The best resource to practice for the International History Olympiad Qualifying Exam are the Battery Exam questions from past Olympiads that are posted here. Note that for the Varsity and Junior Varsity Divisions, the International History Olympiad Qualifying Exam difficulty will be akin to the Battery Exams from past Olympiads which are shown on the linked page.

Note that the Middle School and Elementary Division version of the Olympiad Qualifying Exam will be significantly easier and more in line in terms of difficulty with the  International History Olympiad Practice Qualifying Exam as shown here:

You can also use our Asian, European, Australian, New Zealand or Canadian study guides, sample and past questions (they are very similar, only the regional content varies, so they can be useful even if you live in other parts of the world).