Syllabuses
Syllabuses for Geometry and Topology
Syllabuses on Algebra, Number Theory and Combinatorics
Syllabuses on Analysis and Differential Equations
Syllabuses on AppliedMathematics,Computational Mathematics,Probability and Statistics
Qualify exams from US universities
Harvard: http://www.math.harvard.edu/graduate/index.html#qualifying
Berkeley:http://math.berkeley.edu/index.php?module=documents&JAS_DocumentManager_op=viewDocument&JAS_Document_id=6
Stanford: http://math.stanford.edu/quals/oldquals.htm
UCLA: http://www.math.ucla.edu/grad/handbook/hbquals.shtml
U of Michigan:http://www.math.lsa.umich.edu/graduate/qualifiers/index.html
John Hopkins University: http://www.mathematics.jhu.edu/new/exams/syllabus_exams.htm
U of Wisconsin Madison:http://www.math.wisc.edu/graduate/quals.htm
UCI:http://www.math.uci.edu/graduate/exam.php
Putnam examination: http://www.math.niu.edu/~rusin/problems-math/
Georgia Institute of Technology, For math: http://www.math.gatech.edu/academics/graduate/sample-comprehensive-exams for aco: http://www.aco.gatech.edu/descript.html#Comprehensive%20Examination
2010 exam
2011 exam