You could generate a random quiz, using Mathster’s UKMT Mathematics Challenge Online Quiz. Choose Junior, Intermediate or Senior and one of three difficulty levels; you can also choose the number of questions, a time limit and the order the questions are presented in – random or in order of difficulty.
Nrich publish new problems every month. Why not try and get a solution published on their website?
There is a menu specifically for students. You can sign up for an Nrich student newsletter if you want to be notified of new developments on the site. If you have not tried Nrich problems before you may find their recommended starter problems good to try. You can search for problems by topic if you wish.
Underground Mathematics has an extensive collection of questions to get you really thinking about your Mathematics. Suggestions and full solutions are provided but as always make sure you really do everything you can first with the question.
For more problems – try The Math Contest. Students from around the world can submit answers.