Concern has been expressed throughout Europe about the significant deficiencies in the basic mathematical skills of many engineering undergraduates. Mathematics diagnostic tests in the UK, Ireland and Portugal have shown these shortcomings, which provide a challenge to those striving to introduce more innovative educational practices into engineering education, such as projects or real-world problems. Every year, in the Dublin Institute of Technology (Ireland) and the Instituto Superior de Engenharia de Coimbra (Portugal), a diagnostic test is given to incoming first-year students. A comparison showed some potentially interesting differences between these students. In September 2013, a project was undertaken to compare mathematical competencies of incoming engineering students in both countries. A modified diagnostic test was devised and the results were then compared to ascertain if there are common areas of difficulty between students in Ireland and Portugal, or evidence of one group significantly outperforming the other in a particular area.