The key is that you should understand the English word "OF". OF itself could mean differently in English according to the context.
In this case, I think the reason is that 高考（exam） can not owner a day logically. Similarly in English, the exam's day is logically incorrect. However, 'OF' in English could be used when referring to the day, moment when something happened. For example, the day of the accident. So, in "the day of the exam", it does not express the ownership, but the exam happened in that day or the day in which the exam happened.
Unlike English, we don't have "OF" phrase. So, in Chinese, to interpret "the day of the exam" is equally to interpret "the exam happened in that day" or "the day in which the exam happened". We can use the prep phrase 在...那天，and then it will become 在高考那天. If you omit 在, it will become 高考那天.
On the other hand, OF could be interpreted differently in Chinese according to the context. It could be ...的 denoting the ownership or a prep phrase. For example, "the length of the bench": 凳子的长度. a cup of tea: 一杯茶（you shouldn't translate this to 一杯的茶）.
In summary, there is not a dedicated equivalent in Chinese for the word "OF". You have to make it differently according to the context.