I am going to underline only the possible answers ... only the possible for me.
1. If you are thinking of going abroad on vacation, you should begin ___ collecting information from travel agencies.
2. The audience was amused ___ seeing the clown fall off the stage.
3. Ann was very angry ___ finding her son asleep instead of working.
4. A young woman has to be careful ___ giving her address and phone number to strangers.
5. A politician has to be clever ___ manipulating people into giving him their votes.
6. She is conscious ___ her husband having a love affair with his secretary.
7. A personnel manager must be skilled ___ dealing with people's relationship problems.
8. I'm sick ___ looking after your children! Maybe you should hire a babysitter.
9. Mrs. Henderson felt guilty ___ sending her young children to boarding school.
IS it a problem if your students have to choose more than one correct answer? True, it is a bit heavier to be tested this way but ... make them sweat.