The issue of searching for new methodological approaches to the systematization that will encourage the increase of students’ motivation to learn mathematics under the competency-based approach is considered in this article. The research analyzes the existing works on the increase in students’ motivation to learn Mathematics, in particular, the use of cross-curricular connections while forming students’ competency. Competency-based problems, systematized according to the topic of the 10th grade “Functions, their features and graphics”, were determined as the tools to measure students’ competency and a method to form their motivation to learn mathematics. The use of such methods as the initial research and information gathering, systematization and structural analysis of the problems, data processing allowed the authors of the article to systematize the problems for school subjects of the 10th grade that demonstrate cross-curricular connections of Mathematics with other learning subjects and allow showing the advantages of the mathematical modeling in researching real processes. The research shows the realization of cross-curricular connections in time and such connections as parallel learning, perspective connections, use of the mathematical modeling method are shown. An experiment was held in order to prove the efficiency of implementing a system of the problems to demonstrate the use of the function in different tasks of natural subjects. The results proved that the implemented system of problems considerably influences the increase in students’ motivation to learn mathematics.