Mathematical competitions are like sport: Practice makes the champion!
Junior training with Kangourou (English, French, German)
Kangourou is an international mathematical competition: what you can do is try the test from a past edition and see how well you do. Then read the solutions and learn what was not yet clear to you! If you do not understand a solution, just ask us (or your math teacher)!
You can find multiple choice exercises (in French) on the website of the
Kangourou.
More precisely, look at the following pages with the exercises and solutions from old competitions:
2021;
2020;
2019;
2018;
2017;
2016;
2015;
2014;
2013;
2012;
2011;
2010;
2009;
2008;
2007;
2006;
2005;
2004.
And here are the old exercises (in German) from
Känguru der Mathematik.
Here the Kangaroo in English:
exercises and
solutions.
Beaver/Castor competition
Castor informatique France (interactive website in French).
Beaver contests (past problems in English).
Junior and Advanced training with OMB/BxMO problems (French, English)
The website of the OMB (Olympiade mathématique belge) contains
junior exercises
and
advanced exercises in French. You can try to solve these problems and send us your solution to be corrected!
At an advanced level, you can find
very advanced exercises from the past editions of the Benelux Mathematical Olympiads, in English and French.
Junior and Advanced training with the British Olympiads (English)
On
this website you find past problems (and the solutions) for various competitions, in English, at various levels: Junior, Intermediate, Senior. Selecting each competition there is a link to past problems, with solutions (look at the section 'Preparing for the Challenge'). See also the website from the
British Olympiads.
Junior and Advanced training with the Swiss Olympiads (English, French, German)
On this
page you can find a list of exercises from past editions of the Swiss mathematical olympiads, with solutions. By the way, you can find some resources (in French) also on the website of the
French Olympiads.
Do not miss to participate in the Online World Math Contest, available in English, French, and German
here.
Advanced training with mathraining (French)
If you are training for mathematical competitions (and you understand French), then we expect you to work with the wonderful interactive website
(non-commercial, made by the mathematician Nicolas Radu for pupils)
www.mathraining.be.
You can make a login and then freely access the material. There you find:
- Concise explanations of the theory.
- Multiple choice and calculation exercises (meant to check that you understood the theory).
- Very difficult problems : These are meant as personal challenges for high-level training.
Notice that in mathraining there is also a Forum to ask for hints, so you should not give up!
Advanced training with the art of problem solving, e.g. AIME (English)
The most comprehensive compendium of exercises related to mathematical contests (of many countries!) is
artofproblemsolving.com/community/ .
We recommend you this site to train for the AIME test.
You find
here problems and solutions
of the AIME competition of the past years.
If you want to have a look at the very very very advanced problems from the famous IMO, see
this page (the solutions are contained in the 'shortlist' pdf): here you can try to understand the solutions and learn the mathematics behind it.
If you do not understand a solution, you can ask us!
Advanced training with EGMO (many languages)
On the EGMO website you find, for every past edition, the
problems in very many languages.
Moreover, going into the homepage of the individual years you should also find the solutions. And some solutions are also discussed in the
blog.
Books
Solving Mathematical Problems: A Personal Perspective by Terence Tao;
Problem Solving Strategies by Arthur Engel;
Les olympiades de mathématiques by Tarik Belhaj Soulami;
Mathematical Olympiad Challenges and
Mathematical Olympiad Treasures by Titu Andreescu;
IMO Compendium by Djukić, Janković, Matić, and Petrović.
Notice that these books are available at the public library in Campus Belval, by the University of Luxembourg. More books are under way, and you can also suggest the books that you would like to have...