Teenagers could also gain a C through only answering questions designed for G, F and E difficulty. In one paper, the C boundary was set at 25 per cent.

The revelations have led to accusations that the new exam, to be taken by virtually every pupil in England and many in Wales from September, has been dumbed down. And they will do little to assuage employers’

concerns that pupils are able to achieve top passes without having mastered key aspects of the subject.

Westminster is going ahead with the changes even though an expert evaluation of the trial concluded that it was not possible to tell, from a pupil’s grade, how much maths they know.

Maths GCSE courses are to change from September amid concerns that the exam’s structure has demotivated many teenagers.

Under the current “three-tier” system, pupils on the lowest tier can achieve only a D at best, which teachers argue gives them little incentive to work hard.

A new “two-tier” arrangement has been under trial, with pilots in Welsh schools, in which every pupil has the chance to achieve a C. Two versions were tested last summer. Ministers opted for the model which, according to an independent evaluation report, gave lower-ability pupils a better chance of a higher grade.

In the trial, the top-tier papers (grades A* to D) saw 80 per cent of the questions set at B grade difficulty or below. Yet pupils only needed 67 per cent to get an A.

The report said: “A candidate could get an A without doing any grade A questions. There was concern the two-tier structure would lack challenge for the most able.”

England is switching to the two-tier model in September, but the old three-tier-style maths course will remain an option in Wales for the September 2006 cohort only.