Maths Olympiad Prep

Library /Selection Examinations for the IMO

Selection Examinations for the IMO

37 problems here, rated 7.5 to 9.2 on our scale (National Olympiad, round 2 to IMO level). 37 of them ask for a proof. Years covered: 2012–2015.

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