Answer:
1. Convenció.
2. Escribiste.
3. Animaron.
4. Invitamos.
5. Publicaste.
6. Dieron.
7. Presentamos.
8. Hizo.
Explanation: Just to elaborate a little on the answer, it can be added that in this passage they are asking you to use the past tense of the verb, since at least some of the sentences are describing events for the past. Just to provide a few examples, in sentence 1 it says that the dance teacher convinced the best dancers to participate (the sentence in Spanish does not use the infinitive, but the Imperfect Subjuntive). In sentence 2 it says that the person did not write in the newspaper that the organising commitee was incompetent. The other sentences do not reveal the tense, but since I do not have more information about your assignment, I have used the past tense—specifically the "Pretérito Perfecto Simple" in Spanish—in all of them.