I know how important these tests are to our students, their parents and teachers and I am extremely upset at any distress that may have been caused

Christina Townsend, Edexcel chief executive

But 6,466 students in other subjects - who had been told they had failed - were upgraded to a pass.

The error, by the applied qualifications provider, Edexcel, was caused by a single pass mark being put into computers instead of different pass marks for each of the six tests.

The mistake was uncovered by the regulator, the Qualifications and Curriculum Authority, in a routine assessment which identified a discrepancy when the results were compared with those of other exam boards.

All of the students concerned had been sent personal letters of apology, a spokeswoman for Edexcel said.

Free re-sit

Those students who have learnt that they have not yet passed the tests have been automatically entered for the May re-sit and will be offered a second re-sit - free of charge - in July, if necessary.

The company's chief executive, Christina Townsend, said: "We are very sorry that this has happened."

"I know how important these tests are to our students, their parents and teachers and I am extremely upset at any distress that may have been caused.

"Our job now is two-fold: first to encourage and provide extra incentive to those who have discovered that they have not passed and secondly, to ensure that this never happens again," she said.

A helpline number for students, parents and teachers is 020 7758 5353.