An investigation into optional tests at the end of primary school for high-flying students has highlighted a huge variation in pass rates between English and maths.

Just 2 per cent of children entered for the level 6 test in reading secured a pass, figures show. In the maths test, however, 34 per cent made the grade.

The study on level 6 tests, carried out by academics at Sheffield Hallam University, discovered that schools were frustrated at the lack of guidance on how to select students for the special assessments. Schools were confident in assessing students across the spectrum of level 5 but not in deciding whether they were meeting level 6 criteria.

However, schools had their reasons for choosing to use the level 6 tests, telling researchers that they wanted to provide an extra challenge for their most able students and that they were anxious about Ofsted’s reaction if students were not entered.

Level 6 tests were scrapped in 2003 but reintroduced in 2012. A number of schools consulted by the researchers said they would be stricter about which students they entered for the tests in future.

The researchers said that the “very low pass rate” for reading, the difficulty in selecting students and a scepticism among secondaries suggested that changes to the tests were needed. A new assessment might attempt to identify the top 10 per cent of students, the academics said.