Age-related cognitive impairment have increased dramatically in recent years, which has risen the interes in developing screening tools for mild cognitive impairment and Alzheimer's disease. Speech analysis allows to exploit the behavioral consequences of cognitive deficits on the patient's vocal performance so that it is possible to identify pathologies affecting speech production such as dementia. Previous studies have further shown that the speech task used determines how the speech parameters are altered. We aim to combine the impairments in several speech production tasks in order to improve the accuracy of screening through speech analysis. The sample consists of 72 participants divided into three equal groups of healthy older adults, people with mild cognitive impairment, or Alzheimer's disease, matched by age and education. A complete neuropsychological assessment and two voice recordings were performed. The tasks required the participants to read a text, and complete a sentence with semantic information. A stepwise linear discriminant analysis was performed to select speech parameters with discriminative power. The discriminative functions obtained an accuracy of 83.3% in simultaneous classifications of several levels of cognitive impairment. It would therefore be a promising screening tool for dementia.