Official figures released yesterday show the percentage of secondary schools reporting results for 14-year-olds increased from 2 per cent last year to more than 20 per cent this year.
For tests for seven-year-olds, the increase was from 18 per cent last year to 52 per cent.
Next year's tests for all 7-, 11- and 14-year-olds will be changed after reports from the School Curriculum and Assessment Authority showed that pupils could not understand the language in some maths and science questions.
External markers costing £8m will be introduced next year to answer teachers' criticisms that they are too time-consuming to mark. However, the National Union of Teachers has said it will continue its boycott.
Nick Tate, the authority's chief executive, said: "The message to teachers boycotting the tests is that they are missing a great deal of information about their own pupils and the effectiveness of their own teaching."
The report says some pupils had difficulty understanding technical terms such as magnetic and conductor in the context of a question about electricity.
Fourteen-year-olds will be given an extra 15 minutes to read the English paper because teachers complained pupils did not have enough time. Weaknesses pinpointed by the tests include knowledge of physics for 11-year-olds, probably because the subject hasnot traditionally been taught in primary schools.
Among 14-year-olds there are problems in arithmetic, especially in placing the decimal point and in fractions and percentages.
Seven-year-olds had difficulty adding up five coins, £1, 50p and three 20ps.
Almost all 11-year-olds entered for the main spelling test spelt cold, looked and power correctly. Illuminated and reference were spelt correctly by 29 per cent and 37 per cent respectively.
In maths, 11-year-olds did well on arithmetic but not on questions requiring explanation or probability.In science, they knew about the movement of the Earth and the Moon but not about circuits.Reuse content