Investigations have been launched in England and Wales into claims that some examiners gave teachers unfair advice on GCSE and A-level questions.
The Daily Telegraph said it had filmed an examiner telling teachers at a seminar which questions to expect.
The Welsh exam board has suspended two people, but insists the claims relate to a misunderstanding of advice.
The prime minister's spokesman has said the exam system is in urgent need of reform.
And the Education Secretary Michael Gove says the claims "confirm that the current system is discredited".
The boards involved are investigating - as are England's exams regulator Ofqual and the Welsh government - which regulates exams taken in Wales.
Ofqual said exams should be run in a way that was "fair and open to all".
The Telegraph said it had secretly filmed a chief examiner telling teachers, who had each paid up to £200 to attend the seminar, which questions their pupils could expect in forthcoming exams.
It said the advice appeared to go far beyond standard "guidance".
The newspaper said its undercover reporters went to 13 meetings organised by exam boards used by English schools.
It alleged that teachers were "routinely" given information about future exams, including questions, syllabus areas to focus on and even the specific words or facts students must use to win marks.
It quoted a named examiner at a seminar on GCSE history as telling teachers that a compulsory question in the exam "goes through a cycle".
He gives the subjects for the forthcoming exam, adding: "We're cheating, we're telling you the cycle."
When told that this information was not in the course specification, the examiner said: "No, because we're not allowed to tell you," according to the paper.
Mr Gove said he had asked the new chief executive of Ofqual, Glenys Stacey, to investigate and report back within two weeks.
He said: "As I have always maintained, it is crucial our exams hold their own with the best in the world. We will take whatever action is necessary to restore faith in our exam system. Nothing is off the table."
Mrs Stacey said: "It's right that awarding bodies provide support and guidance for teachers, it's not right if they're selling privileged access to inside information."
Ofqual says it might consider "pulling" certain exam papers or questions in up-coming exams.
The prime minister's official spokesman said: "We are very clear that our exam system needs fundamental reform.
"The revelations we have seen today show our current system is discredited. We are very clear we will take whatever action is necessary to restore faith in the exam system."
The WJEC exam board, one of those named, said: "Most of the issues raised... relate to an incomplete understanding of the generic advice on teaching approaches given in good faith at professional development sessions with the aim of enhancing students' appreciation of the subjects studied and their assessment."
It added that the courses described in the article were "by no means secretive" as the information was freely available on its public website to ensure teachers and students were not disadvantaged in cases where teachers were unable to attend.
Another board, Edexcel, said examiners' contracts stated that no discussion of the content of future exams should take place.
"Any breach of this clear contractual obligation is something we would take extremely seriously, and act on. On this basis, we are speaking to those examiners identified... in order to fully understand the context and complete nature of the conversations they had at these events," it said.
Teachers and head teachers say both schools and the exam boards are working under "intense pressure" .
Russell Hobby, general secretary of the National Association of Head Teachers said: "For too long we have judged schools on their ability to exceed crude thresholds of exam passes, but this was only ever a proxy for a great education.
"As today's allegations suggest, passes can be achieved in good ways and bad ways.
"As long as the system is managed on crude data and cruder incentives, these risks will be rife: market forces crowd out ethics, and league tables crowd out judgement.
"These events remind us that the profit motive sits uncomfortably with the values of education."
Shadow education secretary Stephen Twigg said the Telegraph's allegations were "extremely serious" and the investigation by Ofqual must "leave no stone unturned".
"Parents rightly expect that their children are taking tests on a level playing field with others. The government must act quickly and decisively to ensure faith in A-levels and GCSEs," he said.
Chris McGovern, chairman of the Campaign for Real Education, said the system needed to change: "What we need to do is stop having examination boards competing against each other. What we have to do is to have one single examination board.
"You wouldn't dream of having, say, different boards offering driving licences. You've got to have one exam board, like most countries do, so that there's some integrity to the system. Without that, I'm afraid, it's just going to carry on getting worse."