time.

A guide to using geogebra

Some of my geogebra files: load these into geogebra and see what they do.

- the y = mx+c straight line
- solving equations graphically (the lines are f and g, type in new definitions such as f: x+y=1 or g: y = x^2 and see what happens

Microsoft Mathematics is free and can be used like a graphical calculator, both for calculations and graphs. Unlike most calculators, it understands complex numbers.

Scilab is an open-source equivalent to the widely used MATLAB numerical analysis package. It lets you plot experimental data, experiment with calculations, write programs and do design simulations.

Available for Windows, Mac and Linux.