Improved GMAT by 100 points - supplemental essay needed?

I personally believe that there is no reason to address this in an essay. The more attention you bring to it, the more it can be dwelled on. I generally believe that schools and adcoms will see your 740 and move right past it. You got the checkmark for "excellent GMAT" and they will move onto the next areas of your application with no reserves. You also run the risk in an essay of sounding like you're making excuses for the first test instead of giving yourself credit for an excellent change in study habits, and strong drive. You really did turn it around, and didn't let the GMAT beat you. It will be easy to see that when they see your top score, and the first test will be attributed to a bad day. I'm not a professional, but its my personal opinion that you shouldn't bring attention to potential weaknesses unless there is nothing you can do to change it (for example an F on transcript). You killed the GMAT, and that is the score you'll report. Your 640 should get little to no attention. If you get asked about it in an interview, explain that a course correction in quant study really made all the difference.

If you do choose to write an essay, make sure to give yourself credit. Don't blame the first test on bad circumstances. It was a challange that you overcame with hard work and effort, and thats how it should be portrayed. Congrats on your killer score.