Here is a folder with past NAT Fall Startup tests from 2007 to 2015 for practice. Problems, answers, and solutions are included.

Art of Problem Solving (AoPS) is an amazing community for math competitors. They have online classes in a variety of math topics, forums for discussing math competitions, and many more resources.

Art of Problem Solving (AoPS) publishes many well written books for math competitions. Specifically, the books "Art of Problem Solving: Volume 1" and "Art of Problem Solving: Volume 2" are excellent for preparation for the AMC 10/12, AIME, and other tournaments.