Perfect forms of modal verbs

Paraphrase the following sentences using the words provided so that the meaning changes as little as possible. Use perfect forms of modal verbs.

1. I'm sure that John went to London last year.
John must ........................................................................... last year.
2. It's impossible that you saw Jane at the gym. She hates sports.
You .............................................. Jane at the gym. She hates sports.
3. You bought ten oranges although it wasn't necessary.
You ............................................................................... ten oranges.
4. It's bad that you told Lilly about her husband's affairs.
You oughtn't ............................................ about her husband's affairs.
5. I didn't help Jim because he didn't ask me.
If Jim ................................................................................... done it.
6. It was a bad idea to have that old car repaired.
You shouldn't ..................................................................... repaired.
7. She was free to visit me during my duty hours (but she never did).
She could ....................................................... during my duty hours.
8. At the end of the week our course will be over.
By the end of the week we ............................................ our course.
9. Perhaps this book belonged to Grandma.
This book ................................................................... to Grandma.
10. It's certain that Tim took your umbrella by mistake.
Tim ................................................... taken your umbrella by mistake.

KEY
1. have gone to London, 2. can't have seen, 3. needn't have bought, 4. to have told Lilly, 5. had asked me to help him, I would have, 6. have had that old car, 7. have visited me, 8. will have completed, 9. may/might have belonged, 10. must have

While making this exercise I got a little help from this website: http://www.learnamericanenglishonline.com/Yellow%20Level/Y12%20Perfect%20Modals.html
I also had a look at this book: Close, R.A. 1975. A Reference grammar for students of English. London: Longman.