The objective of this study is to characterize the academic achievement of students based on an analysis of constructed response items in high school mathematics from the 2015 National Assessment of Educational Achievement(NAEA) to enhance teaching and learning efficiency. Towards this end, the responses of 7,468 students in the sample-based assessment were classified by type and further analyzed in connection with problem-solving process. According to the study results, proficient-level and lower-level students expressed difficulty with determination of points of internal division in a coordinate plane and with analysis of maximum and minimum quadratic functions. Advanced-level students showed insufficient understanding of procedures for formulation of distance between points and lines and methods to calculate maximum and minimum values based on domain in the quadratic function.