intermediate school vs secondary education

intermediate school

noun
  • A school for children that serves grades between elementary school and high school, and occasionally between the former and middle school. These grades vary from anywhere from grade 4 to grade 8. 

secondary education

noun
  • Education that follows primary education and leads to either employment or college / university education. 

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