Here's the correct form for each sentence, using gerunds or infinitives as required:

### I. Give the correct form
1. We decided **to buy** a new car.
2. They’ve got some work **to do**.
3. Peter gave up **smoking**.
4. He’d like **to fly** an aeroplane.
5. I enjoy **writing** picture postcards.
6. Do you know what **to do** if there’s a fire in the shop?
7. Avoid **making** silly mistakes.
8. My parents wanted me **to be** home at 11 o’clock.
9. I dream about **building** a big house.
10. I’m hoping **to see** Lisa.

### III. Give the correct form
1. The children prefer **watching** TV to **reading** books.
2. The boys like **to play** games but hate **to do** lessons.
3. Would you like **to go** now or shall we wait until the end?
4. I can’t find my favorite book. You **see** it?
5. We used **to dream** of a television set when we (be) small.
6. Would you mind **showing** me how **to send** an email?
7. He always thinks about **going** swimming.
8. She dislikes **doing** a lot of housework.
9. My children enjoy **reading** books.
10. She looked forward **to seeing** you.

### IV. Give the correct form
1. They are used to **preparing** new lessons.
2. By **working** day and night, he succeeded in **finishing** the job in time.
3. His doctor advised him **to give up** **smoking**.
4. Please stop **talking**. We will stop **to eat** lunch in ten minutes.
5. Stop **arguing** and start **working**.
6. I like **to think** carefully about things before **making** a decision.
7. Ask him **to come** in. Don’t keep him **standing** at the door.
8. Did you succeed in **solving** the problem?
9. Don’t forget **to lock** the door before **going** to bed.
10. Don’t try **to persuade** me. Nothing can make me **change** my mind.