$ gnome-terminal --maximize
Take a look at
$ gnome-terminal --help
$ gnome-terminal --help-window-options
etc. to see what else you can do.
So you want to run your application inside a maximized GNOME terminal? The easiest way is to seperate launching the application from the code itself.
Write a shellscript wrapper which runs
gnome-terminal --maximize -x my_typing_tutorial. Then set up the shortcut (or whatever) to run this script, instead of your binary.
Note this gives you a chance to detect if gnome-terminal isn't installed, and try starting konsole or xterm instead. It also means that a user can edit the start script if it doesn't work on their system, without having to re-compile your binary.
Note that I'm not addressing the question of how to maximize an existing terminal - if I were the user, I'd hate a program that messed up my window geometry without asking.