Few Sentences

A exersice in my workbook.
You need to choose between last/the last/latest:

have you heard the latest news?
where were you last week?
last time I saw him he was very cheerful.
The Tempest was one of shakespeare's last plays.
What a beautiful car! is that the latest model?
According to the latest report nobody was injured.
That was the last we saw of her.

Thanks in advance!