首字母不需要，因为它不是专有名词而是普通名词，中文意思是n. 中学，中等学校（英国14-17岁的学生）

To attach the preparatory to the senior school these three classes were known officially, on speech days and in reports, as upper, middle, and lower second.

senior school首写不需要大写字母。大写字母一般用于特定的学校名称。