A bamboozling question about a crocodile stalking its prey was one reason the pass mark for Higher maths had to be lowered, a report has found.
The pass mark for the new-look Higher maths was cut to just 34% because the exam was harder than expected.
A report for the Scottish Qualifications Authority (SQA) said the main problem was the overall difficulty of the exam - not individual questions.
But a former principal assessor said the exam was not fit for purpose.
A question about a crocodile stalking its prey became particularly notorious - with the SQA acknowledging in its report that it had "proved to be challenging for most candidates".
However, it was possible to solve the problem - as DLBmaths demonstrates on YouTube.
Jim Reid, who was responsible for setting the maths exam until 2012, told BBC Scotland that alarm bells about this year's paper should have been ringing at a very early stage.
Mr Reid said: "Given the checks and balances that are in place, at a very early stage alarms 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."
Mr Reid said he had seen the pass marks for the exam going back to the 1960s but had never seen one anything like as low as 34%.
He added: "To reduce it to that level really says the paper was unfit for purpose."
Mr Reid, along with other members of the team who set the paper, left the SQA in 2012.
He said: "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, from the principal assessor in maths, gives specific comments on some of the questions, including the one about the crocodile and another about the time it took a frog and a toad to escape from a well.
However, it said this question did not, in fact, pose a particular challenge to candidates, with the report saying it "met expectations".
The report said this question directly contributed to the lowering of the pass mark.
The main reason the pass mark came down was the first paper in the exam, which replaced a multiple choice paper in the old-style Higher and proved "more challenging than intended for candidates of all abilities."
The average marks reveal just how challenging many candidates found the questions. On average, candidates scored just 24.8 out of a possible 60 marks in the first paper and 32.1 out of 70 in the second.
Every year, the marks needed to pass or achieve a particular grade are adjusted up or down to ensure consistency. However, a pass mark as low as 34% in a major subject is thought to be unprecedented.
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. We are committed to the continuous development and improvement of our qualifications and assessments for the benefit of all candidates."