This report describes three open-ended response types that should broaden the conception of mathematical problem solving embodied in computerized-adaptive admissions tests. The Mathematical Expressions response type presents single-best answer problems that call for an algebraic formalism, the correct rendition of which may take an infinite number of surface forms. Generating Examples presents loosely structured problems which may have many good answers, taking the form of a value, letter pattern, expression, equation, or list. Graphical Modeling problems ask the examinee to represent a given situation by plotting points on a grid, where there may be a single-best answer or multiple correct responses. Finally, these three basic types can be combined to form extended constructed-response problems. For each of the three basic types, this paper gives example items, describes the examinee interface and approach to automatic scoring, and reports available findings.