For all of these codes, you need to hold L1 and R1 and enter them at the options menu in living room:

Fastest Cars:
Triangle,Triangle,Triangle,Triangle.

So for the fastest cars (above) cheat to work, you need to go to the options menu, hold down L1 and R1 and then press the triangle button four times! Use a similar method for the rest of the cheat codes.

Triangle,Triangle,Square,Square - Blow up vehicles in one hit

Square,Square,Square,Square - Faster Cars

Circle,Circle,Circle,X - More camera angles

Triangle,X,Triangle,X - Infinate car health

Square,Square,Square,Triangle - Press horn to do a giant leap in your car

Circle,X,Circle,Triangle - Grid Mode

X,Circle,X,Circle - All reward cars

X,Square,Square,Triangle - Credits

Triangle,Triangle,Circle,Square - Speed meter Display

Circle,Circle,Triangle,Square - Red Brick Car

X,X,X,X - Night Mode

Triangle,Circle,Triangle,Circle - Tripping Mode

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Unlock Cars
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Level 1(homer):rocket car (in gold mansion driveway)
Level 2(Bart):Monorail (up stairs downtown)
Level 3(lisa):boat (on big boat)
Level 4 (marge):Quad (in king trailer park)
Level 5 (Apu):Monster truck (near foantain it's on display)