Most applicants are required to take a written admission assessment, either pre-interview or at interview. Full information about this can be found on the University website (http://www.undergraduate.study.cam.ac.uk/applying/admissions-assessments).
For Mathematics and Music there will be an assessment (in addition to any University admissions assessment), which is specific to Downing College and will take place at Downing College if the applicant is invited to interview:
Mathematics: A written test, lasting 30 minutes, will take place during the day of the interview. Sample questions can be found here.
Music: A written test, lasting one hour, will precede the interview and test basic harmony, counterpoint and essay-writing skills.