I would recommend going through the posted problem set (and get as many samples as you can) and determining which you are very comfortable with and which you are not. Then I would focus in the areas where I am not good or very slow and try improving your knowledge and speed there.
I would do the exam several times and see if your approach to improving speed and accuracy is working. Keep asking yourself which you are good and which you are not and keep improving the weaknesses.
You could even seek other current and former students that took the exam and ask them how they prepared for the exam to get first hand advice. Maybe even talk to the exam organizers and inquire about additional topics and study materials. There is likely a topical list of books or mathematical areas from the exam writers on such reference materials for you to concentrate and focus on.
I looked at some samples on the main web site and it looks like the typical problems focus in areas like (logical reasoning, graphical analysis, analytical and numerical ability,
quantitative comparisons, series formation, puzzles, etc.), so I would certainly seek out materials in these areas to practice understanding, speed and accuracy.
I would also recommend purchasing some problem solving books that have problems on a similar level (although finding exact ones is hard). For example, you can peruse these online and see if any fit your criteria and seek out similar materials.
Problem-Solving Strategies, Arthur Engel
Problem Solving Through Problems, Loren C. Larson
Putnam and Beyond, Razvan Gelca, Titu Andreescu
Mathematical Olympiad Challenges, Titu Andreescu, Razvan Gelca
Along with actual sample exams like the one you posted, I would also do the problems in these books, look at the approaches and then practice, practice, practice in order to improve your weak areas, speed and accuracy.
Lastly, there are probably web sites like Putnam that could provide more practice problems and maybe you can refer to them for more study and learning tips. The Mathematical Association of America has a website that might provide additional materials since they do math competitions and provide problems and study tips.
Regards and great luck to you!