Learn Spanish (Latin America): ¿Completaste el trabajo ayer?

The ending -aste tells you it is the preterite (completed past) tense for tú (informal you). For regular -ar verbs like completar, you drop the -ar and add -aste to say you completed or did you complete.

Why is there no word for did in the Spanish sentence?

Spanish does not use helper verbs like do or did to ask questions. The past tense meaning is built directly into the verb completaste. The upside-down question mark at the beginning and the tone of your voice do the rest of the work!

Why doesn't completaste have an accent mark? I thought past tense verbs usually have them.

In the preterite tense for regular -ar verbs, only the yo form (like completé) and the él/ella/usted form (like completó) get written accent marks. The tú form (completaste) never takes an accent mark because the spoken stress naturally falls on the second-to-last syllable (com-ple-TAS-te).

What is the role of ayer in this sentence?

The word ayer means yesterday. It is a very common time marker used with the preterite tense because it clearly shows that the action was started and completely finished in the past, past making it a perfect fit for this verb form.