Background: Many contributing factors, both domain specific and domain general, influence children's performance in school achievement. Aims: This research aims to verify the importance of kindergarten measures of cognitive abilities and numerical competence in the role of predicting mathematical school achievement at the end of first grade. Sample and Methods: A total of 70 children (38 females and 32 males) took part in the study. We tested the children at the beginning of their last year of kindergarten (time 1) on the following cognitive abilities: IQ, phonology, counting skills, verbal short-term memory, visuo-spatial short-term memory, working memory, and processing speed. Then, we tested the same children at end of their last year of kindergarten (time 2) on a measure of numerical competence and at the end of their first year of primary school (time 3) on a test of math achievement. Results: Path analysis models revealed the direct influence of working memory and processing speed on predicting numerical competence in pre-schoolers and the influence of processing speed and verbal IQ on predicting math achievement in first graders. Moreover, this study found a direct link between numerical competence and math achievement. Conclusions: Both domain-specific and domain-general factors contribute to determining math achievement at the end of first grade. (Contains 3 tables and 2 figures.)