All trainee teachers will be given five chances to pass a new numeracy test, including questions such as: "What percentage of 60 is 36?"

All trainee teachers will be given five chances to pass a new numeracy test, including questions such as: "What percentage of 60 is 36?"

Ministers are introducing the tests this year as part of their campaign to raise standards in teacher training. The questions are designed to help with problems teachers will meet in their daily work: how to work out truancy targets, how to use a graph to compare their school's test results with the national average and even how to work out their expenses.

Though the questions are all about paperwork, they were ordered by ministers who are worried about teachers' basic classroom skills.

Critics said the numeracy test is unnecessary and warned that it might put off badly needed recruits. Teachers already need at least a grade C in mathematics at GCSE and some teacher trainers argue that the simplest way to improve maths standards would be to raise that to a B.

Teachers who finish their training courses this year will not be able to teach for more than a year unless they pass the numeracy test. They will be allowed five attempts at the test, starting in June this year.

From next year, no teacher will be allowed to qualify without passing the numeracy test. They will be allowed four attempts. Tests in literacy and IT will also be introduced next year. The new numeracy test will be harder than GCSE but not as difficult as A-level.

This year's tests, which will be taken on 1 June, will be pencil and paper. In future, teachers will be able to sit the test whenever they wish by calling up computerised test papers. The tests, which will last no more than 45 minutes, will also be marked by computer.

The Teacher Training Agency, which is publishing the sample questions today on its website, said it is working on ways of ensuring that people cannot break into the computerised tests in advance. It will also check candidates' identities to ensure that student teachers have not enlisted friends to sit the tests.

Frankie Sulke, the agency's head of teacher training, said she believes student teachers will be reassured when they see the questions.

"There is an increasing need for all teachers to be able to do the kinds of tasks we are talking about," she said. "The tests will give the public the assurance which ministers are looking for that every teacher has a high level of numeracy, literacy and IT [skills]."

Nigel Gates of the Association of University Teachers said: "The test is unnecessary. Primary school trainees already have a huge amount of maths in their course and to make even maths graduates sit them is ludicrous. Secondary modern language teachers are never going to teach maths but they will have to pass the test."

A spokeswoman for the National Union of Teachers said: "This will discourage older people from going for a change of career and younger people from going into teaching at a time when there are desperate shortages."

Thirty-six is 60 per cent of 60.