试卷 refers to the physical paper itself. Don't confuse with 考试 (kǎoshì, the exam/act of testing). You take a 考试 and write on a 试卷.
culture
China's exam culture (考试文化) dates back to the imperial examination system (科举, kējǔ). Even today, exams like 高考 (gāokǎo, college entrance exam) are defining events in students' lives.