Hi Larry, 

Sadly, it doesn't follow that passing the Senior Candidate exam would have defined Rebecca as a student at the University of Oxford.  Apparently the Senior exam was for under-18s, and the Junior exam for under-15s.  So these would have been early precursors of what we in the UK now call A levels and GCSE respectively, both part of the General Certificate of Education.  (It seems A levels would broadly correspond, in US terms, to a grade 12 high school diploma - although I may be mistaken here, I'm not familiar with the US system.)  Those who passed the Senior Exam were given the title "Associate in Arts".

There are fuller narratives here:
https://www.bodleian.ox.ac.uk/__data/assets/pdf_file/0011/194960/Associate-in-Arts,-A-History.pdf  

and here:
https://archive.org/details/someaccountofori00acla 

Peter Lobbenberg, London