Preparing for Mathematics Olympiad

I'd recommend that you visit the Art of Problem Solving's (AoPS) website: I've linked you to their "resource" page with articles you can download (they are freely accessible.) The website is a "hub" for very motivated students of mathematics, many of whom engage in competition math. The site hosts mathematics resources, curricula, on-line forums, and a "bookstore". So feel free to explore the vast site.

Given the topics you specifically mention, I'll link you to some pdf notes on Number Theory; it's about 40-some odd pages, covering the topics you mention, and more. I'll also link you to a pdf entitled Olympiad Number Theory: an Abstract Perspective. You'll find at least two (freely accessible) notes in pdf on inequalities available for downloading, at the linked page at the top. Here's one of those: Inequalities.

Enjoy!

Buy AoPS books starting from pre algebra and work your way to precalculus... Then just buy practice amc, aime, and usamo tests from the MAA website:

Also I recommend reading the book polynomials by Barbeau as well as Art and Craft of Problem Solving.

For a lighter read go through the Barron's E-Z series in each math subject before touching the AoPS volume. This will make your transition from learning topics to learning to problem solve a lot easier.

These following books are good: