Breakdown of Половина студентов не сдала экзамен, таковы результаты.
не
not
студент
student (m)
экзамен
exam
результат
result
Questions & Answers about Половина студентов не сдала экзамен, таковы результаты.
Why use таковы instead of такие in this sentence?
Таковы is the short form of the demonstrative pronoun такой (such). In this sentence, it acts as the predicate to sum up a situation ("such are the results"). While you could grammatically use такие, the short form таковы is the standard, much more natural choice in Russian for making this kind of concluding statement.
Why does таковы take the plural ending -ы?
The predicative pronoun таков must agree in gender and number with the noun it points to. Because it refers to результаты (results), which is plural, it takes the plural form таковы.
Since студентов is plural, why is the verb сдала in the feminine singular?
The core grammatical subject of that clause is the noun половина (half), which is feminine singular. When a subject consists of половина plus a noun in the genitive plural, the verb typically agrees strictly with половина, taking the feminine singular form.
Why do we use the perfective verb сдала here? Wouldn't the imperfective be better for a negative sentence?
For exams, the verb aspect completely changes the meaning of a negative sentence. The imperfective не сдавать means "not to take" the exam at all. The perfective не сдать means the attempt to pass was not successful, which translates to "failed" the exam. Since they failed, the perfective is required.