1. Always pay attention to the mini map. It's the most important thing for junglers. You need to know where the enemy jungler is and try to plan things around where he is. If he's ganking mid then show mid and hopefully you can turn on him.
2. Keep a lot of early pressure. Amumu is very good at the early ganks because of his q. Don't throw your q out immediately, wait for when you can hit it for sure so you can secure the kill.
3. The easiest camps for Amumu to kill are raptors and wolves. FOCUS THOSE 2. Use raptor smite to clear wards. Wolves if you think enemy jungler will try lots of invades.
4. Initiate fights. Whether it's a flash q ultimate or something else, TRY TO CREATE FIGHTS. You excel at this and can get lots of carries cc'ed down.
5. Right now junglers are the easiest role to carry games. Carrying doesn't mean getting lots of kill. KDA doesn't mean that much. What matters is you create chances for your team to kill the enemy. Set up plays.
6. Don't flame. Don't type. Only use pings.
7. Check my amumu stats on a website. He truly is the ultimate carry.