I'm looking for some mathematics that will challenge me as a year $12$ student. I am an upcoming year $12$ student, school holidays are coming up in a few days and I've realised I'm probably going to be extremely bored. So I'm looking for some suggestions.
I want a challenge, some mathematics that I can attempt to learn/master. Obviously nothing impossible, but mathematics is my number $1$ favorite thing and I really want something to keep me busy and something that can further my understanding of mathematics. Also I would be interested in any mathematical focused book suggestions.
So far in school I've done the usual:
Matrices, transformation matrices, Sine Cosine and Tangent (graphs and proofs), lots and lots of parabolas/quadratics, statistics, growth and decay, calculus intro, Calculus derivation and integration, vectors, proof by induction and complex numbers.
Any suggestions would be heavily appreciated.

You could look at some of the  Questions tagged recreational-mathematics, soft-question and big-list (sort them by "votes").
