Strathclyde University, which made the claim, has set up a Maths Skills Support Centre to help students who are at risk of leaving because they cannot cope with maths course work.
It returns the spotlight to the level of skills pupils learn at school and whether these are sufficient to prepare them for a university education.
Last week, The Herald revealed Dundee University's concerns over years of poor maths and science learning in secondary schools.
The institution said the problem was particularly acute in so-called Stem subjects such as science, technology engineering and mathematics – which are vital to the country's future economic success. Professor Martin McCoustra, chairman in chemical physics at Heriot-Watt University, said his institution had to run top-up maths lessons for first-year students.
The latest warning is revealed in Strathclyde's outcome agreement with the Scottish Funding Council, which sets out the objectives it will work towards in return for its public funding.
The document states: "Students on courses which included a mathematics component and who had not undertaken mathematics in the year immediately preceding entry were twice as likely to fail to be retained beyond first year than those who had studied mathematics immediately prior to university. In response, the university created the Maths Skills Support Centre to support undergraduate students with their mathematical studies."
The university also sets out details of a project to encourage more students from deprived backgrounds to study engineering. It has set up the Engineering Education Scheme to provide opportunities for pupils in S5 and S6 to work on scientific, engineering and technological problems through six-month industry projects.
"Through this scheme, the university is given early access to students with high academic potential, including those from schools that historically have not sent large numbers of pupils into higher education," the outcome agreement states.