They are worried that bright children will be defined solely as those capable of tackling the maths and problem-solving papers.

Sheila Dainton, policy adviser to the Association of Teachers and Lecturers, said new theories of intelligence went beyond the limited applications found in the new tests.

“We are concerned about the way world-class tests define intelligence. What about world-class poets or world-class writers?”

The maths tests encourage pupils to think more deeply about the topics they have covered in lessons.

The problem-solvng papers draw on science, design and technology, and maths. They require pupils to develop strategies to reach a solution. The questions are set in everyday situations (see examples above).

The Qualifications and Curriculum Authority has developed paper tests and a different set of interactive questions that are available on its website. Answers are also provided.

“Some children come up with the answers so fast, you can’t understand how they did it,” said Martin Ripley, project director of the QCA world-class tests project. “In other cases, schools could help children develop strategies.”

Details and more sample questions can be found at www.qca.org.ukworld-class-tests