Answer:
1. She was determined to find out the truth.
2. His letter gave them an idea.
3. The Prime Minister will have to give a speech at the conference tomorrow.
4. They could've saved her from the fire, but the ladder didn't reach her window.
5. I was supposed to meet her outside.
6. When he married her, she must have been no more than sixteen years old.
7. When she was a child, she was so shy, she would hide under the table at the sight of a visitor.
8. Your mother is used to changing her mind, my dear.
9. She would better not try to cheat next time.
10. I'd rather not go there.