1) Ann has to leave school early tomorrow. She has a dentist appointment after school. Здесь has to обозначает то что ей нужно было уйти раньше, тогда как may означает что она может уйти раньше, но не должна
2) If Ben gets permission from his parents, he may study in France next year. Здесь как раз must не походит, потому что это означает что он должен будет учиться, а он может
3) Kate should have studied a lot for the history exam. He got very high mark.
Переводится как «должно быть она занималась много»
4) Students mustn’t run in the school corridors. It’s against the rules. Это строгое правило, тут всегда must
5) You can raise your hand and wait before you ask a question.
Тут на самом деле зависит от контекста Если ученик решил отвечать без очереди, учитель может сказать You MUST raise your hand Ты должен поднять руку и ждать пока тебя не спросят
А можно интерпретировать как if you want to ask smth, you can raise your hand То есть ты можешь поднять руку.
Tom, Thanks for offering to chair tomorrow’s meeting for me. Apart from Sally and Dave, the sales staff …needn't.. attend, but the Personnel people …mustn't.. miss it, as several matters concern them. You …needn't.. mention the new offices – we can deal with that later and you …needn't.. discuss the changes in the computer course timetables since they’re not urgent. Don’t forget that you …mustn't.. mention the visit by inspectors – we don’t want people panicking. You …mustn't.. forget to bring up the matter of the Smithson contract, and you also …mustn't.. leave out the new manager’s appointment. You …needn't.. go into details unless people have questions. But remember you …mustn't.. give anyone the idea that their job is at risk because of this. Make it clear that employess …needn't.. speak unless they want to. Last but not least, you …mustn't.. mention the staff-party Mr. Jones wants to announce that himself. By the way, you …needn't.. take notes, as my secretary will be there to do that. Thanks, Laura.