prep school vs public school

prep school

noun
  • A private or public school intended to prepare its students to get into prestigious universities. 

  • A private primary school which prepares its pupils for the common entrance examination most commonly at the age of thirteen, and subsequent entry into public school. 

public school

noun
  • Certain private schools, particularly (initially) any grammar school operated apart from the personal lands of its students or (from the 19th century) the feepaying secondary schools which developed from or were modelled upon them; a British boarding school 

  • A publicly funded and administered school; (UK, Ireland) such schools in the context of other countries 

How often have the words prep school and public school occurred in a corpus of books? (source: Google Ngram Viewer )