Maths Olympiad Prep

Library /NMO Selection Tests for JBMO

NMO Selection Tests for JBMO

65 problems here, rated 4.5 to 7.7 on our scale (AIME to National Olympiad, round 2). 65 of them ask for a proof.

Algebra 12Combinatorics 16Geometry 22Number theory 15
#TopicDiffTypeYear
1 Geometry 4.5 proof — open
2 Algebra 4.6 proof — open
3 Number theory 4.7 proof — open
4 Number theory 4.7 proof — open
5 Number theory 4.8 proof — open
6 Algebra 4.8 proof — open
7 Algebra 4.9 proof — open
8 Number theory 4.9 proof — open
9 Combinatorics 4.9 proof — open
10 Algebra 5.0 proof — open
11 Geometry 5.0 proof — open
12 Geometry 5.1 proof — open
13 Geometry 5.1 proof — open
14 Algebra 5.1 proof — open
15 Geometry 5.2 proof — open
16 Geometry 5.3 proof — open
17 Algebra 5.3 proof — open
18 Algebra 5.3 proof — open
19 Geometry 5.3 proof — open
20 Number theory 5.4 proof — open
21 Number theory 5.4 proof — open
22 Number theory 5.4 proof — open
23 Number theory 5.5 proof — open
24 Geometry 5.5 proof — open
25 Geometry 5.6 proof — open
26 Number theory 5.7 proof — open
27 Geometry 5.7 proof — open
28 Geometry 5.7 proof — open
29 Algebra 5.7 proof — open
30 Number theory 5.8 proof — open
31 Combinatorics 5.8 proof — open
32 Algebra 5.9 proof — open
33 Number theory 5.9 proof — open
34 Geometry 5.9 proof — open
35 Geometry 5.9 proof — open
36 Number theory 5.9 proof — open
37 Geometry 6.0 proof — open
38 Number theory 6.0 proof — open
39 Combinatorics 6.1 proof — open
40 Combinatorics 6.1 proof — open
41 Algebra 6.1 proof — open
42 Combinatorics 6.1 proof — open
43 Algebra 6.1 proof — open
44 Combinatorics 6.1 proof — open
45 Geometry 6.2 proof — open
46 Algebra 6.2 proof — open
47 Geometry 6.3 proof — open
48 Geometry 6.4 proof — open
49 Geometry 6.4 proof — open
50 Number theory 6.5 proof — open
51 Number theory 6.5 proof — open
52 Combinatorics 6.7 proof — open
53 Combinatorics 6.7 proof — open
54 Combinatorics 6.7 proof — open
55 Geometry 6.8 proof — open
56 Combinatorics 6.8 proof — open
57 Geometry 6.8 proof — open
58 Combinatorics 7.1 proof — open
59 Combinatorics 7.1 proof — open
60 Combinatorics 7.1 proof — open
61 Combinatorics 7.2 proof — open
62 Geometry 7.3 proof — open
63 Geometry 7.4 proof — open
64 Combinatorics 7.4 proof — open
65 Combinatorics 7.7 proof — 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.