Pupils could achieve an A grade in trials of new GCSE maths exams without answering any of the hardest questions, The TES can reveal.
Teenagers could also gain a C through answering questions designed only as of G, F and E difficulty. In one paper, the grade 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 from September, has been dumbed down.
And they will do little to assuage employers' concerns that pupils can achieve top passes in maths or English without having mastered key aspects of the subjects.
The Government is going ahead with the changes even though an expert evaluation of the trial concluded that it was not possible to tell from their grade how much maths pupils know.
Maths GCSE courses are to change from September, as ministers react to fears that the exam's structure has demotivated hundreds of thousands of teenagers.
The present "three-tier" system means pupils on the lowest one can achieve only a D at best, which teachers have argued gives them little incentive to work hard.
A new arrangement has been piloted 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, gave lower-ability pupils a better chance of achieving a higher grade.
In the trial, the top-tier papers, covering the grades D to A*, saw 80 per cent of the questions set at B grade difficulty or below. Yet pupils needed only 67 per cent to get an A, and 81 per cent for an A*.
The report said: "A candidate could get a grade A without doing any grade-A questions. There was a lot of concern that the two-tier trial exam structure would prove to lack challenge for the most able."
Some 55 per cent of questions were set at D or C difficulty. But pupils needed only 49 per cent for a grade B. The report said schools might consider encouraging pupils to take GCSEs and AS-levels early if they felt GCSEs were too easy for brighter youngsters.
The Qualifications and Curriculum Authority has reacted by promising to increase the number of more difficult questions when the exam is launched for real.
But maths experts said it was still likely that pupils would be able to gain grade A* without doing any A* work.
Maths GCSEs have been plagued by low grade boundaries.
Two years ago, The TES revealed how pupils could get a grade A with 45 per cent on one Edexcel paper. An official inquiry found employers said grade Bs or Cs were virtually worthless as a guide to pupils' abilities. The latest revelations suggest the new exam has not solved this problem.
Ministers will therefore have to rely on separate new functional skills maths tests, which all teenagers will have to pass to gain a GCSE from 2009, to ensure that pupils are proficient in areas such as basic numeracy.
Some have predicted that these new tests might be harder to pass than today's maths GCSE.
A Maths Association source said: "A lot of people are concerned that (the new structure) has been set up to provide an easier route to grade C."
Tony Gardiner, reader in mathematics at Birmingham university and a past president of the MA, said: "The two-tier GCSE will dumb down. It's obvious."
Only 20 per cent of the questions on the higher-tier trial papers would be at A or A* difficulty, so brighter pupils would spend a "minute amount of time on anything that's of any interest", he said.
But a QCA spokeswoman said there had been no change to the teaching content and that the two-tier model was designed to ensure everyone could achieve a C, provided they reached the required standard. "The two-tier model will also be designed to ensure it challenges the brightest candidates," she said.