Be + infinitive: I am to ...

You are to do your homework before you can go out.You are not to leave this house without my permission. Is that clear?
At the end of the course, all students are to take a written exam.

Do these sentences sound formal or informal?

1 plans and (official) arrangements: He is to visit Nigeria
We use this structure in a formal style to talk about official and other plans and arrangements.

• The President is to visit Nigeria next month.
• We are to get a 10 per cent wage rise in June.
• I felt nervous because I was soon to leave home for the first time.

2 'fate': We were to meet again
Another use is to talk about things which are/were 'hidden in the future', fated to happen.

• I thought we were saying goodbye for ever. But we were to meet again, many years later, under very strange circumstances.

3 pre-conditions: If we are to get there in time ...
The structure is common in if-clauses, when the main clause expresses a pre-condition - something that must happen first if something else is to happen.

• If we are to get there by lunchtime we had better hurry.
• He knew he would have to work hard if he was to pass his exam.

4 orders: You are to do your homework
The structure is used to give orders, often by parents speaking to children.

• You are to do your homework before you watch Tv.
• She can go to the party, but she's not to be back late.

5 be + passive infinitive: It is not to be removed
Be + passive infinitive is often used in notices and instructions. (am/are/is (not) to be + past participle)

• This cover is not to be removed.

Sometimes only the passive infinitive is used.

• To be taken three times a day after meals. (on a medicine bottle)

Some other common expressions with be + passive infinitive:

• There's nothing to be done. She was nowhere to be found.
• I looked out of the window, but there was nothing to be seen.

6 in conditional sentences when talking about preconditions for something to happen

• If we are to catch that train, we shall have to leave now.
• If we are to solve the world's pollution problems, we must address environmental issues now.

7 frequently used in newspaper, radio and television reports to refer to future events. It expresses near certainty that what is forecast will happen

• A man is to appear in court later this morning charged with the murder of the footballer, Darren Gough.
• The Ministry of Trade and Industry has announced that it is to move three thousand jobs out of the capital and re-locate them in the North East.
• Work is to begin this week on the new bridge across the Nile north of Aswan.

8 be to + perfect infinitive is sometimes used to show that a planned event did not materialise:

• He was to have appeared in the West End show but broke his collar bone during rehearsals.
• Mr Jones was to have spoken at the meeting, but he had to cancel because of his illness.
• Sammy was to have married Sarah but then Jamie came along and the engagement ring he had given her was returned.
• I was to have started work last week, but I changed my mind.

Note that this structure exists only in present and past tenses. We cannot say that somebody has been to go somewhere, or will/must be to go somewhere. Participle structures (being to go) are not possible either.

[source: Practical English Usage & BBC Learning English]