This research is qualitative descriptive which aims 1) to describe the ability of solving mathematical problems of students in terms of the level of prior knowledge of mathematics and cognitive styles of students, 2) to describe the ability of solving mathematical problems in terms of the level of prior knowledge of mathematics students, 3) to describe the ability solving mathematical problems in terms of students' cognitive style. The results of this study were 1) Subject style FI cognitive ability in problem solving sequence, clearly and analytically. because the ability to lower the accuracy of less than 2) Subject FD think thoroughly but because of the ability initially so that the subject early ability high to resolve a given problem, while having a low ability can not resolve a given problem, 3) Based on the style of cognitive subject can resolve problems, have prior knowledge of mathematics is high but the workmanship is subject FI neater and analytical, while on the subject of FD solution is in shambles and many coretannya, 4) subject capable of beginning low with the FI can think of steps that must be taken even if there is a mistake in solving a given problem FD subject while the subject is simply not complete, 5) the relationship between cognitive styles and abilities early. Cognitive styles are influenced by high and low initial capability seemingly solving mathematical problems, namely, the truth and the truth calculation steps completion. While the initial capability is affected by the FI and FD cognitive style seemingly solving mathematical problems, namely, the result of his work in which the subject is more analytical and sequential FI and have their own perception of the subject while the FD is more intuitive and chaotic in solving a given problem