A mathematically driven system which can be used to diagnose a student's strengths and weaknesses and provide studying strategies based on these strengths and weaknesses. The invention bases studying suggestions not on raw test scores or on simple metrics such as "percent correct", but on the student's potential to increase their test score by studying a particular topic. The inventive method includes the steps of administering an exam with composite questions relating to a subject and an associated study strategy therefor; analyzing results of said exam to diagnose strengths and weaknesses of a student with respect to said subjects and strategies; and outputting data with respect to optimal strategies for the student with respect to said subjects.