Selection of students for places at universities mainly depends on GCSE grades and predictions of A-level grades, both of which tend to favour applicants from independent schools. We have therefore developed a new type of test that would measure candidates' "deep learning" approach since this assesses the motivation and creative thinking that we look for in university students. We recruited 526 applicants to Oxford University and gave them a short commentary test and a learning style questionnaire. Specific deep learning approach questions correlated with results in the new test, and both predicted whether the candidate subsequently obtained a place at Oxford. Furthermore high scores on one open-ended commentary question, demanding arguments in favour of a case, produced a greater than 70% chance of obtaining a first class degree at the end of their course irrespective of the candidates' type of school attended or GCSE scores. Candidates from State schools scored as well as those from Independent schools in both tests. Thus our test seemed to index candidates' potential to succeed at a highly selective university, and might usefully be added to current selection procedures for such universities.