Here are the completed sentences with the verbs in the correct tense, along with explanations for each:

1. Tom (not buy) his favorite newspaper yesterday.
**didn’t buy**
*Past simple, negative form to indicate an action that did not happen in the past.*

2. By the end of this year, Mr. Pike (retire) from that company.
**will have retired**
*Future perfect tense to express that the action will be completed by a certain point in the future.*

3. You (go) to the cinema right now.
**are going**
*Present continuous tense to indicate an action happening right now.*

4. Jack (find) his car key at 9 p.m. yesterday.
**found**
*Past simple form for a completed action in the past.*

5. They (not watch) this cartoon last night.
**didn’t watch**
*Past simple, negative form indicating that the action did not happen.*

6. He (talk) about his daughter now.
**is talking**
*Present continuous to show an action happening right now.*

7. There (be) a lot of people in the room last year.
**were**
*Past simple form used for a completed state in the past.*

8. While I (paint) the chair yesterday, Susan (visit) me.
**was painting** / **visited**
*Past continuous for an ongoing action interrupted by a completed past action.*

9. We (open) the door, then (drink) some water.
**opened** / **drank**
*Past simple for sequential actions in the past.*

10. We rushed to the station but we (be) too late.
**were**
*Past simple to indicate a completed state in the past.*

11. In the afternoon Leo often (watch) TV or (go) out.
**watches** / **goes**
*Present simple for recurring actions.*

12. Which countries (use) the euro as their currency?
**use**
*Present simple for a general fact.*

13. One of my sisters (live) in Australia.
**lives**
*Present simple for a general fact.*

14. When I left for school this morning, it (rain).
**was raining**
*Past continuous for an ongoing action in the past.*

15. His hair looks short. He (have) a haircut.
**has had**
*Present perfect to indicate an action that has relevance to the present.*

16. By next February I (write) my third book.
**will have written**
*Future perfect tense for an action that will be completed by a future date.*

17. I hope it (stop) raining before the match starts.
**stops**
*Present simple for a future dynamic situation.*

18. If nothing is done, one million species that are alive today (become) extinct in twenty years.
**will become**
*Future simple for a prediction based on a current condition.*

19. If your passport isn’t valid any more, you (not be able) to go abroad this month.
**won’t be able**
*Future simple negative for an inability due to a condition.*

20. Up to now, the teacher (give) our class five tests.
**has given**
*Present perfect for an action completed in the past with relevance to the present.*

21. Unless it (rain), we’ll go out tonight.
**rains**
*Present simple for conditionals.*

22. By the time I get up tomorrow, the sun (already rise).
**will have risen**
*Future perfect for an action that will be completed before another future action.*

23. Life (become) automated by 2100.
**will have become**
*Future perfect for a change expected by a certain future time.*

24. At this time next week, we (play) soccer again.
**will be playing**
*Future continuous to indicate an ongoing future action at a specific time.*

25. As soon as I hear anything about Barbara, I (let) you know.
**will let**
*Future simple for a future promise based on a condition.*

26. When he (be) young, he never (bother) too much about his appearance.
**was** / **bothered**
*Past simple for completed actions in the past.*

27. Since Mr. Hassan (become) president, both taxes and unemployment (increase).
**became** / **have increased**
*Past simple for a completed action and present perfect for an action continuing into the present.*

28. By the end of this century, we (use) up most of the world’s oil supplies.
**will have used**
*Future perfect for an action projected to be completed by a specific future time.*

29. I (study) English from 8 to 10 tonight.
**will be studying**
*Future continuous for an ongoing action at a specific time in the future.*

30. I always (play) tennis in the morning, but today I (play) volleyball instead.
**play** / **am playing**
*Present simple for habitual actions and present continuous for a current action happening instead.*

Feel free to ask if you have any questions about specific verbs or tenses!