Breakdown of Hast du die Aufgabe noch nicht gemacht?
du
you (informal singular)
machen
to make, to do
haben
to have
nicht
not
Questions & Answers about Hast du die Aufgabe noch nicht gemacht?
Why is gemacht at the very end of the sentence?
In the German Perfekt tense, the verb splits into two parts. The helper verb (here, Hast) takes the normal verb position, but the past participle (gemacht) is pushed all the way to the very end of the sentence. This creates a "sentence bracket" that hugs all the other information (du die Aufgabe noch nicht).
How is the word gemacht formed from the verb machen?
gemacht is the past participle of the regular verb machen (to do/make). For regular (also called "weak") verbs, you take the stem of the verb (mach), put ge- at the front, and add -t to the end. So: ge- + mach + -t = gemacht.
Why does the sentence use noch nicht instead of just nicht?
The combination noch nicht is the standard German way to express "not yet" (literally: "still not"). While nicht alone would simply mean "Have you not done the task?", adding noch adds the "yet".
Why does the sentence start with Hast?
Because this is a yes/no question. Just like in the present tense, you form a yes/no question in the Perfekt tense by moving the conjugated verb to the very front of the sentence. Here, the conjugated verb is the helper verb Hast.