Every pupil in England will have to carry out currency conversions, be able to retrieve data from a spreadsheet and master basic algebra to gain a good GCSE in maths, The TES can reveal.
Teenagers might have to convert bills from euros into sterling or to estimate the chance of an unpredictable event happening as part of new "functional skills" tests to be incorporated into GCSEs from 2009.
They are also likely to be asked to estimate lengths, areas and volumes of objects, to do basic mental arithmetic and to decide whether or not a set of data supports a particular conclusion.
The new tests will assess the ability of students to think for themselves, with problems set in "real world" contexts. This has been welcomed as a departure from the more routine tasks currently assessed at GCSE.
But exam boards and subject experts are already warning that ministers will have to brace themselves for a fall in pass rates as thousands of pupils may struggle with the new exams.
Mike Cresswell, director general of Britain's biggest exam board, AQA, said: "It is likely, if you introduce a new hurdle that pupils must clear to gain a pass, that pass rates will fall.
"The likelihood of that being interpreted as a fall in standards is high."
The new tests are being introduced amid concerns from employers and universities that pupils are gaining top GCSE grades despite lacking basic reading, writing and mathematical skills.
Last week, an independent survey of 250 university admissions tutors raised concerns that school leavers' linguistic skills were declining, while many undergraduates struggled with number.
The functional skills, which pupils will also have to complete to gain one of the Government's new vocational diplomas, could make the GCSE a tougher exam for thousands of teenagers.
The tests are likely to be set at national curriculum level 6. This corresponds to the current difficulty level of GCSE. But maths experts say the greater emphasis on problem-solving could make them more demanding.
A source said: "The questions are likely to be less routine than those at GCSE, and less susceptible to coaching.
"This could be a problem, because it would mean a lot of kids who under the current system would get a grade C could not now collect it because they had not passed the test."
As well as answering questions in test conditions, pupils could be required to complete a portfolio or open-ended problem-solving question. Pupils could also be required to pass an easier test, set at national curriculum level 4, in order to gain a GCSE grade G. Three "entry level" tests, set at levels 1 to 3, will be available for secondary special educational needs pupils.
GCSEs and key stage 2 and 3 national maths tests feature a mix of questions set in real-life contexts and more theoretical problems. For example, a recent GCSE paper asked pupils to calculate the probability of Serena Williams winning two tennis matches against her sister, Venus, given the likelihood of her winning one match.
Ministers want to use the new tests to guarantee that teenagers have the basic maths skills they need in the workplace. It is also hoped that they will give more scope for lateral thinking.
Marion Seguret, senior policy adviser at the Confederation of British Industry, said that it would be necessary to look at the tests in detail before deciding whether the skills to be assessed were exactly what employers wanted.
The QCA is to hold consultation meetings on the outline of the new test from next Thursday. However, it was still not releasing the contents to the public this week.