Конечно, я помогу вам разобраться с этими предложениями и объясню, как правильно использовать инфинитив после глаголов. В английском языке есть несколько глаголов, после которых мы используем инфинитив с частицей "to" (to + verbo). Ниже я приведу разбор каждого предложения с объяснением.
He made me (do) it all over again.
— Используем инфинитив без "to" после глагола "make" в значении заставлять.
— Правильно: He made me do it all over again.
— Объяснение: "made" — глагол, требующий инфинитива без "to" после себя.
Her father made her (learn) the lessons.
— Аналогично "made," требующий инфинитив без "to."
— Правильно: made her learn the lessons.
If you want us (make) the work quickly you should let us (start) at once.
— После "want" используется "want" + "to" + глагол.
— После "let" — "let" + объект + "do" — без "to."
— Правильные варианты: want us to make the work quickly (или "want us to finish" — зависит от контекста), и "let us start at once."
В данном случае правильное решение:
— If you want us to make the work quickly, you should let us start at once.
Would you like me (read) now?
— После "would like" обычно идет инфинитив с "to."
— Правильно: Would you like me to read now?
They won't let us (leave) the classroom till our control work has been checked.
— После "let" — "let" + объект + "do" без "to."
— Правильно: let us leave.
He wouldn't let the children (play) in his study.
— Аналогично: let + объект + "do" без "to."
— Правильно: let the children play.
Please let me (know) the results of your exam as soon as possible.
— После "let" — без "to."
— Правильно: let me know.
He made us (wait) for two hours.
— После "made" — без "to."
— Правильно: made us wait.
I let him (go) early as he had done his task.
— После "let" — без "to."
— Правильно: let him go.
I'd like him (enter) the university but I can't make him (do) it.
— После "like" — "like" + "to" + глагол.
— После "make" — без "to."
— Правильно: I'd like him to enter the university, but I can't make him do it.
I want her (learn) English.
— После "want" — "want" + "to" + глагол.
— Правильно: I want her to learn English.
I heard the door (open) and saw my friend (come) into the room.
— После "heard" и "saw" можно использовать инфинитив без "to" или герундий.
— В данном случае "heard" + объект + инфинитив без "to" — правильный вариант.
— Аналогично и "saw."
— Правильно: I heard the door open and saw my friend come into the room.
I heard her (play) the piano.
— Аналогично: heard + her + инфинитив без "to" — "play."
— Правильно: I heard her play the piano.
I saw him (go out) of the house.
— После "saw" — инфинитив без "to."
— Правильно: saw him go out of the house.
The teacher advised us (use) dictionaries.
— После "advised" — обычно "advice" или "advise" с инфинитивом с "to."
— Правильно: The teacher advised us to use dictionaries.
Her father doesn't allow her (go) to the cinema alone.
— После "allow" нужен инфинитив с "to."
— Правильно: doesn't allow her to go to the cinema alone.
We expect our basketball team (win) next game.
— После "expect" — "expect" + "to" + глагол.
— Правильно: expect our basketball team to win next game.
We don't want you (tell) anything.
— После "want" — "want" + "to."
— Правильно: want you to tell.
I saw them (open) the window.
— Аналогично предыдущим — инфинитив без "to."
— Правильно: saw them open the window.
That is too difficult for you to do, let me (help) you.
— После "let" — "let" + объект + "do" без "to."
— Правильно: let me help you.