On Ph.D. Qualifying Exams
These are the sets of qualifying/preliminary examinations of US universities that I collected some time ago for the same purposes as you. (Dave L. Renfro points out in a commentary below that he compiled a similar list a decade ago, the following includes new departments, updated old broken links and removes unavailable sources). These exams are of much help and some even include solutions!:
- University of Arizona Ph. D. Qualifying Exams
- Arizona State University Qualifying Examinations
- University of Alabama Qualifying Exams.
- University of Alabama at Birmingham Qualifying Exams
- SUNY Albany Ph.D. Preliminary Examinations.
- University of California-Berkeley Preliminary Examinations.
- Boston University Preliminary Exams.
- University of Colorado-Boulder Prelim Exams.
- Columbia University Qualifying Exams.
- University of Connecticut Prelim Exams.
- University of California-Davis Exams.
- University of California-Irvine Exams
- University of California-Riverside Exams
- University of Florida Graduate Exams.
- University of Georgia-Athens Qualifying Exams.
- Harvard University Qualifying Exams.
- University of Illinois at Urbana-Champaign Comprehensive Exams.
- Indiana University-Bloomington Tier I Examinations.
- University of Iowa Qualifying Exams.
- Iowa State University Qualifying Exams
- Johns Hopkins University Qualifying Exams.
- Kansas State University Qualifying Exams.
- University of California-Los Angeles Qualifying Exams.
- Louisiana State University Comprehensive Exams.
- University of Maryland Qualifying Exams.
- University of Massachussetts-Amherst Qualifying Exams.
- University of Michigan-Ann Arbor Qualifying Review Examinations.
- University of Minnesota Prelim Exams.
- University of Missouri-Columbia Qualifying Exams.
- University of Nebraska-Lincoln Qualifying Exams.
- University of New Mexico Qualifying Exams.
- University of North Carolina at Chapel Hill Comprehensive Ph.D. Exams (requires one to log in).
- Northeastern University Qualifying Examinations.
- Northwestern University Preliminary Examinations.
- Ohio State University Qualifying Exams.
- Oklahoma State University Comprehensive Exams.
- University of Oklahoma Qualifying Exams.
- Pennsylvania State University Qualifying Exams.
- University of Pittsburgh Preliminary Exams.
- Purdue University Qualifying Exams.
- University of Rochester Preliminary Exams.
- Rutgers University-New Brunswick Qualifying Exams and oral exams.
- Stanford University Qualifying Exams.
- Syracuse University Prelim and Qualifying Exams.
- Temple University PhD. Exams.
- University of Texas at Austin Preliminary Exams.
- Texas A & M University Qualifying Examinations.
- University of Utah Qualifying Examinations.
- University of Washington Preliminary Examinations.
- University of Wisconsin-Madison Qualifying Exams.
Some old qualifying exams from Harvard: http://www.math.harvard.edu/quals/index.html
Try the collection at Texas A&M University. Although I am not a student of the university, I used the collection to practice for my own qualifying exams. Here is the link: http://www.math.tamu.edu/graduate/phd/quals.html.