I am working with a student who is very interested in math competitions, and I am teaching him Algebra I. I feel like doing competition problems related to a given topic is an excellent way to force him to apply the concept in a non-standard way, so I try to do it as much as possible. The main problem which I encounter with this approach is the difficulty of finding good problems related to a given topic. Skimming old competitions such as the AMC occasionally yields something interesting, but that involves sifting through a lot of problems to find just a few. I have looked at the AOPS Alcumus program to find problems related to a specific problem and that has worked fairly well, the only problem being the slow pace at which I can read through the Alcumus problems due to the format. It would be excellent if there were a place where I could simply download a list of competition problems organized by topic and select the ones which I thought were most relevant and interesting. Does a list like this exist? Thanks
I don't know if such a list exists, but I can recommend other math competitions - specifically the waterloo contests: http://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf
Hope this is helpful in some way.
My answer here to a different question has a link to some "college-level contest" problems that are arranged by topic as you request.
The issue is that these contest problems are not really "Algebra I" exactly. So this may be helpful only to future readers, not to you personally, because they are sorted by topic just well enough that you will find that "Algebra I" is not well-represented.
Topics in that link, as of 2019:
- Extremal Principle
- Number Theory
- Modular Arithmetic
- Pigeonhole Principle
- Sequences and Series
- Generating Functions