To achieve an A, brighter students had to score just 45 per cent on two papers of an Edexcel maths exam. The papers were taken by 80,000 pupils and more than half got an A or A*.
Across three higher-tier papers, candidates needed an average of 51 per cent to achieve an A, while a mark of 22 per cent earned a C. Only 0.7 per cent of those entered failed to achieve a C.
The figures were described as "ludicrous" by a leading maths expert, and even Edexcel admitted it may have been possible for some students to achieve As without having mastered a central topic such as algebra. Roger Porkess, who developed the first modular maths A-level syllabus, said:
"These grade boundary figures are incredibly low. It's ludicrous."
Doug French, of the Maths Association, said: "To give pupils a paper in which they can get a high-grade pass on less than half marks seems crazy.
This suggests pupils can achieve A grades by missing whole swathes of maths."
Edexcel said the boundaries reflected the fact that the papers consisted entirely of questions targeted at brighter students. But the revelation will provoke more claims of dumbing down.
Last month, the Confederation of British Industry renewed its criticism that many teenagers were leaving school with an inadequate grasp of basic arithmetic.
That claim has been backed by the head of an 18-month government maths inquiry. Professor Adrian Smith agreed GCSEs were virtually worthless as a guide to achievement.
However, Edexcel rejected any suggestion that standards were falling. Its maths GCSEs are offered at three difficulty levels: higher, intermediate and foundation. Taken as a whole, only 14 per cent of maths candidates achieved A or A-star, it said.
Among those taking the higher-tier papers, this figure was 54 per cent. The board admitted it was "uncomfortable" that the grade boundaries had been set so low. But it said this was inescapable given the structure of maths GCSE, set by the Qualifications and Curriculum Authority.
In higher-tier papers, a quarter of questions are targeted at C grade students, a quarter at B grade, a quarter at A and a quarter at A-star.
Edexcel said this meant that a C-grade pupil scoring 13 per cent was effectively scoring 52 per cent on questions they would have been expected to answer. A grade students had to score 60 per cent on questions targeted a A, B and C grades.
Marks required for an A this summer for a similar higher-tier qualification, offered by the Assessment and Qualifications Alliance board, equated to 61 per cent, and for a C, 28 per cent.
A new, two-tier maths GCSE is currently under investigation, but critics say the papers' design means grade boundaries could be just as low in the future.