A new approach to the study of fundamental components of intellectual abilities is presented. It is based on the most universal principles of intellectual development - differentiation and integration - and on S. L. Rubinstein's hypothesis of analysis and synthesis being the core of intellectual abilities. Purposeful selection of indices characterizing analysis and synthesis processes' qualities as manifestations of differentiation and integration of cognitive structures and as a display of their ability to differentiate and to integrate arousal is discussed. The results of experimental study of first- and second-graders' learning success in connection to analysis' quality are shown: the more delicate perceptive and semantic analysis is needed, the more close is the connection.