Alzheimer’s disease (AD) is associated with deficits in a number of cognitive processes and executive functions. Moreover, abnormalities in the electroencephalogram (EEG) power spectrum develop with the progression of AD. These features have been traditionally characterized with montage recordings and conventional spectral analysis during resting eyes-closed and resting eyes-open (EO) conditions. In this study, we introduce a single lead dry electrode EEG device which was employed on AD and control subjects during resting and activated battery of cognitive and sensory tasks such as Paced Auditory Serial Addition Test (PASAT) and auditory stimulations. EEG signals were recorded over the left prefrontal cortex (Fp1) from each subject. EEG signals were decomposed into sub-bands approximately corresponding to the major brain frequency bands using several different discrete wavelet transforms and developed statistical features for each band. Decision tree algorithms along with univariate and multivariate statistical analysis were used to identify the most predictive features across resting and active states, separately and collectively. During resting state recordings, we found that the AD patients exhibited elevated D4 (~4–8 Hz) mean power in EO state as their most distinctive feature. During the active states, however, the majority of AD patients exhibited larger minimum D3 (~8–12 Hz) values during auditory stimulation (18 Hz) combined with increased kurtosis of D5 (~2–4 Hz) during PASAT with 2 s interval. When analyzed using EEG recording data across all tasks, the most predictive AD patient features were a combination of the first two feature sets. However, the dominant discriminating feature for the majority of AD patients were still the same features as the active state analysis. The results from this small sample size pilot study indicate that although EEG recordings during resting conditions are able to differentiate AD from control subjects, EEG activity recorded during active engagement in cognitive and auditory tasks provide important distinct features, some of which may be among the most predictive discriminating features.