Standardized tests play a crucial role in the detection of cognitive impairment. Previous work demonstrated that automatic detection of cognitive impairment is possible using audio data from a standardized picture description task. The presented study goes beyond that, evaluating our methods on data taken from two standardized neuropsychological tests, namely the German SKT and a German version of the CERAD-NB, and a semi-structured clinical interview between a patient and a psychologist. For the tests, we focus on speech recordings of three sub-tests: reading numbers (SKT 3), interference (SKT 7), and verbal fluency (CERAD-NB 1). We show that acoustic features from standardized tests can be used to reliably discriminate cognitively impaired individuals from non-impaired ones. Furthermore, we provide evidence that even features extracted from random speech samples of the interview can be a discriminator of cognitive impairment. In our baseline experiments, we use OpenSMILE features and Support Vector Machine classifiers. In an improved setup, we show that using wav2vec 2.0 features instead, we can achieve an accuracy of up to 85%.