Помогите поставить глаголы в скобках в правильную форму согласно правилу согласования времен

1. The engineer was told that he (may) test the device in the afternoon. 
2. It was known that the head of our laboratory (be) a graduate of Moscow University. 
3. They thought that she (graduate) from a technical institute. 
4. Our professor informed us that he (give) the following lecture on quantum mechanics on Monday. 
5. At the meeting it was said that our lecturer (work) at a new programme of laboratory work. 
6. The teacher told us that the term «engineering» (have) many Russian equivalents. 
7. The chief engineer believed that we (work) at that problem for a month the following summer.