Where are we to meet? - We are to meet at the station

You are to finish the work and then you may go.

In this meaning the phrase “ be supposed to do sth ” can be synonymous to the verb “ be to ” meaning that something is expected or required according to a rule, custom or arrangement:

We were supposed to meet at 5 o’clock.

When the previously arranged action is not carried out the perfect infinitive is used:

He was to have made a speech at the meeting, but he fell ill.

2. The verb be to is used to express official instructions, commands, orders with the non-perfect forms of the infinitive of the notional verb:

You are to cross the street under the green light.

Students are to return the books by the end of the school year.

3. The verb be to is used in interrogative sentences to ask about a person’s order or wish:

What am I to do next?

How many times a day am I to take this medicine?

4. The verb be to is used in negative sentences to express strict prohibition:

You are not to leave the room without permission.

5. The verb be to followed by the non-perfect passive infinitive is used to express possibility:

Nothing was to be done under the circumstances.

The key was nowhere to be found.

6. The verb be to followed by the non-perfect infinitive is used to express something thought of as unavoidable, something that is destined to happen:

He was never to see his native town again.

NEED

The verb need can be used both as a modal and as a notional verb. If it is used as a modal verb, the negative and interrogative forms of the present simple can be built with the help of the auxiliary do or without it; it can also take the ending ‘ -s’ in the 3^rd person singular:

You needn't do it. You don't need to do it.

Need I come? Do I need to come?

She hardly needs to tell you about it, does she?

The modal verb need has the following meanings:

1. The verb need is mostly used to express the absence of necessity to fulfill the action of the notional verb. The indefinite infinitive of the notional verb is used:

She needn't hurry, there's plenty of time.

We don't need to go shopping now; there is enough food at home.

The modal verb need is seldom used in affirmative sentences, except with such adverbs as ‘ hardly ’, ‘ scarcely’ which are half-negative in meaning:

He hardly needs to be helped.

I hardly need to explain anything.

When the verb need is used in affirmative sentences it refers to immediate necessities:

I’m hungry; I need to eat something immediately.

The past form negative of the verb need followed by the indefinite infinitive is used to express the absence of necessity in the past, implying that the action of the notional verb was not carried out:

They didn't need to buy anything (and they didn't buy anything).

The present form negative of the verb need followed by the perfect infinitive is used to say that the action of the notional verb was performed though there was no necessity:

He needn't have come so early.

Note: In Modern English ‘ didn't need + indefinite infinitive’ is sometimes used in oral speech to denote an action that was performed though it was not necessary (the verb need is stressed), while ‘ didn't have to + indefinite infinitive ’ is used to say that the action was not necessary and wasn't performed:

You didn’t need to water the flowers because the ground was wet enough.