Test Problems and Solutions XXX Costa Rican Math Olympiad, 2018

Problemas de exámenes y soluciones XXX Olimpiada Costarricense de Matemática, 2018

Abstract

OLCOMA is the Costa Rican Mathematics Olympics Commission. This commission is made up of academics in the area of Mathematics from the Universidad Nacional, the Instituto Tecnológico de Costa Rica, the Universidad de Costa Rica, the Universidad Estatal a Distancia, and the Universidad Autónoma de Costa Rica and by representatives of the Ministry of Public Education and of the Ministry of Science, Technology, Culture and Telecomuncations.

Within the structure of the Costa Rican Mathematical Olympiads, there are three levels of competition. In Level I there are students of seventh year, between 10 and 13 years old, approximately (also the students of primary school that are studying in this level can choose to participate in this level sixth grade). In Level II, students of eighth and ninth years, between 14 and 15 years, approximately, participate. In Level III there are students of tenth, eleventh and twelfth years, plus 15 years old. During the year 2018, we worked with three stages. In the First Elimination, the students resolved to
a single selection test with 25 items. In the II Eliminatory, the classified ones carried out aexam with 12 single-choice questions and three developmental problems. In the Final Stage, the classified students took two tests on consecutive days, each test with three tests developmental problems. The objective of this book is that future participants in Costa Rican Mathematics Olympiads possess reference material.

 The problems listed in this book represent a challenge for those who like to solve mathematical exercises. Each of the problems has the respective solution, so once who try to solve each problem, can compare the procedure carried out with the proposed solution. All the problems of I Eliminatory for each one of the three levels, the problems of II Eliminatory for each one of the three levels, the problems proposed to conform the examinations of the Final Stage and the problems that conformed the examinations of the Final Stage have been incorporated.