1) the major functions of grammar schools
A grammar school is one of several different types of school in the history of education in the United Kingdom and some other English-speaking countries, originally a school teaching classical languages but more recently an academically-oriented secondary school.

The original purpose of mediaeval grammar schools was the teaching of Latin. Over time the curriculum was broadened, first to include Ancient Greek, and later English and other European languages, natural sciences, mathematics, history, geography, and other subjects. In the late Victorian era grammar schools were reorganised to provide secondary education throughout England and Wales; Scotland had developed a different system. Grammar schools of these types were also established in British territories overseas, where they have evolved in different ways.
2)the major functions of vocational school
vocational school (or trade school or career school), providing vocational education, is a school in which students are taught the skills needed to perform a particular job. Traditionally, vocational schools have not existed to further education in the sense of liberal arts, but rather to teach only job-specific skills, and as such have been better considered to be institutions devoted to training, not education. That purely vocational focus began changing in the 1990s "toward a broader preparation that develops the academic" and technical skills of students, as well as the vocational