When I first read the sentence, I automatically placed "a" in the first gap. Both "a" and "the" are possible for the first one, but the meaning of the sentence with "the" is a bit unusual. If I chose "a", I would place a comma before "with...". It's a slightly bad example for a question, unfortunately. "the best teacher" - there can be only one, unique "best" teacher. Always: the + superlative adj. + noun "the school" because the sentence implies that the reader is familiar with Terry, and the fact that he teaches at a particular school. We can imagine that the previous sentences were: "Terry worked for many years as a teacher at St Trinian's School. One day, he took an exam to become an excellent teacher......."

"Terry became the teacher with the best exam results in the school" = "Terry se convirtió en EL profesor con LAS mejores notas de todo EL colegio". The teacher: Porque estas hablando de un profesor entre muchos otros profesores del colegio. En español es igual, tu no dirías "se convirtió en UN profesor con las mejores notas..." hay que decir "en EL profesor con". The best exam results: Es igual que en español "en el profesor con LAS mejores...". In the school: Aquí te estás refiriendo a un colegio en concreto (es igual en español). "the" es para algo concreto (el, la...) "a/an" para cuando hablas en general (un/una), en general es como en español. La dificultad del "the" está en que en inglés hay muchas situaciones en las que no se usa, mientras que en español se usa mucho. Un ejemplo: "A la gente le gusta Melendi" = "People like Menlendi" (como puedes ver en este caso "the" no se usa) Sigue esforzandote, te deseo mucha suerte :D

English has two articles: the and a/an. The is used to refer to specific or particular nouns; a/an is used to modify non-specific or non-particular nouns. We call the THE definite article and A/AN the indefinite article. I think that s why we used 'The', we are talking about a specific person.(Terry), a specific noun and a specific place (school). Hope this helps!

Thank you so much for your answer!

I would also have put 'a' for the first answer as I interpreted the sentence as being about Terry qualifying as a teacher with the best marks in the qualifying exam of all the students in his college.