Learn Arabic (Modern Standard): كم كتابا اشترى الطالب؟

In Arabic, the question word كم (how many) must always be followed by a singular noun, even though we translate it as plural in English. So you literally ask "How many book?".

Why is there an extra alif at the end of كتابا?

That alif holds the "an" sound (tanwin fatha) at the end of the word. After كم (how many), the singular noun must take this specific ending (the accusative case). Since كتاب (book) doesn't end in a tied-t (taa marbuta), we add an alif to hold those two little dashes.

Why does the verb اشترى (bought) come before الطالب (the student)?

This is the standard word order in Arabic verbal sentences! After our question phrase كم كتابا (how many books), we use the Verb-Subject order: first the verb اشترى (bought), and then the person who did the buying, الطالب (the student).

Why don't we need a separate word for "did" like in the English translation?

Arabic doesn't use helper verbs like "do" or "did" to make questions. The past tense verb اشترى by itself handles the action. The question word كم at the beginning is all you need to turn the statement into a question.