Learn Turkish: Öğrenci soruyu cevapladı. - The student answered the question.

The verb stem is cevapla- (to answer). To make it past tense, we add the suffix -dı. We use -dı instead of -di or -du because the last vowel in cevapla- is 'a', which dictates our choice under standard vowel harmony rules. Because the subject is "the student" (a third-person "he/she/it"), we do not add any extra personal ending after -dı.

Why is there a -yu at the end of soruyu?

Soru is the noun for "question". Because it is the specific direct object of the verb here (the student answered "the" question, not just any question), it takes the definite accusative case suffix. Vowel harmony turns this suffix into -u. Since soru already ends in a vowel, we must insert the buffer letter -y- to prevent two vowels from crashing together, giving us soruyu.

I know cevap means "answer" as a noun. Why does the verb start with cevapla-?

You can often turn Turkish nouns into verbs by adding the suffix -la or -le. By adding -la to the noun cevap, we create the verb stem cevapla-, which means the action "to answer". Then the past tense suffix -dı simply attaches to this new stem.