Mike Cresswell, director general of the AQA board, said he was concerned about the design of a new exam, offered by rival board OCR, which allows candidates to achieve a B grade with a score of just 17 per cent.
AQA is raising the matter with the Qualifications and Curriculum Authority, which is advising ministers on extending the trial nationwide from next year. Candidates could achieve the B grade in the top paper of OCR's new "two-tier" exam with 17 per cent, and an A grade with 45 per cent.
Tim Collins, shadow education secretary, said: "This does nothing to reassure teachers, parents and pupils, let alone admissions tutors and employers, that GCSEs are a reliable guide to effort and ability."
OCR said it was misleading to quote the 17 per cent figure. The top papers were designed so that a third of questions are targeted at A-star students, a third at A students and a third at B-grade candidates.
Thus a student scoring 17 per cent on the whole paper was actually achieving around 50 per cent on the B grade questions aimed at them, he said. They were not being assessed on their ability to answer A or A-star questions.
The controversy mirrors that surrounding current maths GCSEs, taken by hundreds of thousands of pupils and offered by AQA, OCR and Edexcel, which the new qualification has been designed to replace.
The outgoing exam features three levels, or tiers, rather than two. It is to be abandoned because of complaints that pupils entered for foundation level cannot achieve a C grade.
Last summer, The TES revealed how pupils could score an A grade on two papers of an old-style Edexcel maths GCSE with just 45 per cent. Again, the boards responded that the design of the papers lay behind the apparently low scores Last year's Smith report on the state of maths in schools warned that reports of low GCSE grade boundaries were damaging perceptions of pupils'
Questions from OCR's new GCSE
1. Solve this inequality 5 + n
11 - 3n
2. The ratio of the volumes of two similar objects is 1:64. What is the ratio of their surface areas?