This research paper investigates the impact of psychological interventions on student performance, specifically within the MIT Integration Bee, a prestigious mathematics competition that challenges students with advanced calculus problems. Conducted across multiple high schools in Texas, the study explores how different motivational techniques, including intrinsic and extrinsic rewards, influence test scores and overall student engagement. The research design includes a comprehensive analysis of motivational strategies, encompassing both baseline and reward-based conditions to assess their effectiveness in enhancing student performance. By examining a diverse sample of high schools from urban and suburban areas, this study aims to provide a holistic understanding of the factors that drive academic achievement in competitive settings. The results have significant implications for educational strategies, particularly in the realm of mathematics education, and highlight the potential for tailored motivational interventions to optimize student engagement and achievement. These findings contribute to the broader discourse on educational psychology, offering insights that could inform the development of more effective teaching practices and policies aimed at fostering a conducive learning environment for students across different educational contexts. In addition, this can potentially be applied to universities as well, breaking way through an exciting part of academics.