middle school vs prep school

middle school

noun
  • A school which crosses the traditional divide between primary school and secondary school. 

  • An educational level or stage between primary school and secondary school. 

prep school

noun
  • 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. 

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

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