We can use do, have and be (Unit 3) as auxiliaries.

With do and have, we use only the base form, -s form or past form (not the -ing form or past participle -- Unit 14) this way.

For the forms of be, look at Unit 16. If you are not sure which form to use each time, look at Unit 15.

Use do + BASE FORM for negatives and questions in one-word verb formations (Units 19, 21).

Money does not grow on trees.
Do they know how to make a fire?
Did you see Halley's Comet?

Use be + -ING FORM for continuous formations.

It is getting colder. (Present -- Unit 22)
Am I taking your seat? (Present -- Unit 22)
He was not driving very fast. (Past -- Unit 23)
I must be dreaming. (with modals -- Unit 27)
We have been swimming. (Perfect -- Unit 24)

Use be + PAST PARTICIPLE for passive formations.

Dates are grown in Arabia.
Were you shocked by the news?
It was not taken yesterday.

Use have + PAST PARTICIPLE for perfect formations.

Traffic has become a big problem. (Present -- Unit 24)
Have you done your homework? (Present -- Unit 24)
I hadn't learnt English before. (Past -- Unit 26)
They have been swimming. (Continuous -- Unit 24)
I must have lost it. (with modals -- Unit 27)

NOTICE: Do, have and be can also be lexical verbs (Unit 3):

Why did[auxiliary] you do[lexical] it?
I have[auxiliary] never been[lexical] there.
Has[auxiliary] he had[lexical] enough?
I am[lexical] tired.

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Exercise 17.1
Exercise 17.2