This study investigates the cognitive skill patterns associated with mathematical problem-solving success among high school students, utilizing data from the initial round of the Ultimath competition. Specifically, we examine the impact of memory retention, measured through a Memory Matrix game, and arithmetic processing speed on participants’ performance in a final round of multiple-choice math questions. Data collected includes participant demographics (high school and year), scores in Memory Matrix (number of correct cells and maximum matrix size achieved), speed arithmetic results, and multiple-choice question accuracy. Our analysis explores two primary hypotheses: that memory and speed-based tasks significantly predict advanced mathematical problem-solving success, and that students in higher grade levels demonstrate greater proficiency across these cognitive tasks. Preliminary findings indicate moderate correlations between memory retention, speed arithmetic and problem-solving ability, with speed arithmetic showing a stronger influence on mathematical performance. Additionally, a weak but statistically significant positive correlation (𝑟s = 0.0996, p=0.0067) was observed between students' high school year and their competition scores, suggesting a slight advantage for students in higher academic years. These findings highlight the different aspects of cognitive skills in competitive mathematics contexts, thereby offering insightful analysis for tailoring instructional plans and identifying STEM talent.

Keywords: Student performance analysis, STEM education, competitive mathematics.