Pupils taking the old maths Higher this year had to score 12 points more than their peers taking the new Higher in order to pass, with students who gained just 34 per cent in the new maths exam achieving a C grade.
The pass mark for the new Higher maths exam was the lowest in at least five years, TESS can reveal.
Scottish Conservatives young people spokeswoman Liz Smith said: "People would understand if modest modifications had been made to pass rates to reflect realistic changes in exams.
"But this reduction is drastic and shows just how badly the Scottish Qualifications Authority got it wrong."
Scottish Liberal Democrat education spokesman Liam McArthur said: "Cutting the pass mark for Higher maths may help those students who persevered, but it will do nothing for pupils who left exams early on after being presented with an exam paper including topics not covered in the coursework.
"Ministers must undertake a full investigation into why this happened."
There was no evidence that pupils had given up because the new Higher was too difficult, the SQA’s director of qualifications development, Dr Gill Stewart, told TESS.
“We have got all the statistical data for every question and every candidate," she added. "On the whole, every question was attempted, and we did not see, for instance, a drop off in pupils attempting questions at the end of the paper.
“Schools and parents encourage pupils, if they are finding a question difficult, to move on to the next one and, if they have got time, come back to the difficult question.”
However, the SQA has admitted that the new Higher maths exam “proved more demanding than intended”, adding that the "grade boundaries were reduced” as a result.
Therefore, to achieve a C in the new Higher maths exam, students had to score 44 out of a possible 130 points; for the old Higher they had to score 56 out of 130. To reach a B for the new Higher, candidates needed 61 out of 130, compared with 72 for the old Higher. To gain an A, pupils had to score 78 out of 130 for the new Higher, compared with 89 for the old exam.
Ultimately, to pass the new Higher, pupils had to gain 34 per cent of the marks, compared with 43 per cent for the existing Higher.