1.Develop an exam that determines a minimum or base ability to take some advantage of the opportunities provided by the scholarship. Randomly select from the pool of students who pass this test.

Or

2. Split the scholarships in half. Half are awarded purely based on ordered rank for scores on an exam. Half are awarded randomly.

I think you need some type of random element to ensure that those who are merely disadvantaged by income or who are later bloomers for their age can be awarded scholarships. The random nature would also eliminate the subjective nature of teacher assessments.

That said, maybe I'm being overly influenced by having just read Outlier by Gladwell. Flawed as I think the book is, it did have some good nuggets.