Contention 1: Exams provide a means to objectively evaluate what a student has learned.
Although many students and teachers dislike grades an exams, there needs to be an objective standard that measures what a student has learned. Without exams, teachers would be forced to resort to two methods of grading. First, they could choose not to assign grades. This, however, does not give employers and colleges a fair method to objectively evaluate whether or not a student is capable of learning the material presented to them and whether or not they have mastered the abilities necessary to carry out specific functions. Second, the teacher could assign grades subjectively. This also undermines the idea of an objective evaluation because it harms students who may anger the teacher for various reasons and aids students with excellent social skills put who have a poor mastery of the material. Exams correct for these flaws by providing for a more objective basis for evaluating what a student has learned.
Contention 2: Exams serve as a feedback mechanism for the teacher. Another reason to give exams to students is that teachers need an objective basis for determining whether or not they have taught a specific section of the material properly. Since the only way to do this is to test the students' mastery of the material, exams can provide teachers with valuable information as to whether or not they need to change their teaching styles or the way that they presented the material. If most students do poorly on questions from a specific unit, for example, teachers will be able to correct their styles and aid students in mastering the proper material.
I gave you net benefits that show that you should negate. Second, not all students find exams stressful, so this is just an unwarranted assertion that you can throw out. Finally, turn this argument...