Bringing out brain activity through the interpretation of EEG signals is a challenging problem that involves combined methods of signal analysis. The issue of classifying mental states induced by arithmetic tasks can be solved through various classification methods, using diverse characteristic parameters of EEG signals in the time, frequency, and statistical domains. This paper explores the results of an experiment that aimed to highlight arithmetic mental tasks contained in the PhysioNet database, performed on a group of 36 subjects. The majority of publications on this topic deal with machine learning (ML)-based classification methods with supervised learning support vector machine (SVM) algorithms, K-Nearest Neighbor (KNN), Linear Discriminant Analysis (LDA), and Decision Trees (DTs). Also, there are frequent approaches based on the analysis of EEG data as time series and their classification with Recurrent Neural Networks (RNNs), as well as with improved algorithms such as Long Short-Term Memory (LSTM), Bidirectional Long Short-Term Memory (BLSTM), and Gated Recurrent Units (GRUs). In the present work, we evaluate the classification method based on the comparison of domain limits for two specific characteristics of EEG signals: the statistical correlation of pairs of signals and the size of the spectral peak detected in theta, alpha, and beta bands. This study provides some interpretations regarding the electrical activity of the brain, consolidating and complementing the results of similar research. The classification method used is simple and easy to apply and interpret. The analysis of EEG data showed that the theta and beta frequency bands were the only discriminators between the relaxation and arithmetic calculation states. Notably, the F7 signal, which used the spectral peak criterion, achieved the best classification accuracy (100%) in both theta and beta bands for the subjects with the best results in performing calculations. Also, our study found the Fz signal to be a good sensor in the theta band for mental task discrimination for all subjects in the group with 90% accuracy.