Here are copies of some MA/PhD qualifying exams from previous years. At the bottom you will also find links to some syllabi describing topics that the three exams may cover. Some of these lists are out of date but they still should give an idea of the range of topics covered by the exams. For more details on the next set of exams consult with this year's instructors of the corresponding 5000-level courses (in algebra, analysis and topology).
The instructors for the 2010 (Spring and Summer) examinations are: Prof Kujawa (Algebra), Prof Grasse (Analysis), and Prof Lee (Topology).