A new study also suggests that institutions want to see applicants with good written English and work experience, and if youngsters are succeeding despite a difficult start in life.
The research, by ACS International Schools, is based on a survey of 99 admissions tutors in the UK and the United States.
It found that around 72 per cent of those questioned said they see a reasonable grasp of maths as an important attribute among applicants, up on 44 per cent last year.
Around 87 per cent value a student who can show that they can think and work independently (up from 72).
Evidence of a passion for a chosen subject (98 per cent) was the quality most highly rated by admissions tutors, followed by evidence of a positive attitude towards study (95 per cent) and good written English (94 per cent).
The study, which asked tutors what they looked for in an applicant besides academic qualifications and grades, found almost half considered evidence of success through a difficult start or background to be important.
Fergus Rose, head of marketing and admissions at ACS International Schools, said: "I think universities are now looking for students who are better equipped to contribute more and cope better with the rigours of university life and learning."