If I keep going on this track, I should be able to go to university without having to write any entrance exams.
この場合、次のような言い方ができますよ。
ーIf I keep going on this track, I should be able to go to university without having to write any entrance exams.
「このままいけば、受験せずに大学に行けるはずだ」
to keep going on this track「このままいく」
to go to university「大学に行く」
without having to write any entrance exams「入学試験を受けることなく」
ご参考まで！
カナダ 
