Early identification of cognitive impairment (CI) is essential for the health and quality of life of older adults. The MyCog assessment utilizes two established iPad-administered tests drawn from the NIH Toolbox® for Assessment of Neurological and Behavioral Function (NIH Toolbox). These tests target key cognitive areas: Picture Sequence Memory (PSM) for episodic memory and Dimensional Change Card Sort Test (DCCS) for executive function/cognitive flexibility. The research included 86 participants and examined various machine learning approaches to improve CI classification. This included conventional classifiers as well as neural network techniques. Following 100 bootstrap iterations, the Random Forest algorithm performed best, achieving strong metrics: precision of 0.803, recall of 0.758, accuracy of 0.902, F1 score of 0.742, and specificity of 0.951. Importantly, the model used a combined score obtained from a 2-parameter higher-order item response theory (HOIRT) framework that combined DCCS and PSM performance. A central conclusion of the work highlights the limitations of depending only on a single fixed threshold for the composite score. Rather, it supports the use of machine learning algorithms that integrate HOIRT-based scores along with additional variables such as age. This strategy offers greater potential for accurate CI prediction, thereby supporting earlier screening and management in older populations.