Cambridge professors will set tough new maths A-levels after the university became the first to intervene in the exams system.
Mathematicians will put together new syllabuses and exam questions as part of the government's reforms to drive up education standards, The Daily Telegraph reports.
It says that Cambridge's department of pure mathematics has outlined how new-style maths A-levels should be structured, in a report sent to the Department for Education.
Under the changes pupils would study A-levels that focus around a series of "key mathematical ideas", such as complex numbers, trigonometry, combinatorics, probability and centres of mass.
The report, by Professor Martin Hyland, head of the department of pure mathematics, argues that changes are needed because "the majority of the talented students which Cambridge is able to recruit do not have sufficient mastery of basic mathematics to enable them to confidently engage with anything other than routine problems".
It said: "Existing A-level curriculums treat topics superficially and the UK has lost the tradition of teaching school mathematics coherently and in depth.
"The effect on Cambridge is acute."
In a key change, it recommends creating "graded sets of problems" for bright teenagers, while resources for lessons will be made available online.
The assessments will be aimed at all students, but the university proposes a "range of demanding questions to challenge the most able," the Telegraph said.
The move by Cambridge is the first since Education Secretary Michael Gove announced earlier this year that he intends to give universities, particularly the most elite institutions, "a far greater role" in designing A-levels in the future, amid concerns that the qualifications are failing to prepare teenagers for degree study.
However, a leading higher education group has said it is against the plan.
Universities UK (UUK) said it does not believe it would be "advisable or feasible" for the sector to "take ownership" of the qualifications.