A performance test would be most appropriate for determining which of the following skills in a student?

A performance test is designed to assess a student's practical skills and competencies through hands-on tasks rather than through theoretical knowledge or written assessments. This type of evaluation is most suitable for skills that require physical demonstration and real-time application.

The ability to give a razor cut specifically involves precise hand movements, an understanding of techniques, and the application of skills in a real-world scenario, all of which can be accurately observed and judged in a performance test setting. The instructor can directly assess the student's technique, the quality of the cut, and adherence to safety and sanitation standards during this practical performance.

In contrast, skills such as writing essays, solving mathematical problems, and conducting research primarily rely on cognitive abilities, analysis, and expression of knowledge, which are better suited for written assessments or discussions. A performance test does not effectively measure these intellectual abilities; it focuses instead on directly observable actions and outcomes that are indicative of practical skills.