Given the increasing threat of adversarial attacks on deep neural networks (DNNs), research on efficient detection methods is more important than ever. In this work, we take a closer look at adversarial attack detection based on the class scores of an already trained classification model. We propose to train a support vector machine (SVM) on the class scores to detect adversarial examples. Our method is able to detect adversarial examples generated by various attacks, and can be easily adopted to a plethora of deep classification models. We show that our approach yields an improved detection rate compared to an existing method, whilst being easy to implement. We perform an extensive empirical analysis on different deep classification models, investigating various state-of-the-art adversarial attacks. Moreover, we observe that our proposed method is better at detecting a combination of adversarial attacks. This work indicates the potential of detecting various adversarial attacks simply by using the class scores of an already trained classification model.