Maths Olympiad Prep

Library /Selection Examinations for the IMO

Selection Examinations for the IMO

41 problems here, rated 7.1 to 9.2 on our scale (National Olympiad, round 2 to IMO level). 41 of them ask for a proof. Years covered: 2012–2015.

Algebra 10Combinatorics 8Geometry 15Number theory 8
#TopicDiffTypeYear
1 Number theory 7.1 proof 2012 open
2 Number theory 7.5 proof — open
3 Algebra 7.6 proof 2012 open
4 Number theory 7.6 proof — open
5 Geometry 7.8 proof — open
6 Algebra 7.8 proof — open
7 Geometry 7.8 proof — open
8 Geometry 7.8 proof 2013 open
9 Geometry 7.9 proof 2012 open
10 Number theory 7.9 proof 2013 open
11 Number theory 7.9 proof 2013 open
12 Combinatorics 7.9 proof 2012 open
13 Number theory 8.0 proof 2015 open
14 Algebra 8.1 proof — open
15 Combinatorics 8.2 proof 2013 open
16 Number theory 8.2 proof — open
17 Geometry 8.3 proof 2012 open
18 Algebra 8.3 proof — open
19 Geometry 8.3 proof — open
20 Number theory 8.3 proof 2015 open
21 Algebra 8.3 proof 2013 open
22 Algebra 8.3 proof 2012 open
23 Algebra 8.3 proof — open
24 Geometry 8.4 proof 2013 open
25 Geometry 8.4 proof 2015 open
26 Combinatorics 8.4 proof 2012 open
27 Algebra 8.4 proof 2015 open
28 Geometry 8.4 proof — open
29 Geometry 8.5 proof 2015 open
30 Combinatorics 8.5 proof — open
31 Geometry 8.6 proof — open
32 Geometry 8.6 proof 2013 open
33 Combinatorics 8.6 proof 2012 open
34 Algebra 8.7 proof — open
35 Geometry 8.8 proof — open
36 Combinatorics 8.8 proof 2013 open
37 Geometry 8.8 proof 2012 open
38 Geometry 8.8 proof — open
39 Combinatorics 8.8 proof — open
40 Combinatorics 9.2 proof 2015 open
41 Algebra 9.3 proof 2015 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.