For English, pupils taking the key stage 3 tests needed to score 30 out of 100 for a level 5.
Teenagers taking the second hardest of four maths papers could achieve level 5 with a score of 32 out of 151, "threshold" marks for the 2006 tests released by the National Assessment Agency showed.
KS3 maths papers set at other tiers of difficulty had pass marks, for level 5, set at 66 per cent, (easiest paper), 37 per cent (second easiest) and 22 per cent (hardest).
And pupils could achieve the highest possible level, 8, with 66 per cent on the hardest paper.
The Mathematical Association has questioned the low grade boundaries needed to achieve key levels in maths tests and GCSEs.
Doug French, president of the association, said: "If someone is getting 20 per cent or so on a paper and they are getting what is effectively a pass, it is not at all clear to me what this demonstrates they can do."
For KS3, the Qualifications and Curriculum Authority has to set seven threshold scores relating to level 5 every year, covering English, maths and science at several "tiers" of difficulty.
Five of these threshold marks fell this year, indicating the assessment agency believed the papers were harder than last year. In English, the figures equalled the lowest on record. All other level 5 thresholds at KS3 have been lower in previous years.
For key stage 2, the level 4 threshold score for English rose from 42 to 43 per cent. Pupils needed only 36 per cent to achieve level four in reading but 50 per cent for writing.In maths, it fell from 48 to 46 per cent. In science, it fell from 53 to 50 per cent.
Pupils needed to score 78 per cent in science, 78 per cent in maths and 70 per cent in English to achieve a level 5 at KS2.
Mick Brookes, general secretary of the National Association of Head Teachers, said the 36 per cent threshold for level 4 in the key stage 2 reading test was depressingly low.
A National Assessment Agency spokesman said: "National tests are not pass-fail, they are used to monitor (a pupil's) progress in the previous three years of learning.
"The thresholds are there to give an indication of whether a child has met a certain ability level.
"Level thresholds on harder papers are usually lower than those on the easier ones."