This research describes the process of construction and psychometric analysis of the COL-TPM test. A test is developed to evaluate the learning of the quadratic function based on types of routine and non-routine mathematical problems, and levels of literal, inferential and critical reading comprehension of high school students from different municipal educational establishments, whose previous phases included literature review, apparent validation, content validity by expert judgment, construct validity, construction of the final version, pilot application, analysis of the discrimination indexes of the problems and reliability. From the psychometric analyses, a test with positive results was obtained in all cases, with appropriate difficulty, discrimination and reliability indexes. However, the experts gave their opinions and/or suggestions on modifications to the problems, and the changes proposed were modifications in the wording of some of the questions and the elimination of others. The final version of the test, which consists of five problems of applications of the quadratic function with ten questions each, subjected to different theoretical and methodological phases, provides certainty about its ability to evaluate in a valid and reliable way, the levels of reading comprehension skills of students, when they are confronted with the resolution of a type of verbal mathematical problem, contextualized to a specific mathematical function.