Many existing deep learning models for natural language processing tasks focus on learning the compositionality of their inputs, which requires many expensive computations. We present a simple deep neural network that competes with and, in some cases, outperforms such models on sentiment analysis and factoid question answering tasks while taking only a fraction of the training time. While our model is syntactically-ignorant, we show significant improvements over previous bag-of-words models by deepening our network and applying a novel variant of dropout. Moreover, our model performs better than syntactic models on datasets with high syntactic variance. We show that our model makes similar errors to syntactically-aware models, indicating that for the tasks we consider, nonlinearly transforming the input is more important than tailoring a network to incorporate word order and syntax.