Dr Rachel Quinlan of NUI Galway, who studied the exam paper, said no one could argue that the controversial trigonometry question in Paper II, which caused such outrage, contained elements not covered by the syllabus.

Nor did she think it was any harder than previous years' questions.

"In my opinion this is a welldesigned question, " Quinlan said. "A maths exam should be able to distinguish deep understanding from more superficial understanding.

This question does exactly that, while people who are not completely at home with the theoretical concept can still answer three-quarters of the question."

Part B of the trigonometry question included a photograph of the great pyramid at Giza in Egypt, instead of the usual diagram.

"To me it seemed that the examiners were trying hard to test both the knowledge and creative thinking of the student, " Quinlan said. "The actual trigonometry required in this question was not very advanced and mostly covered at Junior Cert level."

The examinations commission received complaints last week after students were reportedly thrown into panic during the exam on Monday.

Teachers said the paper was designed to put those who had learned from grindschool notes at a disadvantage over those who were able to employ independent mathematical reasoning.

"Understanding mathematics is more important than the knowledge that one can just rattle it off, " Quinlan said. "It is difficult to get a sense of a student's ability of maths these days, because even if they got a good grade, they may not necessarily have the capacity for independent thinking."

Professor John Carroll, head of mathematical sciences at Dublin City University, agreed that students should be brought beyond rote-learning.

"They need to be challenged. But I believe it is not right to spring it on them. We are seeing a worrying trend in students declining to take higher-level maths and we need to work together to make the syllabus more interesting."