Standardized national exams are normally very highly correlated to academic ability as represented by grades by the same teacher. Actually, where I live, this is essentially the explicit goal of the national exams - they then generate a score that normalizes the difficulty of each teacher and use it both for selection and to evaluate the accuracy of the exam and update it next year.

The data from which I learnt this isn't public AFAIK, but I'm sure similar studies exist for other countries.