Alzheimer's disease (AD) is a common neurodegenerative disorder with no effective treatment currently available, for which the diagnostic process is both costly and time-consuming. Therefore, it is crucial to establish an efficient and non-invasive detecting method. This study focused on the potential applications of speech and drawing as non-invasive biomarkers. Sixty-one participants were recruited and asked to complete a drawing test and three speech tests. By analyzing the features extracted from these tests, we validated the effectiveness of the speech and drawing tests (HC vs. non-HC and MCI vs. AD) in two binary classification tests using machine learning methods. The results demonstrate that combining data from these two tests significantly improves the classification performance of the model compared to the individual tests. In addition, the use of feature selection methods further improved classification performance. This study highlights the potential application of multimodal strategies in the early diagnosis of cognitive impairments. Importantly, speech and drawing detecting tools offer simplicity, speed, and non-invasiveness, which are expected to enhance the preliminary diagnosis rate of AD.