We report on the contents and results for 360 students of a mathematics assessment administered at the start of the second-semester introductory chemistry course required for science and engineering majors at the University of Minnesota. This calculator-free, 20-question, 30-minute, multiple-choice, diagnostic quiz includes questions selected specifically for their relevance to this course, concerning logarithms, scientific notation, graphs, and algebra. For the 325 students in degree-granting programs, significant correlations are reported between their mathematics assessment scores and success in this course, as measured by performance on exams (for which scientific calculators were permitted) and course grades. These observations suggest that responses to the simple questions on this unannounced quiz have some predictive utility as signatures of underlying thinking and learning patterns that are associated with success in this course. In addition, we argue that these results indicate an inadequate degree of mathematics fluency for the majority of the students tested, which can seriously impede their abilities to develop a firm conceptual understanding of quantitative introductory chemistry. Several mathematical and pedagogical misconceptions highlighted by these results are discussed, and possible methods are suggested for enhancing students' mental and pencil-and-paper mathematics skills during, and prior to, their participation in this course. (Contains 3 tables and 7 figures.)