Maths Olympiad Prep

Library /USAMO

USAMO

135 problems here, rated 6 to 8 on our scale (National Olympiad to Shortlist). 20 of them ask for a proof. Years covered: 2009–2010.

Algebra 56Combinatorics 32Geometry 29Number theory 18
#TopicDiffTypeYear
1 Algebra 6.0 answer — open
2 Geometry 6.0 answer — open
3 Geometry 6.0 answer — open
4 Geometry 6.1 answer — open
5 Algebra 6.1 answer — open
6 Algebra 6.2 answer — open
7 Number theory 6.3 proof — open
8 Number theory 6.3 answer — open
9 Number theory 6.3 answer — open
10 Algebra 6.4 answer — open
11 Algebra 6.5 answer — open
12 Geometry 6.5 answer — open
13 Number theory 6.5 proof — open
14 Algebra 6.5 answer — open
15 Algebra 6.6 answer — open
16 Number theory 6.6 answer — open
17 Algebra 6.7 answer — open
18 Algebra 6.7 answer — open
19 Algebra 6.7 answer — open
20 Geometry 6.7 answer — open
21 Geometry 6.7 answer — open
22 Geometry 6.8 answer — open
23 Combinatorics 6.8 answer — open
24 Algebra 6.8 answer — open
25 Geometry 6.8 answer — open
26 Combinatorics 6.8 answer — open
27 Combinatorics 6.8 answer — open
28 Combinatorics 6.9 answer — open
29 Combinatorics 6.9 answer — open
30 Algebra 7.0 answer — open
31 Geometry 7.0 answer — open
32 Algebra 7.0 answer — open
33 Number theory 7.0 answer — open
34 Geometry 7.0 proof 2009 open
35 Geometry 7.0 proof — open
36 Combinatorics 7.0 answer — open
37 Number theory 7.0 answer — open
38 Geometry 7.0 answer — open
39 Combinatorics 7.0 answer — open
40 Combinatorics 7.0 proof — open
41 Geometry 7.0 answer — open
42 Geometry 7.1 answer — open
43 Algebra 7.1 answer — open
44 Number theory 7.1 answer — open
45 Algebra 7.1 answer — open
46 Number theory 7.1 proof — open
47 Number theory 7.1 answer — open
48 Algebra 7.1 answer — open
49 Geometry 7.1 answer — open
50 Combinatorics 7.1 proof — open
51 Algebra 7.1 answer — open
52 Algebra 7.1 answer — open
53 Combinatorics 7.1 answer — open
54 Number theory 7.2 answer — open
55 Algebra 7.2 proof 2009 open
56 Combinatorics 7.2 proof — open
57 Algebra 7.2 answer — open
58 Combinatorics 7.2 answer — open
59 Algebra 7.2 proof 2010 open
60 Geometry 7.2 answer — open
61 Combinatorics 7.2 answer — open
62 Number theory 7.2 answer — open
63 Combinatorics 7.2 answer — open
64 Combinatorics 7.3 answer — open
65 Combinatorics 7.3 proof — open
66 Combinatorics 7.3 proof — open
67 Number theory 7.3 proof — open
68 Algebra 7.3 answer — open
69 Geometry 7.3 answer — open
70 Algebra 7.3 answer — open
71 Algebra 7.3 proof — open
72 Algebra 7.3 answer — open
73 Algebra 7.3 answer — open
74 Combinatorics 7.3 answer — open
75 Algebra 7.3 answer — open
76 Geometry 7.3 proof — open
77 Geometry 7.3 proof — open
78 Geometry 7.3 answer — open
79 Algebra 7.4 answer — open
80 Geometry 7.4 proof 2010 open
81 Algebra 7.4 proof — open
82 Algebra 7.4 answer — open
83 Algebra 7.4 answer — open
84 Algebra 7.4 answer — open
85 Algebra 7.4 proof — open
86 Geometry 7.4 answer — open
87 Geometry 7.4 proof — open
88 Combinatorics 7.4 answer — open
89 Algebra 7.4 answer — open
90 Combinatorics 7.4 answer — open
91 Combinatorics 7.4 answer — open
92 Algebra 7.4 answer — open
93 Combinatorics 7.4 answer — open
94 Geometry 7.4 answer — open
95 Algebra 7.5 answer — open
96 Algebra 7.5 answer — open
97 Number theory 7.5 answer — open
98 Geometry 7.5 answer — open
99 Combinatorics 7.5 answer — open
100 Algebra 7.5 answer — open
101 Geometry 7.5 answer — open
102 Combinatorics 7.5 answer — open
103 Combinatorics 7.5 answer — open
104 Combinatorics 7.5 answer — open
105 Algebra 7.5 answer — open
106 Algebra 7.5 answer — open
107 Algebra 7.5 answer — open
108 Algebra 7.5 answer — open
109 Algebra 7.6 answer — open
110 Algebra 7.6 answer — open
111 Geometry 7.6 answer — open
112 Number theory 7.6 answer — open
113 Geometry 7.6 answer — open
114 Number theory 7.6 answer — open
115 Number theory 7.6 answer — open
116 Algebra 7.6 answer — open
117 Number theory 7.6 answer — open
118 Algebra 7.7 answer — open
119 Algebra 7.7 answer — open
120 Algebra 7.7 answer — open
121 Combinatorics 7.7 answer — open
122 Combinatorics 7.7 answer — open
123 Algebra 7.7 answer — open
124 Combinatorics 7.7 answer — open
125 Algebra 7.7 answer — open
126 Algebra 7.7 answer — open
127 Algebra 7.8 answer — open
128 Combinatorics 7.8 answer — open
129 Combinatorics 7.8 answer — open
130 Geometry 7.8 answer — open
131 Algebra 7.8 answer — open
132 Combinatorics 7.9 answer — open
133 Algebra 7.9 answer — open
134 Algebra 8.0 answer — open
135 Algebra 8.0 answer — open
These are sorted by difficulty within the competition, but they aren't a course. The track is the route through, drawn from all the sources at once.