You've had some good ideas already but may I put in a word for problem-solving taking up a lot of time that could be spent on new stuff? In school they often jump from one bit of stuff to the next and don't do nearly enough solving hard problems with what they already know for optimal mathematical development, IMO. There are lots of resources in the form of books of contest questions, Olympiads etc. - if you need specific stuff I'm sure I or others can help.


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