The 14-19 diploma courses could have a "devastating" impact on the maths ability of school leavers and fail to prepare students for university, curriculum experts warn.
Students opting for the engineering diploma will study only a fraction of the maths they would at A-level, says the advisory group Maths in Education and Industry (MEI).
The engineering course, which has the greatest maths content of all the diplomas starting next month, will deliver just 240 hours of taught maths, compared with 360 hours at A-level, an MEI report showed.
This will leave a gaping hole in maths education and create problems for university courses in numerate subjects.
Roger Porkess, MEI's chief executive, said that if diplomas took off as ministers hope, a teacher shortage would see the maths element being taught by unqualified staff.
"Some of the maths content in the engineering diploma is the same as in AS and A-level," he said. "But in A-level it is given twice as much time. Without it, there is no way the material can be successfully learnt. The maths content of the diplomas generally is not broad enough when you go to university and need to think mathematically."
The independent MEI group has complained that diplomas are being directed at top-performing students, which means that the brightest students could end up dropping A-level maths in favour of special maths units on diploma courses.
"This sets up serious potential problems," the report says. "Indeed, it would not be an overstatement to say that a successful diploma programme would have a devastating effect on mathematics."
Several top universities, including Cambridge, have backed the engineering diploma as good preparation for an engineering degree. But MEI is concerned that the "rich mathematical experience" the present A-level syllabuses offer would be lost to diploma students.
The comments follow an earlier warning by the independent Advisory Committee on Mathematics Education, which said that all level three diplomas (equivalent to A-level) should have maths content.
The committee also voiced concerns that diplomas did not have sufficient content for future maths specialists.
An estimated 20,000 pupils will take up the first five diplomas. To pass, they will have to take GCSE-level functional skills tests in maths. The MEI group questioned whether there would be enough trained maths teachers to cope.
A Department for Children, Schools and Families spokesman said: "The diploma has deliberately been designed for students of all abilities, including those who aspire to go to the top universities.
"A-level maths can be incorporated into advanced diplomas and, for those students who have traditionally taken two maths A-levels, the extended diploma - worth four-and-a-half A-levels - could now be the right choice for them."