The exams are being drawn up in response to employers' concerns that teenagers are leaving school without being able to spell or do simple sums.
A computerised key-skills test in the "functional" aspects of the three subjects is being considered by the Qualifications and Curriculum Authority.
Pupils could also face oral tests in English, as ministers believe that the ability to make presentations and speeches is a vital part of many careers.
Around 800,000 pupils a year would sit the passfail exams whenever they are ready, with questions selected at random from a computerised bank of problems from 2008. The exams will be incorporated into GCSEs and new vocational diplomas. However, pupils will also be able to take them separately.
The tests are modelled on those used to assess adult literacy and numeracy, in which candidates do simple comprehension exercises and basic calculations such as working out percentages.
But subject associations fear the new exams, which are likely to be multiple choice, could be very low-level, offering pupils little opportunity to demonstrate deeper understanding of the subject.
Doug French, of the Mathematical Association, said: "This is very worrying.
If it's a key skills approach, it looks like these qualifications are going to be all about doing sums. We want a deeper, problem-solving approach."
Ministers made clear in February's white paper on 14-19 their intention to react to employers' concerns about poor literacy and numeracy among school-leavers.
They announced then that GCSEs would be toughened to ensure that no pupil could achieve a higher pass without having mastered the "functional"
aspects of the subject. The QCA is to publish an outline of the tests next month for consultation. The TES has seen a copy of presentations the exams watchdog has made to subject associations and academics over the past month.
Paddy O'Hagan, head of the QCA's skills for life and work team, hinted that the tests might be modelled on those for adult basic skills.
Recent questions on these tests have asked candidates to calculate how much butter someone needs to buy to make a batch of scones, given the amount of butter per scone and the number of scones, and to decide what a writer was trying to say in an article about obesity in America.
Learners will be able to sit the functional skills exams without taking GCSEs. But most pupils will take them aged 16 alongside their GCSEs. The tests in English and ICT, incorporating the new functional skills elements, will be launched in 2008, with maths to follow a year later.
However. subject associations fear the "back to basics" approach to teaching could demotivate youngsters. It is possible that the proposed maths test could be changed to put more emphasis on creative problem-solving.
Simon Wrigley, chair of the National Association for the Teaching of English, said the Government still faced serious difficulties defining what it meant by functional English.
"Which aspects of the subject are not functional?" he said.
David Lambert, of the Geographical Association, said: "There's no arguing that basic skills are important, but pupils also need to be inspired to learn well. The Government does not seem to be talking very much about inspirational teaching."
The QCA is to put its plans out to consultation next month.
This week, the Government published a paper setting out its long-term plans for reform of secondary education and the emphasis on functional skills is a central part.