Question

2. At the end of each term,the professor would require that every student          their notebooks (hand)

每个学期末，教授会要求每个学生上交他们的笔记本。

Answer 1

2. (should) hand in动词require表示"要求"之意,后接宾语从句时，从句谓语动词用"should +动词原形".should可以省略。