Introduction Stress is a significant risk factor for cognitive impairments and disorders. Because stress is associated with extraneous cognitive load, we hypothesize that stress will affect cognitive processing. We will address this hypothesis by examining machine learning techniques' capacity on physiological signals to detect stress. Then, we will compare the performance of models trained on physiological signals recorded at different cognitive processing loads. Methodology We invited the subjects to the laboratory two to four weeks before and during the examination week to complete a stress questionnaire and measure their physiological activity (Electroencephalogram - EEG and Electrocardiogram - ECG) while at rest and performing cognitive tasks. Utilizing examination as a stimulus to induce stress response from the subjects, we label segments of signals recorded before examination week "non-stress" - and segments during examination week "stress," resulting in two datasets once at low cognitive load ("rest-rest" dataset) and other at high cognitive load ("task-task" dataset). Several machine-learning models were trained on two datasets to predict if the subject is stressed. Results The accuracy of ExtraTrees, KNN, Random Forest Classifier trained on the "rest-rest" dataset are 85.8%, 72.2%, and 83.1%; while training on the "task-task" dataset, the accuracy is 96%, 92.8%, and 94.6%, respectively. The prediction models also positively correlated with chronic stress questionnaire scores, strengthening their validity in classifying stress. Conclusion and Discussion This result demonstrated the capacity of machine learning techniques to rely on physiological signals to predict stress. The improvement in accuracy of models trained on a high cognitive load dataset compared to models trained on a low cognitive load dataset supports our hypothesis that stress affects cognitive processing.