The concerns centre around the use of “structured” exam questions in which students are led through problems by being given a number of intermediate steps.

The report said that this type of question has become increasingly common, despite the fact that exam boards have twice been asked to scale down its use.

In its last review, conducted eight years ago, the QCA said that the structure made it more difficult for students to demonstrate their ability to solve a multi-stage problem. However, the situation had become worse by 2004, it said, with almost all questions now highly structured and candidates given no scope to develop mathematical arguments.

“Questions (have) become so structured as to become leading,” the report said. There was little attempt to test the construction of rigorous arguments, even though pupils were supposed to be assessed on this.

The report added: “The reviewers commented repeatedly on how the 2004 AS and A2 exam papers had failed to provide candidates with an opportunity to demonstrate their knowledge.”

Some Curriculum 2000 changes, introduced to offer more choice for students, also offer ammunition for critics. The report said students no longer have to take any mechanics at A-level, even though that part of the subject is a foundation for much university maths, physics and engineering study and is not offered at GCSE.

The watchdog also reported that even students with good GCSE results had mastered only some areas of the maths syllabus. In 2004, The TES revealed how pupils could get an A grade at GCSE with only 45 per cent on some papers.

Doug French, of the Mathematical Association, said: “People have been saying this for a long time. If you want people to be able to do maths, it is not good to tell them how to doit in the question. The question now is what the QCA is going to do about it.”