After participating in the Rocky Mountain Area Calculus Bowl, I thought it would be fun to come up with some questions myself. Fair warning: they are quite a bit harder than the ones given in the competition—even the ones from the final round.
The document is set up as a slide presentation, but it is formatted as a PDF file rather than a PowerPoint or Keynote presentation, so it is completely cross-platform and viewable in your browser. The slides alternate between problems and solutions, so you can check your answers immediately. If you want to use these questions in a Calculus Bowl-style competition, feel free! You can use any PDF application on any platform to project the slides. For best results, use a program that allows you to view the next slide on your screen while you're projecting the current slide. This way, you can see the answer to the question that contestants are trying to solve, without having to write down the solutions on paper.