Hidden Go-Kart Mode: To access the Extra Go-Kart mode play through the championship mode and beat the beginners, middle, and high-speed classes. You should get a new car after the last race you win that is a go-kart and then go to the main menu and the first option that was unlockable will say extra.
Formula 1 Mode: To access the Extra Formula 1 mode play through the championship mode and beat all four of the classes with a first place in each race. You will get a new car after the last race. It is a Formula 1 race car. At the menu screen the Extra 2 option will be available.