My take on this: Without the: it's about an exam that you reflect back on and you think after completing it that it was easy. You didn't know before, but now you know it was easy.
With the: you are taking multiple exams. One of them is supposed to be easy. Maybe someone told you that this exam is easy and the others hard. Now when you have taken the exam, you can say "this was the easy exam (out of the group of exams I am taking)". Saying this doesn't say anything about if I really thought the exam was easy after completing it. This could have been the hardest exam for me personally, but it was supposed to be the easy exam. Another possibility is that I am taking two exams and I know that one should be easy and the other hard, but I don't know in which order I will take them. After coming out from the easy exam, I can then say "this was the easy exam".
Context is important.
Now I don't know Czech that well, but it seems to me that we don't want the here.