Where can I find very hard math problems to practice on?

I'm trying to step up my math game and prepare for college-level classes. I feel comfortable with the normal high school math but I want to challenge myself with some very hard math problems. Any recommendations where I could find those? Preferably free problems?

There are several online resources where you can find challenging math problems to help you better prepare for more advanced college-level classes:

1. Art of Problem Solving (AoPS): Renowned among math enthusiasts, AoPS offers a large collection of problems (and detailed solutions) across a broad range of topics in high school math. They also have forums where you can discuss problems with other users.

2. MIT OpenCourseWare (OCW): From the Massachusetts Institute of Technology, this program provides free lecture notes, exams, and videos from actual MIT courses. You'll find a wealth of challenging problems, especially if you check out their upper-level math courses.

3. Khan Academy: While it's often used for its instructional videos, Khan Academy also offers various practice problems along with detailed explanations. Look at the math sections for AP classes or dive into their practice problems for first-year college courses.

4. Putnam Archive: If you're looking for some truly difficult problems, try the Putnam Competition. It's an annual math contest for undergraduate college students in the U.S. and Canada, and it's known for having some of the most challenging problems out there. You can find past problems in the Putnam Archive.

5. Project Euler: This resource offers a series of challenging math-related computational problems that require more than just mathematical insights to solve. If you're interested in the intersection of math and computer science, Project Euler is a great place to test your skills.

Remember, solving challenging problems requires time and patience. It's common to get stuck, but each struggle helps you learn and improve. Good luck with your math journey!