The pass rate had to be lowered to just 34 per cent because the exam was said to be too hard, though the Scottish Qualifications Authority (SQA) blamed overall difficulty, not specific questions.
Jim Reid, who set the maths exam until 2012, told BBC Scotland that alarm bells about the paper should have been ringing long before pupils sat it, with some reduced to tears and condemnation on social media.
Mr Reid said: “Given the checks and balances that are in place, at a very early stage alarm bells should have been ringing regarding the paper and knowing that the overall level of difficulty was far, far in advance of what they were looking for, for a paper of that nature.
“My main concern is at what stage did somebody raise a red flag and say ‘this isn’t proper’.
“If we get to the stage where the exam is sat on the 18th May and that red flag isn’t flown then something has gone seriously wrong at SQA - maybe a lack of experience, maybe producing the paper in too short a time scale.”
He added: “To reduce [the pass rate] to that level really says the paper was unfit for purpose.”
“The Higher maths setting team that walked away in 2012 had between them over 300 years of experience. You were talking lots and lots of experienced people who at the one time, en masse, walked away.”
The SQA report by the current principal assessor said the question about a crocodile stalking its prey - question eight on the second paper - “proved to be challenging for most candidates” and marks were adjusted by seven for that one alone.
More than 10,000 pupils sat the Higher maths exam in 2015. Nearly 20 per cent received an A, and a B and C went to another quarter each. There was no award given to 18.1 per cent of candidates.
The first paper in the exam replaced a multiple choice one in the old-style Higher and was “more challenging than intended”, said the report. Pupils scored an average of just 24.8 out of 60 marks on the first paper and 32.1 out of 70 on the second.
The report concluded: “SQA’s main aim is to be fair to candidates across all subjects and all levels and maintain comparable standards across the years, even as arrangements evolve and change.”
Dr Gill Stewart, SQA Director of Qualifications Development, said: “As we do every year, we consider what went well in the most recent diet, and where we need to make improvements for the future.
“Our external assessment and course reports, which are provided for all subjects at all levels, also highlight ways in which recent exams and coursework may have differed from those of previous years.
“This is to ensure standards remain high.”