Kate went to the airport with her parents and her brother Nick. While they (кажется вы пропустили слово they, когда писали задание) were waiting at the airport, Nick remembered that he had something important to tell Kate. Her friend phoned just as they were leaving to ask what time Kate's flight left. Previously Kate's friend had thought that she wouldn't be all to get to the airport in the time but she turned up while Kate was saying goodbye to her parents. She finally went through passport control and everybody waved (насколько я поняла, то тут должно было быть wave, а не wake, опечатка (?)) goodbye.
1. Kate ( went) to the airport with her parents and her brother Nick. While
they (were waiting) at the airport, Nick ( remembered) that he ( had)
something important to tell Kate. Her friend (phoned) just as they (were
leaving) to ask at what time Kates flight ( left). Previously Kate's
friend (had thought) that she wouldn't be able to get to the airport in time
but she ( turned) up while Kate (was saying) goodbye to her parents. she
finally (went) through passport control and everybody (waved)
goodbye.
2. It (was) the day of his English exam. He ( woke) up and
( looked) at this alarm clock. He (saw) that it (had stopped) raining
during the night. He (realised) he would be late for his exam. He (was) an hour late and exam had already ( begun). When he (was sitting) at the
table, he ( found) that he (had left) his pen at home. He (asked) his
friend to give him a pen. Despite everything (going) wrong
he (passed) his exam.
Источник: интернет.