The “Test of Cognitive Ability” (“TCP”) is a language-free test of reasoning ability that was created at the heart of the Luxembourg Centre for Educational Testing (LUCET). The TCP was initially developed for children at the age of 10 and can be applied in a group context. Since no advanced language-skills are required in order to take this test, it is perfectly suited not only to serve as a cognitive ability screener in a multi-lingual context, but also to study the relationship of cognitive ability and academic success within a demanding school-system that deals with a very complex mixture of student backgrounds (spoken languages, socioeconomic status, culture, etc.). Using traditional intelligence tests with language-based tasks and instructions could, in this context, result in biased data since maximum performance relies on a good understanding of task requirements. Being language-free, the TCP can help in gaining a more precise understanding of academic performance under different circumstances and prevent wrong conclusions as to the fairness of curricular requirements for different student populations. The present contribution will present the Test of Cognitive Potential and give an overview of how the relationship of cognitive ability and academic success varied within different subpopulations of a Luxembourgish sample of 303 4th graders.