Here are a couple of sheets of extension problems aimed at challenging bright students. One was originally aimed at Y11s, and the other at Y12-13. However, many of them do not need knowledge of particularly advanced topics, so could be accessible to younger students.
The aim is as stated at the top of each sheet:
A problem that you can see how to solve straight away isn’t a problem at all.
A problem that you have no idea how to solve even after trying it for half an hour is probably too frustrating.
Hopefully these come in between - enough of a challenge to give you a buzz when you solve it, but not so hard that you never do!
Y11 Extension Problems
Y12-13 Extension Problems