According to the National Association of Head Teachers, which is mounting a campaign to block publication of 11-year-olds’ results, this is further evidence that the national testing system is still at an experimental stage.

Seven-year-olds were expected to grapple with Venn diagrams - based on systems of intersecting circles - in question number 30 of the key stage 1 maths test (see box). Yet, says the union, these diagrams are not even in the national curriculum.

The markers appear to have fared little better than the pupils. Seventy per cent of Surrey schools failed to mark the question correctly, according to the NAHT.

“Secondary maths teachers, heads of department and university professors have all been gob-smacked that anyone should try to give this sort of question to seven-year-olds,” said John Kenward, chair of the NAHT’s curriculum and assessment committee. The association will be taking up the matter with the School Curriculum and Assessment Authority, which set the exam.

Mr Kenward said he gave the question to four secondary heads of maths but only two got the answer correct.

The question is hard chiefly because of its spartan, not to say obscure, presentation. In fact pupils are expected to produce nothing more complex than: any even number; any number below 100; and any number which is both even and below 100. This is not explained.

A SCAA spokeswoman said that the question was only intended for the brightest pupils and that the majority would not even have reached it in the time allowed. She said that Venn patterns are not mentioned by name in the national curriculum, but are covered in a reference to using “a range of diagrams”.